惯性载荷作用下结构拓扑优化

STRUCTURAL TOPOLOGY OPTIMIZATION UNDER INERTIAL LOADS

针对惯性载荷作用下的结构拓扑优化设计问题,基于结构整体柔顺度的灵敏度计算公式的推导,阐述了此类问题目标函数的非单调特征;根据载荷与单元刚度的设计相关性,分析了多种材料插值模型对优化结果和迭代过程的影响.在此基础上,提出可变参数的RAMP模型,对不等式体积约束和纯自重作用下的拓扑优化问题,通过稳定的优化迭代过程得到逼近理论最优解的优化结果.理论分析和数值算例表明,设计相关惯性载荷导致结构柔顺度的灵敏度不再永远为负值,即柔顺度不再是单调减函数;惯性载荷作用下拓扑优化结果并不总是达到体积约束上限,即材料用量越多结构刚度未必越大;已有的ESO和MP类优化方法的优化结果存在明显的区别,而选择适当的材料插值模型能够很好的将两类优化方法的结果统一起来.

Abstract Structural topology design optimization under inertial loads is studied in the paper. Based on the sensitivity scheme of structural compliance, the non-monotonous feature of the objective function is described. Due to the design-depedent effects of loads and element stiffness, various material penalization models are investigated to show their influences on the optimization results and iteration processes. Subsequently, an improved RAMP model with variable parameter is proposed and validated. For the problem with inequality volume constraint under self-weight loading, the optimal solution is obtained in stable convergence way for the first time, also to approach the theoretic solution associated with a void structure without material. Theoretical and numerical results showed that the compliance sensitivity remains no longer to be negative due to the the design-dependent effect of inertial loads. This means that the objective function is non-monotonous. As a result, the inequality volume constraint is not always active at the optimum solution. In other words, less material may lead to a stiffer structure for an optimum material layout. Besides, it is shown that the integration of a proper RAMP model with the BESO method can improve greatly the result so that both BESO and MP methods become consistent for self-weight design problem whereas previously existing optimization results obtained by BESO and MP methods are quite different.