Optimal embedding of rigid objects in the topology design of structures

Extensive published research results exist on the topology design of single-component structures, while multicomponent structural systems have received much less attention. In this article, we present a technique for optimizing the topology of a structure that should be connected to one or more predesigned polygon-shaped components to maximize the stiffness of the overall ensemble. We call it an embedding problem in topology design because predesigned components are to be optimally positioned and oriented within a design region while the connecting structure's topology is optimized simultaneously. Continuous design variables are used to vary the locations of the embedded objects smoothly along with the topology of the connecting structure to apply gradient-based continuous optimization algorithms. A new material interpolation function on the basis of normal distribution function was used for this purpose. An optimality criteria method combined with the steepest descent method was used to minimize the mean compliance to obtain the stiffest structure for a given volume of material for the connecting structure. As a special case of this method, topology optimization of multicomponent structural systems connected with fasteners was also considered. Illustrative examples are presented.