A study of mesh influence on extended finite element cracked plate and finite element plate bending

Abstract

The object of this study is a refining mesh effect on discontinuous structures response. This paper presents a study of mesh influence between cracked and non-cracked plates using extended finite element and standard finite element method, respectively. For the first case, the plate is stressed on one side, in which cracked zone displacements are given for different mesh refinements. The second case study is bending orthotropic and isotropic plates under uniform rectangular impulsive load, in which mesh influence on the structural response is presented. The numerical modelization is done using an isoperimetric quadrilateral element. On one hand, the stiffness linear matrix of a cracked plate is evaluated numerically by adding an enriched shape function to the standard shape function to be able to model discontinuity numerically. On the other hand, for the case of the non-cracked plate, the use of the finite element method with standard shape function is well suited to the numerical design of stiffness and mass matrix. The essence of this study is to show the mesh effect on cracked and non-craked plate response, which is a first step that allows to go even further on monoitoring of our crack evolution.It is a very useful field as any structure in our daily life is subject to a discontinuity (crack) which we must be able to control in order to evoid a future structure collapse.