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Stochastic structural topology optimization: Existence of solutions and sensitivity analyses
Chalmers University of Technology, Göteborg University, Department of Mathematics, 412 96 Goteborg, Sweden.
Chalmers University of Technology, Göteborg University, Department of Mathematics, 412 96 Goteborg, Sweden.
Linköping University, The Institute of Technology. Linköping University, Department of Management and Engineering, Mechanics .
2003 (English)In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, Vol. 83, no 7, 479-492 p.Article in journal (Refereed) Published
Abstract [en]

We consider structural topology optimization problems including unilateral constraints arising from, for example, non-penetration conditions in contact mechanics or non-compression conditions for elastic ropes. To construct more realistic models and to hedge off possible failures or an inefficient behaviour of optimal structures, we allow parameters (for example, loads) defining the problem to be stochastic. The resulting nonsmooth stochastic optimization problem is an instance of stochastic mathematical programs with equilibrium constraints (SMPEC), or stochastic bilevel programs. The existence as well as the continuity of optimal solutions with respect to the lower bounds on the design variables are established. The question of continuity of the optimal solutions with respect to small changes in the probability measure is analysed. For a subclass of the problems considered the answer is affirmative, thus establishing the robustness of optimal solutions. © 2003 WILEY-VCH Verlag GmbH & Co. KGaA.

Place, publisher, year, edition, pages
2003. Vol. 83, no 7, 479-492 p.
Keyword [en]
e-perturbation, Bilevel programming, Robust optimization, Stochastic programming, Stress constraints
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-46415DOI: 10.1002/zamm.200310029OAI: oai:DiVA.org:liu-46415DiVA: diva2:267311
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-13

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Petersson, Joakim

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