Fail-safe truss topology optimization

Mathias Stolpe*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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.
Original languageEnglish
JournalStructural and Multidisciplinary Optimization
Volume60
Issue number4
Pages (from-to)1605-1618
Number of pages14
ISSN1615-147X
DOIs
Publication statusPublished - 2019

Keywords

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

Cite this

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title = "Fail-safe truss topology optimization",
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, Minimum compliance, Second-order cone programming, Semidefinite programming, Truss topology optimization",
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language = "English",
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Fail-safe truss topology optimization. / Stolpe, Mathias.

In: Structural and Multidisciplinary Optimization, Vol. 60, No. 4, 2019, p. 1605-1618.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Fail-safe truss topology optimization

AU - Stolpe, Mathias

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Fail-safe optimal design

KW - Minimum compliance

KW - Second-order cone programming

KW - Semidefinite programming

KW - Truss topology optimization

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