Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
An Educational MATLAB Code for Topology Optimization of Thick-Thin Plates using Arbitrary Polygonal Meshes
Submission Author:
Diego Santos Duarte , BA
Co-Authors:
Diego Santos Duarte, Ivan Menezes
Presenter: Diego Santos Duarte
doi://10.26678/ABCM.COBEM2023.COB2023-1154
Abstract
Arbitrary polygonal finite element meshes have been widely used in topology optimization in the past few years. This class of meshes offers great flexibility for treating complex geometries, as required in most real-world engineering problems. For topology optimization purposes, arbitrary polygonal meshes have been proven to present an efficient performance. Due to the edge-to-edge connections between elements, instead of vertice-to-vertice connections, as in conventional triangular and quadrilateral meshes, the polygonal elements demonstrated not to be susceptible to numerical instabilities such as checkerboard patterns and one-node connections. Another issue on either lower-order triangular/quadrilateral or arbitrary polygonal meshes in Reissner-Mindlin plate formulations is the shear locking, which considerably increases the plate stiffness as its thickness decreases. For the aforementioned conventional meshes, various techniques primarily emerged to circumvent the shear locking occurrence, such as reduced and selective integration. Recently, a few locking solutions have been proposed and studied for arbitrary polygonal meshes. In the context of academic research, the literature available provides codes for topology optimization using polygonal meshes mainly applied to membrane elements. Motivated by the same academic purposes and inspired by the latest scientific contributions, this work aims to provide an educational, concise, and user-friendly MATLAB code for topology optimization of plates using polygonal isoparametric plate elements under the Reissner-Mindlin theory. The shear locking is naturally solved by imposing a generalization of an assumed strain field over the polygonal edges under Timoshenko’s beam assumption. The novel extracts of the proposed code are explained, and possible variations for further user exploration are discussed. To properly illustrate and validate the computational efficiency of the proposed code, some plate benchmark problems are solved in the context of compliance topology optimization.
Keywords
Topology optimization, Polygonal Elements, Plates, Reissner-Mindlin, Compliance Minimization
