# Truss topology optimization considering local buckling constraints and restrictions on intersection and overlap of bar members

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## Abstract

This paper illustrates the application of a two-level approximation method for truss topology optimization with local member buckling constraints and restrictions on member intersections and overlaps. Previously developed for truss topology optimization with stress and displacement constraints, that method is achieved by starting from an initial ground structure, and, combined with genetic algorithm (GA), it can handle both discrete and continuous variables, which denote the existence and cross-sectional areas of bar members respectively in the ground structure. In this work, this method is improved and extended to consider member buckling constraints and restrict intersection and overlap of members for truss topology optimization. The temporary deletion technique is adopted to temporarily remove buckling constraints when related bar members are deleted, and in order to avoid unstable designs, the validity check for truss topology configuration is conducted. By using GA to search in each possible design subset, the singularity encountered in buckling-constrained problems is remedied, and meanwhile, as the required structural analysis is replaced with explicit approximation functions in the process of executing GA, the computational cost is significantly saved. Moreover, for the consideration of restrictions on member intersecting and overlapping, the definition of such phenomena and mathematical expressions to recognize them are presented, and a new fitness function is developed to include such considerations. Numerical examples are presented to show the efficacy of the proposed techniques.

## Keywords

Truss topology optimization Local buckling constraints Intersection and overlap Singular optima Two-level approximation Genetic algorithm## Notes

### Acknowledgments

This research work is supported by the National Natural Science Foundation of China (Grant No. 11672016), which the authors gratefully acknowledge.

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