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On the trajectories of the epsilon-relaxation approach for stress-constrained truss topology optimization
KTH, Superseded Departments, Mathematics.
2001 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 21, no 2, 140-151 p.Article in journal (Refereed) Published
Abstract [en]

We consider the nonconvex problem of minimizing the weight of a linearly elastic truss structure subject to stress constraints under multiple load conditions. The design variables are the cross-sectional areas of the elements, and the stress constraints are imposed only on elements with strictly positive areas. To avoid degenerate feasible domains, it has been suggested that the stress constraints of the original problem should be relaxed by a positive scalar epsilon, leading to the so-called epsilon -relaxed problem. In this paper, the trajectories associated with optimal solutions of the epsilon -relaxed problems, for continuously decreasing values of epsilon, are studied in detail on some carefully chosen examples. The global trajectory is defined as the path followed by the global optimal solution to the epsilon -relaxed problem, and we present two parameterized examples for which the global trajectory is discontinuous for arbitrarily small values of epsilon > 0. From that we conclude that, in practice, a sequence of solutions to the epsilon -relaxed problem for decreasing values on epsilon may not converge to the global optimal solution of the original problem, even if the starting point is on the global trajectory.

Place, publisher, year, edition, pages
2001. Vol. 21, no 2, 140-151 p.
Keyword [en]
topology optimization, stress constraints, singular topologies
URN: urn:nbn:se:kth:diva-20662ISI: 000168915400006OAI: diva2:339358
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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