An introduction to nonlinear finite element analysis / J.N. Reddy.

Format:

Book

Author/Creator:

Reddy, J. N. (Junuthula Narasimha), 1945- author.

Language:

English

Subjects (All):

Finite element method.

Nonlinear mechanics.

Genre:

Textbooks.

Physical Description:

1 online resource (xv, 463 pages) : illustrations

Edition:

1st ed.

Other Title:

Nonlinear finite element analysis

Place of Publication:

Oxford ; New York : Oxford University Press, 2004.

Language Note:

English

Summary:

"This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics - flows of incompressible fluids - and solid mechanics - elasticity, beams, plates and shells. Both geometric as well as material nonlinearities are considered, and static and transient (i.e. time dependent) responses are studied. Detailed theoretical formulations and computer implementation steps, as well as numerical examples for the user to verify and validate self-created computer programs, give the reader a clear understanding of the concepts of nonlinear finite element analyses and allow greater confidence in the formulation and computer implementation of nonlinear equations across many fields of science and engineering. At the same time, the book serves as a prelude to more advanced books on the subject. It will be a useful textbook for graduate students of engineering - in particular, aerospace, civil and mechanical - and applied mathematics, but also a good reference for engineers and scientists working in industry, especially those in the aerospace and automobile industries."--Jacket.

Contents:

Contents; Preface; 1 Introduction; 1.1 Mathematical Models; 1.2 Numerical Simulations; 1.3 The Finite Element Method; 1.4 Nonlinear Analysis; 1.4.1 Introduction; 1.4.2 Classification of Nonlinearities; 1.5 The Big Picture; References; 2 The Finite Element Method: A Review; 2.1 Introduction; 2.2 One-Dimensional Problems; 2.2.1 Governing Differential Equation; 2.2.2 Finite Element Approximation; 2.2.3 Derivation of the Weak Form; 2.2.4 Interpolation Functions; 2.2.5 Finite Element Model; 2.3 Two-Dimensional Problems; 2.3.1 Governing Differential Equation; 2.3.2 Finite Element Approximation

2.3.3 Weak Formulation; 2.3.4 Finite Element Model; 2.3.5 Interpolation Functions; 2.3.6 Assembly of Elements; 2.4 Library of Two-Dimensional Finite Elements; 2.4.1 Introduction; 2.4.2 Triangular Elements; 2.4.3 Rectangular Elements; 2.5 Numerical Integration; 2.5.1 Preliminary Comments; 2.5.2 Coordinate Transformations; 2.5.3 Integration Over a Master Rectangular Element; 2.5.4 Integration Over a Master Triangular Element; 2.6 Computer Implementation; 2.6.1 General Comments; 2.6.2 One-Dimensional Problems; 2.6.3 Two-Dimensional Problems; 2.7 Closure; Problems; References

3 Heat Transfer and Other Field Problems in One Dimension; 3.1 Model Differential Equation; 3.2 Weak Formulation; 3.3 Finite Element Model; 3.4 Solution Procedures; 3.4.1 General Comments; 3.4.2 Direct Iteration Procedure; 3.4.3 Newton's Iteration Procedure; 3.5 Computer Implementation; 3.5.1 Introduction; 3.5.2 Preprocessor Unit; 3.5.3 Processor Unit; 3.6 Closing Remarks; Problems; References; 4 Nonlinear Bending of Straight Beams; 4.1 Introduction; 4.2 Euler-Bernoulli Beams; 4.2.1 Basic Assumptions; 4.2.2 Displacement Field and Strains; 4.2.3 Weak Forms; 4.2.4 Finite Element Model

4.2.5 Iterative Solutions of Nonlinear Equations; 4.2.6 Load Increments; 4.2.7 Membrane Locking; 4.2.8 Computer Implementation; 4.3 Timoshenko Beams; 4.3.1 Displacement Field and Strains; 4.3.2 Weak Forms; 4.3.3 General Finite Element Model; 4.3.4 Shear and Membrane Locking; 4.3.5 Tangent Stiffness Matrix; Problems; References; 5 Heat Transfer and Other Fields Problems in Two Dimensions; 5.1 Model Equation; 5.2 Weak Form; 5.3 Finite Element Model; 5.4 Solution Procedures; 5.4.1 Direct Iteration; 5.4.2 Newton-Raphson Iteration; 5.5 Computer Implementation; 5.5.1 Introduction

5.5.2 Numerical Integration; 5.5.3 Element Calculations; Problems; References; 6 Nonlinear Bending of Elastic Plates; 6.1 Introduction; 6.2 Classical Plate Theory; 6.2.1 Assumptions of the Kinematics; 6.2.2 Displacement Field and Strains; 6.3 Variational Formulation of CPT; 6.3.1 Virtual Work; 6.3.2 Weak Forms; 6.3.3 Equilibrium Equations; 6.3.4 Boundary Conditions; 6.3.5 Stress Resultant-Deflection Relations; 6.4 Finite Element Models of CPT; 6.4.1 General Formulation; 6.4.2 Tangent Stiffness Coefficients; 6.4.3 Some Plate Finite Elements; 6.5 Computer Implementation Aspects and Numerical Results of CPT Elements.

Notes:

Includes bibliographical references and index.

Description based upon print version of record.

ISBN:

0-19-157467-8

9786612354779

1-282-35477-9

OCLC:

502287564