Isogeometric level set topology optimization for elastoplastic plane stress problems

This article aims to utilize IsoGeometric analysis (IGA) and Level set method for topology optimization of elastoplastic plane stress problems. The IGA is employed to model geometry of the problem and calculate unknown displacements by satisfying equilibrium for materially-nonlinear problems. The von Mises elastoplastic material behavior model with and without isotropic strain hardening is utilized. The normal velocity is derived by the pointwise gradient based sensitivity analysis of the Level set function and the control net is updated at each optimization iteration. The reaction-diffusion equation is also employed to update the design variables, which eliminates the signed distance function dependency, and the algorithm provides capability of hole nucleation. The objective is to maximize the toughness of structure, which is defined as the total external work within a specified displacement, while certain amount of material in the design domain is used. In order to demonstrate the ability and efficiency of the proposed method, several numerical examples are presented.