Compliance minimization is a central objective in structural topology optimization, commonly interpreted as the total strain energy of a system. In this work, we examine the influence of alternative compliance formulations based on different norm representations of structural energy. Specifically, we consider three formulations: the classical quadratic compliance, its square-root form corresponding to an l2 norm, and a spectral l1 -norm based formulation derived from the stiffness weighted displacement field. Although these formulations arise from the same stiffness displacement relationship, they generate markedly different optimization landscapes and result in distinct structural topologies. Numerical results indicate that the classical formulation produces well-distributed load paths, whereas the l1 -based formulation promotes sparse and highly localized structural members. These findings underscore the critical role of objective function selection in topology optimization and offer insights into alternative formulations for achieving tailored structural performance.

翻译：柔度最小化是结构拓扑优化的核心目标，通常被解释为系统的总应变能。本研究考察了基于结构能量不同范数表示的替代性柔度公式的影响。具体而言，我们考虑三种公式：经典二次柔度、对应l2范数的平方根形式，以及基于刚度加权位移场导出的谱l1范数公式。尽管这些公式源于相同的刚度位移关系，但它们产生了显著不同的优化景观，并导致截然不同的结构拓扑。数值结果表明，经典公式产生分布良好的载荷路径，而基于l1范数的公式则促进了稀疏且高度局部的结构构件。这些发现强调了目标函数选择在拓扑优化中的关键作用，并为实现定制化结构性能的替代性公式提供了见解。