Topology optimization of elastic contact problems using B-spline parameterization

Abstract

This work extends B-spline parameterization method to topology optimization of elastic contact problems. Unlike the traditional density-based method, design variables directly refer to the control parameters of the B-spline. A continuous pseudo-density field representing the material distribution over the concerned design domain is constructed by means of B-spline parameterization and then discretized onto the finite element (FE) mesh. The threshold projection is further introduced to regularize the B-spline pseudo-density field for the reduction of gray areas related to the local support property of B-spline. 2D and 3D frictionless and frictional problems are solved to demonstrate the effectiveness of the proposed method. Results are also compared with those obtained by the traditional density-based method. It is shown that the B-spline parameterization is independent of the FE model and suitable to deal with contact problems of inherent contact nonlinearity. The optimized configuration with refined details and smoothed boundaries can be obtained.