Shape optimization of an elasto-plastic body for the model with strain- hardening. (English) Zbl 0717.73054

Summary: The state problem of elasto-plasticity (for the model with strain- hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences in time are used. Existence and uniqueness of a solution of the approximate state problem and existence of a solution of the approximate optimal design problem are proved. The main result is the proof of convergence of the approximations to a solution of the original optimal design problem.


74P99 Optimization problems in solid mechanics
65K10 Numerical optimization and variational techniques
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
49J40 Variational inequalities
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