The finite element method in engineering / Singiresu S. Rao.

Format:

Book

Author/Creator:

Rao, S. S.

Language:

English

Subjects (All):

Finite element method.

Engineering mathematics.

Physical Description:

1 online resource (685 p.)

Edition:

4th ed.

Place of Publication:

Amsterdam ; Boston, MA : Elsevier/Butterworth Heinemann, c2005.

Language Note:

English

System Details:

text file

Summary:

Finite Element Analysis is an analytical engineering tool developed in the 1960's by the Aerospace and nuclear power industries to find usable, approximate solutions to problems with many complex variables. It is an extension of derivative and integral calculus, and uses very large matrix arrays and mesh diagrams to calculate stress points, movement of loads and forces, and other basic physical behaviors. Students will find in this textbook a thorough grounding of the mathematical principles underlying the popular, analytical methods for setting up a finite element solution based on those math

Contents:

Front Cover; The Finite Element Method in Engineering; Copyright Page; Contents; Preface; Principal Notation; PART 1: INTRODUCTION; Chapter 1. Overview of Finite Element Method; 1.1 Basic Concept; 1.2 Historical Background; 1.3 General Applicability of the Method; 1.4 Engineering Applications of the Finite Element Method; 1.5 General Description of the Finite Element Method; 1.6 Comparison of Finite Element Method with Other Methods of Analysis; 1.7 Finite Element Program Packages; References; Problems; PART 2: BASIC PROCEDURE; Chapter 2. Discretization of the Domain; 2.1 Introduction

2.2 Basic Element Shapes2.3 Discretization Process; 2.4 Node Numbering Scheme; 2.5 Automatic Mesh Generation; References; Problems; Chapter 3. Interpolation Models; 3.1 Introduction; 3.2 Polynomial Form of Interpolation Functions; 3.3 Simplex, Complex, and Multiplex Elements; 3.4 Interpolation Polynomial in Terms of Nodal Degrees of Freedom; 3.5 Selection of the Order of the Interpolation Polynomial; 3.6 Convergence Requirements; 3.7 Linear Interpolation Polynomials in Terms of Global Coordinates; 3.8 Interpolation Polynomials for Vector Quantities

3.9 Linear Interpolation Polynomials in Terms of Local CoordinatesReferences; Problems; Chapter 4. Higher Order and Isoparametric Elements; 4.1 Introduction; 4.2 Higher Order One-Dimensional Elements; 4.3 Higher Order Elements in Terms of Natural Coordinates; 4.4 Higher Order Elements in Terms of Classical Interpolation Polynomials; 4.5 One-Dimensional Elements Using Classical Interpolation Polynomials; 4.6 Two-Dimensional (Rectangular) Elements Using Classical Interpolation Polynomials; 4.7 Continuity Conditions; 4.8 Comparative Study of Elements; 4.9 Isoparametric Elements

4.10 Numerical IntegrationReferences; Problems; Chapter 5. Derivation of Element Matrices and Vectors; 5.1 Introduction; 5.2 Direct Approach; 5.3 Variational Approach; 5.4 Solution of Equilibrium Problems Using Variational (Rayleigh-Ritz) Method; 5.5 Solution of Eigenvalue Problems Using Variational (Rayleigh-Ritz) Method; 5.6 Solution of Propagation Problems Using Variational (Rayleigh-Ritz) Method; 5.7 Equivalence of Finite Element and Variational (Rayleigh-Ritz) Methods; 5.8 Derivation of Finite Element Equations Using Variational (Rayleigh-Ritz) Approach; 5.9 Weighted Residual Approach

5.10 Solution of Eigenvalue Problems Using Weighted Residual Method5.11 Solution of Propagation Problems Using Weighted Residual Method; 5.12 Derivation of Finite Element Equations Using Weighted Residual (Galerkin) Approach; 5.13 Derivation of Finite Element Equations Using Weighted Residual (Least Squares) Approach; References; Problems; Chapter 6. Assembly of Element Matrices and Vectors and Derivation of System Equations; 6.1 Coordinate Transformation; 6.2 Assemblage of Element Equations; 6.3 Computer Implementation of the Assembly Procedure; 6.4 Incorporation of Boundary Conditions

6.5 Incorporation of Boundary Conditions in the Computer Program

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-280-96441-3

9786610964413

0-08-047050-5

OCLC:

437176623