Comparative Analysis of Compliance-Matrix Induced Norms in Structural Topology Optimization

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.