Shape optimization of elasto-plastic bodies obeying Hencky’s law. (English) Zbl 0616.73081

The paper deals with the shape optimization of two dimensional elasto- plastic bodies obeying Hencky’s law according to the minimum of cost functional. The cost functional is an integral of the yield function. It has been assumed that the body forces, surface loads and material characteristics of an elasto-plastic body are given. To solve the state problem, the principle of Haar-Kármán and piecewise constant stress approximation are used. A convergence analysis of the solution of discrete problem to the solution of the original continuous optimization problem and the existence of an optimal boundary is proved. The paper has a cognizable character, but it is not far from technical applications.
Reviewer: St.Jendo


74P99 Optimization problems in solid mechanics
65K10 Numerical optimization and variational techniques
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
49J40 Variational inequalities
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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