A density-based topology optimization method using radial basis function and its design variable reduction

This article aims to present a novel topological design approach, which is inspired by the famous density method and parametric level set method, to control the structural complexity in the final optimized design and to improve computational efficiency in structural topology optimization. In the proposed approach, the combination of radial basis function and the SIMP formula is introduced to describe the distribution of the fictitious density field in the design domain. By changing the radius and distribution of radial function, the structural complexity can be controlled. Meanwhile, it is found that the proposed method can naturally avoid checkerboard design. In order to improve the computational efficiency affected by the number of design variables, we propose to redefine the support points so that the number of support points is much smaller than that of the observation points of the radial function. It follows that the number of design variables can be reduced to a great extent. Several numerical examples are tested to show the feasibility and effectiveness of the presented method.