Assessment of New Adaptive Finite Elements Based on Carrera Unified Formulation for Meshes with Arbitrary Polygons

Abstract

The meshing technique represents the capability to discretize the domain of interest, to fit the real physical continuum in the best possible way. The most used approach is the finite-element method (FEM), a numerical method to solve partial differential equations. To overcome the classical issues presented by FEM, other models are investigated. The goal is to allow the problem domain to be discretized by elements represented by arbitrary polygons, which can be concave and convex. Moreover, different polynomial consistency is sought within these methods with the possibility to handle non-conforming discretizations, mainly for local refinement and so on. This work aims to present the new adaptive elements, which are finite elements based on Carrera unified formulation, to demonstrate that all the previous capabilities can be done with these new elements, with easy implementation of the relative model. First, a classical patch test is done to investigate the mesh distortion sensitivity. Then, different study cases are presented with more complex meshes combining very distorted concave and convex elements.