简谐力激励下结构拓扑优化与频率影响分析

摘要

研究了简谐力激励下以结构指定位置稳态阶段位移响应幅值为目标函数、结构体积为约束的拓扑优化设计问题.通过在频域上使用模态叠加法求解简谐力激励下的位移响应,分析了激励频率和作用方向对位移响应幅值及其优化结果的影响.引入材料属性的多项式插值惩罚模型,有效消除了动力学拓扑优化局部模态现象.分析了高频激励下位移响应幅值拓扑优化存在的稳定性差、结构不连续等问题,并通过引入附加静位移约束,获得了清晰合理的结构形式.理论分析和算例结果揭示了位移响应幅值优化过程中结构模态的变化规律,验证了该拓扑优化模型的有效性.%In this paper,structural topology optimization is studied under harmonic force excitations.The displacement amplitude at the specified location of a structure is defined as the objective function subjected to the volume constraint.The displacement amplitude is calculated based on modal superposition method and the corresponding sensitivity analysis is derived.In order to avoid localized modes,the polynomial interpolation scheme is introduced to relate material properties to pseudo density variables.In the meantime,the influences of the excitation frequency and direction upon the displacement response are investigated and how the eigen-modes vary in the optimization process is highlighted.Topology optimization of structure under harmonic excitation with high frequency is specially analyzed.More constraints on the static displacements are applied to generate clear structural topology.Numerical optimization examples are finally solved to demonstrate the validity of the proposed optimization procedure.