Mathematical Formulation and Numerical Implementation of a Finite Element with Anisotropic Geometry

A plane quadrangular element with geometric anisotropy has been developed to perform 2D Finite Elements Analyses in cases where high stress concentrations, varying with very different laws along two orthogonal directions, are present. The element has been implemented into a finite element code. To validate the element behavior, analyses in the adhesive of a single lap joint and in a bimaterial interface have been performed, comparing the stress fields obtained with those get from different methodologies (analytical, experimental and numerical with very fine meshes). It has been found that, using the same number of nodes, the analyses with the developed element returned better results with respect to the ones obtained with standard geometric isotropic elements.