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  • 101
    Electronic Resource
    Electronic Resource
    A Chebyshev spectral collocation method using a staggered grid for the stability of cylindrical flows (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 825-833 
    Details
    ISSN: 0271-2091
    Keywords: Spectral collocation ; Chébyshev polynomials ; Staggered grid ; Pressure boundary conditions ; Hydrodynamic stability ; Cylindrical flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A staggered spectral collocation method for the stability of cylindrical flows is developed. In this method the pressure is evaluated at different nodal points than the three velocity components. These modified nodal points do not include the two boundary nodes; therefore the need for the two artificial pressure boundary conditions employed by Khorrami et al. is eliminated. It is shown that the method produces very accurate results and has a better convergence rate than the spectral tau formulation. However, through extensive convergence tests it was found that elimination of the artificial pressure boundary conditions does not result in any significant change in the convergence behaviour of spectral collocation methods.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120903
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  • 102
    Electronic Resource
    Electronic Resource
    Dynamics of liquid membranes. II: Adaptive finite difference methods (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 881-894 
    Details
    ISSN: 0271-2091
    Keywords: Liquid membranes ; Adaptive finite difference methods ; Integrodifferential equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120906
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  • 103
    Electronic Resource
    Electronic Resource
    A solution for the vertical variation of stress, rather than velocity, in a three-dimensional circulation model (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 911-928 
    Details
    ISSN: 0271-2091
    Keywords: Direct stress solution ; Vertical velocity profiles ; Three-dimensional circulation model ; Spectral methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A simple technique is presented that allows a numerical solution to be sought for the vertical variation of shear stress as a substitute for the vertical variation of velocity in a three-dimensional hydrodynamic model. In its most general form the direct stress solution (DSS) method depends only upon the validity of an eddy viscosity relation between the shear stress and the vertical gradient of velocity. The rationale for preferring a numerical solution for shear stress to one for velocity is that shear stress tends to vary more slowly over the vertical than velocity, particularly near boundaries. Consequently, a numerical solution can be obtained much more efficiently for shear stress than for velocity. When needed, the velocity profile can be recovered from the stress profile by solving a one-dimensional integral equation over the vertical. For most practical problems this equation can be solved in closed form.Comparisons are presented between the DSS technique, the standard velocity solution technique and analytical solutions for wind-driven circulation in an unstratified, closed, rectangular channel governed by the linear equations of motion. In no case was the computational effort required by the velocity solution competitive with the DSS when a physically realistic boundary layer was included.The DSS technique should be particularly beneficial in numerical models of relatively shallow water bodies in which the bottom and surface boundary layers occupy a significant portion of the water column.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650121002
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  • 104
    Electronic Resource
    Electronic Resource
    Masthead (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130101
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  • 105
    Electronic Resource
    Electronic Resource
    Conference diary (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 131-134 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130108
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  • 106
    Electronic Resource
    Electronic Resource
    Masthead (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130201
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  • 107
    Electronic Resource
    Electronic Resource
    A study of upstream-weighted high-order differencing for approximation to flow convection (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 167-199 
    Details
    ISSN: 0271-2091
    Keywords: Finite difference ; High-order schemes ; Numerical diffusion ; Solution unboundedness ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is concerned with a number of upstream-weighted second- and third-order difference schemes. Also considered are the conventional upwind and central difference schemes for comparison. It commences with a general difference equation which unifies all the given first-, second- and third-order schemes. The various schemes are evaluated through the use of the general equation. The unboundedness and accuracy of the solutions by the difference schemes are assessed via various analyses: examination of the coefficients of the difference equation, Taylor series truncation error analysis, study of the upstream connection to numerical diffusion, single-cell analysis. Finally, the difference schemes are tested on one- and two-dimensional model problems. It is shown that the high-order schemes suffer less from the problem of numerical diffusion than the first-order upwind difference scheme. However, unboundedness cannot be avoided in the solutions by these schemes. Among them the linear upwind difference scheme presents the best compromise between numerical diffusion and solution unboundedness.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130204
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  • 108
    Electronic Resource
    Electronic Resource
    Solution of the 3D linear hydrodynamic equations using an enhanced eigenfunction approach (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 235-250 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A method is presented for solving the 3D hydrodynamic equations in homogeneous sea regions using the Galerkin approach in the vertical with a mixed basis set. The basis set is composed of eigenfunctions of the eddy viscosity profile and a fixed function through the vertical, the amplitude of which is related to the externally applied surface wind stress. By this means the high-shear near-surface layer, which has previously been difficult to resolve using eigenfunction expansions, is accurately represented in the solution.The computational advantages of this approach compared with other basis functions, in terms of computer time and memory, and the ease of implementation on parallel processors with vector facilities are briefly discussed.The accuracy of the method and the choice of the additional function is demonstrated for the problem of wind-induced currents in a rectangular sea region.Calculations clearly show that for wind-induced currents this new approach is significantly more accurate than the ‘classical’ eigenfunction method. Also, the new method retains the advantages of the eigenfunction approach, namely insight into the mechanisms involved and ease of implementation on vector-parallel computers, together with minimization of computer time and memory.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130207
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  • 109
    Electronic Resource
    Electronic Resource
    Transonic viscous-inviscid interaction by a finite element method (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 309-319 
    Details
    ISSN: 0271-2091
    Keywords: Viscous-inviscid interaction ; Shock wave-boundary layer interaction ; Boundary layers ; Finite element method for flow problems ; Zonal methods ; Choked viscous flows ; Stream function-vorticity formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A method is outlined for solving two-dimensional transonic viscous flow problems, in which the velocity vector is split into the gradient of a potential and a rotational component. The approach takes advantage of the fact that for high-Reynolds-number flows the viscous terms of the Navier-Stokes equations are important only in a thin shear layer and therefore solution of the full equations may not be needed everywhere. Most of the flow can be considered inviscid and, neglecting the entropy and vorticity effects, a potential model is a good approximation in the flow core. The rotational part of the flow can then be calculated by solution of the potential, streamfunction and vorticity transport equations. Implementation of the no-slip and no-penetration boundary conditions at the walls provides a simple mechanism for the interaction between the viscous and inviscid solutions and no extra coupling procedures are needed. Results are presented for turbulent transonic internal choked flows.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130304
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  • 110
    Electronic Resource
    Electronic Resource
    A boundary integral equation method for Navier-Stokes equations - application to flow in annulus of eccentric cylinders (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 355-369 
    Details
    ISSN: 0271-2091
    Keywords: Boundary integral equation method ; Navier-Stokes equation ; Method of characteristics ; Hamel flow ; Eccentric cylinder annulus ; Rotating cylinders ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A novel Navier-Stokes solver based on the boundary integral equation method is presented. The solver can be used to obtain flow solutions in arbitrary 2D geometries with modest computational effort. The vorticity transport equation is modelled as a modified Helmholtz equation with the wave number dependent on the flow Reynolds number. The non-linear inertial terms partly manifest themselves as volume vorticity sources which are computed iteratively by tracking flow trajectories. The integral equation representations of the Helmholtz equation for vorticity and Poisson equation for streamfunction are solved directly for the unknown vorticity boundary conditions. Rapid computation of the flow and vorticity field in the volume at each iteration level is achieved by precomputing the influence coefficient matrices. The pressure field can be extracted from the converged streamfunction and vorticity fields. The solver is validated by considering flow in a converging channel (Hamel flow). The solver is then applied to flow in the annulus of eccentric cylinders. Results are presented for various Reynolds numbers and compared with the literature.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130307
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  • 111
    Electronic Resource
    Electronic Resource
    A numerical method for subcritical and supercritical open channel flow calculation (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 437-464 
    Details
    ISSN: 0271-2091
    Keywords: Free surface flow ; Spillways ; Subcritical and supercritical steady flow ; Marching finite volume method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A marching finite volume method is presented for the calculation of two-dimensional, subcritical and supercritical, steady open channel flow including the usually neglected terms of slope and bottom friction. The channel flow will be assumed to be homogeneous, incompressible, two-dimensional and viscous with wind and Coriolis forces neglected. A hydrostatic pressure distribution is assumed throughout the flow field. The numerical technique used is a combination of the finite element and finite difference methods. A transformation is introduced through which quadrilaterals in the physical domain are mapped into squares in the computational domain. The governing system of PDEs is thus transformed into an equivalent system applied over a square grid network. Comparisons with other numerical solutions as well as with measurements for various open channel configurations show that the proposed approach is a comparatively accurate, reliable and fast technique.
    Additional Material: 33 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130404
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  • 112
    Electronic Resource
    Electronic Resource
    An axisymmetric model of separated flow about a sphere using discrete vortices (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 809-823 
    Details
    ISSN: 0271-2091
    Keywords: Axisymmetric flow ; Sphere Vortices ; Discrete vortices ; Cloud in cell ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A procedure for the calculation of the starting flow around a sphere in a uniform stream is presented. The flow field is simulated by a flow of ideal fluid with embedded vorticity. With the assumption that the flow remains symmetric, the vorticity field is approximated by a number of discrete circular line vortices. The image vortices to satisfy the boundary condition for the normal component of velocity on the surface of the sphere are determined by Butler's sphere theorem. The Stokes streamfunction is used for the field description. The motion of vortices is tracked by the vortex-in-cell method, the cells being formed by square grids.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120902
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  • 113
    Electronic Resource
    Electronic Resource
    Conference diary (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 909-910 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120908
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  • 114
    Electronic Resource
    Electronic Resource
    Unsteady flow calculation in a radial flow centrifugal pump with spiral casing (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 895-908 
    Details
    ISSN: 0271-2091
    Keywords: Unsteady flow ; Vortex method ; Boundary element method ; Centrifugal pump ; Spiral casing ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The prediction of the two-dimensional unsteady flow established in a radial flow centrifugal pump is considered. Assuming the fluid incompressible and inviscid, the velocity field is represented by means of source and vorticity surface distributions as well as a set of point vortices. Using this representation, a grid-free (Lagrangian) numerical method is derived based on the coupling of the boundary element and vortex particle methods. In this context the source and vorticity surface distributions are determined through the non-entry boundary condition together with the unsteady Kutta condition. In order to satisfy Kelvin's theorem, vorticity is shed at the trailing edges of the impeller blades. Then the vortex particle method is used to approximate the convection of the free vorticity distribution. Results are given for a pump configuration experimentally tested by Centre Technique des Industries Mécaniques (CETIM). Comparisons between predictions and experimental data show the capability of the proposed method to reproduce the main features of the flow considered.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120907
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  • 115
    Electronic Resource
    Electronic Resource
    Development of a parallel computational fluid dynamics algorithm on a hypercube computer (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 947-963 
    Details
    ISSN: 0271-2091
    Keywords: Computational fluid dynamics ; Parallel computing ; Parallel processing ; Domain decomposition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: One of the main factors limiting the widespread use of computational fluid dynamics codes for engineering design is their very large requirements both in terms of computer memory and CPU time. Distributed memory parallel computers offer both the potential for a dramatic improvement in cost/performance over conventional supercomputers and the scalability to large numbers of processors that is required if performance beyond that of current supercomputers is to be achieved. As part of an evaluation to explore the potential of such machines for computational fluid mechanics applications, a concurrent algorithm for the solution of the Navier-Stokes equations has been developed and demonstrated on a hypercube parallel computer. The algorithm is based on a domain decomposition of a well-established serial pressure correction algorithm.The algorithm is demonstrated on both a 32-node scalar and eight-node vector Intel iPSC/2 for complicated two-dimensional laminar and turbulent flow problems with different grid sizes and numbers of processors. Speed-ups relative to a single processor of 12.9 with 16 processors and 20.2 with 32 processors are achieved on a scalar iPSC/2, demonstrating the parallel efficiency of the algorithm. Measured performance on a 32-node scalar iPSC/2 exceeds one-sixth that of a Cray X-MP running the original serial algorithm. The performance of the algorithm on an eight-node vector iPSC/2 exceeds that of the larger scalar hypercube and is about one-fifth that of the Cray X-MP. With cost/performance more than 10 times better than the Cray, these results dramatically show the cost effectiveness of vector hypercubes for this class of fluid mechanics algorithm.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650121004
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  • 116
    Electronic Resource
    Electronic Resource
    Algebraic grid generation for complex geometries (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 1-31 
    Details
    ISSN: 0271-2091
    Keywords: Grid generation ; Surface generation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An efficient computer programme called GRID2D/3D has been developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2D and 3D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation. The distribution of grid points within the spatial domain is controlled by stretching functions and grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For 2D spatial domains the boundary curves are constructed by using either cubic or tension spline interpolation. For 3D spatial domains the boundary surfaces are constructed by using a new technique, developed in this study, referred to as 3D bidirectional Hermite interpolation.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130102
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  • 117
    Electronic Resource
    Electronic Resource
    Multidomain collocation techniques for a viscous compressible flow (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 643-653 
    Details
    ISSN: 0271-2091
    Keywords: Spectral multidomain method ; Patching methods ; Viscous compressible flow ; Shock structure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a viscous compressible flow problem to which an equilibrium solution, in terms of density and velocity, can be given implicitly by elementary functions. The corresponding initial boundary value problem is solved by time discretization by the Crank-Nicolson method, Newton linearization and space discretization using multidomain Chebyshev collocation techniques. The physical interval is covered by subintervals of equal length. Each subinterval utilizes the same number of collocation points and each interface consists of one or two points. Six ways of patching are tested. All of them yield solutions with spectral accuracy for a few time steps, but only three are stable in the long run. Details of the density evolution are illustrated.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130507
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  • 118
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    Finite element solution of the incompressible Navier-Stokes equations by a Helmholtz velocity decomposition (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 135-144 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Finite element solution methods for the incompressible Navier-Stokes equations in primitive variables form are presented. To provide the necessary coupling and enhance stability, a dissipation in the form of a pressure Laplacian is introduced into the continuity equation. The recasting of the problem in terms of pressure and an auxiliary velocity demonstrates how the error introduced by the pressure dissipation can be totally eliminated while retaining its stabilizing properties. The method can also be formally interpreted as a Helmholtz decomposition of the velocity vector.The governing equations are discretized by a Galerkin weighted residual method and, because of the modification to the continuity equation, equal interpolations for all the unknowns are permitted. Newton linearization is used and at each iteration the linear algebraic system is solved by a direct solver. Convergence of the algorithm is shown to be very rapid. Results are presented for two-dimensional flows in various geometries.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130202
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  • 119
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    Masthead (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130301
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  • 120
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    A coupled multigrid-domain-splitting technique for simulating incompressible flows in geometrically complex domains (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 269-286 
    Details
    ISSN: 0271-2091
    Keywords: Unsteady ; Navier-Stokes ; Domain decomposition ; Schwarz ; QUICK ; Multigrid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper describes a domain decomposition numerical procedure for solving the Navier-Stokes equations in regions with complex geometries. The numerical method includes a modified version of QUICK (quadratic upstream interpolation convective kinematics) for the formulation of convective terms and a central difference scheme for the diffusion terms. A second-order-accurate predictor-corrector scheme is employed for the explicit time stepping. Although the momentum equations are solved independently on each subdomain, the pressure field is computed simultaneously on the entire flow field. A multigrid technique coupled with a Schwarz-like iteration method is devised to solve the pressure equation over the composite domains. The success of this strategy depends crucially on appropriate methods for specifying intergrid pressure boundary conditions on subdomains. A proper method for exchanging information among subdomains during the Schwarz sweep is equally important to the success of the multigrid solution for the overall pressure field. These methods are described and subsequently applied to two forced convection flow problems involving complex geometries to demonstrate the power and versatility of the technique. The resulting pressure and velocity fields exhibit excellent global consistency. The ability to simulate complex flow fields with this method provides a powerful tool for analysis and prediction of mixing and transport phenomenon.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130302
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  • 121
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    Announcements (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 401-402 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130309
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  • 122
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    Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 371-399 
    Details
    ISSN: 0271-2091
    Keywords: Incompressible fluids ; Streamlines ; Streamfunction ; Vortex flows ; Trust-region (TR) algorithm ; Newton-Raphson method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130308
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    Numerical analysis of convection-diffusion with chemical reaction by combined finite and boundary element methods (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 465-479 
    Details
    ISSN: 0271-2091
    Keywords: Convective diffusion ; Chemical reaction ; Finite element method ; Boundary element method ; Combined method ; Coupling method ; COD ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical method is presented to analyse a steady convection-diffusion problem with a first-order chemical reaction defined on an infinite region. The present method is based on the combined finite element and boundary element methods. For one- and two-dimensional examples in an infinite region the numerical results by the present method are in excellent agreement with the exact solutions. As a practical application, the simulation of the concentration distribution of the chemical oxygen demand at Kojima Bay is carried out.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130405
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    Spurious, zeroth-order entropy generation along a kinked wall (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 1113-1129 
    Details
    ISSN: 0271-2091
    Keywords: Steady Euler equations ; Subsonic flow ; Entropy error ; Local truncation error ; Global discretization error ; Singularity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical entropy generation is studied in the case of steady, subsonic Euler flow along a kinked solid wall. For a standard upwind finite volume discretization the numerical entropy error, a component of the global discretization error, appears to be zeroth-order in mesh size. Two possible causes of the zeroth-order entropy error are studied. First an investigation is made of the local truncation error on a kinked grid. Although this error also appears to be zeroth-order in the neighbourhood of the kink, it probably does not cause the zeroth-order entropy error. Next a study is made of the existence of a singularity in the exact solution. Probably, the Euler flow solution is singular at the kink in the wall. The form of this likely singularity is unknown. Therefore the construction of a computational method which uses a priori knowledge about the singularity is not possible. Finally it is shown by numerical experiments that the subsonic Euler flow along a kinked wall still can be computed with vanishing entropy errors by using an appropriate sequence of continuously curved walls which converge to the kinked wall in the limit of zero mesh width.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130904
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    Masthead (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650131001
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    Investigation of use of reach-back characteristics method for 2D dispersion equation (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 841-855 
    Details
    ISSN: 0271-2091
    Keywords: Two dimension ; Dispersion ; Characteristics method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The use of the Holly-Preissmann two-point scheme has been very popular for the calculation of the dispersion equation. The key to this scheme is to use the characteristics method incorporating the Hermite cubic interpolation technique to approximate the trajectory foot of the characteristics. This method can avoid the excessive numerical damping and oscillation associated with most finite difference schemes for advection computation. On the basis of the fundamental idea of the Holly-Preissmann two-point scheme, a new technique is introduced herein for the computation of the two-dimensional dispersion equation. This new scheme allows the characteristics projecting back several time steps to fall on the spatial or temporal axis, while the characteristics foot is still solved by the Holly-Preissmann two-point method. The diffusion portion of the dispersion equation is solved by the commonly used Crank-Nicholson method. The calculation for these two processes consisting of advection and diffusion is carried out separately but consecutively in one time step, a method known as the split operator algorithm. A hypothetical model was constructed to demonstrate the applicability of this new technique for the calculation of the pure advection and dispersion equation in two dimensions.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130703
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    Prediction of wake in a curved duct (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 907-916 
    Details
    ISSN: 0271-2091
    Keywords: Wake curvature ; k-ε model of turbulence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Experimental data on the development of an aerofoil wake in a curved stream are compared with calculations based on the k-ε model of turbulence with standard constants and with the model constant Cμ dependent on the local curvature. The mean velocity profile is asymmetric, the half-width of the wake is more on the inner side of the curved duct than on the outer side, and the turbulent shear stress decreases rapidly on the outer side. The standard k-ε model is able to satisfactorily reproduce this behaviour. Making Cμ dependent on the local radius improves the agreement on the inner side but slightly worsens it on the outer side.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130708
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    An adjoint variable method for sensitivity analysis of non-linear elastic systems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1649-1667 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adjoint variable method for design sensitivity analysis of non-linear elastic systems is presented. The method uses domain parameterization and a mutual form of the Hu-Washizu energy principle, and extends results reported in a recent work for linear elastic systems to non-linear elasticity. Non-linearities due to finite deformations and non-linear, hyperelastic constitutive models are considered. In contrast to other methods for non-linear sensitivity analysis, the present formulation can be applied with force, displacement or mixed approximate solution methods.The mutual energy expression used in the adjoint sensitivity derivation is developed from a non-linear extension of the Hu-Washizu energy functional and yields a linear governing equation for the adjoint system. This has important ramifications for the computational cost of a sensitivity analyses of non-linear systems: excluding the cost of determining the response of the system, the cost of a sensitivity analysis for a non-linear system is essentially the same as that for a linear system. Finite element implementation of the resulting sensitivity expressions is discussed, and two numerical examples are presented. The first example involves large deformations of a Mooney-Rivlin body, while the second involves design sensitivity analysis for mixed solution methods.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310813
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    Lagrange constraints for transient finite element surface contact (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 103-128 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach to enforce surface contact conditions in transient non-linear finite element problems is developed in this paper. The method is based on the Lagrange multiplier concept and is compatible with explicit time integration operators. Compatibility with explicit operators is established by referencing Lagrange multipliers one time increment ahead of associated surface contact displacement constraints. However, the method is not purely explicit because a coupled system of equations must be solved to obtain the Lagrange multipliers. An important development herein is the formulation of a highly efficient method to solve the Lagrange multiplier equations. The equation solving strategy is a modified Gauss-Seidel method in which non-linear surface contact force conditions are enforced during iteration. The new surface contact method presented has two significant advantages over the widely accepted penalty function method: surface contact conditions are satisfied more precisely, and the method does not adversely affect the numerical stability of explicit integration. Transient finite element analysis results are presented for problems involving impact and sliding with friction. A brief review of the classical Lagrange multiplier method with implicit integration is also included.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320107
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    An adaptive procedure for stabilizing convergence quality in frequency-constrained design optimization of bar structures supporting non-structural massThis work was presented in part at the Second NASA/Air Force Symposium on Multidisciplinary Analysis and Optimization in Hampton, Virginia on September 28-30, 1988 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1-27 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an improved optimality criteria (OC) method for minimum-weight design of bar structures supporting non-structural mass and subjected to multiple natural frequency constraints and minimum gauge restrictions. The convergence quality of the OC method hinges on both the number of active constraints retained and the choice of a proper step size. This being the case, a criterion, which uses previous scaled designs to ‘adaptively’ tune the step size, is established with the purpose of dissolving the (sometimes violent) oscillations of scaled design weights in the iteration history. As the step size is tuned, the convergence rate is descreased. Hence, a modified Aitken's accelerator, which extrapolates from previous scaled designs to obtain an improved one, is used. Its effect is to both increase the overall rate and reduce the net cost of convergence by reducing the number of repeat finite element analyses. The method presented here is used to qualitatively survey the convergence of several OC recursive schemes compositely used to resize and to evaluate the Lagrange multipliers. Design examples are presented to demonstrat the method. The method is adaptable, as it eliminates the need for adjustments of internal parameters during the redesign stage.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320102
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    Generalized numerical integration of moments (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 129-147 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Sampling points and weighting coefficients of the Gaussian type are presented for integrands typically encountered in axisymmetric finite elements. The proposed method is a generalization of Gaussian Integration of Moments for non-zero limits of integration. The method achieves one extra order of accuracy in the integration of polynomials as compared with the Gauss-Legendre method with the same number of sampling points. Although the locations of sampling points require the solution of non-linear equations, analytical solutions are presented for the cases of one and two sampling points. Special cases of these general expressions are shown to include both Gauss-Legendre integration corresponding to an integration range at a considerable distance from the axis of symmetry, and Fishman integration corresponding to an integration range whose lower limit lies on the axis of symmetry.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320108
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    A numerical study of the deviation of the crack ending at the interface in a multilayer (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 171-181 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The study of the deviation of a crack reaching the interface separating two materials in a multilayer in a 4-point deflection is considered. This study is based on the use of special isoparametric finite elements.1 (The elements surrounding the crack tip have nodes placed at a distance α from the crack tip, and in this way we impose a singularity of the stresses in the neighbourhood of the crack.)The Erdogan2 criterion that estimates the deviation angle shows that this angle is a function of the initial angle of the crack, and the properties of each component of the multilayer.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320110
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    Petrov-Galerkin finite element model for compressible flows (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 255-274 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Petrov-Galerkin method for the solution of the compressible Euler and Navier-Stokes equations is presented. It is based on the introduction of an anisotropic blancing diffusion in the direction of the local direction of propagation of the scalar variables. The local direction in which the anisotropic diffusion is introduced is uniquely determined, and the magnitude of the balancing diffusion is automatically calculated locally using a criterion that is optimal for one-dimensional transport equations.The algorithm has been implemented using four-noded bilinear elements with forward Euler and second-order Runge-Kutta methods of integration in time. Several applications are presented and show the stability and approximation properties of the method.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320203
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    Multiple scale finite element methods (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 969-990 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New temporal and spatial discretization methods are developed for multiple scale structural dynamic problems. The concept of fast and slow time scales is introduced for the temporal discretization. The required time step is shown to be dependent only on the slow time scale, and therefore, large time steps can be used for high frequency problems. To satisfy the spatial counterpart of the requirement on time step constraint, finite-spectral elements and finite wave elements are developed. Finite-spectral element methods combine the usual finite elements with the fast convergent spectral functions to obtain a faster convergence rate; whereas, finite wave elements are developed in parallel to the temporal shifting technique. Therefore, the spatial resolution is increased substantially. These methods are especially applicable to structural acoustics and linear space structures. Numerical examples are presented to illustrate the effectiveness of these methods.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320504
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    Multi-domain two- and three-dimensional thermoelasticity by BEM (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 991-1008 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computationally advantageous multi-domain boundary element formulation is presented for uncoupled thermoelastic analysis of two- and three-dimensional isotropic media. Particular integrals capable of representing exactly a quadratic temperature distribution in both two and three dimensions are employed. These particular integrals are derived using an orderly approach. When temperature data are provided at discrete points, the best fit quadratic distribution is generated in the least square error sense which, together with a multi-domain approach, makes it possible to represent an arbitrary temperature distribution within acceptable bounds. Numerical examples are given to show the efficiency and effectiveness of the present formulation, which is now incorporated in a general purpose boundary element code named GPBEST.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320505
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    The Lanczos algorithm applied to unsymmetric generalized eigenvalue problem (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1009-1026 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Application of the two-sided Lanczos recursion to the unsymmetric generalized eigenvalue problem is presented. The system matrices are real and unsymmetric. Therefore, the recursions are performed in real arithmetic and complex arithmetic is employed in the QR algorithm used to extract the eigenvalues of the transformed tridiagonal matrix. The biorthonormal transformation of the unsymmetric generalized eigenvalue problem is considered in detail with appropriate proofs presented in Appendices. Issues relating to the computer implementation of the unsymmetric generalized eigenvalue problem are discussed. The example problems solved demonstrate the working of the algorithm in extracting the complex and/or real eignevalues of an unsymmetric system of matrices. Also, the algorithm is applied to extract a few of the eigenvalues of a large fluid-structure interaction problem, and the results are compared with the eigenfrequencies extracted by an unsymmetric subspace iteration procedure presented in the literature.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320506
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    A method of finite element tearing and interconnecting and its parallel solution algorithm (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1205-1227 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented. The spatial domain is partitioned into a set of totally disconnected subdomains, each assigned to an individual processor. Lagrange multipliers are introduced to enforce compatibility at the interface nodes. In the static case, each floating subdomain induces a local singularity that is resolved in two phases. First, the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution. Next, the contributions of these modes are related to the Lagrange multipliers through an orthogonality condition. A parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and Lagrange multipliers, which completes the solution of the problem. When implemented on local memory multiprocessors, this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory. Moreover, unlike parallel direct solvers, it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320604
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    Parallel/vector improvements of the frontal method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1267-1281 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present, discuss, and report on the performance of two combined parallel/vector frontal algorithms which have been incorporated in a production finite element code. Two parallelization strategies are described. The first approach is algebra driven and is recommended for the solution of problems with a large bandwidth on a coarse grain configuration. The second strategy is targeted for finer grain systems; it blends the first one with a substructuring technique that is based on a careful partitioning of the finite element mesh into a series of subdomains. Using only 4 IBM 3090/VF processors, the proposed algorithms are shown to deliver speed-ups as high as 17 with respect to a serial non-vectorized frontal solver.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320607
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    Stochastic design sensitivity in structural dynamics (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1247-1265 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method to analyse stochastic design sensitivity for problems of structural dynamics is presented. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element context. An alternative form of the constraint functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations exicited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition technique: the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, whereas the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient; they can be readily adapted to fit into the existing finite element codes whose element derivative matrices can be explicitly generated. A number of numerical results for the deterministic and stochastic sensitivity analysis of beams and shells illustrates the paper.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320606
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    Adaptive analysis of thin shells using facet elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1283-1301 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive mesh refinement (AMR) procedure is used in static thin shell analysis using triangular facet shell elements. The procedure described herein uses the h-version of adaptive refinement based on an error estimate determined by using the best guess values of bending moments and membrane forces obtained from a previous solution. It includes the use of a relaxation factor to achieve better convergence. Some examples are presented to illustrate this method. The results obtained are compared with those of uniform mesh refinement (UMR).
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320608
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    An algorithm for three-dimensional convection and diffusion with very different horizontal and vertical length scales (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1303-1319 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is developed and tested for the numerical solution of the three-dimensional convection - diffusion equation appropriate for the marine environment, in which the horizontal and vertical scales differ by one or two orders of magnitude. The algorithm splits the horizontal and vertical parts of the process, treating the horizontal convection and diffusion explicitly and the vertical convection and diffusion by an implicit finite element method that is unconditionally stable. The overall stability conditions on the algorithm are discussed and its accuracy is verified through a number of test problems whose exact solutions are known.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320609
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    Announcement (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1365-1368 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320613
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    Delamination buckling of laminated plates (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1321-1337 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The subject of this paper is the buckling of laminated plates, with a pre-existing delamination, subjected to in-plane loading. Each laminate is modelled as an orthotropic Mindlin plate. The analysis is carried out by a combination of the finite element and asymptotic expansion methods. By applying the finite element method, plates with general delamination regions can be studied. The asymptotic expansion method reduces the number of unknown variables of the eigenvalue equation to that of the equation for a single Kirchhoff plate. Numerical results for the critical buckling load are presented for several examples. The effects of the shape, size and position of the delamination on the buckling load are studied through these examples.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320610
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    Modelling of structures by finite elements Volume 1: Elastic solids; Volume 2: Beams and plates. In French: Modelisation des structures par elements finis Volume 1 : Solides elastiques [Price: 150 FR.]; Volume 2 : Poutres et plaques [Price 200 FR.] by Jean-Louis Batoz and Gouri Dhatt, Editions Hermes, Paris, France, 1990 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1363-1363 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320612
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    An alternating technique for evaluating weight functions for 3-D surface flaws in finite solid bodies (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1339-1361 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient method, based on the Schwarz-Neumann alternating technique, is presented for computing weight functions of a general solid (3-D as well as 2-D), with embedded or surface-flaw configurations. The total rate of change of the crack-opening displacements, due to simple perturbations of crack-dimension characteristics, is conveniently decomposed into the infinite-domain and boundary-correction parts. The former is determined from available analytical solutions of ideal-shaped cracks, whereas the latter is computed numerically by imposing nil boundary-traction requirements for the displacement field corresponding to the weight functions. Numerical examples, with solutions for 3-D weighted-average and local stress intensity factors, indicate that the proposed method is very accurate and efficient.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320611
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1369-1370 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320614
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    Three-dimensional full Navier-Stokes solvers for incompressible flows past arbitrary geometries (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1427-1451 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The computation of the three-dimensional viscous flow past several geometries is investigated. An iterative technique resting on the fully elliptic mode is applied to the Reynolds-Averaged Navier-Stokes Equations written in a non-orthogonal curvilinear body-fitted co-ordinate system. Results of the computation are compared with available experiments.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310713
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310801
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1471-1474 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310718
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    In memoriam: Lothar Collatz (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1475-1476 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310802
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    Announcement (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1476-1476 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310803
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    Preface (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 651-651 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320402
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320401
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    Shape reconstruction and volume meshing for complex solids (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 665-675 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The reconstruction of a solid surface from a series of cross-sections and the generation of a volume mesh that conforms with a prescribed surface are issues that arise in numerous applications. We describe an approach to both these problems that is based on the generation of a tetrahedral mesh which automatically captures a triangulation of the surface points. A simple algorithm for introducing a set of interior points permits a simple partition of the volume mesh into two disjoint sets of tetrahedra such that one set determines the interior of the solid while the second determines the exterior.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320404
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    A comparison of adaptive-grid redistribution and embedding for steady transonic flows (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 653-663 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In recent years, numerical analysts have increasingly turned to adaptive-grid techniques to efficiently obtain highly-accurate solutions to partial-differential equations. This paper presents a comparison of two distinct grid-adaptation approaches, grid-point redistribution and grid-embedding, applied to two-dimensional, steady, inviscid, shocked flows. Grid redistribution is accomplished through a control function approach applied to the elliptic-grid generator while the embedding approach consists of a fixed global grid and an automatically chosen number of irregularly shaped, embedded regions. For both techniques, the Euler flow equations are integrated to steady state using Ni's Lax-Wendroff-type integrator to predict the flow fields about a variety of isolated airfoil configurations. The application of a common integration scheme as well as a common adaptive control function leads to a direct comparison of the effectiveness of the two adaptation approaches for the types of problems tested.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320403
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    Adaptive finite element methods for hyperbolic systems with application to transient acoustics (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 677-707 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of the hyperbolic systems of equations governing transient acoustics by adaptive finite elements and various finite difference time discretization schemes is addressed. Emphasis is placed on the use of a class of implicit Runge-Kutta methods for temporal approximations.
    Additional Material: 31 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320405
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    Automatic three-dimensional mesh generation by the finite octree technique (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 709-749 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An octree-based fully automatic three-dimensional mesh generator is presented. The mesh generator is capable of meshing non-manifold models of arbitrary geometric complexity through the explicit tracking and enforcement of geometric compatibility and geometric similarity at each step of the meshing process. The resulting procedure demonstrates a linear growth rate with respect to the number of elements and can be easily integrated with any geometric modeller through a set of geometric operators.
    Additional Material: 34 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320406
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    An adaptive finite element method for transient compressible flows with moving boundaries (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 751-765 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A description is given of an adaptive finite element method for the simulation of two dimensional compressible flows with moving boundaries. The method is implemented on an unstructured triangular grid and the mesh adaptation is achieved by local grid regeneration, using an error estimation procedure coupled to an automatic triangular mesh generator. Two numerical examples are included to illustrate the numerical performance of the method.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320407
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    Finite element analysis of heat transfer and flow problems using adaptive remeshing including application to solidification problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 767-781 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An error estimation technique for adaptive finite element analysis of heat conduction problems is described. The performance of this technique is demonstrated using a two-dimensional steady-state linear benchmark problem with a known analytical solution. A transient non-linear heat conduction problem involving solidification is then solved as a typical practical application. Some preliminary investigations for error indicators in flow problems are presented.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320408
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    Paving: A new approach to automated quadrilateral mesh generation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 811-847 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new mesh generation technique, paving, which meshes arbitrary 2-D geometries with an all-quadrilateral mesh. Paving allows varying element size distributions on the boundary as well as the interior of a region. The generated mesh is well formed (i.e. nearly square elements, elements perpendicular to boundaries, etc.) and geometrically pleasing (i.e. mesh contours tend to follow geometric contours of the boundary). In this paper we describe the theory behind this algorithmic/heuristic technique, evaluate the performance of the approach and present examples of automatically generated meshes.
    Additional Material: 42 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320410
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    Adaptivity and mesh generation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 783-810 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The objective of achieving economically finite element solutions of specified accuracy is now within reach. The importance of this objective is finally recognized by commercial code originators and efforts directed at automating the process are meeting with success.Three essential ingredients are here necessary. These are: (i) economical and efficient a posteriori error estimating processes; (ii) close prediction of the refinement necessary for a specific accuracy to be achieved so that numerous trial and error solutions can be avoided; (iii) implementation of the predicted refinement.With h and h-p adaptive processes Step (iii) requires powerful mesh generator facilities capable of achieving meshes of specified density.The paper considers all three aspects, introducing some novel concepts in error estimation and discussing in some detail the problem of mesh generation. As such, it introduces the other papers of this special issue, which discuss various aspects in more detail.
    Additional Material: 19 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320409
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    Automated adaptive two-dimensional system for the hp-version of the finite element method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 867-893 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an automated, adaptive finite element modelling system based on the hp-version of the finite element method. Error estimation and correction indication procedures with an automatic mesh generator and a p-version analysis code are combined to provide a computationally efficient modelling environment. Error prediction techniques are employed to find the best combination of finite element discretization, h-, and overall polynomial order, p-, needed to achieve the prescribed level of accuracy. The automated adaptive modelling results demonstrate the capability of the modelling system of predicting discretizations to perform a p-version finite element analysis to achieve prescribed levels of accuracy in the most efficient manner.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320412
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    A new approach to the development of automatic quadrilateral mesh generation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 849-866 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A methodology for the automatic mesh generation of quadrilateral elements is proposed. The methodology is based on the facts that (i) a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides, (ii) a quadrilateral can be formed by two triangles which share a common side. By taking advantage of the techniques developed in an existing automatic triangular mesh generator, quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest. In particular, an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described. Techniques to improve the quality of the generated quadrilateral meshes are introduced. The robustness and versatility of the mesh generator are demonstrated by a variety of examples.
    Additional Material: 21 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320411
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 939-941 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320415
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320501
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    Adaptivity for compressible flow computations using point embedding on 2-D structured multiblock meshes (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 895-919 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structured meshes which consist of a single curvilinear network of lines and points have limited flexibility when applied to geometrically complicated domains. To alleviate this constraint the idea of multiblock structured meshes has been proposed. This approach subdivides the domain of interest into regions, each of which can be mapped into a transformed space equivalent to a rectangle. The connections between these regions define the mesh topology. By a suitable subdivision of the domain, multiblock grids, which are globally unstructured between blocks, but provide a structured grid within blocks, can be used to discretize highly complex geometrical domains. This technique has been used to great effect, both in two and three dimensions. However, structured meshes are not naturally amenable to adaptivity techniques based upon local point addition. This paper describes a method, based upon the quadtree data structure, which allows for local point refinement on multiblock meshes for use with flow algorithms for the simulation of compressible flow around aerospace geometries. The basic concepts of multiblock meshes, the use of the quadtree data structure, together with the treatment within the flow algorithm of locally embedded meshes, will be discussed.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320413
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    A modified Euler method for dynamic analyses (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 943-955 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modified version of the well known Euler method for numerical integration is presented, and its application in analyses of the dynamic response of structures is discussed. This modified method was first introduced in 1981, and it has been reported that it was discovered by accident. When first introduced, however, valuable information related to the accuracy, stability and merits of the method were not provided. It is shown that the modified Euler method has features that make it an attractive approach for applications in dynamic analyses of structures. Accuracy and stability analyses are made for the method by considering free-vibrational responses of linear, undamped, single-degree-of-freedom systems. The method is explicit and extremely easy to use. However, it is conditionally stable. Applications of the method are also made which illustrate its usefulness and inherent simplicity. Furthermore, comparisons of the modified Euler method and the Newmark beta method are reported which elucidate the relative merits of these methods.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320502
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    Elastic stress analysis of three-dimensional solids with small holes by BEM (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 369-384 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An advanced level development of the boundary element method is presented for the elastic stress analysis of a three-dimensional solid containing a large number of small diameter, tubular shaped holes. The formulation has been developed such that these holes can be modelled by a system of curvilinear line elements, resulting in substantial savings in both data preparation and computing costs. This is accomplished by assuming a variation in the displacement field along the circumference defined in terms of trigonometric functions together with a linear or quadratic variation of displacements along the longitudinal direction.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310210
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    Experimental and finite element simulation methods for rate-dependent metal forming processes (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 345-367 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An experimental procedure and a finite element simulation method for rate-dependent metal forming processes are developed. The development includes the formulation of a tangential stiffness matrix for an axisymmetric solid finite element with four node, eight degree of freedom, quadrilateral cross-section. The formulation includes the effects of elasticity, viscoplasticity, temperature, strain rate and large strains. The solution procedure is based on a Newton-Raphson incremental-iterative method which solves the non-linear equilibrium equations and gives temperatures and incremental stresses and strains. Three examples are studied. In example 1, finite element simulation for the upsetting of a cylindrical workpiece between two perfectly rough dies is performed and the results are compared with alternative finite element solutions. In examples 2 and 3, both experimental and finite element studies are performed for the upsetting of a cylindrical billet and the forging of a ball, respectively. Annealed aluminium 1100 workpieces are used in both examples. For the finite element analysis, uniaxial compression tests are first performed to provide the material properties. The tests generate elastic moduli and two sets of stress-strain curves (quasi-static and constant strain rate), which are used to establish a rate-dependent material model for input. For both examples 2 and 3, comparisons between the experimental and finite element simulation results for the forming force vs. die displacement relations and also for the deformed configurations show good agreement. The versatility of finite element methods allows for displaying detailed knowledge of the metal forming process, such as the distributions of temperature rise, yield stress, effective stress, plastic strain, plastic strain rate, forming forces and deformed configurations, etc. at any instance during the forming process.
    Additional Material: 23 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310209
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    Fluid-structure interaction analysis by the finite element method-a variational approach (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 463-491 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We have developed a finite element method for analysing non-linear and linear fluid-structure interaction problems by working directly from a variational indicator based on Hamilton's principle. We restrict our analyses to inviscid, irrotational and isentropic fluid flows. The variational indicator includes the fluid potential energy due to gravity, which is often ignored. This and the fact that we consider our domain to be variable provide us with the capability to model free surfaces.We demonstrate the effectiveness of both linear and non-linear finite element formulations in analysing a variety of fluid-structure interaction problems.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310305
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    Announcements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 819-820 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310412
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310501
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 821-824 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310413
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    Geometrical representation and integration in BIE analysis (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 803-817 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Boundary representation by straight lines and circular arcs is described, and the error introduced through the common representation of circular arc boundaries by quadratic geometrical shape functions is investigated. This error is shown to be in some cases the major contributor to the total error. An even more significant advantage of exact boundary representation is that it permits many of the required integrations to be performed analytically, rather than by using Gaussian quadrature. For example, all integrations in any rectilinear domain can then be evaluated analytically. This generally produces an increase in accuracy, and a saving in the computing time required to assemble the coefficient matrices. In slender domains both this increase in accuracy and saving in computing time are very marked, as analytical integrations permit the use of very much coarser discretization than would be required for numerical quadrature.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310411
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    Modified formulations for nine-d.o.f. plane triangles that include vertex rotations (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 825-835 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper considers various procedures that yield improved stiffness matrices for plane triangular elements. Each element has nine d.o.f. and vertex nodes only. Some of the resulting elements are non-classical constant strain triangles while others have more competent displacement fields. Numerical examples suggest that the nine-d.o.f. element can either be formulated more efficiently or made more accurate, but probably not both at the same time.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310502
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    Large deflection elastic-plastic analysis of cylindrical shells using the finite strip method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 837-857 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite strip method is extended to the non-linear, static analysis of cylindrical shells. Large deflection effects are incorporated via first-order non-linearities in the strain-displacement relations, and material non-linearities are included via the von Mises yield criteria and associated flow rule. Numerical results are presented for various example problems including the diaphragm supported cylindrical shell-roof problem, an axisymmetric cylindrical shell loaded by radial pressure, the cylindrical shell-roof problem with clamped curved ends and a pressure loaded cylindrical panel clamped all round. The results are compared with known results from analytical and/or finite element analyses. The results indicate that a single bending mode in the strip direction is sufficient in most cases to yield engineering accuracy for preliminary design purposes.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310503
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    Closed form stiffness matrices and error estimators for plane hierarchic triangular elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 879-894 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Closed form expressions for the stiffness matrix and a simple error estimator and error indicator are derived for plane straight sided triangular finite elements in elasticity problems. The calculation of the error estimator is performed on an element by element basis, and is found to be very accurate and efficient. In general, the solutions for benchmark problems using the error indicators for selective refinement of the regions show accelerated convergence when compared to the convergence rate of solutions using uniform mesh refinement. Evaluation of the stiffness matrices and error estimators using explicit formulations is found to be several times faster than numerical integration.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310505
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    Delaunay versus max-min solid angle triangulations for three-dimensional mesh generation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 987-997 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Delaunay triangulation has been used in several methods for generating finite element tetrahedral meshes in three-dimensional polyhedral regions. Other types of three-dimensional triangulations are possible, such as a triangulation satisfying a local max-min solid angle criterion. In this paper, we present experimental results to show that max-min solid angle triangulations are better than Delaunay triangulations for finite element tetrahedral meshes, since the former type of triangulations contains tetrahedra of better shape than the latter type. We also describe how mesh points are generated and triangulated in our tetrahedral mesh generation method.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310511
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1027-1030 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310514
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    Improved formulations of Qcs6 hybrid element for enhancing computational efficiency (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 999-1008 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article discusses two alternative methods of formulating the recently proposed quadrilateral plane element Qcs6, which is based on a generalized functional with multiple stress fields. The first method is derived by an extended Hu-Washizu Principle with the presence of incompatible modes and enforcement of energy orthogonality, while the second one is established on a non-conventional discrete local stress smoothing. Both methods can be applied to other structural element formulations with enhanced efficiency.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310512
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310601
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    Transient scattering of elastic waves by three dimensional non-axisymmetric dipping layers (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1009-1026 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Scattering of elastic plane waves by three dimensional non-axisymmetric multiple dipping layers embedded in an elastic half-space is investigated by using a boundary method. The dipping layer is subjected to incident Rayleigh waves and oblique incident SH, SV and P waves. For the steady state problem, spherical wave functions are used to express the unkown scattered field. These functions satisfy the equation of motion and radiation conditions at infinity but they do not satisfy the stress free boundary conditions on the surface of the half-space. The boundary and continuity conditions are imposed locally in the least-square sense at points on the layer interfaces and on the surface of the half-space. The transient response is constructed from the steady state solution by using Fourier synthesis.Numerical results are presented for both steady state and transient problems. Steady state problems include solutions for two non-axisymmetric dipping layers in the form of a prolate. Transient responses are presented for one and two dipping layer models subjected to incident wave signals in the shape of a Ricker wavelet. It is shown that change in azimuthal orientation of the incident wave may significantly change the surface response of the dipping layer. For the transient problem, response comparison of one and two dipping layers indicates that the addition of an extra layer may also completely change the response characteristics of the alluvium. In particular, the delay in arrival of much larger amplitude surface waves by two dipping layers in comparison with other geometrically compatible models demonstrates the importance of the detailed three dimensional modelling of layered irregularities.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310513
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    An adaptive descent method for non-linear viscoplasticity (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1031-1054 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A forming model based on a viscoplastic flow formulation is derived which includes the effects of small elastic strains. A significant feature of the formulation is its reliance on the dominant inelastic material characteristics in the formation of the stiffness matrix for large strain problems. The resultant non-linear system of equations is solved by an adaptive descent method which combines the rapid convergence of Newton's method near the solution with the robustness of a method of successive approximations. The use of the adaptive descent method effectively extends the viscoplastic flow formulations into the nearly rate-insensitive range of behaviours exhibited, for example, by metals at low temperature, where slow convergence of the non-linear solution algorithm has traditionally hampered their use.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310602
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    Direct determination of periodic solutions of the dynamical equations of flexible mechanisms and manipulators (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1691-1710 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method based on finite elements, characterized by generalized strains as functions of the nodal co-ordinates, is the basis for the computer program SPACAR for the kinematic and dynamic analysis of flexible multibody systems. This program allows also the evaluation of the linearized dynamical equations, which makes possible the implementation of a method for the direct determination of stationary and periodic solutions and of a continuation method for these solutions if some parameter is varied. As an illustration, these methods are applied to a Duffing equation, a double pendulum and a slider-crank mechanism with an elastic connecting rod.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320811
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    Dynamic analysis and computer simulation of variable-mass multi-rigid-body systems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1711-1725 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we present a general procedure for analysing the motion of a multi-rigid-body system that is capturing and/or ejecting mass. The motivations for this work are given in the introductory section, followed by a description of the mathematical model we have used to represent a variable-mass system. Using a control volume approach, the differential equations of motion are derived in vector-dyadic form. The non-linear scalar components of these equations have been encoded into a Fortran-77 program that uses a fourth-order Runge-Kutta algorithm to compute a numerical solution for the motion of a given physical system; we describe the development of this simulation program and its use of the conformal rotation vector to represent orientations. An application of the program to the dynamic analysis of a specific variable-mass problem is presented, and a comparison of the numerical results to an analytical solution is used to assess the accuracy of the software. In the concluding section, the advantages and limitations of the underlying formulation are discussed.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320812
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    An approach to dynamics and control of orbiting flexible structures (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1727-1748 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A relatively general formulation for studying the dynamics of an arbitrary spacecraft with interconnected flexible bodies is developed accounting for thermal deflection, transient system inertias, shift in the centre of mass, shear deformations, rotary inertias and geometric non-linearities. The computer implementation has been carried out through symbolic manipulation of the equations of motion. Versatility of the formulation is indicated through application to problems of contemporary interest.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320813
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    Systematic construction of equations of motion for rigid-flexible multibody systems containing open and closed kinematic loops (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1749-1766 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A systematic method for formulating the equations of motion for multibody systems containing rigid and flexible bodies is presented. The method of using joint co-ordinates to derive the minimum number of equations of motion is utilized for rigid bodies and the finite element method is employed for flexible bodies. The equations of motion for flexible bodies are simplified into several steps using (a) a lumped mass assumption, (b) static condensation and (c) modal superposition. The combined rigid and flexible body formulation can be used to simulate dynamic response in a variety of applications such as ride handling, rollover and the crash analysis of vehicles, space structures, and biomechanical problems.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320814
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    A modular multibody analysis capability for high-precision, active control and real-time applications (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1767-1798 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computationally oriented formulation and its solution procedures for the analysis of rigid-flexible multibody dynamics systems are presented. The present formulation adopts a set of dual co-ordinate systems, an inertially fixed one for the measure of translational motions and a body-based one for rotational motions. The origins of these co-ordinate systems are located at the centres of rigid bodies and at the nodal points of flexible bodies for implementation ease. The flexibility is modelled by an intrinsic spatial beam theory which is approximated by transverse-shear deformable linear beam elements. The solution of the resulting equations of motion including system constraints is obtained by a partitioned procedure, which solves first for the constraint force vector, then the generalized co-ordinates for the rigid and flexible components, and finally interaction quantities such as active control forces, manoeuvring space ranges and corrections due to state measurements, with each solution stage being processed by the corresponding separate module. A central feature of the present capability is its high accuracy of the analysis results by demanding the energy conservation throughout the various stages of response analyses. Several examples are included to demonstrate the capabilities of the present analysis software both on sequential and parallel machines.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320815
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1683-1686 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310815
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    Mapped infinite elements for exterior wave problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 207-209 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320112
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    An implicit finite-element method for high-speed flows (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 183-205 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fast algorithm is presented for constructing continuous lines, made up of element sides, which pass once through each node of a general unstructured triangular mesh and which are generally aligned in prescribed directions. The lines are used as the basis of an adaptive fully implicit unstructured grid procedure for the solution of two-dimensional problems of steady compressible inviscid and laminar viscous high-speed flows, where the equation system is solved by line relaxation using a block tridiagonal equation solver. For three-dimensional laminar viscous simulations it is proposed to utilize an implicit/explicit finite-element formulation. In the vicinity of solid walls a grid exhibiting structure in the normal direction is employed while, away from this region, the grid will be totally unstructured. In the structured region, lines in the normal direction to the wall are readily identified, while lines in the surfaces parallel to the solid wall are constructed using the proposed two-dimensional procedure. The implicit algorithm is then used in the structured region and the equation solution is achieved via line relaxation. An explicit form of the solution algorithm is used elsewhere. To illustrate the performance of the proposed method, solutions are obtained for both transonic inviscid and transonic and hypersonic laminar viscous problems in two dimensions. The application of the proposed procedure to the solution of three-dimensional hypersonic laminar viscous flow over a double ellipsoid configuration is also described.
    Additional Material: 17 Ill.
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    Authors' reply (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 213-213 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320114
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    Announcements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 217-218 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320117
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    Analytical and computational models of shells (CED-Vol. 3), edited by Ahmed K. Noor, Ted Belytschko and Juan C. Simo, The American Society of Mechanical Engineers, New York, 1989. No. of pages: 640 (hard bound). ISBN 0-7918-0373-2. Price: $95.00 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 215-215 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320116
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    An indirect BIM for static analysis of spherical shells using auxiliary boundaries (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 313-325 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Boundary integral approaches, which are known for their mathematical sophistication and elegance as well as their ability to reduce the problem dimensions by one, suffer from drawbacks associated with their performance in the vicinity of the boundaries. Such behaviour is the result of the unavoidable, in most cases, discretization of the boundary on one hand, which consequently results in the reduction of the integral problem to an algebraic one, and of the tedious evaluation of singularities that are present in most kernels on the other. The sensitivity of solutions of shell problems using a special form of boundary integral method is studied. Such an approach hopes to achieve a better representation of the solution near the boundaries by utilizing fictitious surface lines to perform the kernel integrations. Lastly, the performance of the integral formulation is examined through some representative examples.
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    URL: http://dx.doi.org/10.1002/nme.1620320206
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    Phase-space representation of iterative design processes (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 327-346 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A large variety of design optimization methods have been proposed in recent years. Comparison of the relative performance of each method is a difficult task, and attempts to do so are often based on a limited number of numerical experiments. Recently, a ‘basins of attraction’ construction has been proposed as a graphical tool for investigating global performance of iterative design optimization methods, and as a basis for comparison of different methods. The phase-space representation presented in this paper is a companion to the basins of attraction construction. Basins of attraction reveal the relationship between starting design and final outcome of the solution process; the phase-space construction reveals that nature of the paths connecting the starting design and final outcome. The two constructions complement one another in summarizing the performance of design optimization processes. Both constructions are demonstrated in this paper, applied to the optimal design of an elastic grillage structure using Newton's method and the stress ratio method.
    Additional Material: 21 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320207
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    The finite element solution of elliptical systems on a data parallel computer (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 347-362 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A study is conducted of the finite element solution of elliptic partial differential equations on a data parallel computer. A nodal assembly technique is introduced which maps a single node to a single processor. The system of equations is first assembled and then solved in parallel using a conjugate gradient algorithm for unsymmetric, non-positive definite systems. Using this technique and a massively parallel machine, problems in excess of 100k nodes are solved.Results of electromagnetic scattering, governed by the 2-d scalar Helmholtz equation, are presented for both an infinite cylinder and an airfoil cross-section. Solutions are demonstrated for a wide range of object sizes. A summary of performance data is given for a set of test problems.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320208
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    Derivatives of tangential stiffness matrices for equilibrium path descriptions (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1093-1113 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes how several procedures, based on expressions from analytical elastic stability theory, are introduced as numerical tools in a general Finite Element program for geometrically non-linear structural analysis. Especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm. These include improved predictions for the step-wise solution of equilibrium states, identification of critical points and accurate descriptions of initial post-bifurcation behaviour.For two plane beam and bar elements, formulations have been developed giving analytical expressions for these derivatives. The corresponding numerical approximations, needed in other element types, are also discussed. The paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies. Some numerical examples, showing different types of behaviour, are analysed and discussed.
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    URL: http://dx.doi.org/10.1002/nme.1620320511
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    Physical shape functions in finite element analysis of moderately thick plates (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1115-1135 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new rectangular finite element for moderately thick plates is presented. The element is based on the concept of physical shape functions, i.e. functions which contain in themselves physical and geometrical properties of the element. The analytic formulae of stiffness, geometric stiffness and mass matrices are presented for isotropic material. The element is free from locking and zero energy modes not corresponding to rigid body motions.Several examples are presented for static, initial stability and free vibration problems.
    Additional Material: 17 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320512
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    Electronic Resource
    An adaptive finite element method for transient compressible flows (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1145-1159 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive finite element method for the solution of time dependent strongly compressible flows in two dimensions is described. The computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid, using an error estimation procedure coupled to an automatic triangular mesh generator. Problems involving shock propagation are solved to illustrate the numerical performance of the proposed approach.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320514
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