Wavelet-based interpolation algorithm for topology extraction of compliant mechanisms

An important issue is to extract a practicable topology from the solution to the topology optimization design of a compliant mechanism. However, there exist checkerboard patterns in most topology results, which makes topology extraction very difficult. In this investigation, a wavelet-based interpolation algorithm, which directly works with the optimization result to extract a checkerboard-free topology, is proposed. Firstly, auxiliary variables, which are mapped from topology variables, are decomposed by an orthogonal wavelet into approximation and detail coefficients. Secondly, the approximation coefficients are served as reference data for a cubic spline interpolation. The approximation coefficients are reconstructed after the interpolation. In order to evaluate the goodness of the algorithm proposed and determine an optimal resolution level selected in the wavelet decomposition, a method based on a volume constraint of the topology optimization is considered. Numerical simulation is carried out on a compliant force inverting mechanism. Simulation results show that the algorithm proposed is an effective remedy for checkerboard patterns in topology solutions and as a result a desired topology is extracted.