Cameron Talischi

TL;DR: A simple and robust Matlab code for polygonal mesh generation that relies on an implicit description of the domain geometry and the centroidal Voronoi diagrams used for its discretization that offers great flexibility to construct a large class of domains via algebraic expressions.

TL;DR: This work focuses on the linear elasticity equations in three-dimensions and elaborate upon the key concepts underlying the first-order VEM, and presents several numerical studies in order to verify convergence of the VEM and evaluate its performance for various types of meshes.

TL;DR: An efficient Matlab code is presented that includes a general finite element routine based on isoparametric polygonal elements which can be viewed as the extension of linear triangles and bilinear quads and features a modular structure in which the analysis routine and the optimization algorithm are separated from the specific choice of topology optimization formulation.

TL;DR: Polygonal meshes constructed from Voronoi tessellations are considered, which in addition to possessing higher degree of geometric isotropy, allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities.

TL;DR: In this paper, the authors propose and explore an alternative approach to model finite elasticity problems in two dimensions by using polygonal discretizations, which consist of a piecewise constant pressure field and a linearly complete displacement field at the element level.