Название: An Introduction to Finite Element Analysis Using Matlab Tools
Автор: Shuvra Das
Издательство: Springer
Год: 2023
Страниц: 228
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB

This book is an attempt to develop a guide for the user who is interested in learning the method by doing. There is enough discussion of some of the basic theory so that the user can get a broad understanding of the process. And there are many examples with step-by-step instructions for the user to quickly develop some proficiency in using FEA. We have used Matlab and its PDE toolbox for the examples in this text. The syntax and the modeling process are easy to understand and a new user can become productive very quickly. The PDE toolbox, just like any other commercial software, can solve certain classes of problems well but is not capable of solving every type of problem. For example, it can solve linear problems but is not capable of handling non-linear problems. Being aware of the capabilities of any tool is an important lesson for the user and we have, with this book, tried to highlight that lesson as well.

In this text we are introducing some basic concepts of Finite Element Method (FEA) and Matlab as a tool for performing FEA analyses. There are two ways to use Matlab for FEA work. The core calculations in FEA centers around Matrix operations. Matlab is very well suited for performing these types of calculations; Matlab’s origin is from Matrix operations. For simpler problems users can use Matlab commands to perform these analyses very easily or develop and use Matlab codes to automate the process of FEA problem setup and solution. Matlab also has a PDE Toolbox (partial differential equation toolbox). This toolbox is used to solve many types of linear physical problems using the FEA method. Particularly, this toolbox is very useful for solving linear Finite Element problems with applications in domains such as structural mechanics, heat transfer and electromagnetics. The PDE toolbox is capable of performing the various steps that were iden- tified in this chapter, such as geometry and meshing, boundary condition application, solving a variety of equation types, and post processing. In this text we have included examples of both type of work. For some of the simpler and earlier examples we use basic Matlab command to develop code for solving certain problems. And for problems that are a little more involved we have demonstrated the use of the PDE toolbox.

In the following sections we will review some basic matrix operations that are core features for any FEA work and introduce the PDE toolbox. Like with every other Matlab module, there is extensive documentation on the PDE toolbox available online for users to refer to. We are not trying to be comprehensive or exhaustive in this introduction. So users will benefit a lot by using Matlab resources.