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A finite element method for problems in perfect plasticity using discontinuous trial functions. (English) Zbl 0572.73076

Nonlinear finite element analysis in structural mechanics, Proc. Europe- U.S. Workshop, Bochum 1980, 307-329 (1981).
[For the entire collection see Zbl 0453.00049.]
We propose a finite element method of displacement type for problems in perfect plasticity where we use a finite element space \(V_ h\) of piecewise polynomial functions with no requirement on inter-element continuity. In order to be able to approximate a discontinuous solution u of a plasticity problem accurately with functions in \(V_ h\), the finite element mesh will have to fit the discontinuities of u. Thus, since the location of these discontinuities is in general not known in advance, one would like to use some kind of adaptive technique where according to the results of computations the finite element mesh is successively modified. In this note we do not consider this more general problem but concentrate on analyzing the proposed method in the case of a given mesh.
An outline of the note is as follows: In Section 2 we formulate the problem, in Section 3 we introduce the finite element method and prove a convergence result, and finally in Section 3 we give the results of some numerical experiments in one space dimension.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)

Citations:

Zbl 0453.00049