DOCUMENTA MATHEMATICA, Extra Volume ICM III (1998), 707-716

Michal Kocvara and Jochem Zowe

Title: Free Material Optimization

Free material design deals with the question of finding the stiffest structure with respect to one or more given loads which can be made when both the distribution of material and the material itself can be freely varied. We consider here the general multiple-load situation. After a series of transformation steps we reach a problem formulation for which we can prove existence of a solution; a suitable discretization leads to a semidefinite programming problem for which modern polynomial time algorithms of interior-point type are available. Two numerical examples demonstrates the efficiency of our approach.

1991 Mathematics Subject Classification: 73K40;\,90C90;\,90C25

Keywords and Phrases: Structural optimization; Material optimization; Topology optimization; Semidefinite programming

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