A new adaptive penalization scheme for topology optimization

In the product development process topology optimization can successfully be applied in the early product design stages. In this work a new penalization scheme for the SIMP-method (Solid Isotropic Material with Penalization) is presented. One advantage of the presented method is a linear density-stiffness relationship, which has advantages for self-weight or eigenfrequency problems. The optimization problem is solved through derived optimality criteria (OC), which is also introduced in this paper. The derived OC uses no sensitivities of the optimization function but is equivalent to the classical OC in the case of no penalization. In the case with penalization we present an objective function for the penalty factor. By maximizing the objective function in each iteration, we get an adaptive penalty factor. Numerical experiments show, that the adaptive penalty factor leads to better optimization results then a fixed penalty factor. The presented topology optimization method is implemented in the commercial FEM package ANSYS under the name TopoAD. One useful extension of TopoAD is the concept of “meta elements”, which is also presented in this paper.