基于等效静载荷和模态跟踪的结构拓扑优化

摘要

为实现结构动态多目标下的拓扑优化设计,以特定模态固有频率最大化和动态柔顺度最小化加权函数为目标,提出动力特性和动力响应综合目标的渐进结构拓扑优化模型.基于等效静载荷原理,将结构的动刚度拓扑优化设计问题转换为多载荷工况静态刚度拓扑优化设计问题.基于模态跟踪技术,保证结构指定模态在渐进优化过程中的一致性.构建归一化目标函数避免不同性质目标函数的量纲与量级差异,融和渐进结构优化方法构造动态多目标下的连续体渐进结构拓扑优化算法.数值算例结果表明:所提出的动态多目标渐进结构优化方法对结构动力学拓扑优化问题具有一定的适用性,拓展了渐进结构优化方法在动力学拓扑优化设计的应用领域.%A multi-objective optimization technique in continuum topology is proposed to simultaneously consider the maximization of corresponding fundamental eigenfrequency with the desired modal shape and the minimization of the dynamic compliance by evolutionary structural optimization.Based on equivalent static load method,the structural optimization design in dynamic stiffness is transformed to that of multi-loading case in static stiffness.A mode-tracking method is proposed to ensure the consistence of the desired mode during the optimization process.The comprehensive objective function is normalized to avoid the dimensional and numerical magnitude difference among diverse objective functions.Subsequently the multi-objective dynamic programming scheme for continuum topology is implemented to obtain optimal topologies based on evolutionary structural optimization.The numerical results indicates that the proposed multi-objective dynamical evolutionary structural optimization method is feasible in the topological optimization of dynamic performance,and hence can be extended to the application of original evolutionary structural optimization theory to dynamic optimization in structural topology.