基于位移和应力灵敏度的结构拓扑优化设计

STRUCTURAL TOPOLOGICAL OPTIMIZATION BASED ON DISPLACEMENT AND STRESS SENSITIVITY ANALYSES

针对仅有应力约束以及含位移和应力约束的重量最小结构拓扑优化问题,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,通过形成和引进新的位移和应力约束限,自动构建设计变量移动限.将结构应力约束归并为几个最可能的有效应力约束,大大减少了应力灵敏度的分析量.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,构建了其等效的优化模型.结合位移和应力灵敏度分析,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.

Stress constrained topology optimization problem has not been paid the same attention as the minimum compliance problem in the literatures. The traditional minimum compliance formulations offer some obvious advantages to avoid dealing with a large number of highly non-linear constraints. This could be considered crucial, if one takes into account the large number of design variables, i.e. inherent to topology optimization. However, one can also argue that this gives rise to several important drawbacks since no constraints are imposed on stresses and displacements, for example, multiple load cases cannot be considered; different solutions are obtained for different restrictions; the final design could be unfeasible in practice. This paper deals with topology optimization of continuum structures with stress and displacement constraints or with only stress constraints, based on the ICM method and the evolutionary structural optimization method. New displacement and stress constraint limits are formed and introduced into the optimization model at the beginning of each optimization iteration sub-loop, so that moving limits of design variables can be easily constructed. Instead of all stress constraints, only the most potential effective stress constraints are considered. In this way, stress sensitivity analysis is much less costly. Moreover, the element deletion 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 element restorable functions, some elements with artificial material property are inserted around the cavities and boundaries of the structure optimized. Meanwhile, an equivalent topological optimization model is developed. Incorporating displacement and stress sensitivity analyses, a new continuum： structural topological optimization method is also proposed. Two simulation examples demonstrate that the proposed method is of validity and effectiveness.