Formation of periodic ribbed or lattice structures in topology optimization assisted by biological pattern formation

Abstract

Periodic porous structural features such as ribs are commonly adopted in the construction of strong and light weight structures. This paper presents a method to create and control periodic structures in topology optimization. The developed method is a resonant coupling of topology optimization and biological pattern formation. The pattern formation excites spacial waves that provide triggers for forming ordered periodic structures in the topology optimization. The period is well controllable, which allows structural designers to choose a suitable period according to non-structural requirements like productivity or styling. Optimization trials for wide cantilevers and in-plane shear-loaded plates successfully demonstrated the creation of the intended periodic structures. The obtained periodic structures exhibit superior rigidity. The proposed method does not force the formation of a periodic structure when an ordered periodic structure is not appropriate. The present work also discovered a phenomenon in conventional topology optimizations. Numerous optima and spontaneous symmetry breaking occur when the loading condition has translational symmetry, i.e., uniformity along an axis. Under such conditions, conventional optimizations create porous structures with an uncertain period. This paper also presents MATLAB code for the proposed method.