# Fail-safe truss topology optimization

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## 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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