基于动响应约束的结构材料优化设计

Topology optimization of micro structures with random vibration responses constraints

针对于随机荷载作用下动响应为约束的结构材料优化问题,基于结构拓扑优化思想,提出了一种变动响应约束的结构材料优化方法。采用分式有理式和幂函数识别结构材料单元特性参数,以微观单元拓扑变量倒数为设计变量,导出了频率及振型对微观单元设计变量的一阶导数,进而得到了随机荷载作用下结构均方响应的一阶近似展开式。结合变约束限的思想,建立了以结构质量作为目标函数,均方响应作为约束条件的连续体微结构拓扑优化近似模型,并采用对偶方法进行求解。对典型结构进行了考虑单个和多个动响应约束的结构材料优化设计,优化所得结果验证了该方法的有效性和可行性。

A structural material optimization method with varied random dynamic responses constraints was proposed to solve the problem of structural material optimization under random excitations, based on the structural topology optimization technology. By using the conventional rational approximation and power interpolation for material properties and masses and selecting the reciprocals of topological variables of micro structural elements as design variables, the first order derivatives of frequency and modal shape with respect to the design variables were derived. And the one order approximate explicit functions of dynamic responses were further achieved. Integrated with the idea of varied constraints, a topological optimization model of micro structures was built by taking the structural mass as the objective function and the dynamic responses as constraint functions. Then, a dual solving method was introduced. Several numerical examples were presented to verify the proposed optimization algorithm and the microstructures of cellular materials were obtained. © 2017, Editorial Office of Journal of Vibration and Shock. All right reserved.