Geodesic
Shape optimization of an elasto-plastic body for the model with strain- hardening
Applications of Mathematics, Tome 35 (1990) no. 5, pp. 373-404
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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.
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.
DOI : 10.21136/AM.1990.104419
Classification : 49J40, 65K10, 65N30, 73E05, 73E99, 73V25, 73k40, 74P10, 74P99, 74S05, 74S30
Keywords: domain optimization; time-dependent variational inequality; elasto-plasiicily; finite elements; uniqueness; state problem; optimal design; piecewise linear approximations of the unknown boundary; hardening parameter; backward differences in time; convergence 
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     title = {Shape optimization of an elasto-plastic body for the model with strain- hardening},
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Pištora, Vladislav. Shape optimization of an elasto-plastic body for the model with strain- hardening. Applications of Mathematics, Tome 35 (1990) no. 5, pp. 373-404. doi: 10.21136/AM.1990.104419

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