Introduction to Finite Elements in Engineering (3rd Edition) - Hardcover

Chandrupatla, Tirupathi R.; Belegundu, Ashok D.

Hardcover

ISBN 10: 0130615919 ISBN 13: 9780130615916

Publisher: Pearson, 2002

Synopsis

This book provides an integrated approach to finite element methodologies. The development of finite element theory is combined with examples and exercises involving engineering applications. The steps used in the development of the theory are implemented in complete, self-contained computer programs. While the strategy and philosophy of the previous editions has been retained, the Third Edition has been updated and improved to include new material on additional topics. Chapter topics cover fundamental concepts, matrix algebra and gaussian elimination, one-dimensional problems, trusses, two-dimensional problems using constant strain triangles, axisymmetric solids subjected to axisymmetric loading, two-dimensional isoparametric elements and numerical integration, beams and frames, three-dimensional problems in stress analysis, scalar field problems, dynamic considerations, and preprocessing and postprocessing. For practicing engineers as a valuable learning resource.

About this title

About the Author

Tirupathi R. Chandrupatla is Professor and Chair of Mechanical Engineering at Rowan University, Glassboro, New Jersey. He received the B.S. degree from the Regional Engineering College, Warangal, which was affiliated with Osmania University, India. He received the M.S. degree in design and manufacturing from the Indian Institute of Technology, Bombay. He started his career as a design engineer with Hindustan Machine Tools, Bangalore. He then taught in the Department of Mechanical Engineering at LLT, Bombay. He pursued his graduate studies in the Department of Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin and received his Ph.D. in 1977. He subsequently taught at the University of Kentucky. Prior to joining Rowan, he was a Professor of Mechanical Engineering and Manufacturing Systems Engineering at GMI Engineering & Management Institute (formerly General Motors Institute), where he taught for 16 years.

Dr. Chandrupatla has broad research interests, which include finite element analysis, design, optimization, and manufacturing engineering. He has published widely in these areas and serves as a consultant to industry. Dr. Chandrupatla is a registered Professional Engineer and also a Certified Manufacturing Engineer. He is a member of ASEE, ASME, NSPE, SAE, and SME.

Ashok D. Belegundu is a Professor of Mechanical Engineering at The Pennsylvania State University, University Park. He was on the faculty at GMI from 1982 through 1986. He received the Ph.D. degree in 1982 from the University of Iowa and the B.S. degree from the Indian Institute of Technology, Madras. He was awarded a fellowship to spend a summer in 1993 at the NASA Lewis Research Center. During 1994-1995, he obtained a grant from the UK Science and Engineering Research Council to spend his sabbatical leave at Cranfield University, Cranfield, UK.

Dr. Belegundu's teaching and research interests include linear, nonlinear, and dynamic finite elements and optimization. He has worked on several sponsored projects for government and industry. He is an associate editor of Mechanics of Structures and Machines. He is also a member of ASME and an Associate fellow of AIAA.

From the Back Cover

Now in its third edition, Introduction to Finite Elements in Engineering provides an integrated approach to finite methodologies through the integration of exercises and examples involving engineering applications. The steps used in the development of the theory are implemented in complete, self-contained computer programs, while retaining the strategies and philosophies of previous editions. It serves as a primary textbook for senior undergraduate and first-year graduate students as well as an invaluable learning resource for practicing engineers.

Hallmark Features:

• Over 250 illustrations integrated throughout the text.
• Problem formulation and modeling emphasized in each chapter.
• Practical examples and problems.
• Pre- and post-processing concepts discussed in the last chapter.

New to the Third Edition:

Additional programs and source code on a companion CD
Includes complete self-contained computer programs with source codes in Visual Basic, Excel-based Visual Basic, MATLAB, QUICKBASIC, FORTRAN, and C.

Excerpt. © Reprinted by permission. All rights reserved.

The first edition of this book appeared over 10 years ago and the second edition followed a few years later. We received positive feedback from professors who taught from the book and from students and practicing engineers who used the book. We also benefited from the feedback received from the students in our courses for the past 20 years. We have incorporated several suggestions in this edition. The underlying philosophy of the book is to provide a clear presentation of theory, modeling, and implementation into computer programs. The pedagogy of earlier editions has been retained in this edition.

New material has been introduced in several chapters. Worked examples and exercise problems have been added to supplement the learning process. Exercise problems stress both fundamental understanding and practical considerations. Theory and computer programs have been added to cover acoustics, axisymmetric quadrilateral elements, conjugate gradient approach, and eigenvalue evaluation. Three additional programs have now been introduced in this edition. All the programs have been developed to work in the Windows environment. The programs have a common structure that should enable the users to follow the development easily. The programs have been provided in Visual Basic, Microsoft Excel/Visual Basic, MATLAB, together with those provided earlier in QBASIC, FORTRAN and C. The Solutions Manual has also been updated.

Chapter 1 gives a brief historical background and develops the fundamental concepts. Equations of equilibrium, stress-strain relations, strain-displacement relations, and the principles of potential energy are reviewed. The concept of Galerkin's method is introduced.

Properties of matrices and determinants are reviewed in Chapter 2. The Gaussian elimination method is presented, and its relationship to the solution of symmetric banded matrix equations and the skyline solution is discussed. Cholesky decomposition and conjugate gradient method are discussed.

Chapter 3 develops the key concepts of finite element formulation by considering one-dimensional problems. The steps include development of shape functions, derivation of element stiffness, formation of global stiffness, treatment of boundary conditions, solution of equations, and stress calculations. Both the potential energy approach and Galerkin's formulations are presented. Consideration of temperature effects is included.

Finite element formulation for plane and three-dimensional trusses is developed in Chapter 4. The assembly of global stiffness in banded and skyline forms is explained. Computer programs for both banded and skyline solutions are given.

Chapter 5 introduces the finite element formulation for two-dimensional plane stress and plane strain problems using constant strain triangle (CST) elements. Problem modeling and treatment of boundary conditions are presented in detail. Formulation for orthotropic materials is provided. Chapter 6 treats the modeling aspects of axisymmetric solids subjected to axisymmetric loading. Formulation using triangular elements is presented. Several real-world problems are included in this chapter.

Chapter 7 introduces the concepts of isoparametric quadrilateral and higher order elements and numerical integration using Gaussian quadrature. Formulation for axisymmetric quadrilateral element and implementation of conjugate gradient method for quadrilateral element are given.

Beams and application of Hermite shape functions are presented in Chapter 8. The chapter covers two-dimensional and three-dimensional frames.

Chapter 9 presents three-dimensional stress analysis. Tetrahedral and hexahedral elements are presented. The frontal method and its implementation aspects are discussed.

Scalar field problems are treated in detail in Chapter 10. While Galerkin as well as energy approaches have been used in every chapter, with equal importance, only Galerkin's approach is used in this chapter. This approach directly applies to the given differential equation without the need of identifying an equivalent functional to minimize. Galerkin formulation for steady-state heat transfer, torsion, potential flow, seepage flow, electric and magnetic fields, fluid flow in ducts, and acoustics are presented.

Chapter 11 introduces dynamic considerations. Element mass matrices are given. Techniques for evaluation of eigenvalues (natural frequencies) and eigenvectors (mode shapes) of the generalized eigenvalue problem are discussed. Methods of inverse iteration, Jacobi, tridiagonalization and implicit shift approaches are presented.

Preprocessing and postprocessing concepts are developed in Chapter 12. Theory and implementation aspects of two-dimensional mesh generation, least-squares approach to obtain nodal stresses from element values for triangles and quadrilaterals, and contour plotting are presented.

At the undergraduate level some topics may be dropped or delivered in a different order without breaking the continuity of presentation. We encourage the introduction of the Chapter 12 programs at the end of Chapter 5. This helps the students to prepare the data in an efficient manner.

We thank Nels Madsen, Auburn University; Arif Masud, University of Illinois, Chicago; Robert L. Rankin, Arizona State University; John S. Strenkowsi, NC State University; and Hormoz Zareh, Portland State University, who reviewed our second edition and gave many constructive suggestions that helped us improve the book.

Tirupathi Chandrupatla expresses his gratitude to J. Tinsley Oden, whose teaching and encouragement have been a source of inspiration to him throughout his career. He also expresses his thanks to many students at Rowan University and Kettering University who took his courses. He expresses his thanks to his colleague Paris vonLockette, who gave valuable feedback after teaching a course from the second edition. We thank our production editor Fran Daniele for her meticulous approach in the final production of the book.

Ashok Belegundu thanks his students at Penn State for their feedback on the course material and programs. He expresses his gratitude to Richard C. Benson, chairman of mechanical and nuclear engineering, for his encouragement and appreciation. He also expresses his thanks to Professor Victor W Sparrow in the acoustics department and to Dongjai Lee, doctoral student, for discussions and help with some of the material in the book. His late father's encouragement with the first two editions of this book are an ever present inspiration.

We thank our acquisitions editor at Prentice Hall, Laura Fischer, who has made this a pleasant project for us.

Tirupathi R. Chandrupatla
Ashok D. Belegundu

Edition details

• Publisher: Pearson
• Publication date: 2002
• ISBN 10: 0130615919
• ISBN 13: 9780130615916
• Binding: Hardcover
• Language: English
• Edition number: 3
• Number of pages: 453