基于整体应变的柔顺机构多目标拓扑优化设计

摘要

针对传统方法在拓扑优化中会出现局部应变集中的缺陷，提出了一种基于整体有效应变的柔顺机构多目标拓扑优化方法。该方法不再以应变能最小作为目标函数，而是以整体有效应变最小来表征机构的刚度最大，从而将应变均匀地分布在整个系统中。考虑到柔顺机构对刚度和柔度的要求，以整体有效应变最小化和互应变能最大化为目标建立了多目标拓扑优化模型，在变密度法的基础上，利用妥协规划法研究了柔顺机构的多目标优化问题。其中，目标函数的灵敏度分析采用伴随矩阵求解方法，并采用移动渐进算法求解拓扑优化问题。最后，通过柔顺夹钳设计的数值算例来说明该方法的有效性和先进性。结果表明，该方法能够减少基于传统优化方法的结构中的局部大应变，从而有效提升柔顺机构的可靠性。%To overcome the disadvantages of the traditional topology optimization method ,a global effective strain based multi‐objective topology optimization method of compliant mechanisms was presented .Under this method ,a global effective strain function was minimized to represent structural rigidity ,rather than minimizing the strain energy as the objective function .Thus the strain could be well distributed within the whole mechanism ,instead of concentrating on compli‐ant joints to cause a localized high strain .Considering the requirement of rigidity and flexibility on compliant mechanism ,the multi‐objective topology optimization problem that defined the ob‐jective as minimizing the global effective strain and maximizing mutual strain energy was estab‐lished .Based on the solid isotropic material with penalization approach , the compromise pro‐gramming method was used to study the multi‐objective optimization problem of compliant mech‐anisms .The sensitivity of the objective functions was analyzed by the adjoint metrix method . The multi‐objective topology optimization problem was solved using the algorithm of moving as‐ymptotes .Finally ,this method was further investigated and realized with a numerical example to show its correctness and effectiveness .The results show that the global effective strain based to‐pology optimization method can effectively reduce localized high strain of the traditional method to improve the reliability of the compliant mechanism .