A method for setting the objective function in the problem of the topological optimization of three-dimensional structures using a density gradient

We give a method and algorithm that optimizes the shape of structural elements. The goal is to minimize the mass of the structural element and to prevent stresses from exceeding the specified limit.The proposed approach is based on an iterative finite-element analysis of structural elements. At each iteration, the material is redistributed within the design space using the gradient method, which solves the problem of minimizing a specially designed target function. This function includes three terms, one of which depends on the density gradient. The aim of introducing this target function is to improve the robustness of optimization procedure and to avoid the occurrence of checkerboard structures.The developed algorithm is implemented as a software module that performs the topological optimization of structures. Several model problems are described.A comparative analysis of the results obtained using this module and the results obtained earlier shows that the proposed approach revealed their common features, and in some cases eliminated their shortcomings. The sharpness of boundaries of optimized structures is improved.