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An Introduction to Linear and Nonlinear Finite Element Analysis
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An Introduction to Linear and Nonlinear Finite Element Analysis

An Introduction to Linear and Nonlinear Finite Element Analysis

A Computational Approach

Prem K. Kythe, Dongming Wei

446 pages, parution le 24/11/2003

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

Contents

  • 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

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