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  • Engineering General  (3,144)
  • Wiley-Blackwell  (3,144)
  • 1990-1994  (3,144)
  • 1
    Electronic Resource
    Electronic Resource
    Computation of outflow flux for convection-dominated transport equations (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 639-647 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An a posteriori point-wise outflow flux recovery scheme which capitalizes on the hyperbolic nature of convection-dominated transport models is proposed. The scheme is seen to be robust in that it can be applied to any upwind finite-difference or finite-element approximation, and gives a superconvergent approximation to the outflow flux.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090803
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  • 2
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    Application of iterative global/local finite-element analysis. Part 2: Geometrically non-linear analysis (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 757-766 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A geometrically non-linear global/local technique was developed and tested. This technique uses separate global and local finite-element models. Iteration is used to enforce equilibrium between the global and local models. The results of this initial study suggest that the technique can be used to reduce both computer memory and CPU requirements.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090906
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  • 3
    Electronic Resource
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 785-785 
    Details
    ISSN: 1069-8299
    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/cnm.1640090909
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  • 4
    Electronic Resource
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    Consistent concept for line search algorithms in combination with arc-length constraints (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 773-784 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general line search concept is presented, which can be applied for the solution of non-linear equations in the presence of constraint conditions as in arc-length methods in a consistent manner.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090908
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  • 5
    Electronic Resource
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    Two problems with GGP generalized geometric programming algorithm (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 767-772 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The generalized geometric programming algorithm GGP has been found to be one of the better algorithms for optimizing algebraic functions subject to algebraic constraints. The paper discusses two problems with the GGP algorithm presented by Avriel et al. (1980). The first problem is that, because of the way that constraint tolerances are checked, the checks may pass even when a constraint is violated beyond the acceptable tolerance. This problem can affect an acceleration technique suggested for the algorithm. This paper presents two possible solutions to this problem. The second problem is the algorithm's weakness in handling equality constraints. This problem seems to especially affect the ‘Phase I’ part of the algorithm, which finds a feasible solution from a random starting point. While extensions have been made to get around this limitation, no discussion on why the original algorithm has problems with equality constraints has been made. This paper discusses why the problems exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090907
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  • 6
    Electronic Resource
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    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/cnm.1640091001
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  • 7
    Electronic Resource
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    Matrix filter for correcting experimental data (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 797-803 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a filtering algorithm which corrects the results of measurements of certain physical quantities if any additional information about the measured values is known. The algorithm is very effective in one-dimensional as well as in two-dimensional problems where additional constraints are presented in the form of differential equations. For example, this technique can be used to correct the measurements of certain dynamic quantities if some information about motion of examined bodies is known. It can also be used to correct the strain field measurements if the conditions of continuity of strain field are included.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091003
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  • 8
    Electronic Resource
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    Finite-element computer simulation of atmospheric convection with anisotropic eddys (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 805-814 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer simulation is made of cellular convection in an anisotropic atmosphere in an attempt to more closely approximate the observed values with those obtained from mathematical models. A finite-element Galerkin technique, with Taylor approximation and Crank-Nicolson, is employed and comparisons are made with the author's earlier finite-element models of isotropic convection and with finite-difference models. It is found that postulates from physics on the effect of anisotropy on cellular atmospheric convection, with its increase in the aspect ratio, are well modelled with this finite-element technique.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091004
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  • 9
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    Application of augmented Lagrangian techniques for non-linear constitutive laws in contact interfaces (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 815-824 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of micromechanically based constitutive equations for contact interfaces leads to technically relevant parameters to ill-conditioned finite-element equations. In the paper an augmented Lagrangian technique is employed to overcome this difficulty and to provide a good converging algorithm.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091005
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  • 10
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    Finite-element analysis of elastic contact between a shell of revolution and a rigid plate (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 883-888 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Elastic contact between a thick shell of revolution and a rigid plate in the case when the plate is brought into contact with the shell by giving a finite displacement to the plate is analysed by the finite-element method. Field-consistent higher-order strain-displacement relations with vanishing shear stresses on the surfaces are used. A finite element based on these relations is developed and used for the analysis. The contact conditions are imposed by use of the Lagrangian multipliers method, and the resulting minimization problem is solved iteratively. This procedure will lead to reduced memory requirements and computation time.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091104
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  • 11
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    Computation of isotropic tensor functions (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 889-896 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An explicit formulation and a procedure for the computation of isotropic tensor-valued tensor functions is discussed. The formulation is based on a spectral decomposition in terms of second-order eigenvalue bases, which avoids the costly computation of eigenvectors. As an important result a compact structure of the fourth-order derivatives of general second-order isotropic tensor functions is presented.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091105
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  • 12
    Electronic Resource
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 933-935 
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    ISSN: 1069-8299
    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/cnm.1640091110
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  • 13
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    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/cnm.1640091201
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  • 14
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    Macro finite element using subdomain integration (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 937-949 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For some heterogeneous materials, it is not practical to model the microstructure directly using traditional finite elements. Furthermore, it is not always accurate to use homogenized properties. Macro elements have been developed which permit microstructure within a single element. These macro elements performed well in initial tests.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091202
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  • 15
    Electronic Resource
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    Mapping of finite elements around corner singularities of the quasi-harmonic equation (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 957-974 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with the solution of the quasi-harmonic equation by the finite element method in a domain with corners on its boundary. A mapping technique, which can be used for locating the nodes of standard isoparametric elements in a subgrid (patch) of finite elements in the vicinity of a corner singularity point, is presented. The equations of the mapping are based on the analytical singular solution of the problem. Some analytical and numerical results to show the efficiency of the technique are presented.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091204
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  • 16
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    Arbitrary Lagrangian-Eulerian thermomechanical finite-element model of material cutting (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 975-987 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An arbitrary Lagrangian-Eulerian model is described for the prediction of metal flow in a steady-state forming process. The formulation is shown to be capable of dealing with free surface and boundary friction; the coupling with thermal effects is also considered. The numerical techniques are based on the finite elements for spatial discretization of the momentum equation and on an explicit integration scheme for discretization relative to time. The mass and energy equations are integrated by a finite-volume method. Details on the application to an orthogonal cutting process are given in the final Section of the paper.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091205
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  • 17
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    Optimization analysis of the three-level time schemes (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 951-956 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure was implemented to determine the optimum values for the two parameters of the Zienkiewicz three-level time schemes which could be utilized for the numerical solution of a system of ordinary differential equations. A multivariable search method was implemented to estimate optimum values for these parameters. The resultant optimum three-level time scheme produced very accurate results, satisfied physical reality, and did not produce any oscillations for the various problems that were investigated. The optimum values for the two parameters β and γ in the three-level scheme were β = 0·50005 and γ = 1·0007. A comparison was made between this optimum scheme and other existing three-level time schemes. The optimum scheme demonstrated superior results for all the problems that were analysed. However, the results of the optimization analysis produced a set of optimum parameters that were identical to the values that would reduce the general three-level time scheme into a central-difference two-level time scheme, i.e. β = 1/2 and γ = 1.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091203
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  • 18
    Electronic Resource
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    New assumed natural strain formulation of the shallow shell element (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 989-1004 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new efficient formulation of the 36 degree-of-freedom conforming shallow shell element of an arbitrary triangular shape is presented. This formulation is based on natural co-ordinates and independently assumed natural strain fields, and applied to shallow shell analysis. The 3-node element incorporates the normal displacement and its first and second derivatives plus the tangential displacements and their first derivatives at each vertex. A closed form of the element stiffness matrix is achieved. The form of the stiffness matrix derived in this formulation explicitly reveals the essence of the shallow shell theory.The presented approach results in avoiding definite integrals and matrix inversions, and permits operation with lower-order numerical matrices, which are the same for all elements. The example applications presented demonstrate that accurate predictions of stresses as well as displacements are obtained with only a few elements.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091206
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  • 19
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    Locking-free straight beam element based on curvature (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 1005-1011 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The formulation of a straight beam element to eliminate the shear locking phenomenon is presented. The element is based on curvature so that the bending energy is fully represented, and the shear strain energy is incorporated into the formulation by the equilibrium equation. Four examples are chosen to verify the concept of the element employed and its capability of the analysis. The solutions obtained reveal that the element describes the behaviour of the straight beam quite exactly and efficiently, showing no locking and that it is also applicable to the analysis of both thin and thick straight beams.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091207
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  • 20
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 1013-1015 
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    ISSN: 1069-8299
    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/cnm.1640091208
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  • 21
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    Masthead (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
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    ISSN: 1069-8299
    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/cnm.1640100101
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  • 22
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    Iterative computation of second-order derivatives of eigenvalues and eigenvectors (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 1-9 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative method is introduced for computing second-order partial derivatives (sensitivities) of eigenvalues and eigenvectors of matrices which depend on a number of real design parameters. Numerical tests confirm the viability of the method and support our theoretical analysis. Alternative methods are reviewed briefly and compared with the one proposed here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100102
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  • 23
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    Semi-Loof element for plate instability (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 11-19 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the formulation of the semi-Loof element the rotation of the tangent plane is derived from the interpolation of the transverse displacement, while the rotation of the normal is interpolated separately by another set of shape functions. The geometric stiffness matrix can be formulated by use of either of the two rotation representations. It is demonstrated that the use of the tangent plane representation in the geometric stiffness matrix is far superior to the common form at present.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100103
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  • 24
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    Least-squares T-elments: Equivalent FE and BE forms of a substructure-oriented boundary solution approach (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 21-32 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient solution to boundary-value problems may be based on the application of a suitably truncated T-complete set of Trefftz functions over individual subdomains and on linking the fields by a least-squares procedure. Although it yields a symmetric system of linear equations, this approach as originally presented by Zielinski and Zienkiewicz is not suited for implementation into FE codes. The present paper presents two equivalent formulations, which take respectively the form of the finite (FE) and non-conventional boundary-element (BE) approach. Both allow the resulting simultaneous equations to be assembled following the standard direct stiffness methods and can readily be implemented into existing FE codes.As in the conventional p-method, the accuracy may be controlled within large limits without increasing the number of elements. The present approach allows substantial saving in computer time in comparison with the so-called hybrid-Trefftz (HT) elements, though the assumed displacement fields are identical. The practical efficiency of the new T-element approach is assessed on the problem of stress concentration in a symmetrically compressed perforated panel.
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    URL: http://dx.doi.org/10.1002/cnm.1640100104
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  • 25
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    High-order polynomial interpolation in boundary integral equation analysis (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 167-178 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A sixth-order polynomial shape function is developed for BIE analysis. The function is applied over only three-noded elements, but with the support for the function extending over adjacent elements. This avoids the oscillations near the ends of the range which otherwise are characteristic of high-order polynomial interpolation. Various test problems are explored, and it is shown that results as accurate as those from conventional quadratic elements are obtained with larger nodal spacings, and thus giving the potential for significant reductions in matrix storage requirements and solution times.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100208
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  • 26
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    Accurate finite element method for steady and quasisteady lifting aerofoil (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 155-166 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation based on superposition is proposed for a lifting aerofoil in incompressible potential flow. An accuracy improvement technique for the singularity at the aerofoil trailing edge is discussed. It is shown that the quarter-node quadrilateral element can be readily employed to simulate this singularity. It is also demonstrated that the circulation in the flow field can be easily represented by a single constraint equation rather than introducing an artificial cut line in the mesh. The influence of finite-element mesh size on solution accuracy and the correct form of the boundary condition have been investigated as well. Numerical examples are given for both steady and quasisteady Joukowski aerofoils of various thicknesses and at a range of incidences. In all test cases, good agreement is observed between the analytical solution and the numerical result.
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    URL: http://dx.doi.org/10.1002/cnm.1640100207
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  • 27
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    Masthead (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
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    ISSN: 1069-8299
    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/cnm.1640100301
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  • 28
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    A 3D element for non-linear analysis of solids (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 183-194 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An 8-node element (HMITC) for 3D non-linear analysis of solids is presented. The new element is based on an element developed by Wilson and Ibrahimbegovic, that incorporates incompatible modes, and on the method of mixed interpolation of tonsorial components. The HMITC element does not contain spurious zero energy modes and satisfies Irons' Patch Test. The numerical experimentation indicates that the HMITC has good performance even with distorted meshes.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640100302
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  • 29
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    Space-time oriented streamline diffusion methods for non-linear conservation laws in one dimension (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 203-215 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we consider an explicit finite-element method, with elements adaptively oriented in space-time, for the solution of one-dimensional conservation laws, extending previous work dealing with linear convection-diffusion and incompressible flow. In particular we consider Burgers' equation and the compressible Euler equations.
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    URL: http://dx.doi.org/10.1002/cnm.1640100304
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  • 30
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    Neural-network-based approximations for solving partial differential equations (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 195-201 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method, based on neural-network-based functions, for solving partial differential equations is reported in the paper. Using a ‘universal approximator’ based on a neural network and point collocation, the numerical problem of solving the partial differential equation is transformed to an unconstrained minimization problem. The method is extremely easy to implement and is suitable for obtaining an approximate solution in a short period of time. The technique is illustrated with the aid of two numerical examples.
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    Cyclic symmetry in boundary elements (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 217-225 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient algorithm for consideration of axial and cyclic symmetry in the boundary-element method is presented. The appropriate transformation relationships was derived. The algorithm is then implemented in a boundary element program for the analysis of 2D elastostatic problems. Through analysis of typical problems the validity of the algorithm and its implementation is verified. A high level of accuracy and substantial reduction in computer time and storage was achieved.
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    Explicit variable time-step method for implicit moving boundary problems (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 227-235 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The diffusion of oxygen into an absorbing medium as an example of an implicit moving boundary problem has been dealt with by a number of authors using various numerical techniques, and, where appropriate, approximate analytical expressions. To evaluate the time for complete absorption, extrapolation is usually employed. An unconditionally stable explicit numerical scheme that avoids the limitations of such methods is presented and tested herein. Unlike existing schemes this method is fully numerical; it avoids the large array size, generally required for existing methods, by using a variable-length time step. The time for complete absorption emerges from the final step in the normal computing procedure with no recourse to extrapolation. Furthermore, owing to the implicit condition prevailing at the moving boundary, no iterations are needed to evaluate the time step required for the moving boundary to move a single space increment. The numerical results obtained compare very favourably with those due to earlier authors.
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    Boundary-element solution of some structural-acoustic coupling problems using the multiple reciprocity method (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 237-248 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In the paper we have developed a new formulation for solution of structural-acoustic coupling problems by boundary elements using the multiple reciprocity method. It is assumed that the structure is composed of plate components and is excited by the external or the internal noise source. The efficiency of the proposed formulation becomes especially remarkable if the boundary-value problem is to be solved repeatedly for different values of frequency. The accuracy of the numerical computations has been compared with the analytical solution in a test example.
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    Homogenization and effective elastoplasticity models for periodic composites (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 257-265 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Techniques for stress- and strain-controlled in situ homogenization of inelastic periodic composites are presented. The results of homogenization computations on a specific elastoplastic composite solid are then employed to validate the form of an orthotropic elastoplasticity model with a tensorial kinematic hardening law.
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    Lagrange multiplier approach for evaluation of friction in explicit finite-element analysis (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 249-255 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An algorithm for evaluation of friction in general contact-impact interfaces is described. The algorithm is based on an explicit finite-element method. Coulomb's friction law is assumed. The defence node algorithm is used such that the sticking condition can be imposed with the Lagrange multiplier method even in explicit dynamic analysis. The algorithm is supposed to be applicable in general situations, including large deformations of the contact-impact bodies and large relative sliding between the contact-impact boundaries. Numerical results are presented to demonstrate the performance of the algorithm.
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    Conference diary (1994)
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    Communications in Numerical Methods in Engineering 10 (1994), S. 275-277 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Masthead (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/cnm.1640100401
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    General forming of transition elements (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 267-273 
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    Notes: A generalization of the r(1-m)/m strain singularity of higher-order isoparametric elements is presented. It is shown that, by variable placement of the side nodes between their original and singular positions, the point of singularity sensed by the element can be controlled. The transition elements have a strain singularity outside their domain. The singular and non-singular elements are elements are special cases of the general mapping. The transition elements, together with the singular isoparametric elements, can be used for solving crack problems.
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    Some geometric problems related to fracture-control in complex structures (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 279-290 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In the design of members with flaws, it is necessary to keep the stress intensity factor K of any sharp crack below the fracture toughness Kcr of the materials. Stress-intensity factor equations for the more common basic specimen geometries and various loading conditions are available in the literature. The application of these equations to complex structures involves geometric problems such as the identification of the outline of each member and the sizing of the equivalent specimen for each flaw. The paper gives a response to such difficulties.
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    Modified simplex optimization program (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 303-312 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A simple, yet storage-effective ‘linear’ programming code is given. The assumption of non-negative variables is bypassed without increasing the size of the problem. Furthermore, the objective is allowed to be summed over not just linear, but also concave, functions. A specific truss topology optimization example is shown.
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    Fourth-order difference method for quasilinear Poisson equation in cylindrical symmetry (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 291-296 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We propose in this paper a nine-point, fourth-order difference method for the numerical solution of the quasilinear Poisson equation \documentclass{article}\pagestyle{empty}\begin{document}$$ Au_{zz} + \frac{1}{r}u_r + Bu_{rr} = f\left({r,z,u,u_r,u_z} \right) $$\end{document} with appropriate boundary conditions. The method is based on five evaluations of f. The numerical results of four problems obtained using this method are listed. The results demonstrate the fourth-order accuracy of the method.
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    Use of central-difference operators for solution of singularly perturbed problems (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 297-302 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Singularly perturbed second-order elliptic equations with boundary layers are considered. These may be considered as model problems for the advection of some quantity such as heat or a pollutant in a flow field or as linear approximations to the Navier-Stokes equations for fluid flow. Numerical methods composed of central-difference operators on special piece-wise-uniform meshes are constructed for the above problems. Numerical results are obtained which show that these methods give approximate solutions with error estimates that are independent of the singular perturbation parameter. An open theoretical problem is posed.
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    Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 313-320 
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    Keywords: Engineering ; Engineering General
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    Notes: In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
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    Universal matrices with new infinite elements for quasiharmonic equation (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 321-331 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new approach to developing serendipity quadrilateral infinite elements is presented. Using these elements universal matrices for quasiharmonic equation are developed. For a particular member of the family these matrices are independent of the size and shape of the element. Using these matrices the element stiffness matrix can be generated in a simpler manner by taking into account the size and shape of the element.
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    Accelerated modified Newton-Raphson iteration-based finite-element solution of structural problems involving non-linear deformation behaviour (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 333-338 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new global secant relaxation (GSR)-method-based improvement procedure is used to improve the overall convergency performance of the modified Newton-Raphson iteration in carrying out the solution of discrete systems resulting from the finite-element discretization of a certain class of structural problems involving non-linear deformation behaviour.
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    A simulation of free-surface electrohydrodynamic flow (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 339-353 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Theoretical and experimental analysis of free-surface electrohydrodynamic flow is fragmented and incomplete. Simulation studies of this phenomenon are further limited by the inherent complexities in the modelling process. In this note a mathematical model is developed to analyse free-surface electrohydrodynamic flow in two dimensions, and preliminary results of the simulation are described. The configurations examined include electrified conducting surfaces, the dielectrophoretic forces, and a conducting jet. The simulation is compared with analytical results in the first two investigations and is shown to be quite accurate. In the last simulation it is demonstrated that in the initial formation of a conducting jet, a 10 per cent increase in applied voltage results in about a 10 per cent increase in fluid velocity.
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    Conference diary (1994)
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    Communications in Numerical Methods in Engineering 10 (1994), S. 355-357 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Announcements (1994)
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    Communications in Numerical Methods in Engineering 10 (1994), S. 359-360 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Masthead (1994)
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    Communications in Numerical Methods in Engineering 10 (1994) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Improvement on dual reciprocity boundary element method for equations with convective terms (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 361-371 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The dual reciprocity boundary element method, first proposed by Nardini and Brebbia (1982, 1985), is a powerful technique for solving elliptic partial differential equations. Adopting this approach, a singular volume integral, which needs to be evaluated with a traditional boundary element method, can be converted into a boundary integral. However, when the governing equation is of a certain type, this conversion fails due to the singularities being introduced inside the physical domain and on the boundary arising by differentiating distance functions. We avoid these artificially created singularities by constructing a transformation which leads to improved numerical results.
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    A direct solver for the least-squares problem arising from GMRES(k) (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 743-749 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This is a study about one of the core questions in the GMRES(k) method regarding the obtaining of vector yk for the least-squares problem, argminy |Hky - β(n)e1|2 (see Saad and Schultz1). We propose a simple but efficient approach to the resolution of this problem and a low cost computation of the residual and the residual norm, including both in a complete and detailed FGMRES(k) algorithm. The whole algorithm of minimization only involves two backward substitutions with triangular matrices and a dot product. The residual and the residual norm are computed, making use of results in the least-squares problem.
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    Conference diary (1994)
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    Communications in Numerical Methods in Engineering 10 (1994), S. 759-760 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Announcements (1994)
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    Communications in Numerical Methods in Engineering 10 (1994), S. 761-762 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Masthead (1994)
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    Communications in Numerical Methods in Engineering 10 (1994) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/cnm.1640101001
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    A combined octree/delaunay method for fully automatic 3-D mesh generation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 37-55 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Fully automatic three-dimensional mesh generation is a fundamental requirement for automating the numerical solution of partial differential equations. Two techniques in particular - the octree and Delaunay approaches - have been used towards this end. A method that combines both approaches to fully automatic mesh generation is presented here. The resulting algorithm provides the linear growth rate and divide-and-conquer approach of the octree method with the simplicity and optimal properties of the Delaunay triangulation.
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    A hybrid/mixed model for non-linear shell analysis and its applications to large-rotation problemsThis work is supported by National Science Foundation, under Research Grant Number EET-8714628 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 407-446 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Adopting an updated Lagrange approach, the general framework for the fully non-linear analysis of curved shells is developed using a simple quadrilateral C0 model (HMSH5). The governing equations are derived based on a consistent linearization of an incremental mixed variational principle of the modified Hellinger/Reissner type with independent assumptions for displacement and strain fields. Emphasis is placed on devising effective solution procedures to deal with large rotations in space, finite stretches and generalized rate-type material models. In particular, a geometrically exact scheme for configuration update is developed by making use of the so-called exponential mapping algorithm, and the resulting element was shown to exhibit a quadratic rate of (asymptotic) convergence in solving practical shell problems with Newton-Raphson type iterative schemes. For the purpose of updating the spatial stress field of the element, an ‘objective’ generalized midpoint integration rule is utilized, which relies crucially on the concept of polar decomposition for the deformation gradient, and is in keeping with the underlying mixed method. Finally, the effectiveness and practical usefulness of the HMSH5 element are demonstrated through a number of test cases involving beams, plates and shells undergoing very large displacements and rotations.
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    Formulation of implicit finite element methods for multiplicative finite deformation plasticity (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 483-514 
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    Keywords: Engineering ; Engineering General
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    Notes: Some constitutive and computational aspects of finite deformation plasticity are discussed. Attention is restricted to multiplicative theories of plasticity, in which the deformation gradients are assumed to be decomposable into elastic and plastic terms. It is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non-symmetric even for associated plastic flow. Both explicit (i.e. no equilibrium iteration) and implicit finite element formulations are considered. An assumed strain formulation is used to accommodate the near-incompressibility associated with fully developed isochoric plastic flow. As an example of explicit integration, the rate tangent modulus method is reviewed in some detail. An implicit scheme is derived for which the consistent tangents, resulting in quadratic convergence of the equilibrium iterations, can be written out in closed form for arbitrary material models. All the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly. Examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method.
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    Model reduction for thermal diffusion: Application of the Eitelberg, Marshall and aggregation methods to a heat transmission tube model (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 599-617 
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    Keywords: Engineering ; Engineering General
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    Notes: This study, dealing with model reduction for thermal diffusion, describes the numerical techniques used: the Eitelberg, Marshall and aggregation methods. The non-linear model of a heat transmission tube, to which these methods are applied, is then described, pointing out the necessary initial algebraic treatment for reduction. Finally the outputs of the complete model and of several reduced ones are compared for some characteristic variations of the inputs. For this problem, the Eitelberg and Marshall methods, which can be used with a high coefficient of reduction, are well adapted.
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    Singular behaviour near an interface crack tip of power law hardening materials using The Finite Element Iterative Method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 699-717 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Finite Element Iterative Method (FEIM) is extended to the analysis of asymptotic fields of materials with non-linear behaviour. It is used in the investigation of the asymptotic field of an interfacial crack of power law hardening materials. The material is assumed to deform according to the total deformation theory of plasticity. The results of the analysis provide evidence to support the hypothesis that the asymptotic field can be cast in the form of the HRR-singularity multiplied by a function of the product form. This function can be written as a series of oscillatory functions, similar to those encountered in an elastic field, each of which is valid over a substantial range of the process zone. The real part of these terms depends on the loading mode, process zone size as well as material properties; it is, however, very small compared to the HRR-singularity. The imaginary part which gives the phase shift is much smaller than the elastic value and is a weak function of the hardening power and the size of the process zone of interest; it eventually vanished at extremely small distances.
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    Consistent force resultant distributions in displacement elements with varying sectional properties (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 775-783 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Force fields computed directly from strains calculated in a displacement type finite element description of a structural element of varying sectional rigidities show extraneous oscillations. The origin of these oscillations is traced to the fact that the displacement type finite element procedure determines strains derived from the displacement field in a least squares correct sense and that force resultants computed using these strain fields and the actual sectional rigidities result in unwanted oscillations. It is necessary to introduce the concept of redistributed assumed force resultant fields that maintain a ‘consistent’ relationship to the strain fields and also are orthogonal to these strain functions. In this paper, the Hu-Washizu theorem is invoked to justify the introduction of an orthogonally correct reconstituted assumed force resultant field which will then be free of extraneous oscillations. The quadratic isoparametric tapered bar element serves to illustrate the underlying principles.It follows that the extremely general Hu-Washizu principle is the most practical procedure of implementing an assumed force resultant, assumed strain displacement type formulation to introduce consistency and thereby remove problems associated with field-inconsistency (such as cause locking in constrained media elasticity) and force resultant oscillations due to varying sectional properties.
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    Improved hybrid solid element with a traction-free cylindrical surface (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 801-809 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New 8-node solid elements with two parallel faces and one traction-free cylindrical surface are derived using the assumed stress hybrid model. Six new expressions of stress components are developed by using four stress functions and cylindrical co-ordinates, so that the normal stress σz on the plane perpendicular to the two parallel faces varies as a parabola, and the assumed stress field satisfies the equilibrium equations as well as the traction-free conditions over the cylindrical boundary. The assumed stress field also satisfies the compatibility conditions when the new element is degenerated into the 2-dimensional case. Examples have clearly demonstrated that these present special elements are far superior in predicting the stress concentration factors, the distributions of circumferential stresses and the normal stress σz.
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    Explicit integration for three-dimensional degenerated shell finite elements (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 861-880 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Explicit integration across the thickness for three-dimensional degenerated shell finite elements is analysed. For this purpose a modifed formulation is proposed. The Jacobian matrix of the physical-parameter spaces transformation is decomposed into a product of ‘in-middle-surface’ and ‘out-of-middle-surface’ terms. This enables an expansion to be carried out of the strain-displacement matrix into power series of the thickness variable. Explicit integration is then performed and the corresponding formulae of the stiffness and mass matrices are given. The possibility of ‘locking’ for thin structures is explained. The analysis is applied to homogeneous and multilayered structures. Numerical applications for linear problems are given in the last part of the paper.
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    A semi-analytical method for time-domain analyses of dam-reservoir interactions (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 913-933 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Non-linear responses of dam-reservoir systems are not well understood, because of the lack of an exact time-domain solution for the far field (extending to infinity) of the fluid. This paper presents a procedure for efficient time-domain analyses. It is based on a semi-analytical solution and is suitable for the determination of the interactive behaviour of dam-reservoir systems.In this formulation, the fluid domain is divided into a near (to the dam) field, which is finite, and a far field extending to infinity. Arbitrary shapes of the upstream face of the dam, and of the bottom of the reservoir floor in the near field, are presumed. Furthermore, the far field is assumed to have a constant depth. The irregular near field is modelled by using the finite element method. A time-domain semi-analytical solution is obtained for the far field. For a vertical dam subjected to earthquake and ramp loadings, numerical solutions obtained compared well with the piecewise exact form of the analytical solution.
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    Advanced development of time-domain BEM for two-dimensional scalar wave propagation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1003-1020 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An improved formulation for solving 2D transient scalar wave propagation problems by the Boundary Element Method (BEM) is presented. The kernels presented are simpler and better behaved than those that have appeared in the published literature. An appropriate set of temporal shape functions for linear variation is used. For spatial variations isoparametric quadratic elements are used. All of these represent significant improvements over the present level of sophistication in the analysis of 2D transient scalar problems. The algorithm is implemented in a general purpose boundary element code known as GPBEST.
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    Time-domain radiation boundary for analysis of plane Love-wave propagation problem (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1049-1063 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method of modelling the radiation effect in a time-domain finite element analysis of semi-infinite solids is proposed. The domain to be analysed is divided into a finite, interior region and a semi-infinite, exterior region. The standard finite elements are used to model the interior region. An infinite element is used to model the semi-infinite region. The main feature of the proposed method is the selection of semi-infinite shape functions to develop the infinite element. A procedure is proposed whereby the necessary shape functions are derived directly from frequency-domain analytical mode shapes. The interior and exterior regions are coupled by enforcing displacement continuity at the interface. The validity of the method is demonstrated in this paper by analysing a two-dimensional, linear (damped), anti-plane, shear-wave (plane Love-wave) propagation problem. The results obtained by the proposed method are compared with those obtained by direct finite element analysis with a fixed boundary placed sufficiently far from the location of loading to avoid wave reflections.
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    A new implementation of the Lanczos method in linear problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 141-159 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Lanczos algorithm has proved to be a powerful solution method not only for finding the eigenvalues but for solving linear systems of equations. In this work a new implementation of the algorithm is presented for solving linear systems of equations with a sequence of right-hand sides. The versions of the method proposed in the past treat the right-hand side vectors successively by keeping the tridiagonal matrix and the orthonormal basis in fast or secondary storage. The new technique handles all approximations to the solution vectors simultaneously without the necessity for keeping the tridiagonal matrix or the orthonormal basis in fast or secondary storage. Thus, when the first solution vector has converged to a required accuracy good approximations to the remaining solution vectors have simultaneously been obtained. It then takes fewer iterations to reach the final accuracy by working separately on each of the remaining vectors.
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    A non-proportional loading finite element analysis of continuum damage mechanics for ductile fracture (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 197-209 
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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 the development of a finite element analysis based on an anisotropic model of continuum damage mechanics theory proposed recently by the authors for ductile fracture under non-proportional loading. The condition of non-proportional loading is formulated by introducing a dynamic co-ordinate system of principal damage allowing the principal direction of damage during the loading to rotate accordingly.The finite element analysis developed under non-proportional loading is applied to predict the crack initiation load of a centre-cracked plate under uniform loading. The predicted load agrees satisfactorily with those determined experimentally with centre-cracked thin plates made of aluminium alloy 2024-T3. The analysis also reveals under non-proportional loading the hysteresis effect of the principal directions of damage and stress. In addition, the influence of varying anisotropic damage coefficients on the crack initiation load and the crack tip displacement profile is also examined. The larger the degree of the anisotropy, the higher the crack initiation load. The magnitude of the crack tip displacement profile is found to be proportional to the degree of material anisotropy.
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 449-452 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Non-linear optimization technique for partial solution of generalized eigenvalue problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 473-482 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an alternative to the subspace iteration and Lanczos techniques, both of which are now used to solve partial eigenvalues and eigenvectors of large generalized linear first order symmetric matrix systems. It is based on non-linear optimization of a modified Rayleigh quotient. The elements of the eigenvector are the decision variables. Orthogonality constraints with respect to the two matrices are incorporated in the sequential unconstrained optimization scheme. By imposing normality with respect to one of the matrices, the Hessian matrix reduces to a much simpler form for which the Woodburry transformation may be used. This, in combination with the fact that the banded structure of the matrices is maintained, results in a number of operations of the same order as the two standard methods. Shifting is readily integrated. Numerical comparison with existing techniques demonstrate the practicality of this method.
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    Importance and use of rigid body mode in boundary element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 453-472 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The superposition of a rigid body mode on a body should result in a corresponding change in displacement values but should not affect the stresses. However, in the numerical solution by the boundary element method (BEM) large errors may be obtained for displacements and stresses if a rigid body mode is present in the input data. To eliminate the effects of the rigid body mode on the numerical accuracy of the solution, the fundamental solutions for displacements must be correctly interpreted and used. The rigid body mode may be unknowingly present in the boundary condition data. It may be present because the boundary data are not known accurately. Or it may be present if the displacement values at the support have been computed from a separate analysis. A rigid body mode may arise due to the collocation nature of satisfying the boundary conditions. The point values of the applied load at the collocation point may not satisfy equilibrium. Or the point values of the specified displacements may not satisfy the condition of zero translation and rotation. For bodies under pure traction, we know that the analytical solution can contain an arbitrary amount of rigid body mode. Numerically, however, some unknown value is assigned to this rigid body mode. It might be desirable (for example in limit analysis) to eliminate the rigid body mode from the displacements to obtain deformation of a point with respect to a point on the body. In addition, knowledge and elimination of the rigid body mode is necessary for the implementation of a scheme described by this author in an earlier work. The importance of the earlier work is that it reduced the sensitivity of the BEM to changes and errors in the input data. In this paper the causes, and the effects of the rigid body mode on the BEM, the correct interpretation of the fundamental solution for displacements and an algorithm for determining and accounting for the rigid body mode are discussed. A numerical example validates the ideas in this paper for the indirect version. The algorithm for the direct version is presented without a numerical example in the Appendices.
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    A panel method computation for oscillating aerofoil in compressible flow (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 559-578 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A panel method using source and doublet singularity has been proposed to solve for subcritical aerodynamics of a two dimensional steady and unsteady aerofoil. The source singularities are placed on the aerofoil surface. The doublet singularity is distributed by a function along the chordline of the aerofoil; this distribution is further projected downstream into infinity.The aerodynamics of an oscillating aerofoil is investigated. The governing unsteady linearized potential equation has a Hankel function as its fundamental solution, which is a source type function. A combination of source and doublet singularity is therefore used for solving the unsteady compressible problem by means of the panel method, this methodology being an extension of a steady aerofoil formulation. Incremental effects of profile change in aerofoil and wake geometry are accounted for. A surface boundary condition is applied on the stationary mean aerofoil surface with time dependent geometrical changes accounted for. An unsteady Kutta condition of equal pressure across the trailing edge is assumed. Results are presented on the aerodynamic influence of Mach number, oscillating frequency parameter, angle of incidence and change of pivoting point. Results are also compared with linear theory, a subsonic experimental result and a subcritical solution of a transonic model.
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    A new approach in non-linear mechanics: The large time increment method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 647-663 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non-linearities and is tested on some examples in elastoplasticity. The method considerably reduces the number of transfers between local and global levels, hence the numerical cost of calculation is also diminished.
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    Vibration analysis of fluid-solid systems using a finite element displacement formulationThis research was sponsored by the Lawrence Livermore National Laboratory under contract CERDA LLNL-1513603. This support and the interest of Dr G. L. Goudreau are gratefully acknowledged. (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 683-698 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This report presents a finite element solution for the vibration interaction between an inviscid fluid and a solid. The equation of motion governing the inviscid fluid is expressed in terms of the displacements. This ensures that compatibility and equilibrium will be satisfied automatically along the interface of the coupled systems. To suppress circulation modes with non-zero energy, reduced integration is used when computing the element stiffness matrix contributed by the fluid. In addition, a projection is used on the element mass matrix in order to remove the spurious modes which result from the use of reduced integration. Numerical examples for both fluid and coupled fluid-solid systems are performed and the results are shown.
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    A dynamic contact buckling analysis by the penalty finite element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 755-774 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper deals with the application of the finite element method to dynamic contact buckling problems. The penalty function method is applied to incorporate the contact conditions in the equation of motion and a trial-and-error method is employed to obtain the converged contact state. Numerical examples are analysed to show the effectiveness and the validity of the method, and it is applied to a dynamic buckling problem involving contact phenomena.
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    The dynamic response of compliant materials to an impulsive pressure field (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 811-831 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The dynamic interaction between a compliant material and an impulsive pressure field, periodic in space and instantaneous in time, was examined as a first step at modelling the interaction between organized structures in a turbulent boundary layer and a compliant surface. The interaction, modelled two-dimensionally, was treated dynamically by matching the pressure forces to the surface stresses in the compliant material at each instant of time. A new boundary element method was formulated to model the compliant material which was treated as a linear isotropic material, elastic in dilatation and viscoelastic (Standard) in shear. The inertial forces and viscoelastic creep stresses have been included in this formulation as transient body forces. The elastic interaction was characterized by a non-dimensional threshold velocity, above which the elastic instabilities grew temporally and spatially in the downstream direction to produce a non-linear breakdown of the interaction. Freestream velocities as high as 9CT (shear wave speed) were found to produce stable elastic interactions. Thinner materials produced smaller amplitude waves of higher frequencies that grew more rapidly than those in thicker materials. The stability characteristics were independent of the location of the compliant material with respect to the spatial distribution of the pressure pulse. For viscoelastic interactions, the stability curve, which serves as a bound on the types of materials capable of producing drag reduction, shows distinct regions of elastic types of interactions (Class B) and damping dominated interactions (Class A) as a function of the constants of the rheological model describing the compliant material. Class A disturbances in these interactions show slower growth or decay than Class B disturbances.
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 909-912 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    A finite element formulation for the coupled thermoviscoelastic response of solid-fluid systems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 953-968 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The coupled thermoviscoelastic response of a solid-fluid system is computed by a finite element formulation which involves only temperature and displacement fields. The Laplace transform with respect to time is applied to the coupled equations. This results in a global matrix in the transform domain that is symmetric and banded and the time response is obtained by numerical inversion of the transformed solution. Also, this formulation permits the use of fractional derivatives to model viscoelastic material behaviour.
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    A subspace forward iteration method for solving the quadratic eigenproblem associated with the FDE formulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 935-951 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the development of an efficient and numerically stable algorithm for accurately computing the eigensolutions of the quadratic real symmetric eigenproblem arising in the finite dynamic element (FDE) formulation. Closely related to the subspace forward iteration method, the proposed scheme is well suited to extracting the lowest natural frequencies and associated mode shapes of large practical eigenproblems, takes full advantage of the banded configuration of the stiffness, inertia and dynamic correction matrices involved in the eigenproblem and ensures a monotonic convergence from above to the required eigenpairs. A shifting technique for convergence acceleration and an eigenpair verification scheme are also presented. Numerical examples are shown demonstrating the excellent performance of the solution procedure.
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    Application of the boundary element method to non-linear diffusion with reaction problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1021-1031 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integral solution method based on the concept of the direct boundary element technique has been applied to develop a solution procedure for problems of diffusion with a non-linear reaction in one dimension. The non-linearity is handled by a process of quasi-linearization over subintervals or elements in the main domain of integration. The weighting functions are defined for each subinterval such that the discretization is exact for the corresponding linear problem. This leads to a new powerful and simple method for the solution of this class of problems. A banded global matrix is obtained with both the concentration and its gradient as the unknown variables, and the problem is solved in an iterative manner. Illustrative results are presented for a test problem of diffusion with a second order reaction in an infinite slab, an infinite cylinder and spherical geometries. The accuracy of the method for situations with a sharp concentration gradient is demonstrated. The technique can also be used to numerically compute the solution in the boundary layer for fast reactions.
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    Flow through fissured porous media with deformable matrix (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1079-1094 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An approach, which is based on the double porosity concept and takes into account pore deformation, has been presented to derive a set of coupled differential equations governing the behaviour of fissured porous media. This approach has resulted in a set of non-linear (variable coefficient) differential equations. Various coefficients involved in the formulation have been explicitly defined in terms of measurable physical parameters. The finite element technique has been employed as the numerical tool for the solution of these equations. The results based on the proposed non-linear formulation have been compared with those of previously presented linear (constant coefficient) formulations. It is found that, in relatively rigid formations, the linearity assumption is quite reasonable and can successfully model the behaviour of fissured porous media. However, in very deformable formations, the linearity assumption could lead to a significant level of error in the numerical solutions.
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    Validation of structural computation codes in elastoviscoplasticity (1990)
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1109-1130 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses various procedures for the implementation of viscoplastic constitutive equations in Finite Element Codes. The set of constitutive equations that has been used is described. Several kinds of implementation, using various numerical techniques, are proposed. Validations of these implementations and comparisons between them are investigated by means of a set of simple but comprehensive examples.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290514
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    A finite element methodology to predictage-related mechanical property and structural performance changes in high performance polymers (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1159-1175 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The treatment of ageing processes in polymers by the finite element (FE) method is described. The development of this analytical method is motivated by the need to assess the effects of ageing on the structural performance of polymers and polymeric composites, particularly when the structures are large and expensive to replace. Also, there is a need to assess the effectiveness of corrective action options when ageing problems do occur, which can be treated by this method. The method describes the treatment of multiple, reactive chemical species in multi-layered polymeric materials by the finite element method. Example problems featuring the simultaneous diffusion and chemical reaction are illustrated: a simple problem of binary diffusion and reaction with comparison of numerical to exact results, and the staged ageing/structural analysis of a solid rocket motor.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290604
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    Application of the zienkiewicz-zhu error estimator for plate and shell analysis (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1281-1298 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An effective and efficient error estimation scheme for finite element plate and shell analysis is presented. The error estimate method proposed is applicable to all the plate and shell elements developed using either classical plate and shell or continuum mechanics theories. The global error in energy norm is computed by summing all the elemental errors. The method is well suited for adaptive mesh refinement as the error contribution for each element is known. Demonstration examples using uniform and adaptive refinement schemes for both the plate and shell analysis show the effectiveness of the method proposed.
    Additional Material: 25 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290612
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    An approach to the generation of triangular grids possessing few obtuse triangles (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1299-1321 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A triangular mesh generator is presented which makes extensive use of side swapping and mesh smoothing to create a grid with few obtuse triangles. To perform the above task a data structure is presented which holds full adjacency information both for nodes and elements. It is shown how this data structure is employed in the process mesh generation, and how the methods of computational geometry such as region decomposition are used not only to decompose a complex region, but also to reflect the boundary grading into the interior the region. Algorithms are provided to show the mechanism of these processes and practical examples are given to support the approach.
    Additional Material: 26 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290613
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    Least-squares characteristics and finite elements for advection-dispersion simulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1343-1358 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of characteristics is combined with the method of least-squares to solve the advection equation within the finite element framework. Fourier mode analysis shows that the numerical scheme is stable and accurate even when a linear basis function is used. However, in practical application, the involvement of using numerical quadrature in this method can produce numerical instability, depending on the value of the Courant number used. It is found that using C1 continuous Hermitian cubic basis functions in the scheme reduces the degree of instability significantly and produces high accuracy. When being used in a split-operator approach, this method combines naturally with the standard finite element method and results in a highly accurate scheme for advection-dispersion simulation.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290615
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    A robust self-starting explicit computational methodology for structural dynamic applications: Architecture and representations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1441-1454 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Conventional approaches for computational structural dynamics (CSD) relevant to time-integration methods involve first employing the classical Galerkin formulations for the spatial discretization to yield a set of ordinary differential equations in time and then employing finite difference approximations for deriving the appropriate step-by-step algorithms. And, almost all of the widely advocated (existing) step-by-step schemes for structural dynamics require an initial acceleration vector to be specified (evaluated) in addition to displacement and velocity vectors for starting the schemes. Unlike the above, in this paper we introduce new representations and architecture towards providing not only direct self-starting features with the elimination of acceleration computations but also for enhancing the computational architecture itself via several other inherent distinguishing characteristics. Thereby, a robust and effective methodology of computation is presented which is an extension of our previous efforts (see Tamma and Namburu3). In particular, to illustrate the basic concepts, in this paper we focus attention on the development of explicit time-integration formulations. The methodology involves expressing the governing dynamic equations of motion in conservation form, and firstly temporal discretization is accomplished in the spirit of Lax-Wendroff-type formulations. Therein, discretization in space is accomplished by introducing stress-based representations and employing the classical Galerkin scheme, and, quite naturally, we advocate employing finite elements as the principal computational tool because of its several inherent advantages. The stability and accuracy of the proposed formulations and the several added distinguishing features are briefly highlighted. Considerations on the effects of damping are additionally included and the introduction of general boundary conditions in a natural setting permits an effective generalized architecture for general applications. Numerical test models are presented to validate the overall developments for computational structural dynamics.
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    URL: http://dx.doi.org/10.1002/nme.1620290705
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    Two-dimensional mesh generation, adaptive remeshing and refinement (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1501-1526 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the generation of unstructured triangular meshes by the advancing front technique. We also employ the technique to discretize surfaces. A simple and effective algorithm for the specification of element sizes is described. A similar idea is then applied to adaptive remeshing where a completely new mesh is created on the basis of the isolines of a certain important variable. The isolines are obtained from the FE-calculation based on the previous mesh. In this paper, attention is focused on the Poisson's equation. The optimal a priori error estimate for the problem is used to estimate the number of isolines needed for the remeshing. When the estimated error exceeds the tolerance in only a small part of the domain, the adaptive procedure is switched automatically to an adaptive refinement.
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    URL: http://dx.doi.org/10.1002/nme.1620290709
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    Development of an automatic, two-dimensional finite element mesh generator using quadrilateral elements and Bezier curve boundary definition (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1551-1567 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the development of an automatic, two-dimensional, quadrilateral element mesh generator. The methodology is based on the looping algorithm developed in part by Dr M. L. C. Sluiter. Bezier curves are used to define the boundaries of the parts to be meshed. The required interaction by the user is reduced to specifying the boundary geometry, the preferred element size and the refinement coefficient. Transition elements are automatically generated between regions of varying element sizes. The ability to offset specified boundary curves insures well-conditioned elements along the boundary. Meshes for several sample geometries are presented to illustrate the versatility of the mesh generator.
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    A class of mixed assumed strain methods and the method of incompatible modesResearch supported by AFOSR under contract nos. 2-DJA-544 and 2-DJA-771 with Stanford University (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1595-1638 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A three-field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within this frame-work, incompatible elements arise as particular ‘compatible’ mixed approximations of the enhanced strain field. The conditions that the stress interpolation contain piece-wise constant functions and be L2-ortho-gonal to the enhanced strain interpolation, ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation. The preceding conditions are formulated in a form particularly convenient for element design. As an illustration of the methodology three new elements are developed and shown to exhibit good performance: a plane 3D elastic/plastic QUAD, an axisymmetric element and a thick plate bending QUAD. The formulation described herein is suitable for non-linear analysis.
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    Solution of radiative problems using variational based finite element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1701-1714 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The calculation of temperature distributions for systems exchanging radiation heat requires as a first step the determination of the heat fluxes caused by radiation at its surfaces. The functional of the variational principle is the starting point of a numerical solution method.By using finite element procedures a system of linear equations is derived, which supplies an approximation of the radiosity. Having the radiosity, the heat flux at the surfaces, which governs the boundary condition for the temperature distribution in the structure, can be calculated. A method of determining the view-factors using the concept of the finite element method is also given.
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    Dynamics of multibody systems, A. A. Shabana, Wiley, New York, 1989. No. of pages: 480. ISBN 0-471-61494-7. price £39.30/$63.20 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1797-1797 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620290812
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    A use of linear programming for the analysis of plane strain rigid-plastic flow (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1-12 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes an application of linear programming for the analysis of plane strain rigid-plastic flow. First, linear programming and the theory of a rigid-plastic material are briefly revised. The implementation of linear programming for rigid-plastic flow is then described. The method is to subdivide the material into rigid triangular blocks which may slide upon each other, dissipating energy at a rate proportional to the rate of sliding. Many different modes of deformation are possible; linear programming is used to select the mode that gives the least rate of total energy dissipation. The indentation of a strip by blunt-nosed indenters is used as an example. Results of the linear programming method are compared with the exact slip line field solutions.
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    URL: http://dx.doi.org/10.1002/nme.1620300102
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    A new approach to boundary modelling for finite difference applications in solid mechanics (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 99-113 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Procedures for extending the useful scope of the finite difference method in solid mechanics applications are presented. The improvements centre around the introduction of the physical nature of the deformations into the equations used to formulate the approximate solution. This is accomplished by evaluating the coefficients of Taylor series expansions for the displacement approximations in terms of rigid body motions, strains and derivatives of strains. This procedure is demonstrated with plane stress applications. The ability to interpret the derivative approximations physically allows the fictitious nodes typical of the finite difference method to be rationally incorporated into the model as a means of enforcing traction boundary conditions. An example problem is solved using both regular and irregular meshes. The displacements and stresses compare well with finite element solutions.
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 201-205 
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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.1620300112
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    Trust region methods for structural optimization using exact second order sensitivity (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 275-293 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of multiplier algorithms for structural optimization has been significantly improved by using trust regions. The trust regions are constructed using analytical second order sensitivity, and within this region, the augmented Lagrangian φ is minimized subject to bounds. Evaluation of first and second derivatives of φ by the adjoint method does not require derivations of individual (implicit) constraint functions, which makes the method economical. Eight test problems are considered and a vast improvement over previously used multiplier algorithms has been noted. Also, the algorithm is robust with respect to scaling, input parameters and starting designs.
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    New predictor/corrector algorithms with improved energy balance for a recent formulation of dynamic vehicle/structure interaction (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 223-253 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new class of predictor/corrector algorithms is proposed to solve the complex system of differential equations that arises from a Galerkin spatial discretization of the equations of motion in a recent formulation of dynamic vehicle/structure interaction. The applicability of the concept of a building-block vehicle/structure interaction model developed in our previous work - where the vehicle nominal motion is not prescribed a priori, but is part of the unknown motion of the system - is demonstrated through the construction of a simple vehicle model. In the new algorithms, the presence of the accelerations of the vehicle component is eliminated in the predictor structural equations, making these equations different from the corrector structural equations. The special treatment of the predicted axial motion that provides an artificial damping to eliminate unstable oscillations in the numerical results as proposed in the old algorithms is avoided. Accurate results from numerical simulations using the new algorithms are obtained, and there are no unstable oscillations that were observed in some other predictor/corrector schemes. The system energy balance is also better preserved compared with the old algorithms.
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    Direct evaluation of singular integrals in elastoplastic analysis by the boundary element method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 295-311 
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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 new method for the direct and accurate evaluation of strongly singular integrals in the sense of Cauchy principal values and weakly singular integrals over quadratic boundary elements in three-dimensional stress analysis and quadratic internal cells in two-dimensional elastoplastic analysis by the boundary element method. A quadratic triangle polar co-ordinate transformation technique is applied to reduce the order of singularity of the singular integrals. Next, a form of Stokes' theorem is introduced in order to remove the singularity in the Cauchy principal value integrals; therefore, the evaluation of these integrals can be carried out by standard Gaussian quadrature. Numerical examples of 2-D elastoplastic problems and a 3-D elastic problem show the effectiveness and efficiency of the method.
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    Projection methods in flexible multibody dynamics. Part II: Dynamics and recursive projection methods (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1941-1966 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this paper the kinematic relationships between the absolute, elastic and joint accelerations are developed. In this paper, these kinematic equations are used with the generalized Newton-Euler equations and the relationship between the actual and generalized reaction forces to develop a recursive projection algorithm for the dynamic analysis of open-loop mechanical systems consisting of a set of interconnected rigid and deformable bodies. Optimal matrix permutation, partitioning and projection methods are used to eliminate the elastic accelerations while maintaining the inertia coupling between the rigid body motion and the elastic deformation. Recursive projection methods are then applied in order to project the inertia of the leaf bodies onto their parent bodies. This leads to an optimal symbolic factorization which recursively yields the absolute and joint accelerations, and the joint reaction forces. The method presented in this paper avoids the use of Newton-Raphson algorithms in the numerical solution of the constrained dynamic equations of open-loop kinematic chains since the joint accelerations are readily available from the solution of the resulting reduced system of equations. Furthermore, the method requires only the inversion or decomposition of relatively small matrices and the numerical integration of a minimum number of co-ordinates. Open-loop multibody robotic manipulator systems are used to compare the results and efficiency of the recursive methods with that of the augmented formulations that employ Newton-Raphson algorithms.
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    URL: http://dx.doi.org/10.1002/nme.1620351003
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    Coupling finite elements and magnetic networks in magnetostatics (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1991-2002 
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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 new method for computing non-linear magnetostatic fields is introduced, which allows the simultaneous coupling of a finite element structure with a magnetic network. Combining the advantages of both methods while avoiding their drawbacks, this coupling yields both an accurate and time-efficient computation.The traditional method of the unknown mesh fluxes is applied for the solution of the magnetic network. The finite element solution, on the other hand, is based on a classical first-order interpolation of the unknown vector potential. The coupling is established by a proper organization of the unknowns on the boundary common to the finite element and network regions. In this way, a single system of non-linear equations is obtained.Moreover, it is shown that the coupled system of equations is equivalent to a single finite element system if generalized base functions are allowed. Consequently, various results from finite element theory may be applied. For instance, the matrix governing the iteratively linearized system of equations can directly be shown symmetrical and positive definite.Finally, the field inside a permanent magnet motor is calculated with the coupled method. Although the number of unknowns is dramatically reduced compared to a full FE calculation, the same level of accuracy is achieved. Hereby, the benefit of the coupled method is clearly proved.
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    A consistent model for first-order moderate rotation plate theory (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 2049-2066 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The first-order shear deformation plate theory can be used in the small strain and moderate rotation non-linear elasticity by defining correctly the displacement vector form. In this paper, the problem of the consistency between the displacement vector form and the finite strain tensor approximation is analysed. Then, a new moderate rotation theory is proposed. The variational form of the governing equations is derived for the beam and the plate problems in a consistent way. Then, an iterative numerical procedure based on the finite element method and the secant striffness matrix is developed in order to solve the non-linear differential equation problem. Computations are made for one- and two-dimensional structures, in order to assess the performance of the von Kármán, finite elasticity, classical and the proposed moderate rotation theories.
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    URL: http://dx.doi.org/10.1002/nme.1620351008
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