提出了一种考虑组件保形要求的组件布局-结构拓扑的多组件结构系统布局优化设计方法。在传统的多组件结构系统布局优化设计基础上，定义了组件设备的弹性应变能函数并用其定量衡量组件设备的弹性变形程度，在多组件结构系统布局优化过程中，采用组件设备的弹性应变能函数作为其保形设计约束，以实现抑制承载组件变形的设计目的。解析了组件设备保形设计约束对结构拓扑及组件布局设计变量的灵敏度，研究了组件保形设计约束与结构系统整体刚度之间的消长关系，分析了组件保形约束对组件布局及支撑结构材料拓扑分布的影响，在考虑组件保形设计约束的挂架系统布局优化模型中引入了系统的质心位置约束并完成了其解析灵敏度求解。通过数值算例，实现了考虑组件保形、材料用量分数、质心位置约束的多组件结构系统布局优化设计。数值算例的计算结果表明，引入组件保形约束的多组件结构系统布局优化设计方法能够有效抑制传力路径上参与承载的组件设备的弹性变形，实现组件设备的保形设计。
A formulation considering the shape-preserving design of components for the integrated layout and topology optimization design of a multi-component structural system is proposed. Based on the conventional integrated layout and topology optimization design of a multi-component structural system, the static strain energy of the movable component is defined to illustrate and measure its elastic deformation. To suppress the warping deformation of load-carrying components in the design of multi-component structural systems, the proposed static strain energy of the movable component is treated as a design constraint of the optimization model, also called shape-preserving design constraint of the movable component. The analytical design sensitivity of the shape-preserving design constraint of components to the topological design variable and the component layout design variable is given, the wane and wax relationship between the shape-preserving design constraint of the movable component and the global stiffness discussed, the influence of the shape-preserving design constraint of the movable component on its supporting structure studied, and the centroid position constraint of the structural system is introduced into the optimization design of the multi-component structural system considering component shape-preserving design constraints. By conducting numerical examples, we achieve the design results taking the shape-preserving design constraint of movable components, material usage fractions and centroid position constraint into account. The design results show that the proposed shape-preserving design constraint of movable components is effective in suppressing the elastic deformation of load-carrying components for the integrated layout and topology optimization design of multi-component structural systems. The desired shape-preserving design of movable components can be obtained using the proposed formulation.
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