New method for controlling minimum length scales of real and void phase materials in topology optimization

Minimum length scale control on real and void material phases in topology optimization is an important topic of research with direct implications on numerical stability and solution manufacturability. And it also is a challenge area of research due to serious conflicts of both the solid and the void phase element densities in phase mixing domains of the topologies obtained by existing methods. Moreover, there is few work dealing with controlling distinct minimum feature length scales of real and void phase materials used in topology designs. A new method for solving the minimum length scale controlling problem of real and void material phases, is proposed. Firstly, we introduce two sets of coordinating design variable filters for these two material phases, and two distinct smooth Heaviside projection functions to destroy the serious conflicts in the existing methods (e.g. Guest Comput Methods Appl Mech Eng 199(14):123–135, 2009). Then, by introducing an adaptive weighted 2-norm aggregation constraint function, we construct a coordinating topology optimization model to ensure distinct minimum length scale controls of real and void phase materials for the minimum compliance problem. By adopting a varied volume constraint limit scheme, this coordinating topology optimization model is transferred into a series of coordinating topology optimization sub-models so that the structural topology configuration can stably and smoothly changes during an optimization process. The structural topology optimization sub-models are solved by the method of moving asymptotes (MMA). Then, the proposed method is extended to the compliant mechanism design problem. Numerical examples are given to demonstrate that the proposed method is effective and can obtain a good 0/1 distribution final topology.