敏度分层过滤策略克服连续体拓扑优化荷载病态问题

针对工程结构中所承受载荷幅值之间相差多个数量级,使用传统拓扑优化方法所得结果中较小载荷传递路径消失的荷载病态现象,提出一种简单有效的敏度分层过滤策略.将各载荷以幅值大小进行分层,并计算各载荷对结构对应的应变能数值.在此基础上,引入比较判断系数和放大应变能影响系数,将各灵敏度以大小进行分层,对不同层次灵敏度进行不同的过滤以取得多载荷作用下最佳材料布局.本文敏度分层过滤策略是在Solid Isotropic Material with Penahiation(SIMP)框架下提出的,并使用Optimality Criteria(OC)方法进行求解.使用二维和三维算例验证了所提策略的有效性,表明该策略可以有效克服荷载病态现象,为结构设计中得到完整传力结构布局提供重要指导.

Strategy of Sensitivity Hierarchical Filtering for Overcoming Load Sickness Phenomenon of Continuum Topology Optimization

To solve the phenomenon of load sickness in which the transfer path of the weak load disappears by using the traditional topology optimization method, a simple and effective strategy of sensitivity hierarchical filtering was proposed. The loads were stratified by magnitude, and the strain energy corresponding to the structure was calculated. On this basis, two coefficients were introduced, which were used for comparison and amplifying the influence of strain energy. Then, the sensitivities were stratified on the basis of degree, and the sensitivity of different stratification was filtered by different filters to obtain the optimal material layout under multi-load. The strategy was proposed in the framework of SIMP and solved by OC method. Both two-dimensional and three-dimensional numerical examples were presented to show the effectiveness of the proposed strategy, demonstrating that the strategy can effectively overcome the phenomenon of load sickness, and provide important guidance for the completed structural force distribution of the structure.