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  • 101
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 102
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 191-198 
    ISSN: 0271-2091
    Keywords: Compressible Boundary Layer ; Stagnation Point Flow ; Boundary Value Problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The non-linear two-point boundary value problem for three-dimensional compressible boundary layers is solved through the application of a boundary value technique for a range of parameters characterizing the nature of stagnation point flows. The analytical boundary conditions, at infinity, are applied at the edge of the computational mesh with iterations on the size of the domain. The solutions obtained show excellent agreement with the established similarity solutions for three-dimensional flows. The present method has the potential advantage of yielding the wall values of f″w, g″w and θ′w as a part of the solution, contrary to the previously used ‘shooting’ methods. The algorithm is computationally simple and numerically stable and extremely suitable for engineering design applications.
    Additional Material: 1 Ill.
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  • 103
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 145-161 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 8 Ill.
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  • 104
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 163-168 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fully discrete stability and accuracy analysis of some algorithms for the one-dimensional heat equation is presented. Results illustrate that 2-pass explicit schemes which simultaneously employ lumped and coupled capacity matrices are capable of improved performance over the standard 1-pass explicit scheme.
    Additional Material: 1 Ill.
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  • 105
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 193-193 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 106
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 194-195 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 107
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 108
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 585-600 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generally applicable and simple joint/interface element for three- and two-dimensional finite element analysis is presented. The proposed element can model joints/interfaces between solid finite elements and shell finite elements. The derivation of the joint element stiffness is presented and algorithms for the treatment of nonlinear joint behaviour discussed. The performance of the element is tested on typical problems involving shell-to-shell and shell-to-solid interfaces.
    Additional Material: 13 Ill.
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  • 109
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 601-616 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The displacement of a slightly compressible liquid by another in a porous medium has been modelled. This problem, which involves a moving boundary, has been numerically solved for the one-dimensional case by using the Galerkin method. State and parameter estimation have been carried out using the extended Kalman filter.
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  • 110
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 637-661 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For a linear elastic structure, the first variations of arbitrary stress, strain and displacement functionals were explicitly expressed in terms of variations of material stiffness parameters within specified domain, in References 1 and 2, by using the solutions for primary and adjoint systems. In this paper, explicit expressions for second variations are derived for the case when the material stiffness or compliance variations depend on a set of parameters. These expressions arc obtained in terms of variations of stiffness or compliance parameters by using the solutions of two additional sets of adjoint systems. Furthermore, the variation of local stress, strain or displacement is considered. Several illustrative examples are provided for the first- and second-order sensitivity analysis of beams.
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  • 111
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 691-711 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a solar energy application involving thermal storage, one of the heat transfer situations is that of combined convection in vertical annuli for rather complex wall thermal boundary conditions. Predictive data of a high order of reliability are needed for incorporation within the suite of programs treating the whole problem.The program reported here treats the complete equations for combined free and forced convection in a vertical annulus. It allows for viscosity and density variation with temperature, and a variable heat flux or temperature at the walls. It was developed from a similar program for circular tubes.Comparisons are made with published data for velocity profiles and heat transfer performance. These are good, and show the step-wise energy balance method is necessary and valid.The strategy of generation of the required data is explained, together with sample output. These data are themselves analysed computationally; the performance equations agree with original predictions typically to within ± 11 per cent, with a standard deviation of around 2 per cent.The working fluid is water with 37 per cent ethylene glycol. Upward heated and downward cooled flows give aided combined convection. For the given design, laminar flow is predicted for the Reynolds number range 1800-2200.
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  • 112
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 723-732 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 7 Ill.
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  • 113
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 713-721 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: At present there are many general methods of approximating a possibly nonlinear operator equation by a finite equation system. The most commonly applied methods are the finite element and the finite difference. Numerous papers (e.g. References 9 and 10) have dealt with a comparison of these methods.In Reference 12 the Galerkin finite difference method (GFDM) is developed. The GFDM is a special finite element method designed t o solve nonlinear and possibly coupled partial differential equations numerically. It consists of a finite difference scheme derived from a Galerkin finite element method through the use of special local basis functions and a special grid.In this paper, we are concerned with extending the GFDM to derive ‘normal’ difference schemes. e.g. five-point schemes on two-dimensional domains for a general class of operators, even in nonlinear cases.Using GFDM or the finite element method on two-dimensional regions generally leads to at least 7- or 9-point schemes as well as expensive approximations of the nonlinear terms. Often, numerical integration is necessary. These computational costs are due to the non-orthogonality of the continuous and differentiable local basis functions that are needed in this case.The basic idea of the multi-bases approaches, which are the major concern in this paper11, is to reduce the smoothnessproperties ofthelocal basis functions in favour oftheir orthogonality. Thiscan beachieved with the help of so-called transfer operators which map the non-orthogonal and differentiable basis onto an only bounded but orthogonal basis.
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  • 114
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 115
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 779-787 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The eigenvalue problem for the Laplace operator is numerical investigated using the boundary integral equation (BIE) formulation. Three methods of discretization are given and illustrated with numerical examples.
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  • 116
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 789-800 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The five-spot waterflooding problem has been modelled as a two-dimensional moving boundary problem with a sharp interface separating the water and oil regions. The Galerkin method was used to solve for the shape and movement of the interface, as well as for the pressures in the reservoir. Having obtained a working model, the extended Kalman filter was then used to estimate the interfacial position when using corrupted pressure measurements from a single sensor in the field.
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  • 117
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 801-824 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Mixed finite element procedures with triangular and quadrilateral elements are evaluated and applied for nonlinear elastic and elastic-plastic analysis of some engineering problems. The elastic-plastic analysis involves implementation of von Mises, Drucker-Prager and Cap models. A number of special techniques such as symbolic programming, utilization of dihedral symmetry and the frontal solution are used to achieve computational economy. The procedure is also adopted for simulation of construction sequences in geomechanics such as excavation involving stress-free surface. The proposed procedures are evaluated and verified with respect to closed-form solutions, other finite element (displacement) procedures and field observations.
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  • 118
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 825-835 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many plane stress finite elements which can exactly represent rigid-body and constant-strain modes are too stiff in their response to the simple flexural action of a beam. This problem has received considerable interest. In this paper we explore a new interpretation of the problem and show that the poor bending response of the original 4-node plane stress quadrilateral can be quantitatively predicted by an error model.
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  • 119
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 853-881 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two methods are compared for integrating the strains that can arise in finite element solutions for Eulerian velocity fields associated with large strain material forming processes. With the Galerkin formulation, partial differential equations for the deformation gradient are solved over the entire domain based on a weighted residual; with the streamline integrated technique, the corresponding ordinary differential equations are integrated along characteristic lines. Both methods have yielded accurate integrations for the radial flow and planar rolling problems studied. A finite element technique is also presented for ensuring that the free surfaces of the fluid flow are streamlines. This technique has been used for ensuring proper boundary conditions in the rolling analysis.
    Additional Material: 16 Ill.
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  • 120
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 837-851 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Orthogonal curvilinear co-ordinates represent the logical choice for description of the middle surface of the majority of shells in engineering practice. By means of orthogonalization of originally skew parameter lines at integration points for shell analysis by the finite element method (FEM), the remaining minority can be treated without having to resort to skew curvilinear co-ordinates. Therefore, it does not seem to be worth while to extend existing computer codes for shell analysis by the FEM, restricted to orthogonal curvilinear co-ordinates, to general curvilinear co-ordinates. Depending on the structure of such a code, this extension may require a substantial amount of recoding. (However, it is advisable to consider general curvilinear co-ordinates if a new computer code for shell analysis by the FEM, based on thin- or thick-shell theory, is written).Based on these considerations, the concept of ‘discrete orthogonalization of parameter lines’ has been developed. It is presented in this paper and applied to the analysis of a hyperbolic paraboloid groined vault subjected to dead load. In the numerical investigation it is demonstrated that treating skew parameter lines incorrectly as orthogonal has a significant effect on the results for the displacements and the internal forces.
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  • 121
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 899-908 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Non-Newtonian fluid motion generated by a vertical porous hot plate in the presence of a transverse magnetic field is studied when viscous and ohmic dissipations are significant. When the temperature of the plate is very large, a general differential approximation for the radiative flux enables the asymptotic flow, valid far away from the tips of the plate, to reduce to a set of nonlinear and coupled ordinary differential equations. The solutions of these differential equations are studied for both small and large values of the absorption coefficient. The temperature, velocity and magnetic field distributions are discussed quantitatively. A primary conclusion of the analysis is that the distributions of temperature, velocity and magnetic field are much larger for a fluid with a large absorption coefficient than for a fluid with a small absorption coefficient.
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  • 122
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 941-957 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The inelastic behaviour of elasto-plastic materials is nonlinear, path-dependent, and is a function of the total plastic strain. For finite strain problems, the total inelastic strain in Lagrangian co-ordinates cannot be decomposed additively. A generalized logarithmic strain which is formulated in ‘updated’ Lagrangian coordinates and obtained by numerical integration of the Lagrangian strain rate is therefore introduced in this paper. By the use of this strain measure, which is additively decomposable, the plasticity model proposed by the authors can be extended to the finite strain range. It is shown that by correlating the generalized plastic modulus in the constitutive relations with the experimental uniaxial true stress-logarithmic strain diagrams, the inelastic behaviour of steel structures subjected to nonproportional loading can be analyzed numerically by using the finite element method.
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  • 123
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 967-970 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 124
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 971-972 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 125
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 973-974 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 126
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 127
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1067-1075 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The pressure pattern of nonlinear airflow through a filled grain bin is obtained by numerically solving the partial differential equation modelling the flow. The finite element method as implemented in an IMSL package - TWODEPEP - is used to obtain the numerical approximation to the solution. The predicted isopressure lines are compared with other published computational results and with the experimentally measured values. It is shown that some features of the experimental isopressure patterns can be obtained computationally by using solution techniques that are more accurate than the ones used so far.
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  • 128
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1187-1204 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modification to a conventional critical state model is described which introduces some plasticity in the stress region which is normally fully elastic. The effect is to blur the otherwise sharp distinction between elastic and yielding states. The modification is conceptually simple and does not require any additional material parameters. The model was developed for the dual purpose of providing a more robust constitutive law for finite element applications and to provide a more realistic representation of the soil. Its potential is demonstrated by simulating the response of a plane strain sample tested over a range of loading and unloading stress paths. The results are in accordance with expectations from physical tests. Further, they show that the model has some potential for at least the first few cycles of cyclic loading. A finite element boundary value analysis of an excavation is also described. This shows how the model copes with the severe test of stress paths which unload while yielding. Finally, the model is used to match stress-strain curves obtained from large-scale laboratory tests on a compacted clay. Close agreement with three of the five tests was obtained using a single set of material parameters.
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  • 129
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1205-1228 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A uniform beam element of open thin-walled cross-section is studied under stationary harmonic end excitation. An exact dynamic (transcendentally frequency-dependent) 14 × 14 element stiffness matrix is derived from Vlasov's coupled differential equations. Special attention is paid to the computational problems arising when coefficients vanish in these equations because of symmetric cross-section, zero warping stiffness, etc. The dynamic element stiffness matrix is established via a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices. A static stiffness matrix is also derived and the associated consistent mass and geometric stiffness matrices are given. Modal masses are evaluated. A FORTRAN program and a numerical example are included.
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  • 130
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1229-1251 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently, a new type of infinite elements which uses r-1 decay was proposed. They were applied to exterior wave problems and good results were obtained. In two-dimensional problems, however, it was necessary to move the origin of the r-1 decay in order to model the outgoing wave more accurately, because it decays roughly as r-1/2. In this paper, the mapped infinite elements with r-1/2 decay and the necessary numerical integration procedure are presented. These elements do not require any artificial movement of the origin. Several example problems are solved. The results show that the infinite elements with r-1/2 decay here give much more accurate values than the infinite elements with exponential decay and any damper elements.
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  • 131
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1253-1267 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the size variable-independence of the equilibrium equations in matrix format, a rational reduced basis reanalysis and an approximate reanalysis method are presented. Because the redundancy of structures is often low, and the decomposed coefficient matrix is known, these techniques can be advantageous in the structural optimization process. Several truss structures are studied for the purpose of numerical illustration.
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  • 132
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1521-1533 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple and logical finite element formulation is presented for the analysis of rings and sectors, with Timoshenko effects. The elemental properties are derived from the governing differential equation of motion using the Galerkin method. A quintic polynomial, satisfying the compatibility of derivatives up to second order, has been used for the ring finite element. The interpolating function is the same as for a thin ring. The efficiency of the formulation has been illustrated by the numerical results presented.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1535-1546 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The calculation of sensitivity derivatives of solutions of iteratively solved systems of algebraic equations is investigated. A modified finite difference procedure is presented which improves the accuracy of the calculated derivatives. The procedure is demonstrated for a simple algebraic example as well as an element-by element preconditioned conjugate gradient iterative solution technique applied to truss examples.
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  • 134
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1547-1553 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For about a decade, each and every researcher who used isoparametric quadratic elements to solve fracture mechanics problems employed only incomplete versions of these elements. Although complete formulations of isoparametric elements are almost as available as incomplete ones in general-purpose finite element computer programs, no attempt to use complete formulations has been seen yet. The purpose of this paper is to show how the complete quadratic isoparametric elements can be employed in the field of fracture mechanics.
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  • 135
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1555-1555 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 136
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1577-1581 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient method for solving algebraic equations is given. The linear equations are solved only once and iterations are performed on the non linear equations. If an initial approximation to a desired root is available, then it is utilized in the solution process. Results of some computational experiments are given.
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  • 137
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1583-1599 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold: (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1803-1812 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we introduce finite element methods of Petrov-Galerkin type for the approximate solution of two-point boundary-value problems for singularly perturbed, second-order, ordinary, linear differential equations. We write down Petrov-Galerkin methods on a uniform mesh which have asymptotic error estimates, as the mesh size tends to zero, whose magnitude is independent of the singular perturbation parameter. This is in marked contrast to standard finite element methods which do not possess such a property on a uniform mesh. For these, typically, the error on a fixed uniform mesh blows up as the singular perturbation parameter tends to zero.This robust behaviour of these Petrov-Galerkin methods for singularly perturbed problems is achieved by choosing trial spaces of standard piecewise polynomial type, while the test spaces consist of hinged piecewise polynomials.We consider self-adjoint and non-self-adjoint two-point boundary-value problems with Dirichlet boundary conditions. We define hinged test spaces for both types of problem. We then introduce a number of sample problems and we present numerical solutions of these sample problems using a Petrov-Galerkin method with the appropriate hinged test space.
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  • 139
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1833-1852 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: There are many physical phenomena which can be handled by the Helmholtz equation. The equation explains certain phenomena of wave propagation. This paper presents a new finite element method to analyse surface wave motion. The characteristic point of this method is that the interpolation equation is chosen to satisfy the governing Helmholtz equation using trigonometric functions. This follows that the variational functional to be minimized can be formulated such that the integration is limited to the boundary of the element. The numerical solutions obtained are compared with analytical and experimental solutions. From these comparative studies, it is concluded that the present method provides a useful tool for the analysis of surface wave motion.
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  • 140
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1887-1896 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Reynolds' equation, which governs the pressure distribution in the oil film of a lubricated bearing, has been solved numerically using finite difference and finite element methods. The latter depends on finding the integral formulation of the Reynold's equation, which is minimized to determine the pressure distribution. The finite control volume method uses the basic flow equations, assumes a given interpolation function for the pressure and, by considering the net flow towards each nodal point, the geometry stiffness is obtained which is identical to the element stiffness matrix obtained by the classical finite element approach. The motivation of the finite control volume method (FCVM) lies in the fact that the calculus of variation, a stumbling block for solution of certain flow problems, is not considered.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2169-2187 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical programming approach is discussed for the finite element-analysis of two-phase undrained problems in the field of geomechanics. This approach enables us to account for the possible development of partially saturated zones in the geotechnical medium, due to the attainment of a given lower limit in the pore pressure distribution. Two alternative formulations are presented, both of them in terms of linear complementarity and quadratic programming problems, and the computational advantages of one of them are illustrated. The main characteristics of a step-by-step solution technique are presented. Finally, the solutions of some test problems are discussed and compared with those deriving from the traditional analyses in which the development of partial saturation is neglected.
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  • 142
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2201-2219 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A higher-order shear deformation theory is used to analyse laminated anisotropic composite plates for deflections, stresses, natural frequencies and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, and requires no shear correction coefficients. A displacement finite element model of the theory is developed, and applications of the element to bending, Vibration and stability of laminated plates are discussed. The present solutions are compared with those obtained using the classical plate theory and the three-dimensional elasticity theory.
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  • 143
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1561-1576 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper. Reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well-known trapezoidal and midpoint rules to fit the present context. Other integration schemes such as the radial return, mean normal and closest point procedures are particular cases of this general formulation. The meaning of first and second-order accuracy in the presence of the plastic consistency condition is examined in detail, and the criteria derived are used to identify two second-order accurate members of the proposed algorithms. A general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed. With the aid of this methodology, the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule. Finally, numerical examples are presented that illustrate the performance of the algorithms.
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  • 144
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1601-1623 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Various mathematical programming methods for structural optimization are studied. In a companion paper, these methods have been studied based on certain theoretical considerations. In this paper, the methods are studied based on solving a set of test problems. The methods that are studied include recursive QP, feasible directions, gradient projection, SUMT and multiplier methods. Various computer codes have been developed, and are studied together with some existing programs such as CONMIN and OPTDYN. The test problems considered have 3-47 design variables and 3-252 constraints. The evaluation criteria consist of studying the accuracy, reliability and efficiency of a code. It turns out that globally convergent algorithms (multiplier methods, in particular) are very reliable but not efficient. Primal algorithms (like CONMIN), which are not proved to be globally convergent, are efficient but not reliable.
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  • 145
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2027-2048 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper sets the stage for the implementation of the Fixed-Point Iteration (FPI) to nonlinear finite element analysis as an alternative to the existing Newton-Raphson Method (NRM) or its derivatives. The superiority of the former method over the latter one is such that it enables one to obtain nonlinear structural static or dynamic responses without inverting the structural stiffness matrix.In the first part of the paper, a new convergence correction/acceleration factor has been developed for the FPI when applied to a single nonlinear algebraic equation. This new factor causes the iteration function of the equation under consideration to rotate about an axis that passes through one of its fixed points or roots. Using this observation, the slope of the iteration function can be adjusted in the neighbourhood of a specific root to ensure the convergence of the FPI. It is found that the optimum choice of the new factor corresponds to a zero slope, evaluated at the root, of the iteration function. The rate of convergence and the error estimate of this form of the FPI is developed and compared with the NRM. The equilibrium positions of a nonlinear loaded softening spring have been obtained by both methods as an illustrative numerical example to measure the effect of the new factor on the convergence rate.The second part of the paper extends the above concept to find the solution of a linear system of algebraic equations using the FPI. This leads to a better diagonal approximate inverse for the Jacobi iteration, or method of simultaneous displacements. If the elements of the solution vector of a specific system are all equal, the new Jacobi iteration becomes an exact method and the solution is obtained in one iteration. The concept is also extended to the Gauss-Seidel iteration, or method of successive displacements. Systems involving symmetric as well as nonsymmetric coefficient matrices have been used as numerical examples and are presented. For future implementation to nonlinear finite element analysis, the active column or the skyline (or the non-zero profile) FPI algorithms are developed for programming considerations.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2099-2126 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general class of time-dependent co-ordinate transformations is introduced in a variational formulation for evolution problems. The variational problem is posed with respect to both solution and transformation field variables. An approximate analysis using finite elements is developed from the continuous variational form. Modified forms of the variational functional are considered to ensure the deforming mesh is not top irregular. ODE system integrators are utilized to integrate the resulting semidiscrete systems. In Part I we consider the formulation for problems in one spatial dimension and time, including, in particular, convection-dominated flows described by the convection-diffusion, Burgers' and Buckley-Leverett equations. In Part II the extension of the method to two dimensions and supporting numerical experiments are presented.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 2145-2155 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The shear locking problem for the bilinear degenerated thick shell elements, when used in the context of thin shell structures, can be overcome by a generalized displacement method presented in this paper. The transverse shear energy in the degenerated thick shell elements is totally suppressed by introducing discrete Kirchhoff constraints in each element. The constrained variational problem based on the nodal displacement space is transformed into an unconstrained one based on a so-called generalized displacement subspace. It is shown that shear looking phenomena completely disappear and no degradation of results is observed as the ratio of thickness to span approaches zero.
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    International Journal for Numerical Methods in Engineering 21 (1985) 
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    International Journal for Numerical Methods in Engineering 21 (1985), S. i 
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 13-18 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1-11 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: ‘Dynamic’ or ‘viscous’ relaxation procedures have not gained much popularity in finite element analysis in which the direct (Gaussian elimination) solution dominates. Reasons for this are various - the most important being the rather slow convergence generally achieved for such procedures. However, it is possible to accelerate this quite dramatically and a method of doing so is shown in this paper. With the use of such acceleration and the inherent advantages of greatly reduced storage requirements and simplicity of programming, relaxation procedures promise an exciting possibility for the solution of large two- and three-dimensional problems in both linear and nonlinear ranges.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 19-36 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is presented for the design of thin turbomachinery blades with specified whirl velocities across the blade span. The numerical scheme involves iteration between the directs solution of a finite-volume method developed earlier on by Soulis1 and a design solution.The finite-volume method, which is a combination of finite elements and finite differences, solves the three-dimensional, inviscid, steady arid potential flow through turbomachinery blade rows in the incompressible, compressible and transonic flow range. In the design step, the whirl velocity distribution is specified across the blade span (Dirichlet boundary condition). The design procedure yields a new set of co-ordinates for the blade geometry which are used in the next iteration of the direct solution. However, in the present analysis only thin turbomachinery blades are designed, although a fully three-dimensional numerical method is used (the whirl velocity components of the flow field are averaged over the blade suction and pressure surface).The numerical method has been used to design free-vortex thin turbomachinery blades. Results show that the new numerical procedure is a comparatively economic and reliable method for designing thin turbomachinery blades. It may form the baseline for complete three-dimensional turbomachinery blade designs.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 37-63 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Structural reanalysis problems, such as in nonlinear finite element analysis or optimum design, involve progressive changes in the global stiffness matrix and its matrix factors. Although many studies have been devoted to the subject of matrix factor modification, most investigations have dealt with the problem separately from sparse matrix methods. This paper introduces a graph-theoretic model for the forward solution procedure which is applicable for identifying the modified entries of the matrix factors due to changes in the original matrix. Applications of this graph-theoretic model to existing refactorization methods are presented. The relation between substructuring and sparse matrix ordering strategies, and their effects on reanalysis are discussed. Modification of a sparse matrix associated with an n × n finite element grid ordered by the nested dissection scheme is analysed.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 65-88 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A solution procedure for the analysis of planar and axisymmetric-contact- problems involving sticking, frictional sliding and separation under large deformations is presented. The contact conditions are imposed using the total potential of the contact forces with the geometric compatibility conditions, which leads to contact system matrices and force vectors. Some key aspects of the procedure are the contact matrices, the use of distributed tractions on the contact segments for deciding whether a node is sticking, sliding or releasing and the evaluation of the nodal point contact forces. The solutions to various sample problems are presented to demonstrate the applicability of the algorithm.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 89-104 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Relations between displacement models using reduced integration and hybrid mixed models based on the Hellinger-Reissner and the Herrmann principles have been investigated. Five different isoparametric elements are considered for the case of plane stress, plane strain and plate bending elasticity problems.It is proved that the following relations hold for both models, provided the number of terms of a polynomial expressing the stress or strain component in the formulation of the mixed models is equal to the number of integration points of the reduced integration. If the stiffness matrix of the mixed model is evaluated by the identical integration rule with the reduced integration, the stiffness matrices of both models are identical. Thus, both models are equivalent, if the stiffness matrix of the mixed model is integrated exactly by the identical integration rule with the reduced integration.The displacement models using uniform reduced integration and selective reduced integration are equivalent to the mixed models based on the Hellinger-Reissner and the Herrmann principles except for the 6-node element, respectively.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 105-114 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new three-noded triangular element for plate bending is described. The element is based on an earlier stress-smoothed triangular element due to Razzaque,1 but extra internal ‘bubble’ functions are included to make it more flexible. The accuracy of the new element is compared with that of a number of other high-performance triangular elements. It is concluded that the present element and that due to Hansen, Bergan and Syvertsen2 are the two most accurate triangular thin plate elements currently available. The extra lines of FORTRAN required to convert Razzaque's shape function subroutine to that for the new element are given, thus making the new element easy to implement in any general-purpose finite element program.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 115-129 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A vector boundary integral equation (BIE) formulation and numerical solution procedure is presented for problems of three-dimensional elastic wave radiation and scattering from arbitrarily shaped obstacles. The formulation is explicitly in terms of surface traction and displacement, rather than wave potentials, and the BIE on which numerical work is based is written in a form entirely free of Cauchy principal value integrals. Indeed, the subsequent computational process, based on quadratic isoparametric boundary elements, renders all integrals free of singularities, so that ordinary Gaussian quadrature may be used. Numerical examples include scattering from spherical surfaces and radiation from a cube.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 131-143 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A six-node plate bending element has been developed by employing mixed formulation based on a modified Hellinger-Reissner principle and the Reissner-Mindlin plate bending theory. The numerical result indicates that, among the types of assumed independent transverse shear strains considered, a combination of 2α version with either 5α version or 6α version is free of spurious kinematic modes and leads to accurate and reliable solutions even for very thin plates.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 169-182 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A general matrix operator is established for solving linear boundary value problems in slip-line field theory. The operator will enable a wider class of problems to be solved than were previously possible with the matrix slip-line field technique. As an illustration, a range of solutions are generated involving the previously intractable Coulomb friction boundary condition.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 183-191 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A simple approach is proposed to calculate the bifurcation and limit points of structures, talcing into account the pre-unstable behaviour, by the finite element method. The approach is as follows: at each load step, the triangular factorization of the tangent stiffness matrix is checked to determine if the matrix is positive definite or not. When the tangent stiffness matrix is positive definite at a certain load step and non-positive definite at the next load step, the structure is considered to become unstable between the two load steps and an eigenproblem is constructed based on the difference of the tangent stiffness matrices at the two load steps. The critical load and corresponding mode of the structure are then derived from solving the eigenproblem. The proposed procedure is simple and economical, and it can be easily incorporated into a conventional geometric nonlinear analysis computer program. It is implemented in the ADINA program and some sample calculations are shown.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 193-193 
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    International Journal for Numerical Methods in Engineering 21 (1985) 
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 197-209 
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    Notes: Exact expressions are presented for the potentials, at an arbitrary point in space, due to two quadratic distributions in a triangular disc. These expressions are obtained by means of extensions of the analytical techniques previously developed for evaluating the potential integrals for constant and linear distributions. It is shown that the potential due to any quadratic distribution in a triangle may be obtained by using the two expressions derived here, together with an expression for the potential corresponding to a linear distribution. This latter expression was presented in an earlier paper.1 Numerical values obtained through the use of the two expressions are compared with those which result from the numerical evaluation of the potential integrals by triangle quadratures.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 229-238 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 301-315 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new finite element technique for calculating energy release rates is presented. An explicit expression for energy changes due to virtual crack extensions is formulated based on a variation of isoparametric element mappings. Energy release rates are calculated directly from integral expressions evaluated over singular quarter-point isoparametric elements surrounding the crack tip. Since the energy release rates are expressed in variational form, there is no need for the analyst to select a small finite crack extension to simulate a virtual crack extension. The method is shown to produce very accurate solutions even with fairly coarse element meshes. A similar technique for mixed-mode fracture based on mutual potential energy release rates is described.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 285-299 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents a finite element analysis of laminated bimodulus composite thin shells of revolution using a 48 d.o.f. doubly curved quadrilateral finite element. All the three displacements of the shell element reference surface are expressed as products of one-dimensional first-order Hermite interpolation polynomials. The constitutive relationship for a bimodulus composite is assumed to depend on the fibre-direction strain experienced by each orthotropic layer. Consequently the true state of strain and the corresponding constitutive relationship in a bimodulus composite structure are to be determined iteratively. The true state of stress/strain is obtained by specifying a maximum error in the locations of the two neutral surfaces (one along each of the orthogonal reference axes) in the shell. The use of the quadrilateral shell finite element is validated by solving the problem of (i) a freely supported single layer (0°) bimodulus composite square plate and (ii) a freely supported single layer (0°) cylindrical panel, which are subjected to sinusoidal transverse loading and for which analytical solutions are available. Next, the problems of a single layer (90°) pinched cylindrical shell and a single layer (0°) open crown hemispherical shell are solved to show the ability of the present program.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 317-328 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A geometrically nonlinear formulation for a 48 degrees-of-freedom (d.o.f.) quadrilateral shell element is presented. Each of the three displacement functions of u, v and w is based on the bicubic Hermitian polynomial. The surface of the element is modelled using linearized ratronal B-spline functions which may be linked to the geometric data bases generated by the computer-aided design system. The displacement functions and the 48 d.o.f. are expressed in both curvilinear and Cartesian forms, whereas the strain-displacement equations are expressed in curvilinear co-ordinates. The use of Cartesian displacement functions and degrees-of-freedom allow for the proper representation of the six rigid body motions even for the element with nonzero Gaussian curvature, such as a bellows. Two examples are demonstrated: snap-through buckling of a spherical cap and large deflection of a semi-toroidal bellows shell. Results compare well with alternative solutions.
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  • 168
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 329-347 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently developed solid modelling systems for the design of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, solid patches, etc.) and macro solids (combination of primitives)3, 4, 8, 16, 18, 25, 38. To provide an effective structural analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled (usually locally graded) finite element mesh. The purpose of this paper is to describe an interactive solid mesh generation system capable of generating valid meshes of well-proportional tetrahedral finite elements for the decomposition of multiply connected solid structures. The system uses a semi-automatic node insertion procedure to locate element node points within and on the surface of a structure. An independent automatic three-dimensional triangulator then accepts these nodes as input and connects them to form a valid finite element mesh oftetrahedral elements. Although this report makes use of a modeller based on a constructive solid geometry representation (a so-called CSG modeller), the mesh generation strategy elaborated herein is completely general and makes no particular use of the CSG representation.
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  • 169
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 349-359 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The two-dimensional inverse heat conduction problem is solved using the method of dynamic programming. One problem involves determining two unknown heat flux histories imposed on two faces of a slab. Several numerical experiments were performed to ascertain the effects of noise and the weighting parameters.
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  • 170
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 361-365 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 171
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 529-541 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite prism technique introduced by Zienkiewicz and Too4 is extended to include 12-node prism elements and, more importantly, a novel offset beam element. The use of 12-node prism elements enables parabolic strain distributions to be simulated, this being useful for structures which have strongly tapered cross-sections. The offset beam element is used to simulate flexure and torsion of a beam whose centroid is offset from the main structure. The element is specified completely at the nodes of adjacent prism elements and so is not really an ‘element’ in the usual sense.The analysis is applied to thin and thick plates and to shells, with and without edge beams. It is shown to be more versatile than the finite strip method and it requires smaller computer resources than the finite element method. Experimental verification of the analysis is obtained by comparison with measurements for a double-T bridge deck tested by Loo14.
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  • 172
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 543-554 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure to discretize explicit enthalpy formulations for one-dimensional planar phase change problems is derived, which removes numerical oscillations in temperature and phase front position. The technique is based on an enthalpy balance for the control volume containing the phase front in combination with linearized temperature profiles near the phase front. A continuous casting solidification problem and a problem with known analytical solution are applied to demonstrate the effect of the scheme.
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  • 173
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 555-563 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Interpolation of a curved triangular surface element by a complete cubic polynomial that minimizes C1discontinuity is described.
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  • 174
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 579-582 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 175
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 565-578 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present work investigates the efficacy and applicability of interior global orthogonal point collocation method to the axisymmetric nonlinear analysis of elastic circular plates and shallow spherical shells subjected to uniformly distributed transverse load. Spacewise discretisation has been carried out using a polynomial expansion with the zeros of a Chebyshev polynomial as collocation points. Timewise integration has been carried out with Newmark k-β scheme corresponding to average acceleration method. The static response and snap-through buckling results, as well as, the dynamic response and dynamic buckling results under a uniformly distributed step load have been obtained and found to agree closely with the available results.
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  • 176
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 583-584 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 177
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 617-635 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 48 degrees-of-freedom quadrilateral element, including the effect of both material and geometric nonlinearities, is formulated and appropriate numerical procedures are adopted for the development of a systematic and efficient approach for the static nonlinear analysis of general shell structures. The element surface is described by a variable-order polynomial in curvilinear co-ordinates. The displacement functions are described by bicubic Hermitian polynomials in curvilinear co-ordinates. Without being confined to the assumption of axisymmetry, this formulation allows for the treatment of shells with a more general shape and with a complex spread of plastic zones. In the formulation for geometric nonlinearity, the total Lagrangian approach is adopted. Only small strains and small rotations are allowed. In the formulation for plastic deformation, the concept of a layered element model is used. In the inelastic range, the material is assumed to obey the Von Mises yield criterion and the Prandtl-Reuss flow rule. A tangential stiffness formulation is combined with the modified Newton-Raphson iteration method for the solution of nonlinear problems. A systematic choice of examples ranging from fiat plates to cylindrical panels and to spherical caps is solved and compared with available solutions to evaluate the recommended formulations and procedures in terms of their accuracy and efficiency.
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  • 178
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 663-670 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three boundary integral equations for the solution of an important class of elastic slab problems are considered. Some numerical examples are examined in order to illustrate the application of the integral equations to particular boundary-value problems.
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  • 179
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 671-681 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theorems of structural variation for rigidly jointed frames are extended to cover the nonlinear elastic-plastic analysis of frames to collapse. Strain hardening and other material changes are included in the analysis. It is shown that the entire load-deflection history of a frame, following the successive formation of plastic hinges up to and including collapse, is obtained from a single initial elastic analysis.The manner in which these theorems are used to insert real (or plastic) hinges to a frame is presented and details of the manual calculations involved in the elastic-plastic analysis of a portal is given to demonstrate the simplicity of the method. This is followed by a comparison of the results with those obtained experimentaly by Baker and Charlton. The versatility of the method is then demonstrated by altering the shape of a frame before its elastic-plastic analysis.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 683-689 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: As an approximation for the mechanism behind noise emission from a rock drilling rod, the transient damped vibrations of a beam (the drilling rod) in bending and shear is studied. At one end the beam is supported by a distributed damped Winkler-type foundation. In order to determine required transfer function from an applied moment at the other end of the beam, it is divided into two finite elements. Each element is treated as a uniform Rayleigh-Timoshenko beam in an ambient medium. The fast Fourier transform (FFT) technique is utilized. Good agreement between calculated and measured strains is obtained. A single-figure measure which is approximately proportional to the sound power radiated from the vibrating beam is calculated for different damping materials at the supported end. It is found that a relatively high value of the stiffness of the Winkler-type foundation is needed if a significant level of reduction in the sound power radiated from the beam is to be achieved.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 733-761 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a general-purpose computer program for the inelastic analysis of reinforced concrete frames based on the method of imposed rotations. The program is capable of calculating the response of the structure to a given loading and also capable of performing collapse load analysis of the given structure. The program has been tested for a variety of problems and has been found to be extremely efficient compared to the other existing routines with much more limited capabilities. Complete listing and information for using the program has been presented.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 775-776 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 183
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 763-774 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We derive a closed-form expression for the change in the variational indicator of a finite element mesh with respect to perturbations in nodal point co-ordinates. The expression is evaluated very effectively from standard finite element data obtained in one solution, and may be easily programmed as part of a general finite element code. We present the derivation for two- and three-dimensional isoparametric elements used in linear and nonlincar elasticity. The expression has practical applications in the computation of stress intensity factors in fracture mechanics and in the determination of the ‘optimal’ mesh with a given element-node connectivity. We demonstrate both applications by accurately determining the stress intensity factor of a Mode I crack using a finite element mesh which was improved using mesh optimization.
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  • 184
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 777-778 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 185
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 909-928 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of scattering from bodies in free space is formulated using a differential equation approach. The finite element mesh extends outward into the far field region of the scattering body, where the outer boundary condition is evaluated using the asymptotic expression for the scattered field. Numerical results for two scattering bodies are presented and discussed. Non-physical, standing waves appear in the results due to the inadequacy of the outer boundary condition in fulfilling the radiation condition for the scattered field. The differential equation approach does not appear to be competitive with integral equation approaches for thin bodies, but seems promising for handling scattering from thick inhomogeneous bodies into which the field penetrates.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 929-939 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A body-fitted curvilinear co-ordinate system is used to solve the equations of two-dimensional incompressible laminar flow over bluff obstructions by finite differences. Arbitrary conditions at the corner are removed by this method. Results for a backward-facing step are in reasonable agreement with those obtained with conventional mesh systems, and the differences are explained. A treatment of a channel expansion, in comparison with empirical data, is also included. The capability of the present method to handle arbitrary two-dimensional geometries is stressed and demonstrated, using a triangle and a semi-circle as examples.
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  • 187
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 959-965 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The ability of the collapsed Q-8 finite element to model strain singularities is studied in this paper. It is shown that its ability to model an r-1 singularity in strains depends strongly on the element size and number of Gauss points used for sampling stresses inside an element.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 975-999 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A series of direct-integration and model-expansion finite element algorithms for a geometrically and materially nonlinear elastodynamic problem are constructed and analysed. The algorithms are constructed by temporally approximating the individual nonlinear stiffness terms such that discrete conservation laws are obtained. This conservative property has a positive effect in providing a stable appromixation, and in addition allows the stability properties of the algorithms to be easily assessed. Stability and convergence criteria for the algorithms are rigorously established using an energy method.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1167-1167 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1168-1169 
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    International Journal for Numerical Methods in Engineering 21 (1985) 
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1171-1185 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for determining the optimum step-size in numerical differentiation of a tabulated function is described. In test cases it gives an average error of about four times the error in the data; thus, it is more than twice as accurate as previously published methods. A Fortran program is presented.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1361-1362 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1363-1364 
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    International Journal for Numerical Methods in Engineering 21 (1985) 
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1365-1380 
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Previously published literature shows widely different results for the free vibration frequencies of twisted cantilever plates. Inasmuch as it is important to know the vibration characteristics of turbomachinery blades, which may have considerable twist, it would be desirable to have a comprehensive, definitive set of results, and to establish which of the numerous theoretical methods available can adequately analyse such problems. For this purpose, a joint government/industry/university research study was organized. Numerical results were obtained for a set of 20 different twisted plates having various aspect ratios, thickness ratios and pretwist angles. Nineteen distinct theoretical methods were employed, 15 using finite elements, two using shell theory, and two using beam theory. Although some of the best-known computational procedures (especially finite element codes) were used by analysts with great experience, the numerical results obtained showed considerable disagreement. The present paper describes the analytical methods used and exhibits samples of the type of results obtained.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1381-1390 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical scheme has been constructed to simulate the imposition of a step in heat transfer at the surface of a multi-layered substrate. The numerical simulation of this process is carried out by applying an extended version of the Keller Box-Scheme to multi-layered diffusion problems. Numerical calculations show that accurate choice of length and time-scales is critical in determining the behaviour of the heat flow through the substrate. Thus, the results from the numerical simulations are of value to the experimentalist, particularly in determining the accurate shape of the response curves which enable experimental apparatus to be designed effectively. The proposed scheme yields heat fluxes as accurately as temperatures, and can be easily adapted to other related applications.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1391-1401 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The best approach for the numerical determination of stress intensity factors at crack tips in plane and antiplane elasticity problems is frequently the numerical solution of the corresponding Cauchy-type singular integral equation by the Gauss-Chebyshev method, followed by the application of the natural extrapolation formula for the numerical determination of the stress intensity factors. It is shown here that this approach converges for Hölder-continuous and discontinuous (with jump discontinuities) loading distributions along the crack (or cracks) and that in all cases the rate of convergence is greater than that believed up to now. This superconvergence result is based on a theorem on the numerical equivalence of the Gauss-Chebyshev direct method to a relevant indirect method for the numerical solution of Cauchy-type singular integral equations, also proved here. Numerical results in various crack problems corroborate the theoretical ones.
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  • 199
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1403-1426 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a new algorithm to generate interior nodes within any arbitrary multi-connected regions. The boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner. Owing to the generality of the central generation program, the global domain is allowed to be divided into as many irregular subdomains as desired, in order to model closely the actual physical situation. Moreover, the boundaries of the sub-domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner, generating radiating mesh from a prescribed node, generating mesh between two circular arcs, etc. Despite its flexibility and capabilities, data for triangulation have been kept to a minimum by a logical input module; no connectivity information between subregions is needed, and common boundaries are defined once only. All these features have contributed to a powerful method to generate 3-node or 6-node triangular element meshes of great variety within the most irregular heterogeneous regions.
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    International Journal for Numerical Methods in Engineering 21 (1985), S. 1447-1458 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of solving inverse problems of stationary electromagnetic fields is described. It can be applied to problems in non-homogeneous, linear and isotropic environments. The method is based on application of integral equations of the first kind which require regularization because they are ill-posed. Numerical calculations of some selected problems confirm the effectiveness of the proposed method.
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