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Stochastic Material and Topology Design
Author(s) -
Stoeckl G.
Publication year - 2002
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/1617-7061(200203)1:1<478::aid-pamm478>3.0.co;2-g
Subject(s) - mathematical optimization , discretization , stochastic optimization , topology optimization , mathematics , optimal design , stochastic process , topology (electrical circuits) , decomposition , finite element method , computer science , mathematical analysis , engineering , statistics , structural engineering , combinatorics , ecology , biology
In order to find a robust optimal topology or material design with respect to stochastic variations of the model parameters of a mechanical structure, the basic optimization problem under stochastic uncertainty must be replaced by an appropriate deterministic substitute problem. Starting from the equilibrium equation and the yield/strength conditions, the problem can be formulated as a stochastic (linear) program “with recourse”. Hence, by discretization the design space by finite elements, linearizing the yield conditions, in case of discrete probability distributions the resulting deterministic substitute problems are linear programs with a dual decomposition data structure.