摘要:

AbstractNumerical solution of Reissner's model for the bending of elastic plates by an advanced boundary integral equation method is outlined. Construction of fundamental solutions and computational strategy is fully described. Implementation of the resulting one‐dimensional model is illustrated by two test problems, including comparison to analytical solution

ISSN:0029-5981    

DOI:10.1002/nme.1620180102

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe dispersive properties of finite element semidiscretizations of the two‐dimensional wave equation are examined. Both bilinear quadrilateral elements and linear triangular elements are considered with diagonal and nondiagonal mass matrices in uniform meshes. It is shown that mass diagonalization and underintegration of the stiffness matrix of the quadrilateral element markedly increases dispersive errors. The dispersive properties of triangular meshes depends on the mesh layout; certain layouts introduce optical modes which amplify numerically induced oscillations and dispersive errors. Compared to the five‐point Laplacian finite difference operator, rectangular finite element semidiscretizations with consistent mass matrices provide superior fidelity regardless of the wave direct

ISSN:0029-5981    

DOI:10.1002/nme.1620180103

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620180104

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractA system for describing three‐dimensional surfaces in a form suitable for finite element analysis is described. The system makes extensive use of real‐time interactive computer graphics techniques for both input and display. Discrete transfinite mappings are used as the mathematical basis for the surface representation. The mathematical basis and the reasons for choosing this form of representation are discussed. Explicit forms of the mappings based on Lagrange polynomial interpolation functions are presented. Finally, the interactive graphics procedures for defining finite element meshes are descri

ISSN:0029-5981    

DOI:10.1002/nme.1620180105

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractFinite element models provide only approximate results under most loadings. A beam modelled by constant‐strain triangles and loaded by pure moment is a case in point. Yet if the iterative method advanced by Loubignacet al.1is applied to this model, the exact stress field will be generated. The iterative method derives from a parent formulation that can be solved without iteration.2As shown in this paper, the parent formulation contains the sum of two stiffness matrices. One is produced by the customary finite element shape functions. The other is produced by finite difference expressions for strain gradients that are not contained in the shape functions.Loubignac's method produces a stress field that is continous across interelement boundaries. Other methods that seek to impose interelement continuity are noted in the concluding sectio

ISSN:0029-5981    

DOI:10.1002/nme.1620180106

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThis paper introduces the notion of the finite element operator, and shows its application to the evaluation of several upwind finite element schemes. It is demonstrated that these operators supply good qualitative information on the performance of these schemes in an inexpensive as well as visual manner. In addition, this method gives insight into grid dependent effects which often characterize finite element solutions.

ISSN:0029-5981    

DOI:10.1002/nme.1620180107

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractMasters are defined as the degrees‐of‐freedom that are retained in the reduced eigenvalue problem. Various qualitative guidelines to select masters are published in the literature, but it is difficult to apply them to complex structures. In this paper a computational algorithm to select masters for complex structures is presented. This algorithm is based on a guideline14which assures that the associated Guyan reduction process is valid. This algorithm eliminates one degree‐of‐freedom at a time satisfying the guideline, and preserves lower frequencies in the reduced eigenvalue problem. The algorithm presented in this paper is used to select masters for four different structural models. The natural frequencies of the associated reduced eigenvalue problems are calculated and compared with those calculated from the full eigenvalue p

ISSN:0029-5981    

DOI:10.1002/nme.1620180108

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractTwo highly accurate implicit Padé approximations to the transient heat conduction equation are investigated using the conjugate gradient method to solve, for the temperatures. The accuracy and stability of the approximations are discussed and numerical examples are presented showing the relative performance. Comparisons with the Crank‐Nicolson method are also present

ISSN:0029-5981    

DOI:10.1002/nme.1620180109

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe numerical solution of nonlinear partial differential equations plays a very important role in may areas of physics, engineering and biology. In many cases all that is desired is a moderately accurate solution at a few points whcih can be calculated rapidly.In this work, we present a simple and direct technique, the differential quadrature method, which can be applied in various classes of partial differential equations. It produces moderately accurate results for the points of interest, generally few in number, and eliminates the difficulties of programming complex algorithms for the computer, as well as excessive use of storage and computer time. We illustrate this technique with the solution of the model of isothermal reactors with axial mixing. The results are compared with the results obtained by using the finite difference method. It is shown that differential quadrature of order 9 (9 points) provides approximately the same accurate results as the finite difference method (480 points) does.

ISSN:0029-5981    

DOI:10.1002/nme.1620180110

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractA new, simple and effective finite element procedure is presented for the practical solution of heat transfer conditions with phase changes. In this method, a fixed finite element mesh is employed, and a relatively coarse finite element mesh and large time step can be used in the incremental solution. The results of various numerical studies using the algorithm are presented that demonstrate the effectiveness of the procedure.

ISSN:0029-5981    

DOI:10.1002/nme.1620180111

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY