Finite Element Method Basic Concepts and Applications

ISBN-10: 1591690277

ISBN-13: 9781591690276

Edition: 2nd 2005 (Revised)

List price: $159.95
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Description:

This much-anticipated second edition introduces the fundamentals of the finite element method featuring clear-cut examples and an applications-oriented approach. Using the transport equation for heat transfer as the foundation for the governing equations, this new edition demonstrates the versatility of the method for a wide range of applications, including structural analysis and fluid flow. Much attention is given to the development of the discrete set of algebraic equations, beginning with simple one-dimensional problems that can be solved by inspection, continuing to two- and three-dimensional elements, and ending with three chapters describing applications. The increased number of example problems per chapter helps build an understanding of the method to define and organize required initial and boundary condition data for specific problems. In addition to exercises that can be worked out manually, this new edition refers to user-friendly computer codes for solving one-, two-, andthree-dimensional problems. Among the first FEM textbooks to include finite element software, the book contains a website with access to an even more comprehensive list of finite element software written in FEMLAB, MAPLE, MathCad, MATLAB, FORTRAN, C++, and JAVA - the most popular programming languages. This textbook is valuable for senior level undergraduates in mechanical, aeronautical, electrical, chemical, and civil engineering. Useful for short courses and home-study learning, the book can also serve as an introduction for first-year graduate students new to finite element coursework and as a refresher for industry professionals. The book is a perfect lead-in to Intermediate Finite Element Method: Fluid Flow and Heat and Transfer Applications (Taylor & Francis, 1999, Hb 1560323094).
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Book details

List price: $159.95
Edition: 2nd
Copyright year: 2005
Publisher: CRC Press LLC
Publication date: 10/31/2005
Binding: Hardcover
Pages: 324
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.232
Language: English

Introduction
Background
Short History
Orientation
Closure
References
The Method of Weighted Residuals and Galerkin Approximations
Background
Classical Solutions
The "Weak" Statement
Closure
Exercises
References
The Finite Element Method in One Dimension
Background
Shape Functions
Linear Elements
Quadratic Elements
Cubic Elements
Steady Conduction Equation
Galerkin Formulation
Variable Conduction and Boundary Convection
Axisymmetric Heat Conduction
Natural Coordinate System
Time Dependence
Spatial Discretization
Time Discretization
Matrix Formulation
Solution Methods
Closure
Exercises
References
The Two-Dimensional Triangular Element
Background
The Mesh
Shape Functions (Linear, Quadratic)
Linear Shape Functions
Quadratic Shape Functions
Area Coordinates
Numerical Integration
Conduction in a Triangular Element
Steady-State Conduction with Boundary Convection
The Axisymmetric Conduction Equation
The Quadratic Triangular Element
Time-Dependent Diffusion Equation
Bandwidth
Mass Lumping
Closure
Exercises
References
The Two-Dimensional Quadrilateral Element
Background
Element Mesh
Shape Functions
Bilinear Rectangular Element
Quadratic Rectangular Element
Natural Coordinate System
Numerical Integration Using Gaussian Quadratures
Steady-State Conduction Equation
Steady-State Conduction with Boundary Convection
The Quadratic Quadrilateral Element
Time-Dependent Diffusion
Computer Program Exercises
Closure
Exercises
References
Isoparametric Two-Dimensional Elements
Background
Natural Coordinate System
Shape Functions
Bilinear Quadrilateral
Eight-Noded Quadratic Quadrilateral
Linear Triangle
Quadratic Triangle
Directional Cosines
The Element Matrices
Inviscid Flow Example
Closure
Exercises
References
The Three-Dimensional Element
Background
Element Mesh
Shape Functions
Tetrahedron
Hexahedron
Numerical Integration
A One-Element Heat Conduction Problem
Tetrahedron
Hexahedron
Time-Dependent Heat Conduction with Radiation and Convection
Radiation
Shape Factors
Closure
Exercises
References
Finite Elements in Solid Mechanics
Background
Two-Dimensional Elasticity-Stress Strain
Galerkin Approximation
Potential Energy
Thermal Stresses
Three-Dimensional Solid Elements
Closure
Exercises
References
Applications to Convective Transport
Background
Potential Flow
Convective Transport
Nonlinear Convective Transport
Groundwater Flow
Lubrication
Closure
Exercises
References
Introduction to Viscous Fluid Flow
Background
Viscous Incompressible Flow with Heat Transfer
The Penalty Function Algorithm
Application to Natural Convection
Closure
Exercises
References
Appendices
Matrix Algebra
Addition/Subtraction of Matrices
Multiplication of Matrices
Determinant of a Matrix
Inverse of a Matrix
Derivative of a Matrix
Transpose of a Matrix
Units
Thermophysical Properties of Some Common Materials
Dimensionless Groups
Computer Programs
Source Codes
Index
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