Multi-component layout design with coupled shape and topology optimization

Abstract

A Coupled Shape and Topology Optimization (CSTO) method is proposed here to deal with the layout design of the multi-component system. Considering a complex packing system for which several components will be placed in a container of specific shape, the aim of the design procedure is to find the optimal location and orientation of each component as well as the configuration of the structure that supports and interconnects the components. Compared with existing packing design approaches, two significant improvements are made in the CSTO method. On the one hand, a new Finite-circle Method (FCM) is used here to discretize boundaries of all components and the container into a number of circum- circles. Hence geometric constraints can be suitably modelled to avoid the overlap among the components as well as the overlap between the components and the container contour. Besides, the FCM approximation is also convenient to deal with components and the container with concave or some other complex shapes. On the other hand, the design procedure is able to take into account the mechanical performances of the structural system. Here, the location and the orientation of the components will be updated to improve the system rigidity by using shape optimization procedure. Meanwhile, the optimal material layout of the supporting structure in the design domain is designed by topology optimization. Due to the iterative movement of components, the technique of the embedded mesh is used to update the local FE mesh around each component in the design domain and pseudo density design variables assigned to density points instead of finite elements will be used to follow such a FE mesh variation. Several design problems are tested in this paper, and numerical results show the proposed CSTO method extends the actual concept of topology optimization and is efficient to generate reasonable design patterns.