Geodesic
Shape optimization of an elasto-perfectly plastic body
Applications of Mathematics, Tome 32 (1987) no. 5, pp. 381-400.

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Within the range of Prandtl-Reuss model of elasto-plasticity the following optimal design problem is solved. Given body forces and surface tractions, a part of the boundary, where the (two-dimensional) body is fixed, is to be found, so as to minimize an integral of the squared yield function. The state problem is formulated in terms of stresses by means of a time-dependent variational inequality. For approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular finite elements for stress and backward differences in time are used. Convergence of the approximations to a solution of the optimal design problem is proven. As a consequance, the existence of an optimal boudary is verified.
DOI : 10.21136/AM.1987.104269
Classification : 65K10, 65N30, 73E99, 73k40, 74P99, 74S05, 74S30
Keywords: optimal design; model of Prandtl-Reuss; variational inequality of evolution; piecewise linear approximation of the unknown boundary; piecewise constant triangular elements for stress; backward differences in time; convergence; elasto-plasticity; finite elements 
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     author = {Hlav\'a\v{c}ek, Ivan},
     title = {Shape optimization of an elasto-perfectly plastic body},
     journal = {Applications of Mathematics},
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Hlaváček, Ivan. Shape optimization of an elasto-perfectly plastic body. Applications of Mathematics, Tome 32 (1987) no. 5, pp. 381-400. doi : 10.21136/AM.1987.104269. http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104269/

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