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<p>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 nonnegativity of trigonometric functions. Finally, we introduce convex relaxations for the minimization problem and provide promising computational results.</p>

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Truss topology design under harmonic loads: peak power minimization with semidefinite programming

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年2月1日

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  • Shenyuan Ma,
  • Jakub Mareček,
  • Vyacheslav Kungurtsev,
  • Marek Tyburec

摘要

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 nonnegativity of trigonometric functions. Finally, we introduce convex relaxations for the minimization problem and provide promising computational results.