A Simple and Efficient Structural Topology Optimization Implementation Using Open-Source Software for All Steps of the Algorithm: Modeling, Sensitivity Analysis and Optimization

Abstract

This work analyzes the implementation of a continuous method of structural topology optimization (STO) using open-source software for all stages of the topology optimization problem: modeling, sensitivity analysis and optimization. Its implementation involves three main components: numerical analysis using the Finite Element Method (FEM), sensitivity analysis using an Adjoint method and an optimization solver. In order to allow the automated numerical solution of Partial Differential Equations (PDEs) and perform a sensitivity analysis, FEniCS and Dolfin Adjoint software are used as tools, which are open-source code. For the optimization process, Ipopt (Interior Point OPTimizer) is used, which is a software package for nonlinear optimization scale designed to find (local) solutions of mathematical optimization problems. The topological optimization method used is based on the SIMP-Solid Isotropic Material with Penalization interpolation. The considered problem is the minimization of compliance/maximization of stiffness, considering the examples of recurrent structures in the literature in 2D and 3D. A density filtering algorithm based on Helmholtz formulation is used. The complete code involves 51 lines of programming and is presented and commented in detail in this article.

Sequential method of topological optimization in multi-component systems

“…In the sequential method it is also possible to consider the volume constraints individually in each component. As demonstrated by Ferro and Pavanello (2023) using a subclass of Dolfin-Adjoint, it is possible to consider the desired volume for each component individually according to Equation 4. And thus, a comparison considering variations between volumes is also shown at the end of each model.…”