航天结构带频率禁区的动力学拓扑优化设计

Dynamic topological optimal design of aerospace structure with frequencies constraints

针对航天设备中对振动频率有特殊要求的高阻尼支座结构,基于独立、连续、映射(Independent Continuous Mapping,ICM)方法,结合随机振动的虚拟激励方法,建立了具有频率禁区约束的连续体动力学优化模型。该方法通过瑞利商和泰勒展开式对频率禁区进行显式处理,将优化模型转化为二次规划模型;在动力学分析过程中引入虚拟激励方法,通过对偶理论和序列二次规划方法进行了求解。通过对某型支座结构的建模优化,结合数值分析对各项优化指标进行了比对,得到优化结果避开了预设频率禁区,在满足变形约束下使质量降低27.66%,完成了优化任务,验证了本文方法的有效性。

In this paper,the Independent,Continuous and Mapping(ICM)Method and Pseudo Excitation Method(PEM)are used to solve the model of topology optimization for high-damping structures in aerospace engineering.The objective of the topology optimization is to minimize the weight subjected to frequency constraints.Exponential function is adopted as the filtering function of the element weight,mass matrix and stiffness matrix.The optimization model is transferred into a dual optimization model.In this method,Rayleigh quotient and Taylor expansion are used to explicitly deal with the frequency constraints,which is solved by the sequential quadratic programming(SQP).In numerical examples,the topology optimization of an engineering support structure is analyzed,the optimization results avoid the preset frequency constraints,and realize the weight loss of 36.17%under the deformation constraints,which completes the optimization task and verifies the effectiveness of the presented method.