比较基于化整交融应力拓扑优化诸解法的效果

由于单元应力属于局部性能约束, 导致相应的结构拓扑优化存在难以承受的大量约束条件; 尽管化整方法极大地减少了约束数量, 但是优化结果中有少数应力超限现象. 为此, 本文在应力约束的结构拓扑优化中, 瞄准克服应力超限和提高求解效率两个目标, 进行了探索. 提出了乘子法及序列二次规划(SQP)法两种解法, 首先在化整交融(即化整-集成)解法中的m方集成模型应用, 与一阶近似的移动渐近线(MMA)解法进行了求解效率对比. 然后, 在此基础上采用了效果最好的m方集成模型的SQP解法, 建立了求解应力约束下结构体积极小化模型(即s方模型), 将化整交融解法与以往单独的化整解法进行了对比. 结果表明: (1) m方集成模型的3种解法中, 乘子法及SQP法的求解效率远高于MMA法, SQP法的求解效率略高于乘子法; (2) 化整交融解法与化整解法相比, 虽然求解效率相当, 但化整交融解法完全避免了个别约束超限的现象, 在满足应力约束条件下, 得到的最优拓扑结构体积更小, 表现出更强的寻优能力. 

EFFECT COMPARISON OF GLOBALIZATION BLEND BASED-METHODS FOR STESS TOPOLOGY OPTIMIZATION

Because of the local characteristics of element stresses, the corresponding structural topology optimization model has too many constraints. Although a globalization method can dramatically reduce the number of constraints in the optimization model, there exist a few elements whose stresses exceeds the allowable stress of materials in the optimized topology. For stress topology optimization problems of continuum structures, this paper aims to overcome the problems of stress over-limit and to improve the solve efficiency. The multiplier method and sequence quadratic programming (SQP) method are proposed. And an aggregation model, called as the m-model in the globalization blend method (named by the globalization-aggregation method), is solved by the two proposed methods. And the solve efficiency of the two proposed methods are compared with the moving asymptote method (MMA) which solves a series of first-order approximated model. On this basis, the SQP method, the most effective method of solving m-model, is adopted to blend with globalization method to form the globalization blend method, which is adopted to solve the structural volume minimization model under stress constraints (named by the s-model). The globalization blend method is compared with the previous globalization method. The results show that: (1) among the three methods of solving the m-model, the solve efficiency of the multiplier method and SQP method is much higher than that of the MMA method. And the solve efficiency of the SQP method is slightly higher than that of the multiplier method. (2) Although the solve efficiency of the globalization blend method is similar to that of the globalization method, the globalization blend method completely avoids the phenomenon of element stress over-limit. In the condition that all stress constraints are satisfied, the resulting optimized topology obtained by the globalization blend method is lighter than that of the globalization method. The globalization blend method has stronger ability to find the optimal solution.