Study on parameters for topological variables field interpolated by moving least square approximation

This paper presents a new approach to the structural topology optimization of continuum structures. Material-point independent variables are presented to illustrate the existence condition, or inexistence of the material points and their vicinity instead of elements or nodes in popular topology optimization methods. Topological variables field is constructed by moving least square approximation which is used as a shape function in the meshless method. Combined with finite element analyses, not only checkerboard patterns and mesh-dependence phenomena are overcome by this continuous and smooth topological variables field, but also the locations and numbers of topological variables can be arbitrary. Parameters including the number of quadrature points, scaling parameter, weight function and so on upon optimum topological configurations are discussed. Two classic topology optimization problems are solved successfully by the proposed method. The method is found robust and no numerical instabilities are found with proper parameters.