一种考虑位移和应力约束的结构拓扑优化方法

为了研究位移和应力约束以及重量最小的结构拓扑优化问题，基于ICM（独立、连续、映射）方法和渐进结构优化方法的思路，提出了一种考虑位移和应力约束的结构拓扑优化方法．在优化迭代循环的每一轮子循环迭代求解开始时，为了控制拓扑设计变量的变化量，依据结构位移、应力量和其约束限，形成和引进了新的位移和应力约束限．研究了位移线性近似式和应力约束转换表达式，建立了单元删除阚值和几轮迭代循环的单元删除策略．为了确保优化迭代中结构非奇异和方法具有增添单元的功能，在结构孔洞和边界周围引入了一层人工材料单元，并建立了一套有效结构信息到结构最大设计域信息的映射转换方法．结合拉格朗日乘子法，改进了子循环迭代中连续拓扑变量的求解方法，形成了一种新的连续体结构的拓扑优化方法．给出的算例验证了该方法的正确性和有效性．

A structural topological optimization method considering displacement and stress constraints

In order to study structural topological optimization problem with the objective function being the structural weight, displacement and stress constraints, based on the ideas of the ICM method and the evolutionary structural optimization method, this paper proposes a new structural topological optimization method. At the beginning of each optimization iteration sub-loop, in order to control the change quantity of topological design variables, new displacement and stress constraint limits are formed and introduced into the optimization model. A liner displacement approximate formula and the transformation expression of stress constraints are proposed. Moreover, the element removing and adding criterion and a set of structural optimization strategies are given. In order to make the structure optimized be non singular and the proposed method be of an element restorable function, some elements with artificial material property are inserted around the cavities and boundaries of the structure optimized. And a structural characteristics mapping transformation relation between the effective structure and the structural maximum design domain is built. Incorporating the Lagrange multiplier method, a set of solving method for continuous topolog- ical variables of sub-loop iterations is improved, and a new continuum structural topological optimization method is proposed. Several simulation examples show that the proposed method is of validity and effectiveness.