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  • 1985-1989  (2,645)
  • 1965-1969  (1,551)
  • Engineering General  (2,505)
  • Industrial Chemistry  (1,691)
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Year
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  • 201
    Electronic Resource
    Electronic Resource
    Superconvergent derivatives: A Taylor series analysis (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 489-509 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis, based on the use of Taylor series expansions, is developed to determine accuracy estimates for derivatives in one and two dimensions computed by differentiation of a finite-element interpolant or approximation. The analysis clarifies some issues concerning special points at which the derivatives are believed to be exceptionally accurate with higher convergence rates (superconvergence). Moreover, it leads directly to a class of post-processing strategies for the derivatives and offers a more direct constructive approach to the subject.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280302
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  • 202
    Electronic Resource
    Electronic Resource
    Application of differential quadrature to static analysis of structural components (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 561-577 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical technique of differential quadrature for the solution of linear and non-linear partial differential equations, first introduced by Bellman and his associates, is applied to the equations governing the deflection and buckling behaviour of one- and two-dimensional structural components. Separate transformations are used for higher-order derivatives, as suggested by Mingle, thus extending the method to treat fourth-order equations and to include multiple, boundary conditions in the respective co-ordinate directions. Results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods. The application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280306
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  • 203
    Electronic Resource
    Electronic Resource
    A Schwarz alternating procedure using spline collocation methods (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 621-627 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A collocation method is described which obtains an approximate solution to Poisson's equation, δu = f, on an L shaped region. The L shaped region is viewed as the union of two overlapping rectangles. The Schwarz alternating procedure may be employed to reduce the problem to one in which collocation techniques are used on each rectangle. The convergence of the alternating scheme depends upon a discrete maximum principle for collocation methods. Several sample problems are presented to illustrate the order of convergence of this method and to compare it with several existing numerical methods for the L shaped region.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280310
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  • 204
    Electronic Resource
    Electronic Resource
    Weighted residual solutions in the time domain (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 679-685 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Galerkin and subdomain forms of the weighted residual method are used to generate recursive equations in time for the numerical solution of a system of ordinary differential equations. The single-step methods that result from a linear interpolation equation match currently available methods whose stability and oscillation properties are known. A three-level scheme developed by combining two linear elements is shown to be unconditionally unstable. Two of the three schemes obtained using a quadratic interpolation equation and quadratic weighting functions are also shown to be unconditionally unstable. The third scheme is unconditionally stable, but the calculated values for a numerical solution of u̇ + u = 0, u(0) = 1 are not as accurate as the values obtained using the single-step central difference method.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280314
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  • 205
    Electronic Resource
    Electronic Resource
    Computational mechanics '88, theory and applications, S. N. Atluri and G. Yagawa (eds.), Springer-Verlag, New York, 1988. No. of pages: 1260 approx (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 726-726 
    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.1620280318
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  • 206
    Electronic Resource
    Electronic Resource
    Finite element formulation for non-steady-state large deformations with sliding or evolving contact boundary conditions (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 753-768 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method using a material description of the instantaneous configuration, valid for viscoplastic material with large deformations, is presented. In view of numerical tests which were carried out, this material formulation, associated with an implicit integration scheme which proved to be numerically accurate and reliable, is shown to be preferable.An algorithm is developed for resolution of sliding or evolving contact condition problems.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280403
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  • 207
    Electronic Resource
    Electronic Resource
    A new method for modelling reinforcement and bond in finite element analyses of reinforced concrete (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 833-844 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method of representing the steei in finite element analyses of reinforced concrete structures is described in which the steel and the concrete are analysed separately. The forces between the steel and concrete are used In an interative method which brings the two solutions together. The method converges very rapidly and it is shown that the computational effort is principally dependent on the mesh chosen for the concrete. All the steel in a reinforced concrete structure may be easily included without affecting the layout of the concrete mesh. Results, which are given for three practical problems, include detailed steel and bond stresses for all bars.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280408
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  • 208
    Electronic Resource
    Electronic Resource
    Homogenization and pre-integration techniques for multilayer composite and sandwich finite element models (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 257-269 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The multilayer degenerated 3-D shell element, for which the stiffness matrix is calculated by numerical integration ply by ply, gives accurate results even for moderately thick composite panels, but needs an important linear and non-linear generation time when the number of plies is high (N 〉 10). In order to reduce this time some pre-integration and homogenization techniques are investigated. Different pre-integration methods have been reviewed and discussed. Then, two new homogenization methods, based on a series expansion of an equivalent Hooke matrix over the thickness, are presented. Next, simple numerical validation tests of these new methods are discussed, indicating necessary further investigations. Finally, a general discussion about the properties of the pre-integration and homogenization techniques tends to define their respective application domain.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270204
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  • 209
    Electronic Resource
    Electronic Resource
    On a mixed finite element method for clamped anisotropic plate bending problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1351-1370 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with a new mixed finite element method of solution of the bending problem of clamped anisotropic/orthotropic/isotropic plates with variable/constant thickness. This new mixed method gives simultaneous approximations to displacement u and bending and twisting moment tensor (ψij)1 ≤ i, j ≤ 2. Computer implementation procedures for this mixed method are given along with results of numerical experiments on a good number of interesting problems.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280609
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  • 210
    Electronic Resource
    Electronic Resource
    A parallel mesh generation algorithm based on the vertex label assignment scheme (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1429-1448 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this article a new mesh generation algorithm is presented. The algorithm is based on a new approach called the vertex label assignment scheme to provide the information for the mesh generation so that parallel processing becomes possible. The algorithm generates 2D meshes of quadrilaterals on the basis of individual faces; conformity and smoothness of the resultant mesh are automatically assured. Local and selective mesh-refinements are also supported. A regular quadrilateral network which defines the geometry of the problem and an associated subdivision level assignment which specifies mesh density data on the network are the only input information.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280613
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  • 211
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    A unified treatment of superconvergent recovered gradient functions for piecewise linear finite element approximations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 469-481 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Piecewise linear finite element approximations to two-dimensional Poisson problems are treated. For simplicity, consideration is restricted to problems having Dirichlet boundary conditions and defined on rectangular domains Ω which are partitioned by a uniform triangular mesh. It is also required that the solutions u ∊ H3 (Ω). A method is proposed for recovering the gradients of the finite element approximations to a root mean square accuracy of O(h2), both at element edge mid-points and element vertices, using simple averaging schemes over adjacent elements. Piecewise linear interpolants (respectively discontinuous and continuous) are then fitted to these recovered gradients, and are shown to be O(h2) estimates for ∇u in the L2-norm, and thus superconvergent. A discussion is given of the extension of the results to problems with more general region and mesh geometries, boundary conditions and with solutions of lower regularity, and also to other second-order elliptic boundary value problems, e.g. the problem of planar linear elasticity.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270304
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  • 212
    Electronic Resource
    Electronic Resource
    Algorithms for construction of preconditioners based on incomplete block-factorizations of the matrix (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 609-622 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When applying an incomplete block-factorization technique one needs sparse approximate inverses of the successive Schur complements computed throughout the factorization. Here we propose a method for the construction of such sparse approximate inverses. The method has an advantage over earlier versions, in that such approximate inverses of block-tridiagonal matrices can be computed in parallel. Comparative numerical experiments for solving a number of discretized diffusion equations by this preconditioning matrix in a preconditioned conjugate gradient method and earlier versions of incomplete block-factorization preconditioners are presented.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270312
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  • 213
    Electronic Resource
    Electronic Resource
    Multigrid solution and grid redistribution for convection-diffusion (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 655-664 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We examine multigrid solution for convection-diffusion problems in which convective effects are significant. In particular, we consider the case where the fine grid satisfies the associated cell or diagonal dominance condition but coarse grid levels violate this condition. Related numerical experiments are conducted. We also introduce an alternative local elliptic projection technique and compare this with interpolating the error corrections from coarse to fine grids. In addition, we demonstrate the use of grid redistribution and optimization techniques in the multilevel context.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270315
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  • 214
    Electronic Resource
    Electronic Resource
    Multi-level finite element solution algorithms based on multiplicative and additive correction procedures (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 27-41 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Owing to the failure of the finite element analyst to employ a properly refined computational model, the accuracy of preliminary finite element computations is often low. Thus, it is useful to introduce a computational procedure for improving the results obtained from a preliminary finite element solution. Such a procedure is presented in this paper. In this procedure the solution error components are decomposed into two parts. One of the error components is assumed to have a long period variation. The other component is assumed to have a short period variation. Multiplicative and additive correction procedures are introduced to iteratively eliminate the two error components. The multiplicative and additive correction procedures are implemented using multi-level solution techniques.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280105
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  • 215
    Electronic Resource
    Electronic Resource
    A cubic triangular finite element for flat plates with shear (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 109-126 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the development of a straightforward displacement type triangular finite element for bending of a flat plate with the inclusion of transverse (or lateral) shear effects. The element has twenty two degrees of freedom consisting of ten for the lateral displacement of the midplane and six for rotations of the normal to the undeformed midplane of the plate. The latter are taken as independent of the slopes of the deformed midplane in order to include deformation due to transverse shear. The element is fully conforming and may be orthotropic. At interelement boundaries, the element matches adjacent elements both with respect to lateral displacement of the midplane and the rotations of the normal. The result is an efficient ‘linear moment’ triangular element but with transverse shear deformation included. Numerical computations for a number of examples are presented. The results show the element to be more flexible than most other finite element models and agree closely with those from a numerical solution of the three dimensional elasticity equations. The results also converge to those from thin plate theory when the thickness to length ratio becomes small or when the transverse shear moduli are artificially increased.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280109
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  • 216
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    Symmetry-preserving return mapping algorithms and incrementally extremal paths: A unification of concepts (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1839-1853 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work we seek to characterize the conditions under which an elastic-plastic stress update algorithm preserves the symmetries inherent to the material response. From a numerical standpoint, the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality. For the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving. For hardening plasticity, symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations. We show that these restrictions amount to the existence of a pseudo-internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli. In view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and, hence, in symmetric tangents, we address the question of whether any connections exist between the two approaches. We show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280810
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  • 217
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    Coupled use of reduced integration and non-conforming modes in quadratic Mindlin plate element (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1909-1928 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The applications of the reduced integration technique, and the addition of non-conforming modes and their coupling to Mindlin plate elements to improve their basic behaviour are reviewed and the establishment of a series of new plate elements by combined use of these schemes is presented in this paper. The element formulation is based upon the quadratic Mindlin plate concept. The results obtained by new elements converge to the exact solutions very rapidly as the mesh is refined and show reliable solutions even for severely distorted meshes. The new elements have the requisite numbers of zero eigenvalues associated with rigid body modes to avoid spurious zero energy modes. These elements are shown to solve the shear locking problem completely so that they are applicable to a wide range of plate problems, giving a high accuracy for both thick and thin plates.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280814
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  • 218
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    Combined effect of shear and large deformation on stress intensity factors (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1951-1964 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An attempt has been made to study the influence of large deformation on the stress intensity factor in a cracked plate subjected to bending including shear deformation. It is assumed that singular terms for stress resultants and strains in the case of large deformation have the same angular distribution and order of singularity as in the case of a linear problem. With this in view the small deformation singular element has been used at the crack tip region surrounded by large deformation plate bending elements. The finite element analysis, based on total Lagrangian formulation combined with the modified Newton-Raphson technique, has been used to get numerical results. Several examples connected with large deformation of cracked plates subjected to bending are studied. Using the above technique stress intensity factors for linear and non-linear cases have been compared.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280816
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  • 219
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    Free and forced vibrations of plates by boundary and interior elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1977-1994 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A direct boundary element method is developed for the dynamic analysis of thin elastic flexural plates of arbitrary planform and boundary conditions. The formulation employs the static fundamental solution of the problem and this creates not only boundary integrals but surface integrals as well owing to the presence of the inertia force. Thus the discretization consists of boundary as well as interior elements. Quadratic isoparametric elements and quadratic isoparametric or constant elements are employed for the boundary and interior discretization, respectively. Both free and forced vibrations are considered. The free vibration problem is reduced to a matrix eigenvalue problem with matrix coefficients independent of frequency. The forced vibration problem is solved with the aid of the Laplace transform with respect to time and this requires a numerical inversion of the transformed solution to obtain the plate dynamic response to arbitrary transient loading. The effect of external viscous or internal viscoelastic damping on the response is also studied. The proposed method is compared against the direct boundary element method in conjunction with the dynamic fundamental solution as well as the finite element method primarily by means of a number of numerical examples. These examples also serve to illustrate the use of the proposed method.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280902
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  • 220
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2219-2222 
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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.1620280916
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  • 221
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    Upwind techniques via variational principles (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 769-784 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The amount of upwind or magnitude of off-centering needed in the numerical solution of second order differential equations with significant first derivatives is justified more rigorously in this paper by requiring the satisfaction of a variational principle. It will be shown that, for a discrete solution, a set of variational principles can be found which allow the problem to be solved as a self-adjoint system. The technique presented here will give a clear indication of those regions where (i) upwind techniques are not required, (ii) upwind techniques are necessary and sufficient and (iii) upwind techniques are insufficient and artificial viscosity is required.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280404
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  • 222
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    Dynamic three dimensional computations for solids, with variable nodal connectivity for severe distortions (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 817-832 
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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 a three dimensional algorithm for dynamic Lagrangian computations for solids, with variable nodal connectivity to allow for severe distortions. The nodes are analogous to flexible spheres. When they move closer together than their equilibrium distance they generate compressive, repulsive forces. Conversely, when they move apart, they generate tensile attractive forces. Material strength effects are also included. Because a node can be affected only by its ‘neighbour’ nodes, the approach has been designated the ‘NABOR’ approach. The distinguishing feature of this technique is that it is possible to have variable connectivity. A node can acquire new neighbours, thus allowing all forms of distortion. The three dimensional NABOR algorithm has been incorporated as an option into the explicit finite element code, EPIC-3. By using both the NABOR grid and the traditional EPIC-3 finite element grid together, it is possible to perform Lagrangian computations for a wider range of problems.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280407
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  • 223
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    A new implementation of the force method and the optimum design of large trusses (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 893-907 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An implementation of the force method is proposed in which the forces and the displacements are simultaneously obtained by the solution of a sparse symmetric indefinite system. The matrix of coefficients is formed by just the concatenation of the element flexibility and equilibrium matrices. No computational procedure is required to generate the compatibility conditions (or the self-stress matrix) and no partitioning of the force vector is made into a basic set and a redundant set, unlike the conventional force method. A slightly modified sparse unsymmetric system can be written in which the stresses and the displacements are the unknowns. This is used as constraints in the formulation of the minimum weight design problem for large structures under static loading conditions. A sparse generalized reduced gradient package is used as the optimizer. A class of test problems involving large truss structures is solved. The results indicate that the present implementation of the force method is better than the displacement method for the optimum design of large structures.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280412
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  • 224
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    Free-vibration analysis of single-layer and two-layer bimodular beams (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 955-965 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented for determining the natural frequencies and the corresponding mode shapes of isotropic bimodular beams at certain supporting conditions. Although only the lowest three modes of the single-layer and two-layer bimodular beams were studied, in principle, the method may also be used to determine higher-mode natural frequencies and shapes of the multi-layer beams. Numerical analysis shows that the approach is suitable for the free-vibration analysis of clamped/free and hinged/hinged bimodular beams.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280416
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    The finite element method in thermodynamics, by Tai-Ran Hsu, ISBN 004-620013-4, Allen & Unwin, Boston, 1986. No. of pages: 391 + xix (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 980-980 
    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.1620280420
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    A bi-cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 987-999 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical strategies employed in the evaluation of singular integrals existing in the Cauchy principal value (CPV) sense are, undoubtedly, one of the key aspects which remarkably affect the performance and accuracy of the boundary element method (BEM).Thus, a new procedure, based upon a bi-cubic co-ordinate transformation and oriented towards the numerical evaluation of both the CPV integrals and some others which contain different types of singularity is developed.Both the ideas and some details involved in the proposed formulae are presented, obtaining rather simple and-attractive expressions for the numerical quadrature which are also easily embodied into existing BEM codes.Some illustrative examples which assess the stability and accuracy of the new formulae are included.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280502
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    A general finite element for beams or beam-columns with or without an elastic foundation (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1061-1076 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general finite element is derived for beams or beam-columns with or without a continuous Winkler type elastic foundation. The need to discretize members into shorter elements for convergence towards an ‘exact’ solution is eliminated by employing in the derivation of the element exact shape functions obtained from the equation of the elastic line. Inter-nodal values of deflections, bending moments and shear forces are obtained using the exact shape functions and trigonometric series. The effect of heavy compressive or tensile axial forces on bending stiffness is treated as a linear problem by considering the axial force as a constant parameter affecting the stiffness. FORTRAN subroutines to compute the stiffness matrix, equivalent nodal forces, deflected shape, bending moments and shear forces are provided and verified by an example.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280506
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    Stress intensity factors by enriched mixed finite elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1461-1473 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An enriched finite element model for linear elastic fracture mechanics is developed for a mixed variational statement. The independent approximations for the displacement and stress components are enriched by adding the near-field analytic expressions for a cracked body to the polynomial approximations of a conventional element. This allows for an accurate representation of the stress and displacement fields near the crack tip and also results in the direct calculation of the appropriate stress intensity factors. The accuracy of this formulation is demonstrated through several numerical examples.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280615
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    Mathematical models in coastal engineering, Christopher G. Koutitas, Pentech Press, distributed by Wiley, 1988. No. of pages: 156 (hardback). ISBN 0-7273-1313-4. Price £22.50 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1475-1475 
    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.1620280616
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    Masthead (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989) 
    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.1620280701
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    Multi-domain general axisymmetric stress analysis by BEM (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2065-2083 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is well known that there are many benefits in solving axisymmetric solids subjected to non-axisymmetric loading by using Fourier series expansion of field variables. Although many researchers have utilized this technique to solve problems of cooling towers and rocket nozzles, etc. by the Finite Element Method, the BEM formulation and implementation of such a method have been available only recently, mainly due to the efforts of Rizzo and Shippy3 and Mayr et al.4 In this paper these early developments have been generalized further by including more expansion terms, an efficient decomposition of kernels into symmetric and antisymmetric forms, improved evaluation of matrix coefficients and developing more general computer implementation to include surface stress calculations, effects of body forces and extensive substructuring facilities to analyse multi-zone problems.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280907
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    A time-space finite element discretization technique for the calculation of the electromagnetic field in ferromagnetic materials (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2085-2111 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stability of time-stepping methods for parabolic differential equations is mostly a critical issue. Furthermore, solving such equations with a classical time-stepping approach can be very expensive because many small time-steps have to be taken if steep gradients occur in the solution, even if these occur only in a narrow part of the space domain. In this paper we present a discretization technique in which finite element approximations are used in time and space simultaneously for a relatively large time period called a ‘time-slab’. This technique may be repeatedly applied to obtain further parts of the solution in subsequent time-intervals. It will be shown that, with the proposed method, the solution can be computed cheaply even if it has steep gradients and that stability is automatically guaranteed. For the solution of the non-linear algebraic equations on each time-slab fast iterative methods can be used.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280908
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    Eigenproperties of large-scale structures by finite element partitioning and homotopy continuation (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2113-2122 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element partitioning (or substructuring) is employed to estimate the eigenproperties of large-scale structural systems. A homotopy equation is constructed and its solutions are characterized by a number of curves which connect the eigensolutions of the partitions with those of the complete system. A step-by-step tracing procedure is developed to follow these curves. At each step, prediction and correction are performed. The Rayleigh-Ritz procedure and the conjugate gradient method are used as predictor and corrector, respectively. Compared with the sole use of either the Rayleigh-Ritz or gradient methods, the proposed method is more reliable and more efficient for large-scale problems. Numerical implementation is well suited for supercomputers.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280909
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    A finite element model for composite beams undergoing large deflection with arbitrary cross-sectional warpingModified version of a paper presented at the Second International Conference on Basic Rotorcraft Research, February 16-18, 1988, College Park, Maryland, U.S.A. (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2143-2160 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation has been developed to take into account the warping effect of composite beams undergoing large deflection or finite rotation. This formulation is to be used to model combined bending, torsional and extensional behaviour of composite helicopter rotor blades. The new approach can model thin to moderately thick walled composite beams with complicated cross-sections, tapers and arbitrary planforms. The warping effects are incorporated by assuming warping displacements superimposed over cross-sections normal to the beam axis in the deformed configuration of a shear flexible beam. The strain is assumed to vary linearly through the wall thickness. The fixed or total Lagrangian description is adopted in the present formulation and the Newton-Raphson method is used to solve the non-linear equilibrium equation resulting from the finite element approximation. Numerical tests of example problems demonstrate the validity and effectiveness of the present approach.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280911
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    A plate bending element based on a generalized laminate plate theory (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2275-2292 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A plate bending element based on the generalized laminate plate theory (GLPT) developed by the senior author is described and its accuracy is investigated by comparison with the exact solutions of the generalized plate theory and the 3D-elasticity theory. The element accounts for transverse shear deformation and layer-wise description of the inplane displacements of the laminate. The element has improved description of the inplane as well as the transverse deformation response. A method for the computation of interlaminar (transverse) stresses is also presented.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620281006
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    Towards parallel I/O in finite element simulations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2541-2553 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: I/O issues in finite element analysis on parallel processors are addressed. Viable solutions for both local and shared memory multiprocessors are presented. The approach is simple but limited by currently available hardware and software systems. Implementation is carried out on a CRAY-2 system. Performance results are reported.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620281105
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    A mixed-variable continuously deforming finite element method for parabolic evolution problems. Part I: The variational formulation for a single evolution equation (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2583-2607 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The objective of the research presented here was to develop a generic adaptive computational method for porous media evolution problems that involve coupled heat flow, fluid flow and species transport processes with sharply defined phase-change interfaces.In this paper we examine the general least squares variational approach and develop the conceptual framework for a rate least squares variational formulation of a continuously deforming mixed variable finite element method for solving highly non-linear time-dependent partial differential equations. In Part II of this paper1 we extend the formulation given here for a single evolution equation to a system of coupled evolution equations. In Part III2 we discuss in detail the numerical procedures that were implemented in a computer program and present several numerical examples that demonstrate the performance of this computational method.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620281108
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    Status of the finite element method in the thermoforming process (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2681-2693 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The purpose of this article is to review the publications dealing with the application of finite elements in the thermoforming process. Although no attempt has been made to discuss the theoretical aspects of these publications, their general methodologies have been presented. The paper is particularly aimed at readers who are seeking an overall view of the subject and possibly interested in acquiring a CAD system for thermoforming technology.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281112
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  • 239
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    A FORTRAN program for profile and wavefront reduction (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2651-2679 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A FORTRAN 77 program for reducing the profile and wavefront of a sparse matrix with a symmetric structure is described. The implementation is based on an algorithm published previously by the Author and appears in response to a large number of enquiries for the source code. Extensive testing of the scheme suggests that its performance is consistently superior to that of the widely used reverse Cuthill-McKee and Gibbs-King methods. In addition to presenting a complete listing of the program, we also describe how to interface it with a typical finite element code. The scheme is especially useful in finite element analysis where it can be employed to derive efficient orderings for both profile and frontal solution schemes.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620281111
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    Elastic plates: Theory and application, Herbert Reismann, Wiley (New York), 1988. 400 pp, £54.20, ISBN 0 471856010 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2710-2710 
    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.1620281115
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    Multigrid methods: Theory, applications and supercomputing, ed. S. F. McCormick, Marcel Dekker, New York, 1988. Price: $99.75 (U.S.A. and Canada), $119.50 (All other countries). No. of pages: 641 pp (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2711-2711 
    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.1620281118
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    Wind waves evaluation in the Adriatic and Mediterranean seas (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 57-69 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present the results of the implementation of an advanced wave model in the Adriatic and in the Mediterranean Sea. With respect to the first and second generation models, the new approach does not accept any a priori assumption on the spectral shape of the wind waves, this being determined uniquely by the dynamical equilibrium of the various source functions. These include the generation by wind, non-linear interactions and the dissipation due to whitecapping and to bottom friction.The Adriatic is characterized by highly variable wind regimes. Several storms have been hindcasted, testing the model in the various possible meteorological conditions. In this paper we focus our attention on a particular storm that allowed us to verify the shallow water behaviour of the model. For the Mediterranean we concentrate on a heavy storm that occurred in February-March 1986 in the Sicily Channel. The very good results obtained in these two highly different conditions prove the effectiveness of the physical approach to the numerical description of the wind waves evolution.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620270106
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    Modelling coastal/shelf systems with emphasis on long term trends (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 113-127 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Hydrodynamic studies of continental seas have been primarily concerned with tides and storm surges and the associated currents which can have velocities as high as several metres per second.However, the period of the dominant tide is only about half a day and the characteristic life time of a synoptic weather pattern is of the order of a few days. The very strong currents which are produced by the tides and the atmospheric forcing are thus relatively transitory and, over time scales of biological interest, they change and reverse so many times that they more or less cancel out, leaving only a small residual contribution to the net water circulation.Mathematical modelling appears at present as the most reliable approach to the determination of the residual circulation and of the long term transport of nutrients and pollutants in the sea.The residual circulation model developed at the GeoHydrodynamics and Environment Research Laboratory of Liège University (GHER) is described and illustrated by its application to the West-European Continetal Shelf.Residual flow patterns on the shelf, and in particular in the Irish Sea and the North Sea, are presented and shown to be in excellent agreement with the observations.The results are exploited to estimate the typical routes and times of residence of nutrients and pollutants and the subsequent long term changes in shelf ecosystems and in the Belgian coastal zone.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270110
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    Preface (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 1-1 
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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.1620270102
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    Hydrodynamic analysis of the surf zone (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 87-101 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Surf zone processes are one of the most difficult and challenging topics in modern marine science and technology. Because of their scientific and practical (e.g. engineering) importance they have been extensively studied in recent years. Nevertheless, even though the basic equations are known, no complete numerical solution can even be attempted yet. Moreover, there are still many unanswered questions relating to domain definition, well-posedness of the mathematical problem, validity of closure relationships and stability/convergence aspects of the numerical solution.This paper, starting from the basic conservation laws, derives sets of governing equations for the various flow modes present in the surf zone (currents, waves and turbulence). The emphasis will be on physical principles and simplifying hypotheses to show the application field of the different sets of equations. The paper will concentrate on the form and validity of the equations, including also some comments on discretization and numerical solution techniques.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620270108
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    Announcements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 239-240 
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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.1620280117
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    Masthead (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989) 
    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.1620280201
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    A deforming finite element method analysis of inverse Stefan problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 295-313 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A deforming FEM (DFEM) analysis of one-dimensional inverse Stefan problems is presented. Specifically, the problem of calculating the position and velocity of the moving interface from the temperature measurements of two or more sensors located inside the solid phase is addressed. Since the interface velocity is considered to be the primary variable of the problem, the DFEM formulation is found to have many advantages over other traditional front tracking methods. The present inverse formulation is based on a minimization of the error between the calculated and measured temperatures, utilizing future temperature data to calculate current values of the unknown parameters. Also, the use of regularization is found to be useful in obtaining more accurate results, especially when the interface is located far away from the sensors. The method is illustrated with several examples. The effects of the location of the sensors, of the error in the sensor measurements and of several computational parameters were examined.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280205
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    3-D shape optimal design and automatic finite element regridding (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), 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: A unified method for continuum shape design sensitivity analysis and optimal design of mechanical components is developed. A domain method of shape design sensitivity analysis that uses the material derivative concept of continuum mechanics is employed. For numerical implementation of shape optimal design, parameterization of the boundary shape of mechanical components is defined and illustrated using a Bezier surface. In shape design problems, nodal points of the finite element model move as the shape changes. A method of automatic regridding to account for shape change has been developed using a design velocity field in the physical domain that obeys the governing equilibrium equations of the elastic solid. For numerical implementation of the continuum shape design sensitivity analysis and automatic regridding, an established finite element analysis code is used. To demonstrate the feasibility of the method developed, shape design optimization of a main engine bearing cap is carried out as an example.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280209
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    Finite element method for solving mhd flow in a rectangular duct (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 445-459 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method is given to obtain the solution in terms of velocity and induced magnetic field for the steady MHD (magnetohydrodynamic) flow through a rectangular pipe having arbitrarily conducting walls. Linear and then quadratic approximations have been taken for both velocity and magnetic field for comparison and it is found that with the quadratic approximation it is possible to increase the conductivity and Hartmann number M (M ≤ 100). A special solution procedure has been used for the resulting block tridiagonal system of equations. Computations have been carried out for several values of Hartmann number (5 ≤ M ≤ 100) and wall conductivity. It is also found that, if the wall conductivity increases, the flux decreases. The same is the effect of increasing the Hartmann number. Selected graphs are given showing the behaviour of the velocity field and induced magnetic field.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280213
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    Correction (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 479-480 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280218
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    Masthead (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989) 
    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.1620280301
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    Mesh rezoning of 2D isoparametric elements by inversion (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 523-531 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new algorithm is presented for performing mesh rezoning on isoparametric elements used in simulations of non-linear deformation processes. The method uses techniques from elimination theory to solve the parametric inversion problem for each node on the new, undistorted mesh. These parameter values are then used in the elemental shape functions to transfer the nodal state variables from the distorted mesh to each node in the new mesh by interpolation. The method has been implemented for bilinear and biquadiatic elements. The method is based on fundamental finite element approximations, since the interpolation functions which define the element are also used to perform rezoning.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280304
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  • 254
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    A unified approach to solving ill-conditioned matrix problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 609-620 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified approach to solving ill-conditioned matrix problems is presented, concentrating on those problems arising in engineering where measurement inaccuracy is the major source of error. By applying the singular value decomposition, it is shown that regularization with a parameter can be used without squaring the condition number of the matrix. Numerical examples demonstrate that a smaller relative error is attainable using the unified approach over the more standard technique of discarding singular values. Lastly, a simple method is presented for locating the optimal solution using a computed residual.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280309
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  • 255
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    A new C1 finite element: Full heptic (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 667-677 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new C1 finite element complete in 7th degree polynomial basis is described and compared with other C1 elements in an eigen-elements analysis.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280313
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  • 256
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    A stream tube based upper bound approach to plane strain metal forming analysis (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 705-723 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In an attempt to establish a practicable computer based metal forming analysis capability, the classical upper bound theorem has been revisited. The result is an enhanced methodology which holds promise of providing some of the capabilities associated with more sophisticated finite element formulations without the attendant costs. The procedures developed here culminate with two sample applications.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280316
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  • 257
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 727-731 
    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.1620280319
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  • 258
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    On improved hybrid finite elements with rotational degrees of freedom (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 785-800 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A set of three new hybrid elements with rotational degrees-of-freedom (d.o.f.'s) is introduced. The solid, 8-node, hexahedron element is developed for solving three-dimensional elasticity problems. This element has three translational and three rotational d.o.f.'s at each node and is based on a 42-parameter. three-dimensional stress field in the natural convected co-ordinate system. For two-dimensional, plane elasticity problems, an improved triangular hybrid element and a quadrilateral hybrid element are presented. These elements use two translational and one rotational d.o.f. at each node. Three different sets of five-parameter stress fields defined in a natural convected co-ordinate system for the entire element are used for the mixed triangular element. The mixed quadrilateral element is based on a nine-parameter complete linear stress field in natural space. The midside translational d.o.f.'s are expressed in terms of the corner nodal translations and rotations using appropriate transformations. The stiffness matrix is derived based on the Hellinger-Reissner variational principle. The elements pass the patch test and demonstrate an improved performance over the existing elements for prescribed test examples.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280405
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  • 259
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    Analysis of viscoelastic behaviour of transversely isotropic materials (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 845-860 
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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 a constitutive equation to describe the mechanical behaviour of materials, reinforced with unidirectional fibres, is presented. The material behaviour of both matrix and fibres may be viscoelastic. The constitutive equation is a linear relation between the second Piola-Kirchhoff stress tensor and the Green-Lagrange strain tensor. The effective relaxation functions in the constitutive equation are composed of component relaxation functions employing the structural model of Hashin and Rosen. A two-dimensional membrane element incorporating this constitutive equation is implemented in a finite element program. The results of several calculations are presented in order to demonstrate the possibilities of the numerical tool. One calculation concerns a square membrane with a circular hole in its centre. The effect of fibre orientation on deformation and stresses will be displayed for this structure as well as for another membrane structure.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280409
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    A three-dimensional hydraulic fracturing simulator (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 909-927 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The propagation of non-planar hydraulic fractures is modelled using a three-dimensional numerical simulator. This paper describes the different components of the model (stress/displacement analysis, fluid-flow analysis, propagation criterion) with an emphasis on the numerical techniques used. A few examples of out-of-plane fracture geometries are provided.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280413
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  • 261
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    Simplifications using isoparametric elements in flexible linkage analysis (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 967-977 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper concerns finite element techniques applied to the analysis of mechanisms where a rigidity hypothesis for the links is unacceptable. Isoparametric elements may simplify the resulting equations because a good many of the terms arising from derivatives of rotation matrices disappear. Furthermore, the isoparametric approach leads to element matrices where integrations over element volumes do not depend on the gross motion of the linkage.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280417
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 981-985 
    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.1620280422
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    Numerical analysis of two-level finite difference schemes for unsteady diffusion-convection problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1001-1021 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper develops, for linear diffusion-convection model problems, the numerical analysis of some two-time-level second order finite difference schemes: modified centred, upstream weighted, Samarskii explicit and implicit schemes. The stability and related properties - dissipation, amplitude and phase errors, numerical diffusion and dispersion - are studied through Fourier analysis. The behaviour of the numerical solution is analysed from the matrix properties of the schemes with special emphasis on parabolicity and positivity. These analyses allow a comparison of the properties of every scheme, the main criterion being the efficiency of the scheme for strongly convective problems.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280503
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    Consistent higher degree Petrov-Galerkin methods for the solution of the transient convection-diffusion equation (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1077-1101 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of the convection-diffusion equation for convection dominated problems is examined using both N + 1 and N + 2 degree Petrov-Galerkin finite element methods in space and a Crank-Nicolson finite difference scheme in time. While traditional N + 1 degree Petrov-Galerkin methods, which use test functions one polynomial degree higher than the trial functions, work well for steady-state problems, they fail to adequately improve the solution for the transient problem. However, using novel N + 2 degree Petrov-Galerkin methods, which use test functions two polynomial degrees higher than the trial functions, yields dramatically improved solutions which in fact get better as the Courani number increases to 1·0. Specifically, cubic test functions with linear trial functions and quartic test functions in conjunction with quadratic trial functions are examined.Analysis and examples indicate that N + 2 degree Petrov-Galerkin methods very effectively eliminate space and especially time truncation errors. This results in substantially improved phase behaviour while not adversely affecting the ratio of numerical to analytical damping.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280507
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1229-1232 
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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.1620280516
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    A numerical integration approach by weight factors and its accuracy (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1217-1228 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new parabolic approach for numerical integration using weight coefficients is proposed.Several basic approaches for integration have been analysed: linear (trapezoidal), parabolic (new form), Simpson's, Newton-Cotes and Gaussian. The weight coefficients are transformed into the same form for all methods. Simpson's and Newton's formulas (for n = 3) are obtained as special cases of the general parabolic formula. A simple procedure to estimate the accuracy of the integral for final intervals is given.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280515
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  • 267
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    A mixed finite element model for the elastic contact problem (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1249-1264 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The static elastic contact problem is approached using Lagrange multipliers, leading to a mixed finite element problem. A non-linear friction law is introduced explicitly and the non-local character of the friction phenomena is implicitly assumed. In order to avoid stress oscillations near singular points, a perturbed Lagrangian functional is considered. The algorithms herein proposed do not impose nodal dependencies over the contact surfaces, allowing for the independent discretization of both bodies. The method is able to model simultaneous contact over different regions of any geometrical shape. Computer code, examples and results presented here are restricted to axisymmetrical and bidimensional cases.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280603
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    On linear constraints for Newton-Raphson corrections and critical point searches in structural F.E. problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1317-1334 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non-linear mechanical Finite Element (F.E.) problems. An alternative to the normal two-phase solution method is discussed. This method is used to represent different iteration constraints, and in conjunction with the search for critical solution points. Numerical tests are presented, evaluating the efficiency of different iteration constraints for a model problem. Practically useful criteria for critical points are discussed. The basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280607
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    Boundary integration and interpolation procedures for plate bending (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1389-1408 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the direct boundary element method (DBEM) for thin plate bending analysis, the integration of the kernel-shape-function products can lead to complications due to a combination of factors. The first is the existence of a singularity at the source point, leading to the singular kernel, which increases in strength as the integral equation is differentiated once for rotation, again for moment and yet again for shear. The second factor arises from the use of piecewise interpolation polynomials.In the first part of the DBEM analysis where the unspecified boundary values are computed, the numerical procedures are fairly straightforward. It is found in this paper that special care must be taken in calculating internal actions at domain points. The problems which can be encountered are demonstrated, and a modified boundary interpolation procedure is described. Examples are given which show the superiority of the recommended approach.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280611
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  • 270
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    Effective and practical h-p-version adaptive analysis procedures for the finite element method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 879-891 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two practical and effective, h-p-type, finite element adaptive procedures are presented. The procedures allow not only the final global energy norm error to be well estimated using hierarchic p-refinement, but in addition give a nearly optimal mesh. The design of this is guided by the local information computed on the previous mesh. The desired accuracy can always be obtained within one or at most two h-p-refinements.The rate of convergence of the adaptive h-p-version analysis procedures has been tested for some examples and found to be very strong.The presented procedures can easily be incorporated into existing p- or h-type code structures.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280411
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  • 271
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    Computational electromagnetics, Edited by Z. J. Cendes, Elsevier Science Publishers B. V. (North Holland), Amsterdam, 1986. No. of pages: 274 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 979-979 
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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.1620280418
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    A frontal technique for vector computersThe work described in this paper has been carried out in the framework of a 1988 contract between ENEL and CISE (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1635-1644 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: At the kernel of most scientific computations lies the solution of linear equations which, in finite element codes, is often performed by the frontal method. This method, like many algorithms for sparse matrices, is usually implemented with extensive use of indirect addressing which scarcely benefits from vectorization. As a consequence, present application codes only partially exploit the innovative features of supercomputer architectures. This paper describes a new version of the frontal technique which is designed for CRAY-like computers and is well suited to vector processing. Numerical tests have shown that the proposed algorithm is effective in improving the efficiency of finite element solutions on a vector machine.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280712
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    A mixed finite element formulation for Reissner-Mindlin plates based on the use of bubble functions (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1677-1702 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new finite element formulation for Reissner-Mindlin plates, based on the Hellinger-Reissner variational principle, is proposed in which the displacement field is additively decomposed into two parts: a part associated with standard interpolation of nodal degrees of freedom and a part associated with a set of independent bubble functions expressed in terms of generalized parameters. The formulation employs independent approximations for every stress component so that the stress field does not a priori satisfy the homogeneous equilibrium equations. It is shown that the bubble functions provide additional variational constraints on the stress field, resulting in optimal accuracy for the mixed formulation, and also eliminating shear locking in the thin limit. A 4-node and a 9-node element are described in detail. Both elements pass the patch test for mixed elements described by Zienkiewicz et al.1 and are stable in the sense of the Babuška-Brezzi condition. Numerical results indicate that the elements are accurate in displacements and stresses, including transverse shear, and insensitive to mesh distortion.
    Additional Material: 17 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280715
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  • 274
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    A special beam element for the analysis of thin-walled structural components (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1733-1747 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new beam element is described which is capable of depicting the non-linear elastic mode interaction of overall bending/buckling with local buckling in thin-walled beam-columns. In addition to being capable of describing overall biaxial bending and twisting, the element has shape functions which contain implictly the relevant local buckling deformation. The mode interaction occurs by virtue of the non-linear coupling of the overall and local buckling deformation. The local and post-local buckling displacement fields are computed a priori in an efficient manner using the finite strip technique. The modulation of the local buckling amplitudes is also accounted for in the element. In general, the beam element incorporates three companion local modes, all of which may become important in the process of interaction. Examples are presented which illustrate the efficacy of the element for problems involving interaction of local and flexural buckling modes and the combined interaction of local, flexural and flexural--torsional modes.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280803
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  • 275
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    Homogenization and damage for composite structures (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 285-298 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: After presenting shortly the main results of the homogenization theory for periodic media, we give two applications related to damage evaluation and simulation for composite materials: (i) simulation of the evolution of damage by fibre rupture in a unidirectional composite, involving parameters defined on the microscale; and (ii) prediction of debonding near an unloaded boundary in a stratified structure, using boundary layer asymptotic expansions.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270206
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  • 276
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    The application of symbolic computing to the hierarchical finite element method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1181-1204 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: One difficulty associated with the hierarchical finite element method is that of accurately determining the integrals necessary to establish the stiffness and mass matrices of arbitrarily high order elements. This paper describes how such integrals can be calculated exactly using symbolic computing.Results are presented which permit the construction of high order hierarchical finite elements applicable to a variety of problems involving two-dimensional elasticity, and plate and shell bending. Three-dimensional solid or brick elements are not considered.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280513
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    Masthead (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989) 
    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.1620280601
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    Optimum design of composite structures (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 437-448 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270214
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    New techniques for fast hybrid solutions of systems of equations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 455-467 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fast analogue solver with limited precision is used as a preconditioner in an iterative process which develops full digital precision. This hybrid process is highly parallel, and, in principle, it can be faster than digital computations alone. A problematic feature of this process is that the low analogue precision can adversely affect convergence speed. New techniques are introduced to address this limitation. A partial separation of analogue imprecision and poor problem condition is made. Fully parallel digital (smoothing) iterations are introduced to eliminate the effect of random errors which accompany analogue-digital conversion. Application is made to the problem of repeated summation.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270303
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    Adaptive h-, p- and hp-versions for boundary integral element methods (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1335-1349 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently very promising results in a so-called hp-version of the finite element method have been obtained. The basic idea is a balanced combination of mesh refinement and increase of the polynomial degree of the shape functions. This idea is applied to a boundary collocation method in this paper. The new method is compared with adaptive h- and p-versions and it is shown in numerical examples that even in the presence of singularities in the exact solution exponential convergence is obtained.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280608
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    Adaptive 2D finite element simulation of metal forming processes (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1409-1428 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development and integration of available current methods and the development of new methods for an adaptive finite element analysis of metal forming processes are presented. The analysis includes large-strain, elastic-plastic, and thermal effects. Many numerical methods such as mesh generation, simulation of the contact between the workpiece and tool and die, and optimization of the finite element mesh are integrated and incorporated. In addition, an algorithm is developed which can detect certain severely distorted elements where the area of integration is approaching zero. The advantage of correcting these regions of locally distorted elements is demonstrated. These numerical methods are implemented in a finite element program developed for simulating metal forming processes, with the emphasis on automating the analysis. Examples include an axisymmetric stress simulation of a coldheading process, a plane strain simulation of an extrusion process and a plane strain simulation of orthogonal metal cutting, all with noticeable thermal effects. The orthogonal cutting forces and feed forces calculated are compared with two sets of experimental data, with good agreement.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280612
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    Engineering quality software, David J. Smith and Kenneth B. Wood, Elsevier, Amsterdam, No. of pages: 209. ISBN 1-85166-074-7 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1476-1477 
    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.1620280618
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1479-1483 
    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.1620280620
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  • 284
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    Some acceleration methods for iterative computer of derivatives of eigenvalues and eigenvectors (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1505-1519 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of an iterative method for computing partial derivatives of eigenvalues and eigenvectors of parameter dependent matrices may be improved dramatically by various extrapolation methods proposed here. With exact computation, all these extrapolation methods yield the exact solution with a finite number of iterations. Two of these methods, which have not been used before for this problem, are compared with the ∊-algorithms. Numerical examples are given. The methods suggested may be used to obtain either highly accurate estimates or cheap estimates of modest accuracy.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280704
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    PCG methods in transient FE analysis. Part I: First order problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1557-1566 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performances of some PCG (preconditioned conjugate gradient) algorithms are evaluated in the solution of first order time dependent parabolic partial differential equations, such as the heat conduction equation, which have been spatially discretized using finite elements. ‘Consistent mass’ discretizations are preferred by the authors to ‘lumped mass’ ones and various preconditioners are then compared - diagonal, incomplete Choleski and EBE (‘element-by-element’). Recommendations are made and implications for parallel computation outlined.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280707
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  • 286
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    Adaptive time-step control in creep analysis (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1619-1633 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Concerning the integration in time of constitutive relations for Norton-type creep problems two families of algorithms are examined, namely the generalized trapezoidal rule and the generalized midpoint rule. Based on a mathematical concept, the accuracy properties are derived for both stresses and strains. Since the choice of the step-size is crucial for the accuracy of the numerical results, an adaptive step-size procedure is carried out by means of error estimators. Specifically, attention is paid to features arising in the context of a finite element displacement method. Finally, two numerical examples are given to illustrate the effect of the step-size control on the accuracy.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280711
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  • 287
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    A coarse/fine preconditioner for very ill-conditioned finite element problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1715-1723 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the problem of applying the conjugate gradient method to solve-ill-conditioned large algebraic systems of equations resulting from the finite element discretization of some three-dimensional boundary value problems. We present an effective preconditioner for such systems based on a multigrid technique. We assess its performance with examples borrowed from large flexible aerospace structures.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280717
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1725-1729 
    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.1620280718
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    Modelling liquid-solid phase changes with melt convection (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1769-1785 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Methods are described for modelling of phase change processes using the finite element method to simulate freezing and melting including convection in the melt. Evaluation of several enthalply/specific heat methods and time marching schemes is also included. Suppression of velocities in the solid region is described, and example problems are given. Comparison is made to simulations performed by other researchers using finite difference methods. Substantially different results were found for one of these problems, and this result is shown to be caused by numerical problems in the earlier work.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280805
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    Application of the Ritz method to plane elasticity problems for composite sheets with variable fibre spacing (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1813-1825 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The plane stress problem of a parallel fibre, rectangular composite sheet with variable fibre content is investigated. The resulting sheets are governed by partial differential equations that have variable coefficients, which are generally unsolvable exactly. A Ritz method is used to approximate the solution and is checked against known problems having exact solutions. The method is found to determine closely both the displacements and the stresses with fewer than 200 degrees of freedom. It is then applied to two interesting problems for which no exact solutions exist, including that of uniform normal stress applied in the direction of the fibres.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280808
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    The problem of selecting the shape functions for a p-type finite element (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1891-1908 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper addresses the question of the optimal selection of the shape functions for p-type finite elements and discusses the effectivity of the conjugate gradient and multilevel iteration method for solving the corresponding linear system.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280813
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    Free vibration of symmetrically laminated plates using a higher-order theory with finite element technique (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1875-1889 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A C0 finite element formulation of the higher-order theory is used to determine the natural frequencies of isotropic, orthotropic and layered anisotropic composite and sandwich plates. The material properties that are typical of high modulus fibre reinforced composites are used to show the parametric effects of plate aspect ratio, length-to-thickness ratio, degree of orthotropy, number of layers and lamination angle/scheme. The present theory is based on a higher-order displacement model and the three-dimensional Hooke's laws for plate material. The theory represents a more realistic quadratic variation of the transverse shearing strains and linear variation of the transverse normal strains through the plate thickness. A special mass matrix diagonalization scheme is adopted which conserves the total mass of the element and includes the effects due to rotary inertia terms. The results presented should be useful in obtaining better correlation between theory and experiment, and to numerical analysts in verifying their results.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280812
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    Announcement (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1969-1970 
    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.1620280818
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    Analysis of difference diagrams stability approximating a class of one- and two-dimensional non-linear-parabolic field equations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1995-2020 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the stability conditions for difference diagrams applied to the approximation of one- and two-dimensional non-linear field equations. The one-dimensional electromagnetic field is described by vector B and vector E, and the two-dimensional field by magnetic vector potential A.It has been proved that the presence of a lower order of derivatives has a decisive influence on the stability condition of the considered diagrams.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280903
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    A general and effective way for evaluating the integrals with various orders of singularity in the direct boundary element method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2059-2064 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general and efficient technique is developed for the evaluation of the integrals with various orders of singularity, such as occur in the three-dimensional boundary element method (BEM). Generalized (extended) triangle, tetrahedron polar co-ordinate mappings together with two conditions are used to remove the singularity of the integrals, and to evaluate the corresponding non-singular ones in a new numerical space. Triangle and tetrahedron polar co-ordinates in Reference 1 are proved to be a special case of the generalized ones in this paper. With the developed idea, boundary element results converge rapidly towards the analytical solutions for the strongly singular integrals evaluated directly, and the analytical solutions can be gained in principle, even when employing higher order, triangular boundary elements and tetrahedral cells. The generality and practicability of the method are demonstrated in the case of higher order elements, discontinuous elements and large engineering problems.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280906
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    Analysis of the Zienkiewicz-Zhu a-posteriori error estimator in the finite element method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2161-2174 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An a-posteriori error estimator for finite element analysis proposed by Zienkiewicz and Zhu is analysed and shown to be effective and convergent. In addition we analyse wider classes of estimators of which the Zienkiewicz-Zhu estimator is a special case. It is shown that some of these estimators will be asymptotically exact. Numerical evidence is presented supporting the analysis.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280912
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    Stress computations for nearly incompressible materials by the p-version of the finite element method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2175-2190 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the case of nearly incompressible elastic materials the strain energy, the shear stress and the difference of normal stresses can be computed accurately by direct methods when the p-version of the finite element method is used. Computation of the sum of the normal stresses requires special procedures. In this paper such procedures are described and examples are presented.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280913
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    Advanced development of the boundary element method for steady-state heat conduction (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2123-2142 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Considerable progress has been made in recent years toward advancing the state-of-the-art in solid mechanics boundary element technology. In the present work, much of this new technology is applied in the development of a general-purpose boundary element method (BEM) for steady-state heat conduction. In particular, the BEM implementation involves the use of higher-order conforming elements, self-adaptive integration and multi-region capability. Two- and three-dimensional, as well as axisymmetric analyses, are incorporated within a unified framework. In addition, techniques are introduced for the calculation of boundary flux, and for the inclusion of thermal resistance across interfaces. As a final extension, an efficient formulation is developed for the analysis of solid three-dimensional bodies with embedded holes. For this last class of problems, the new BEM formulation is particularly attractive, since use of the alternatives (i.e. finite element or finite difference methods) is not practical. A number of detailed examples illustrate the suitability and robustness of the present approach for steady-state heat conduction.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280910
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    Masthead (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989) 
    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.1620281001
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    Crypto-DOF finite elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 943-954 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New finite elements, called crypto-DOF elements, are introduced, utilizing degrees of freedom that satisfy the differential equation but do not appear explicitly in the discrete equations. The crypto-DOF elements can be advantageous in adaptive finite element techniques, and to approximate singular-type eigensolutions (e.g. in convective diffusion or stress concentration problems) without altering the original mesh or introducing new degrees of freedom. In this paper the crypto-DOF elements, the construction of crypto-DOF element families and selected numerical results are presented.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280415
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