Smoothed Finite Element Methods.

Abstract

In building an advanced engineering system or a product, engineers must undertake a very sophisticated process of modeling, simulation, designing, testing, and construction or fabrication. In such a process, a computer is routinely used as one of the most important tools. This book deals with topics related mainly to modeling and simulation, with a focus on numerical and computational methods. These topics play an increasingly important role in building advanced engineering systems in rapid and cost-effective ways, because modeling and simulation can be performed in a virtual environment on computers without physically building the system. Many computational methods and numerical techniques, such as the finite element method (FEM) [1–3], can be employed to deal with these topics. This book mainly focuses on the development of so-called smoothed finite element methods (S-FEM) that were proposed in the past few years, based on FEM and some mesh-free techniques. This chapter first addresses overall issues related to numerical modeling and simulation and some important common terminologies used in the book. It then discusses major differences in key numerical techniques between S-FEM and the well-known and widely used FEM.