A MATLAB implementation for topology optimization of compliance minimization problems based on the standard finite-volume theory for continuum elastic structures

Resumo

Topology optimization is an important technique for the design of optimum structures. Its main
objective is to determine the best material distribution inside of an analysis domain. In the last three decades, a
significant part of the advances in structural topology optimization has been achieved by employing finite-element

strategies for structural analysis. Therefore, the advantages and disadvantages of this numerical technique are well-
known. For instance, the checkerboard pattern is directly associated with the finite-element method numerical

assumptions, which leads to some artificial stiffness. An alternative to the finite-element method is the finite-
volume theory, which has been shown to be an efficient checkerboard-free numerical technique. Many algorithm

implementations have been published for educational purposes over the last decades to promote topology
optimization strategies. However, most of these algorithms are constructed based on the finite-element method.
Therefore, the present paper proposes a MATLAB® implementation of a topology optimization approach for
compliance minimization problems based on the standard finite-volume theory of linear elastic continuum
structures. A sensitivity filter is also implemented to control the mesh dependence and length scale issues.