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E-raamat: The Finite Element Method: Basic Concepts and Applications with MATLAB, MAPLE, and COMSOL, Third Edition

(University of Nevada, Las Vegas, USA), (University of New Mexico, Albuquerque, USA)
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This self-explanatory guide introduces the basic fundamentals of the Finite Element Method in a clear manner using comprehensive examples. Beginning with the concept of one-dimensional heat transfer, the first chapters include one-dimensional problems that can be solved by inspection. The book progresses through more detailed two-dimensional elements to three-dimensional elements, including discussions on various applications, and ending with introductory chapters on the boundary element and meshless methods, where more input data must be provided to solve problems. Emphasis is placed on the development of the discrete set of algebraic equations. The example problems and exercises in each chapter explain the procedure for defining and organizing the required initial and boundary condition data for a specific problem, and computer code listings in MATLAB and MAPLE are included for setting up the examples within the text, including COMSOL files.



Widely used as an introductory Finite Element Method text since 1992 and used in past ASME short courses and AIAA home study courses, this text is intended for undergraduate and graduate students taking Finite Element Methodology courses, engineers working in the industry that need to become familiar with the FEM, and engineers working in the field of heat transfer. It can also be used for distance education courses that can be conducted on the web.

Highlights of the new edition include:

- Inclusion of MATLAB, MAPLE code listings, along with several COMSOL files, for the example problems within the text. Power point presentations per chapter and a solution manual are also available from the web.

- Additional introductory chapters on the boundary element method and the meshless method. - Revised and updated content. -Simple and easy to follow guidelines for understanding and applying the Finite Element Method.

Arvustused

"I found the book easy to read, clearly written using simple language that novices and experts in the area of Finite Element analysis will probably find amicable. It covers a range of finite element applications that nonstructural engineers and scientists from different fields will appreciate either to start learning about them or as a reference for the day-to-day practice. Overall, I think that this is a great book if the reader is looking for a nonstructural approach, that is also easy to follow and that covers a range of topics that can be useful in different engineering fields and for multiphysicalapplications." Eduardo M. Sosa, West Virginia University, USA





"In the current book, as in the previous editions the basics of the finite element method are introduced in a simple way always followed by illuminating examples. Part of the book focuses in the development of the discrete set of algebraic equations in more than one dimensions originated from concrete real-life problems. The usage of MATLAB, and MAPLE and COMSOL is recommended for especially the multidimensional problems (see the appendices E and F) although FORTRAN, JAVA, C/C++ or other commercially available finite element codes can be used. There are many books in this area. I consider, the third edition of this book to be one of the best for students, researchers and practitioners in this area." Ioannis K. Argyros, Cameron University, Oklahoma, USA

Preface xiii
Authors xvii
Chapter 1 Introduction 1(10)
1.1 Background
1(1)
1.2 Short History
2(2)
1.3 Orientation
4(2)
1.4 Closure
6(1)
References
7(4)
Chapter 2 Method Of Weighted Residuals And Galerkin Approximations 11(20)
2.1 Background
11(1)
2.2 Classical Solutions
12(2)
2.3 The "Weak" Statement
14(12)
2.4 Closure
26(1)
Exercises
26(3)
References
29(2)
Chapter 3 Finite Element Method In One Dimension 31(80)
3.1 Background
31(1)
3.2 Shape Functions
31(8)
3.2.1 Linear Elements
32(3)
3.2.2 Quadratic Elements
35(2)
3.2.3 Cubic Elements
37(2)
3.3 Steady Conduction Equation
39(16)
3.3.1 Galerkin Formulation
39(6)
3.3.2 Variable Conduction And Boundary Convection
45(10)
3.4 Axisymmetric Heat Conduction
55(5)
3.5 Natural Coordinate System
60(17)
3.6 Time Dependence
77(13)
3.6.1 Spatial Discretization
79(2)
3.6.2 Time Discretization
81(9)
3.7 Matrix Formulation
90(3)
3.8 Solution Methods
93(9)
3.9 Closure
102(1)
Problems
103(6)
References
109(2)
Chapter 4 Two-Dimensional Triangular Element 111(82)
4.1 Background
111(1)
4.2 The Mesh
112(4)
4.3 Shape Functions
116(7)
4.3.1 Linear Shape Functions
116(6)
4.3.2 Quadratic Shape Functions
122(1)
4.4 Area Coordinates
123(10)
4.5 Numerical Integration
133(5)
4.6 Conduction In A Triangular Element
138(5)
4.7 Steady-State Conduction With Boundary Convection
143(4)
4.8 The Axisymmetric Conduction Equation
147(3)
4.9 The Quadratic Triangular Element
150(16)
4.10 Time-Dependent Diffusion Equation
166(10)
4.11 Bandwidth
176(5)
4.12 Mass Lumping
181(2)
4.13 Closure
183(1)
Exercises
183(8)
References
191(2)
Chapter 5 Two-Dimensional Quadrilateral Element 193(70)
5.1 Background
193(1)
5.2 Element Mesh
193(2)
5.3 Shape Functions
195(5)
5.3.1 Bilinear Rectangular Element
195(2)
5.3.2 Quadratic Rectangular Element
197(3)
5.4 Natural Coordinate System
200(11)
5.5 Numerical Integration Using Gaussian Quadratures
211(4)
5.6 Steady-State Conduction Equation
215(11)
5.7 Steady-State Conduction With Boundary Convection
226(13)
5.8 The Quadratic Quadrilateral Element
239(14)
5.9 Time-Dependent Diffusion
253(1)
5.10 Computer Program Exercises
254(3)
5.11 Closure
257(1)
Exercises
258(4)
References
262(1)
Chapter 6 Isoparametric Two-Dimensional Elements 263(22)
6.1 Background
263(1)
6.2 Natural Coordinate System
264(2)
6.3 Shape Functions
266(7)
6.3.1 Bilinear Quadrilateral
266(2)
6.3.2 Eight-Noded Quadratic Quadrilateral
268(1)
6.3.3 Linear Triangle
269(1)
6.3.4 Quadratic Triangle
269(1)
6.3.5 Directional Cosines
270(3)
6.4 The Element Matrices
273(4)
6.5 Inviscid Flow Example
277(3)
6.6 Closure
280(1)
Exercises
281(3)
References
284(1)
Chapter 7 Three-Dimensional Element 285(44)
7.1 Background
285(1)
7.2 Element Mesh
285(3)
7.3 Shape Functions
288(10)
7.3.1 Tetrahedron
288(7)
7.3.2 Hexahedron
295(3)
7.4 Numerical Integration
298(3)
7.5 A One-Element Heat Conduction Problem
301(12)
7.5.1 Tetrahedron
303(4)
7.5.2 Hexahedron
307(6)
7.6 Time-Dependent Heat Conduction With Radiation And Convection
313(7)
7.6.1 Radiation
315(3)
7.6.2 Shape Factors
318(2)
7.7 Closure
320(1)
Exercises
321(5)
References
326(3)
Chapter 8 Finite Elements In Solid Mechanics 329(44)
8.1 Background
329(1)
8.2 Two-Dimensional Elasticity: Stress/Strain
329(4)
8.3 Galerkin Approximation
333(16)
8.4 Potential Energy
349(7)
8.5 Thermal Stresses
356(10)
8.6 Three-Dimensional Solid Elements
366(3)
8.7 Closure
369(1)
Exercises
369(2)
References
371(2)
Chapter 9 Applications To Convective Transport 373(82)
9.1 Background
373(1)
9.2 Potential Flow
373(18)
9.3 Convective Transport
391(34)
9.4 Nonlinear Convective Transport
425(5)
9.5 Groundwater Flow
430(16)
9.6 Lubrication
446(6)
9.7 Closure
452(1)
Exercises
452(1)
References
453(2)
Chapter 10 Introduction To Viscous Fluid Flow 455(42)
10.1 Background
455(1)
10.2 Viscous Incompressible Flow With Heat Transfer
456(2)
10.3 The Penalty Function Algorithm
458(3)
10.4 Equal Order: Projection Method
461(2)
10.5 Application To Free And Forced Convection
463(31)
10.6 Closure
494(1)
Exercises
494(1)
References
495(2)
Chapter 11 Introduction To Boundary Elements 497(34)
11.1 Introduction
497(1)
11.2 One-Dimensional BEM
497(12)
11.3 Two-Dimensional BEM
509(16)
11.3.1 Constant Elements
515(7)
11.3.2 Linear Elements
522(3)
11.4 Three-Dimensional BEM
525(1)
11.5 Dual Reciprocity Method
526(1)
11.6 Closure
527(1)
Exercises
528(1)
References
528(3)
Chapter 12 Introduction To Meshless Methods 531(22)
12.1 Background
531(1)
12.2 History Of Mems
532(1)
12.3 Radial Basis Functions
533(3)
12.3.1 Global Versus Local RBFs
534(2)
12.4 The Kansa Approach
536(4)
12.5 Implementation Of The Mem
540(10)
12.5.1 1-D Formulation
540(8)
12.5.2 2-D Formulation
548(2)
12.6 Smooth Particle Hydrodynamics
550(1)
12.7 Closure
550(1)
Exercises
551(1)
References
551(2)
Appendix A: Matrix Algebra 553(8)
Appendix B: Units 561(2)
Appendix C: Thermophysical Properties Of Some Common Materials 563(2)
Appendix D: Nomenclature 565(4)
Appendix E: Matlab® 569(10)
Appendix F: Maple 579(10)
Appendix G: Supplemental Routines Used In Maple And Matlab® Examples 589(12)
Index 601
Dr. Pepper is presently Professor of Mechanical Engineering and Director of the Nevada Center for Advanced Computational Methods at the University of Nevada Las Vegas. He was appointed Distinguished Visiting Professor at the US Air Force Academy where he taught from 2011-2013. He served as an ASME Congressional Fellow in 2004, working for US Senator Dianne Feinstein in Washington, DC. He was Interim Dean of the UNLV College of Engineering in 2002 and served as Chairman of the Department of Mechanical Engineering from 1996-2002. He obtained his B.S.M.E. (1968), M.S.A.E. (1970), and Ph.D. (1973) degrees from the University of Missouri-Rolla (now MS&T). Following graduation, he worked for DuPont at the Savannah River Laboratory in Aiken, SC, where he held various technical and managerial positions. In 1987 he became Chief Scientist of the Marquardt Company, an aerospace propulsion company located in Van Nuys, CA. Dr. Pepper co-founded and was CEO of Advanced Projects Research, Inc., an R&D company involved with development and application of computational methods in fluid dynamics, heat transfer, and environmental transport. He has published over 300 technical papers on fluid dynamics, heat transfer, and environmental transport topics, and authored/co-authored six books on advanced numerical modeling and one on indoor air dispersion. He is a Life Fellow of the American Society of Mechanical Engineers, Associate Fellow of the American Institute of Aeronautics and Astronautics, and a Fellow of Wessex Institute. Dr. Pepper is currently an editor of the J. of Thermodynamics, Associate Editor of Computational Thermal Sciences, was Associate Editor of the ASME J. of Heat Transfer from 2010-2013, and was Associate Editor of the AIAA J. Thermophysics and Heat Transfer from 1990-1997. In 2008, Dr. Pepper was awarded the Eric Reissner Medal for his work in computational methods. In 2010, he received the Harry Reid Silver State Research Medal. In 2011, he received the AIAA Distinguished Service Award and in 2012 the AIAA Energy Systems Award. Dr. Heinrich is Emeritus Professor of Mechanical Engineering in the Department of Mechanical Engineering at the University of New Mexico. He served as Chair of the Department from 2004-2012. Dr. Heinrich previously was a member of the faculty in the Department of Mechanical and Aerospace Engineering at the University of Arizona. He received his undergraduate degree from Universidad Católica de Chile and his Ph.D. in Mathematics/Numerical Analysis from the University of Pittsburgh. He is a Fellow of the ASME and member of the ASEE, and acts as a consultant to several international institutions. He is currently editor, advisor and reviewer for a variety of technical journals, including Computer Methods in Applied Mechanics and Engineering and Progress in Computational Fluid Dynamics. He has been a consultant for several major corporations and published over 100 technical papers in the area of finite element analysis. He is co-author of the book Intermediate Finite Element Method. Fluid Flow and Heat Transfer Applications with D.W. Pepper.