RESEARCH ON TOPOLOGICAL OPTIMIZATION DENSITY FILTERING METHOD BASED ON NODAL DENSITY INTERPOLATION

In density-based topology optimization methods, the numerical instability problems, such as chessboard patter and gray scale elements affect the manufacturability and practicality of optimized structures seriously. In order to eliminate these problems, the paper proposes a modified density filtering method. The proposed method first takes the densities at the center points of square elements as the design variables, and uses the nodal interpolation method to obtain a smooth and continuous material density distribution within the design domain. Then, the average densities of elements are used as the filtered physical densities for structural stiffness calculation. Therefore, the modified density filter is still a linear filtering method, which only requires simple modifications on the basis of classical density filter. The key of the modified density filter lies in utilizing the nearest neighbor principle of Voronoi diagram, which maximizes the density interpolation weight of the nodal density at the center of the target element for any point within the element. Furthermore, by introducing an optimization parameter into the nodal interpolation weight function, the goals of controlling the proportion of grayscale elements and ensuring convergence stability are achieved. Unlike the Heaviside mapping filters, the added optimization parameter does not increase the non-convexity of the optimization problem, resulting in a decrease in the convergence of the optimization solution. And the modified density filter naturally has the characteristic of volume preserving, effectively avoiding the occurrence of iterative oscillation phenomena similar to the Heaviside-type filters. The numerical results of the compliance minimization problem show that the modified density filter can avoid chessboard patter and obtain optimization result close to the ideal 0 ~ 1 distribution by only changing the optimization parameter. Moreover, compared to the Heaviside mapping filters, the proposed method has better robustness and optimization efficiency in the solving process.