An Introduction to Linear and Nonlinear Finite Element Analysis: A Computational Approach

Front Cover
Springer Science & Business Media, Oct 17, 2003 - Mathematics - 445 pages
0 Reviews

Although finite element courses have become more popular in the undergraduate and graduate engineering, science, and applied mathematics curricula, there are very few introductory textbooks geared toward students accustomed to using computers for everyday assignments and research. 'An Introduction to Linear and Nonlinear Finite Element Analysis' fills this gap, offering a concise, integrated presentation of methods, applications, computational software tools, and hands-on programming projects. Suitable for junior/senior undergraduate and first-year graduate courses, the book is aimed at students from a variety of disciplines: engineering, physics, geophysics, and applied mathematics.

Unlike existing texts designed with specific applications to a particular field of mechanical, civil, or chemical engineering, the emphasis here is on interdisciplinary applications. One- and two-dimensional linear and nonlinear initial/boundary value problems are solved using finite element, Newton's, and conjugate gradient methods.  Mathematical theory is kept to a minimum, making the text accessible to students with varied backgrounds.

Features:

* Software tools using Mathematica, Matlab, Fortran, and commercial finite element codes, such as Ansys, integrated throughout the text

* Numerous examples and exercises with diverse applications to linear and nonlinear heat transfer, fluid flows, mechanical vibrations, electromagnetics, and structures

* Supporting material and selected solutions to problems available at the authors' websites: http://www.math.uno.edu/fac/pkythe.html and http://www.math.uno.edu/fac/dwei.html

* Minimal prerequisites: a course in calculus of several variables, differential equations and linear algebra, as well as some knowledge of computers

Primarily a classroom resource, the book may also be used as a self-study reference for researchers and practitioners who need a quick introduction to finite element methods.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Introduction
1
OneDimensional Shape Functions
25
OneDimensional SecondOrder Equation
37
OneDimensional FourthOrder Equation
75
TwoDimensional Elements
89
TwoDimensional Problems
107
More TwoDimensional Problems
137
Axisymmetric Heat Transfer
175
Plane Elasticity
269
Stokes Equations and Penalty Method
297
Vibration Analysis
323
Computer Codes
351
A Integration Formulas
393
Temporal Approximations
405
E Greens Identities
421
G GradientBased Methods
429

Transient Problems
207
Single Nonlinear OneDimensional Problems
241

Other editions - View all

Common terms and phrases

Bibliographic information