A reevaluation of the SIMP method with filtering and an alternative formulation for solid-void topology optimization

The most popular way to introduce the notion of topology into the structural analysis of the topology optimization problem is through the Solid Isotropic Material with Penalization (SIMP) method. The fundamental principle behind its use requires a density design variable dependent material constitutive law that penalizes intermediate density material in combination with an active volume constraint. Here, the SIMP method with filtering is reevaluated, and an alternative topology optimization problem formulation, called the SINH (pronounced cinch) method, is developed that exploits this principle. The main advantages of the SINH method are that the optimization problem is consistently defined, the topology description is unambiguous, and the method leads to predominantly solid-void designs.