考虑组件保形约束的多组件结构系统布局优化

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.