Proportional Topology Optimization algorithm for two-scale concurrent design of lattice structures

In this paper, the Proportional Topology Optimization (PTO) algorithm is extended for two-scale concurrent topology optimization, in which both structure and material cellular micro-structure are subject to design. PTO was originally developed on concept that amount of being distributed an element would be proportional contribution objective function. Sensitivity analysis not required. a optimization problem, two sets design variables defined, one macro-structure micro-structure. Here, function reformulated such each micro-scale variable can determined, facilitating employment PTO. The macroscopic effective elastic tensor evaluated by energy-based homogenization method (EBHM), providing link between macro-structure. Feasibility efficiency proposed approach demonstrated via several benchmark examples three dimensional structures.