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Structural and Multidisciplinary Optimization

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22-12-2017 | RESEARCH PAPER

The equivalent static loads method for structural optimization does not in general generate optimal designs

Authors: Mathias Stolpe, Alexander Verbart, Susana Rojas-Labanda

Published in: Structural and Multidisciplinary Optimization | Issue 1/2018

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Abstract

The Equivalent Static Loads Method (ESLM) is an algorithm intended for dynamic response structural optimization. The algorithm attempts to solve a sequence of static response structural optimization problems approximating the original problem. It is argued in several published articles that if the ESLM converges, then it finds a KKT point of the considered dynamic structural response optimization problem. The theoretical convergence properties of the ESLM are however not as strong as previously reported. We propose and analyze easily reproducible counter examples based on a two-bar truss illustrating that the ESLM in general fails in finding optimal designs to the considered dynamic response problem.

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We use the term KKT point to refer to a feasible point x ^∗ for which there exists positive Lagrange multipliers satisfying the KKT conditions to the studied inequality constrained problem. The term primal-dual KKT point refers to the pair (x ^∗, λ ^∗) satisfying the KKT conditions.

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Title: The equivalent static loads method for structural optimization does not in general generate optimal designs
Authors: Mathias Stolpe
Alexander Verbart
Susana Rojas-Labanda
Publication date: 22-12-2017
Publisher: Springer Berlin Heidelberg
Published in: Structural and Multidisciplinary Optimization / Issue 1/2018
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-017-1884-0

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