# Introduction to the Finite Element Method, Fourth Edition

by: J. N. Reddy, Ph.D.

**Abstract:**An up-to-date, self-contained introduction to the theory and applications of the finite element method. This thoroughly revised classic engineering textbook offers a broad-based overview of the finite element method. Written by a world-renowned mechanical engineering researcher and author, the book shows, step-by-step, how to calculate numerical solutions to steady-state as well as time-dependent problems. You also get detailed problems with worked-out solutions and downloadable programs that can be used and modified for real-world situations. Special attention is paid to applications that are important in bioengineering, fluid and thermal sciences, structural mechanics, and a host of applied sciences. Introduction to the Finite Element Method, Fourth Edition, covers: • Mathematical preliminaries and classical variational methods • 1-D finite element models of second-order differential equations • Applications to 1-D heat transfer and fluid and solid mechanics problems • Finite element analysis of beams and circular plates • Plane trusses and frames • Eigenvalue and time-dependent problems in 1-D • Numerical integration and computer implementation in 1-D • Single-variable problems in two dimensions • 2-D interpolation functions, numerical integration, and computer implementation in 2-D • Flows of viscous incompressible fluids • Plane elasticity • 3-D finite element analysis

Full details

## Table of Contents

**A.**About the Author**B.**Dedication**C.**Preface to the Fourth Edition**D.**Preface to the Third Edition**E.**Preface to the Second Edition**F.**Preface to the First Edition**G.**Symbols and Conversion Factors**1.**General Introduction**2.**Mathematical Preliminaries and Classical Variational Methods**3.**1-D Finite Element Models of Second-Order Differential Equations**4.**Applications to 1-D Heat Transfer and Fluid and Solid Mechanics Problems**5.**Finite Element Analysis of Beams and Circular Plates**6.**Plane Trusses and Frames**7.**Eigenvalue and Time-Dependent Problems in 1-D**8.**Numerical Integration and Computer Implementation**9.**Single-Variable Problems in Two Dimensions**10.**2-D Interpolation Functions, Numerical Integration, and Computer Implementation**11.**Flows of Viscous Incompressible Fluids**12.**Plane Elasticity**13.**3-D Finite Element Analysis

## Expanded Table of Contents

**A.**About the Author**B.**Dedication**C.**Preface to the Fourth Edition**D.**Preface to the Third Edition**E.**Preface to the Second Edition**F.**Preface to the First Edition**G.**Symbols and Conversion Factors**1.**General Introduction**2.**Mathematical Preliminaries and Classical Variational Methods**3.**1-D Finite Element Models of Second-Order Differential Equations**4.**Applications to 1-D Heat Transfer and Fluid and Solid Mechanics Problems**5.**Finite Element Analysis of Beams and Circular Plates**6.**Plane Trusses and Frames**7.**Eigenvalue and Time-Dependent Problems in 1-D**8.**Numerical Integration and Computer Implementation**9.**Single-Variable Problems in Two Dimensions**10.**2-D Interpolation Functions, Numerical Integration, and Computer Implementation**11.**Flows of Viscous Incompressible Fluids**12.**Plane Elasticity**13.**3-D Finite Element Analysis

**Book Details**

**Title: **Introduction to the Finite Element Method, Fourth Edition

**Publisher: **McGraw-Hill Education: New York, Chicago, San Francisco, Athens, London, Madrid, Mexico City, Milan, New Delhi, Singapore, Sydney, Toronto

**Copyright / Pub. Date: **2019, 2006, 1993, 1984 McGraw-Hill Education

**ISBN: **9781259861901

**Authors:****J. N. Reddy, Ph.D.**
is the Oscar S. Wyatt Endowed Chair Professor, a Distinguished Professor, and a Regents Professor of Mechanical Engineering at Texas A&M University. He is a highly cited researcher with an h-index of 100 (per Google Scholar) and the author of 21 books and over 650 journal papers. Dr. Reddy is known worldwide for his significant contributions to the field of applied mechanics for more than 40 years through the authorship of widely used textbooks on linear and nonlinear finite element analysis, variational methods, composite materials and structures, and continuum mechanics. His pioneering work on the development of shear deformation theories that bear his name in the literature, the Reddy third-order plate theory and the Reddy layerwise theory, has had a major impact and led to new research developments and applications. Some of his ideas on shear deformation and on penalty finite element models of fluid flows have been implemented in commercial finite element computer programs like ABAQUS, NISA, and HyperXtrude. Dr. Reddy is a Fellow of all major professional societies of engineering (ASME, AIAA, ASCE, AAM, ASC, USACM, IACM), and has received top mechanics medals from these and other societies (ASME Medal, Raymond D. Mindlin Medal, Theodore von Karman Medal, John von Neumann Medal, William Prager Medal, O. C. Zienkiewicz Medal). He is a Member of the U.S. National Academy of Engineering and a Foreign Fellow of the Canadian Academy of Engineering, Indian National Academy of Engineering, and Brazilian National Academy of Engineering. For additional details, visit http://mechanics.tamu.edu.

**Description: **
An up-to-date, self-contained introduction to the theory and applications of the finite element method.
This thoroughly revised classic engineering textbook offers a broad-based overview of the finite element method. Written by a world-renowned mechanical engineering researcher and author, the book shows, step-by-step, how to calculate numerical solutions to steady-state as well as time-dependent problems. You also get detailed problems with worked-out solutions and downloadable programs that can be used and modified for real-world situations. Special attention is paid to applications that are important in bioengineering, fluid and thermal sciences, structural mechanics, and a host of applied sciences.
Introduction to the Finite Element Method, Fourth Edition, covers:
• Mathematical preliminaries and classical variational methods
• 1-D finite element models of second-order differential equations
• Applications to 1-D heat transfer and fluid and solid mechanics problems
• Finite element analysis of beams and circular plates
• Plane trusses and frames
• Eigenvalue and time-dependent problems in 1-D
• Numerical integration and computer implementation in 1-D
• Single-variable problems in two dimensions
• 2-D interpolation functions, numerical integration, and computer implementation in 2-D
• Flows of viscous incompressible fluids
• Plane elasticity
• 3-D finite element analysis