一种变频率约束限的结构拓扑优化方法

A STRUCTURAL TOPOLOGIC OPTIMIZATION METHOD BASED ON VARYING FREQUENCY CONSTRAINT LIMITS

针对仅频率约束和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,提出了一种变频率约束限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,依据结构频率和其约束限,形成和引进了新的频率约束限。另外,建立了单元删除阈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。结合拉格朗日乘子法,形成了一种新的连续体结构的拓扑优化方法。给出的算例表明该方法没有目标函数的振荡现象,且验证了该方法的正确性和有效性。

For structural topologic optimization problems with an objective function being structural weight and only frequency constraints,based on the ICM method and the evolutionary structural optimization method,a new structural topologic optimization method is proposed.At the beginning of each sub-loop optimization iteration process,in order to control the change quantity of topologic design variables,new frequency constraint limits are formed and introduced into the optimization model.Moreover,the element deletion and adding criterion and a set of structural optimization strategies are given.In order to make the optimized structure be non-singular and the proposed method possess an element restorable function,some elements with artificial material property are inserted around cavities and boundaries of the structure optimized.Combined with Lagrange multiplier method,a new continuum structural topologic optimization method is proposed.Two simulation examples show that there is not any oscillatory phenomenon of the objective function,and the correctness and effectiveness of the proposed method are verified.