On honeycomb representation and SIGMOID material assignment in optimal topology synthesis of compliant mechanisms

This paper introduces a new honeycomb based domain representation and SIGMOID material function to model continuum topology optimization domains with fixed grids. The two-point connectivity ensured with hexagonal cells is shown to circumvent singularities related to checkerboard patterns and point flexures that are typically observed with one-point connected rectangular cells. The novel SIGMOID function is developed to assign the ‘solid’ material for very low values of design variables (probabilities) and ‘void’ material for those further lower than the threshold, thus encouraging the binary material assignment. The performance of the SIGMOID function is compared with the previously proposed SIMP and PEAK material assignment functions. It is shown that both SIMP and PEAK functions can be over-restrictive in that the material is assigned only for probabilities close to one. The proposed modeling is suitable for topology optimization objectives wherein the number of constraints is large and gradient-based algorithms are chosen. Numerous examples on material layout determination for compliant mechanisms are solved with flexibility-stiffness and flexibility-strength multi-criteria formulations to illustrate the essence of this paper.