Introduction to Finite Element Analysis and Design, 2nd Edition
by Nam H. Kim, Bhavani V. Sankar, Ashok V. Kumar
Chapter 9Finite Element Procedure and Modeling
9.6 INTRODUCTION
The finite element method (FEM) is one of the numerical methods of solving differential equations that describe many engineering problems. The FEM, originated in the area of structural mechanics, has been extended to other areas of solid mechanics and later to other fields such as heat transfer, fluid dynamics, and electromagnetism. In fact, FEM has been recognized as a powerful tool for solving partial differential equations and integro‐differential equations, and it is the numerical method of choice in many engineering and applied science areas. One of the reasons for its popularity is that the method results in computer programs versatile in nature that can solve many practical problems with the least amount of training. Obviously, there is a danger in using computer programs without properly understanding the assumptions and limitations of the method, so the objective of this textbook is to provide the readers a sound background on the underlying theory.
In the previous chapters, we developed a variety of finite elements and studied their application in solving problems in solid and structural mechanics. Different elements were used for different types of problems. When a structural problem is given, it is important to understand the following steps: (1) creation of the most appropriate FE model of the given problem; (2) applying the right boundary conditions and the loads; (3) solution techniques available ...