Author | Kythe, Prem K. author |
---|---|

Title | An Introduction to Linear and Nonlinear Finite Element Analysis [electronic resource] : A Computational Approach / by Prem K. Kythe, Dongming Wei |

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |

Connect to | http://dx.doi.org/10.1007/978-0-8176-8160-9 |

Descript | XXIII, 445 p. online resource |

SUMMARY

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. P>

CONTENT

Preface -- Notation -- 1 Introduction -- 1.1 Historical Sketch -- 1.2 Euler-Lagrange Equations -- 1.3 Weak Variational Form -- 1.4 Galerkin Method -- 1.5 -- 1.6 -- 2 One-Dimensional Shape Functions -- 2.1 Local and Global Linear Shape Functions -- 2.2 Local and Global Quadratic Shape Functions -- 2.3 Parametric Coordinates -- 2.4 Hermite Shape Functions -- 2.5 Exercises -- 3 One-Dimensional Second-Order Equation -- 3.1 Galerkin Finite Element Method -- 3.2 Two Dependent Variables -- 3.3 Exercises -- 4 One-Dimensional Fourth-Order Equation -- 4.1 Euler-Bernoulli Beam Equation -- 4.2 Exercises -- 5 Two-Dimensional Elements -- 5.1 Linear Three-Node Triangular Elements -- 5.2 Bilinear Four-Node Rectangular Elements -- 5.3 Global Shape Functions -- 5.4 Triangular Coordinates -- 5.5 Shape Functions on the Sides of a Triangle -- 5.6 Exercises -- 6 Two-Dimensional Problems -- 6.1 Single Dependent Variable Problems -- 6.2 Exercises -- 7 More Two-Dimensional Problems -- 7.1 Heat Transfer -- 7.2 Torsion -- 7.3 Seepage -- 7.4 Fluid Flows -- 7.5 Exercises -- 8 Axisymmetric Heat Transfer -- 8.1 Radial Symmetry -- 8.2 Linear Elements -- 8.3 Linear Elements for Heat Transfer in Fluids -- 8.4 Nonlinear Heat Transfer -- 8.5 Exercises -- 9 Transient Problems -- 9.1 Classical Methods -- 9.2 One-Dimensional Transient Problems -- 9.3 Time-Dependent Heat Conduction -- 9.4 Two-Dimensional Transient Problems -- 9.5 Exercises -- 10 Single Nonlinear One-Dimensional Problems -- 10.1 Newtonโ{128}{153} method -- 10.2 Radiation Heat Transfer -- 10.3 Stress Analysis of Plastic Rods -- 10.4 Power-Law Pressure Driven Flow between Two Plates -- 10.5 Mixing-Length Equation for Turbulent Flow in Pipes -- 10.6 Rayleigh-Ritz and Nonlinear Gradient Methods -- 10.7 Exercises -- 11 Plane Elasticity -- 11.1 Stress-Strain Relations -- 11.2 Constant-Strain Triangular Element -- 11.3 Virtual Displacement Finite Element Model -- 11.4 Weak Form Finite Element Model -- 11.5 Stiffness Matrix and Load Vector -- 11.6 Exercises -- 12 Stokes Equations and Penalty Method -- 12.1 Equality-Constrained Programs and Lagrange Multipliers -- 12.2 Penalty Formulation for Linear Stokes Equation -- 12.3 Penalty Linear Triangular Stokes Element -- 12.4 Penalty Bilinear Rectangular Stokes Element -- 12.5 Penalty Linear Triangular Power-law Stokes Element -- 12.6 Solutions by Conjugate Gradient Methods -- 12.7 Exercises -- 13 Vibration Analysis -- 13.1 Hamiltonian Principle -- 13.2 Free Axial Vibrations of an Elastic Rod -- 13.3 Free Vibrations of a Euler Elastic Beam -- 13.4 Free In-Plane Vibrations of an Elastic Plate -- 13.5 Axial Vibrations of a Plastic Rod -- 13.6 Eigenvalue Problems -- 13.7 Exercises -- 14 Computer Codes -- 14.1 Mathematica Codes -- 14.2 Ansys Codes -- 14.3 Matlab Codes -- 14.4 Fortran Codes -- Integration Formulas -- A Special Cases -- B Temporal Approximations -- C Isoparametric Elements -- D Greenโ{128}{153} Identities -- E Gaussian Quadrature -- F Gradient-Based Methods

Mathematics
Partial differential equations
Applied mathematics
Engineering mathematics
Computer mathematics
Physics
Engineering
Mathematics
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Partial Differential Equations
Theoretical Mathematical and Computational Physics
Appl.Mathematics/Computational Methods of Engineering
Engineering general