摘要:

AbstractThe solution of dynamic contact (elastic impact) problems is complicated by the changing nature of the contact area. If a finite element approach is used, the system matrices vary with the contact area. If the problem is properly formulated, such changes are rank one. Rank one changes produce easily determinable changes in theLDLTdecompositions of the system matrices. This renders a class of dynamic contact problems soluble with the same accuracy and computational effort as is associated with the solution of any dynamic problem using finite element procedures. Consideration of an example problem involving the impact of spring–mass systems confirms this clai

ISSN:0029-5981    

DOI:10.1002/nme.1620200102

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractThe present paper attempts to evaluate the fracture mechanics parameters, the stress intensity factor (K) and Rice's energy integral (J) in plane strain conditions for three‐point bend specimens. Both the parameters have been evaluated by the FEM using higher order isoparametric elements (i.e. quadratic elements). The crack tip elastic singularity (1/√r) has been taken into account by the use of the special crack tip elements of degenerate triangular element type as well as the fine eight‐noded isoparametric plane elements. The stress distribution has been compared with the Westergaard solution in the vicinity of the crack. TheKandJvalues have also been‐compared with the theoretical

ISSN:0029-5981    

DOI:10.1002/nme.1620200103

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA generalized boundary integral equation method for the solution of the Laplace equation is developed based on the Cauchy integral theorem for analytical complex variable functions. Although the approach is complicated by the utilization of complex variable theory, the resulting model involves direct integration along straight‐line boundary segments (elements) rather than using quadrature formulae that are required in current real variable boundary element formulations. Previously published boundary integral equation methods based on the Cauchy integral theorem are shown to be a subset of the generalized model theory developed in this pape

ISSN:0029-5981    

DOI:10.1002/nme.1620200104

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractAn optimum design sensitivity analysis capability is reported which exploits the approximation concepts‐dual method formulation of the minimum weight structural sizing problem. An efficient iterative solution technique is used to facilitate determination of sensitivity derivatives for both primal and dual variables. Estimates on the useful range of parameter perturbations, over which the optimum design sensitivity projections can be expected to yield satisfactory revised optimum designs, are also obtained. Numerical results for several example problems will be presented to illustrate the effectiveness of the capability reporte

ISSN:0029-5981    

DOI:10.1002/nme.1620200105

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractWe present numerical solutions for the following Stefan problems. The half‐spacez>0 is initially filled with liquid at its fusion temperature. The boundaryz= 0, taken to be thexaxis, is maintained at a constant temperature, less than the fusion temperature, forx0, the first problem considers the case of an insulated boundary, and the second problem considers the case of the boundary maintained at the fusion temperature. This gives rise to a solid‐liquid interface curved in the (x,z) pl

ISSN:0029-5981    

DOI:10.1002/nme.1620200106

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractAn optimal control finite element approximation of the penalization type for the solution of incompressible viscous Navier–Stokes equations is presented. This paper has proved the convergence of its minimizing sequence and the existence of the solution for the optimal control problem corresponding to the penalty variational problem of the Navier–Stokes equations. Based on this method and the conjugate gradient algorithm, the program for solving the three‐dimensional Navier–Stokes problem has been developed, and some numerical results have also been p

ISSN:0029-5981    

DOI:10.1002/nme.1620200107

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractA method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions. To produce accurate temporal differencing, the method employs forward‐time Taylor series expansions including time derivatives of second‐ and third‐order which are evaluated from the governing partial differential equation. This yields a generalized time‐discretized equation which is successively discretized in space by means of the standard Bubnov–Galerkin finite element method. The technique is illustrated first in one space dimension. With linear elements and Euler, leap‐frog and Crank–Nicolson time stepping, several interesting relations with standard Galerkin and recently developed Petrov–Galerkin methods emerge and the new Taylor–Galerkin schemes are found to exhibit particularly high phase‐accuracy with minimal numerical damping. The method is successively extended to deal with variable coefficient problems and multi‐d

ISSN:0029-5981    

DOI:10.1002/nme.1620200108

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractIn this paper a straightforward derivation of one‐ and two‐dimensional finite difference forms for general cartesian networks is given. General analytic compact expressions up to third order for first derivatives are specifically derived. General cartesian networks with locally telescoping subnetworks are also introduced and the basic problem of approximating derivative boundary conditions is clarified. The applicability of these general finite difference forms is shown by solving numerically the Laplace problem with mixed Dirichlet–Neumann boundary conditions for an elliptic d

ISSN:0029-5981    

DOI:10.1002/nme.1620200109

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractThe aim of the work reported in this paper is to present the new formulation of the integral equation method for non‐self‐adjoint problems and to apply the method to stability problems of elastic continua subjected to non‐conservative loadings. A general non‐self‐adjoint eigenvalue problem stated in terms of differential operators is transformed into a set of coupled integral equations. Our derivation of integral equations is based on an inverse formulation of a canonical form for the original problem and the corresponding fundamental solution pair. Three well‐known non‐conservative stability problems in elasticity are examined by this integral equation method as illustrative examples. The approximate values of the critical parameters of sample problems demonstrate a sufficient accuracy through a comparison of

ISSN:0029-5981    

DOI:10.1002/nme.1620200110

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY

摘要:

AbstractSteady‐state, free surface seepage through a heterogeneous porous medium underlain by a drain at a finite depth is solved using a fixed domain solution technique. The problems investigated are axisymmetric seepage from a circular pond and plane seepage from a symmetric channel. These ponds and channels may have variable shaped bottoms. Since the Baiocchi transformation was used to define a new dependent variable, the form of the permeability function was restricted to a product of functions of the independent variables. Herein the permeability was chosen to be a function of the depth only. For certain forms of this function, namely those having negative gradients, part of the flowfield becomes unsaturated and this violates the assumed saturation of the flowfield in the flow theory. The governing differential equation, which holds in the sense of distributions, is derived for a fixed solution domain and a simple algorithm (a finite difference successive over‐relaxation scheme with projection) is given to obtain the solution to these free surface problems. Numerous comparisons are made with published results. Rigorous mathematical justification of the methods used herein can be found in the references ci

ISSN:0029-5981    

DOI:10.1002/nme.1620200111

出版商:John Wiley&Sons, Ltd    

年代:1984

数据来源: WILEY