A new multi-p-norm formulation approach for stress-based topology optimization design

Abstract

Although the stress-based topology optimization problem has been extensively studied for continuum structures, it is still an open problem and there is still room for improvements. This work proposes a comprehensive approach for dealing with stresses in topology optimization problems. The SIMP method is used to distribute material along the domain. For limiting the stress, a multi-p-norm formulation is proposed to deal with the local nature of stress and to avoid stress concentration. This function considers many values of p coefficients at the same time while other formulations adopt a specific value for p defined for subregions. As a consequence this formulation can avoid the stress concentrations without being necessary to define sub-regions. In addition, the proposed formulation is load independent because the multi-p-norm is used as the objective function. A SIMP-like formulation is used to address the stress singularity phenomenon and the heaviside projection is used to avoid mesh dependency, checkerboarding, and to control the minimum length-scale. A proper continuation scheme is proposed to all penalization coefficients in order to achieve black-and-white solutions. The optimization problem is solved by using GCMMA. Numerical examples for homogeneous and composite structures are presented to illustrate the proposed formulation.