Designing lightweight yet stiff structures that can withstand vibrations is a crucial task in structural optimization. Here, we present a novel framework for truss topology optimization under undamped harmonic oscillations. Our approach minimizes the peak power of the structure under harmonic loads, overcoming the limitations of single-frequency and in-phase assumptions found in previous methods. For this, we leverage the concept of semidefinite representable (SDr) functions, demonstrating that while compliance readily conforms to an SDr representation, peak power requires a derivation based on the non-negativity of trigonometric functions. Finally, we introduce convex relaxations for the minimization problem and provide promising computational results.
@article{arxiv.2401.16175,
title = {Truss topology design under harmonic loads: Peak power minimization with semidefinite programming},
author = {Shenyuan Ma and Jakub Marecek and Vyacheslav Kungurtsev and Marek Tyburec},
journal= {arXiv preprint arXiv:2401.16175},
year = {2025}
}