考虑地震荷载的框架结构拓扑优化设计

Topology optimization design of frame structure considering seismic load

为研究考虑地震荷载的框架结构拓扑优化设计,引入改进的多项式刚度矩阵惩罚模型和基于低阶模态能的伪模态识别准则和删除措施,综合解决了伪模态问题和惯性荷载作用下结构低密度区域的寄生效应问题;采用Heaviside函数建立了设计变量与物理变量之间的映射关系,并构建了地震荷载作用下以结构模态柔顺度总和最小为目标函数、满足体积约束的框架结构拓扑优化模型;采用移动渐近线方法对优化模型进行了求解。算例的计算结果表明:采用本研究提出的方法可以得到清晰的0/1分布的优化拓扑,且结构的设计域质量对优化结果有很大的影响,这验证了本研究方法的正确性和有效性。

In order to study the topology optimization design of frame structure considering seismic load,the pseudo modal identification criteria and deletion measures based on low order modal energy and the improved polynomial stiffness matrix penalty model were introduced to solve the pseudo modal problems and the parasitic effects of low density areas of the structures under inertial loads.The mapping relationship between design variables and physical variables was established by using the Heaviside function,and the topological optimization model of frame structure was constructed,whose objective function was that the sum of structural modal compliance under the seismic loads was minimal and constraints were the volume constraint.The method of moving asymptotes was used to solve the optimization model.The results of the examples show that the proposed method can obtain a clear 0/1 distribution topology,and the masses of the design domain have serious impacts on the optimization results,which verifies the correctness and effectiveness of the proposed method.