An Introduction to Linear and Nonlinear Finite Element Analysis

A Computational Approach

Prem K. Kythe, Dongming Wei

446 pages, parution le 24/11/2003

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Résumé

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.

Written for:
Advanced undergraduates / 1st-year graduates, instructors, engineers, applied mathematicians

Notation
Introduction
One-Dimensional Shape Functions
One-Dimensional Second-Order Equations
One-Dimensional Fourth-Order Equations
Two-Dimensional Elements
Two-Dimensional Problems
More Two-Dimensional Problems
Axisymmetric Heat Transfer
Transient Problems
Single Nonlinear One-Dimensional Equations
Plane Elasticity
Stokes Equations and Penalty Method
Vibration Analysis
Computer Codes: Mathematica Codes, Ansys Codes, MatLab Codes, Fortran Codes

Appendix A: Integration Formulas
Appendix B: Special Cases
Appendix C: Temporal Approximations
Appendix D: Isoparametric Elements
Appendix E: Green's Identities
Appendix F: Gaussian Quadrature
Appendix G: Gradient-Based Methods
Bibliography
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Prem K. Kythe, Dongming Wei
Parution	24/11/2003
Nb. de pages	446
Format	16 x 24
Couverture	Broché
Poids	775g
Intérieur	Noir et Blanc
EAN13	9780817643089
ISBN13	978-0-8176-4308-9