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Structural and Multidisciplinary Optimization

, Volume 60, Issue 4, pp 1605–1618 | Cite as

Fail-safe truss topology optimization

  • Mathias StolpeEmail author
Research Paper
  • 276 Downloads

Abstract

The classical minimum compliance problem for truss topology optimization is generalized to accommodate for fail-safe requirements. Failure is modeled as either a complete damage of some predefined number of members or by degradation of the member areas. The considered problem is modeled as convex conic optimization problems by enumerating all possible damage scenarios. This results in problems with a generally large number of variables and constraints. A working-set algorithm based on solving a sequence of convex relaxations is proposed. The relaxations are obtained by temporarily removing most of the complicating constraints. Some of the violated constraints are re-introduced, the relaxation is resolved, and the process is repeated. The problems and the associated algorithm are applied to optimal design of two-dimensional truss structures revealing several properties of both the algorithm and the optimal designs. The working-set approach requires only a few relaxations to be solved for the considered examples. The numerical results indicate that the optimal topology can change significantly even if the damage is not severe.

Keywords

Fail-safe optimal design Truss topology optimization Minimum compliance Semidefinite programming Second-order cone programming 

Notes

Acknowledgments

The author would like to sincerely thank two anonymous reviewers for their knowledgeable comments and suggestions that significantly improved the manuscript in terms of contents and presentation.

Funding information

The research presented in this manuscript is funded by Independent Research Fund Denmark through the research project Fail-Safe Structural Optimization (SELMA) with grant no. 7017-00084B.

Compliance with ethical standards

Conflict of interest

The author declares no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.DTU Wind EnergyTechnical University of Denmark (DTU)RoskildeDenmark

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