Topology optimization for compliant mechanism using material point topological variable

To overcome various kinds of numerical instabilities in topology optimization for compliant mechanisms, a method using material point topological variables as design variables is proposed. The material point topological variable can be viewed as natural extension of the nodal density. Based on a modified mesh-independent filtering scheme, a new interpolation function used to construct the topological variable field is presented. The mathematical model of topology optimization for compliant mechanisms is established based on spring model, in which some structural responses are taken as constraint functions. The analytical expressions of various structural responses sensitivity are deduced. The method of moving asymptotes is adopted in the optimization algorithm. The feasibility and generality of the method are demonstrated by some numerical examples.