Research on Post-processing Method of Topology Optimization Model

Abstract

Introduction: Structural topology optimization is an effective structural optimization method, which has become a hot research topic in the field of finite element analysis. The variable density method is usually used to solve the structural topology optimization problem due to the advantages of less design variables and high efficiency. However, this method also has disadvantages such as network dependence and boundary diffusion which would increase the geometric complexity and optimization time cost. In addition, the optimization results often bring a gray transitional boundary, the ideal smooth boundary cannot be obtained by traditional method of curve approximation or curve fitting, and it is impossible to determine whether the boundary extraction and model reconstruction can be successful. At the same time, the optimization model needs to be attached to the grid during topology optimization, so it is unavoidable that the edge of the optimization result has a jagged boundary. This not only increase the manufacturing difficulty, but also increases the complexity of the structure and makes model reconstruction difficult. Aiming at the problems of boundary diffusion and jagged boundary existing in the topology optimized model based on the variable density method, a topology optimization post-processing method using the partition sensitivity filtering and the ordinary least squares is proposed. The partition weighted sensitivity filtering method is to divide the sensitivity filtering area into two parts, and use different weighting factors to weight the inner and outer areas respectively to remove the gray value to obtain a topology optimization structure with clear boundaries. The ordinary least squares curve fitting is to make the sum of the squares of the errors between the extracted boundary points and the fitting points reach the minimum value as much as possible, and the curve formed by the fitting points is an ideal fitting curve, which can make the jagged boundary become smooth. Some typical examples verify the effectiveness and feasibility of the method in suppressing boundary diffusion and solving jagged boundary problems under the conditions of single load, multiple loads and elements with different densities. By analyzing the model before and after post-processing, it is verified that this post-processing method can effectively obtain the topology optimization structure with clear and smooth boundaries, and the stress distribution is more uniform, which can reduce the difficulty of model reconstruction and manufacturing.