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Shape optimization of an elasto-perfectly plastic body. (English) Zbl 0632.73082

Given are body forces, surfaces loads and material characteristics of an elasto-plastic two-dimensional body. It is necessary to find the shape of a part of its boundary, such that a cort functional is minimized. The latter functional is an integral of the square of the yield function over the time-space domain. The model of Prandtl-Reuss is used, which is formulated in terms of a variational inequality of evolution. The solution method is based on piecewise linear approximation of the unknown boundary, piecewise constant triangular elements for stress and backward differences in time. The convergence of the approximation to a solution of the original optimal design problems is proved.
Reviewer: A.Žilinskas

MSC:

74P99 Optimization problems in solid mechanics
65K10 Numerical optimization and variational techniques
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S30 Other numerical methods in solid mechanics (MSC2010)
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References:

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