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.

本文旨在利用等几何分析（IGA）和水平集方法对弹塑性平面应力问题进行拓扑优化。IGA 用于对问题的几何形状进行建模，并通过满足材料非线性问题的平衡来计算未知位移。使用具有和不具有各向同性应变硬化的 von Mises 弹塑性材料行为模型。法向速度由水平集函数的基于逐点梯度的灵敏度分析得出，控制网络在每次优化迭代时更新。反应扩散方程也用于更新设计变量，消除了有符号距离函数依赖性，并且该算法提供了孔成核能力。目标是最大限度地提高结构的韧性，它被定义为指定位移内的总外部工作，同时使用设计域中的一定量的材料。为了证明所提出方法的能力和效率，给出了几个数值例子。