简谐力激励下多组件结构系统的整体优化设计

Integrated layout and topology optimization design of multi-component structure system under harmonic force excitation

多组件结构系统整体优化设计通过协同优化支撑结构拓扑构型和组件布局来使结构系统的位移响应最小。本文提出通过模态加速度法(MAM)求解多组件结构系统的位移响应,并以位移响应值最小作为优化目标;引入多点约束(MPC)方法模拟组件与设计域间的铆钉或螺栓连接形式;采用有限包络圆法(FCM)来避免组件之间及组件与设计域边界产生干涉。建立了多组件结构系统整体优化问题的数学模型,并对动响应目标函数关于设计变量的灵敏度进行了推导。最后,通过几个算例验证了整体优化方法在简谐力激励下求解问题的可行性及其在实际问题中的有效性。

This paper presents an integrated layout and topology optimization of the multi-component structure system under harmonic force excitation.The configuration of the supporting structure and the component layout are simultaneously optimized to minimize the displacement responses that are obtained by using the Mode Acceleration Method（MAM）.The MultiPoint Constraint（MPC）scheme is employed to simulate the rivets and bolts connecting components and supporting structures.The Finite Circle Method（FCM）is used to avoid overlaps among different components and boundaries of supporting structures.The mathematical model for the integrated layout and topology optimization of multi-component structure system is established,and the sensitivities of the objective function to design variables are deduced.Numerical examples are presented to demonstrate the effectiveness and validity of the proposed method for solving problems under harmonic force excitation.