Thermodynamic Topology Optimization of compliant mechanisms including a multi-objective approach to prevent one-node connections

Abstract We integrate compliant mechanisms into our Thermodynamic Topology Optimization framework. By applying Hamilton ’s principle we obtain the governing system of equations for both the physical variables and the design variable, all derived from a single Hamilton functional. In this context, the Helmholtz free energy is modeled by using Betti ’s reciprocal theorem taking into account two load cases. The first load case defines the acting force, while the second load case determines the location where displacement should be maximized. Since a pure SIMP approach results in large intermediate material regions, we introduce a smoothed Heaviside function in order to enforce binary material states. As a consequence, the topology develops one-node connections. To prevent this, we propose a simple but effective multi-objective approach for their avoidance.