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<p>This paper addresses compliance minimization in linear elastic systems by reformulating the task as an equivalent optimization problem that avoids explicit volume constraints. Within a level-set framework, we examine several algorithms for optimizing material distribution. By deriving both shape and topological sensitivities, we obtain the corresponding derivatives that serve as key inputs to the optimization scheme. Our method efficiently updates the level-set function to reallocate material, concentrating it along primary load paths while removing it from low-stress regions. Numerical examples demonstrate the effectiveness of the proposed approach.</p>

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Shape and topology optimization for elasticity system using shape gradients and topological derivatives

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Yixin Tan,
  • Jan Sokolowski

摘要

This paper addresses compliance minimization in linear elastic systems by reformulating the task as an equivalent optimization problem that avoids explicit volume constraints. Within a level-set framework, we examine several algorithms for optimizing material distribution. By deriving both shape and topological sensitivities, we obtain the corresponding derivatives that serve as key inputs to the optimization scheme. Our method efficiently updates the level-set function to reallocate material, concentrating it along primary load paths while removing it from low-stress regions. Numerical examples demonstrate the effectiveness of the proposed approach.