Incompatible finite elements for laminated structures

Abstract

A new family of finite elements is presented for the analysis of layered anisotropic media. The elements are based on the traditional displacement method and make extensive use of incompatible displacement modes and selectable kinematic dimensionality. Several methods for stress recovery are presented and one is selected for general purpose analysis. A simple modification of the nodal strain-displacement matrix is used in a general isoparametric formulation to allow for irregular elements that pass the patch test. Accuracy of the new elements is demonstrated by comparison with an exact elasticity solution for a linear bending problem. Efficiency and other practical concerns are also discussed. Shear locking is avoided by using incompatible displacement modes and results show that the elements can be used for both thick and thin problems. It is also shown that incompatible modes can be selectively included between and within individual elements to locally refine displacement and stress fields. The end products of the proposed methodology are herein called ZORO finite elements.