Topology optimization of periodically arranged components using shared design domains

Abstract

AbstractBuilding structures from identical components organized in a periodic pattern is a common design strategy to reduce design effort, structural complexity and cost. However, any periodic pattern will impose certain design restrictions often leading to lower structural efficiency and heavier weight. Much research is available for periodic structures with connected components. This paper addresses minimal compliance design for periodic arrangements of unconnected components. The design problem discussed here is relevant for many applications where a tightly nested, space-saving arrangement of identical components is required. We formulate an optimal design problem for a component being part of a periodic arrangement. The orientation and position of the component relatively to its neighbours are prescribed. The component design is computed by topology optimization on a design domain possibly shared by several neighbouring components. Additional constraints prevent components from overlapping. Constraint aggregation is employed to reduce the computational cost of many local constraints. The effectiveness of the method is demonstrated by a series of 2D and 3D examples with an ever-smaller distance between the components. Moreover, problem-specific ranges with only little to no increase in compliance are reported.