Numerical Approach: Finite Element Analysis

Abstract

Finite element analysis (FEA) is a widely used computer-based method of numerically solving a range of boundary problems. In the method, a continuum is subdivided into a number of well-defined elements that are joined at nodes, a process known as discretization. A continuous field parameter, such as displacement or temperature, is now characterized by its value at the nodes, with the values between the nodes determined from polynomial interpolation. The nodal values are determined by the solution of an array of simultaneous equations using computational matrix methods, and the accuracy of the results is dependent on the discretization, the accuracy of the assumed interpolation form, and the accuracy of the computation solution methods. The current popularity of the method is based on its ability to model many classes of problem regardless of geometry, boundary conditions, and loading. Modeling the behavior of adhesive joints is complicated by a number of factors, including the complex geometry, the complex material behavior, and the environmental sensitivity. FEA is currently the only technique that can comprehensively address the challenges of modeling bonded joints under realistic operating conditions. However, a reliable and robust method of using FEA to model failure in bonded joints is still to be developed.