Search and Find
Service
The Finite Element Method in Engineering
of: S S RAO
Elsevier Trade Monographs, 2010
ISBN: 9780080952048 , 726 Pages
5. Edition
Format: PDF, ePUB, Read online
Copy protection: DRM
Front Cover
1
The Finite Element Method in Engineering
4
Copyright
5
Dedication
6
Table of Contents
8
Preface
14
Approach of the Book
14
New to this Edition
14
Organization
15
Resources for Instructors
16
Acknowledgments
16
Part 1: Introduction
18
Chapter 1. Overview of Finite Element Method
20
1.1 Basic Concept
20
1.2 Historical Background
21
1.3 General Applicability of the Method
24
1.4 Engineering Applications of the Finite Element Method
26
1.5 General Description of the Finite Element Method
26
1.6 One-Dimensional Problems with Linear Interpolation Model
29
1.7 One-Dimensional Problems with Cubic Interpolation Model
41
1.8 Derivation of Finite Element Equations Using a Direct Approach
45
1.9 Commercial Finite Element Program Packages
57
1.10 Solutions Using Finite Element Software
57
References
59
Problems
60
Part 2: Basic Procedure
68
Chapter 2. Discretization of the Domain
70
2.1 Introduction
70
2.2 Basic Element Shapes
70
2.3 Discretization Process
73
2.4 Node Numbering Scheme
80
2.5 Automatic Mesh Generation
82
References
85
Problems
86
Chapter 3. Interpolation Models
92
3.1 Introduction
92
3.2 Polynomial Form of Interpolation Functions
94
3.3 Simplex, Complex, and Multiplex Elements
95
3.4 Interpolation Polynomial in Terms of Nodal Degrees of Freedom
95
3.5 Selection of the Order of the Interpolation Polynomial
97
3.6 Convergence Requirements
99
3.7 Linear Interpolation Polynomials in Terms of Global Coordinates
102
3.8 Interpolation Polynomials for Vector Quantities
113
3.9 Linear Interpolation Polynomials in Terms of Local Coordinates
116
3.10 Integration of Functions of Natural Coordinates
125
3.11 Patch Test
126
References
128
Problems
129
Chapter 4. Higher Order and Isoparametric Elements
136
4.1 Introduction
137
4.2 Higher Order One-Dimensional Elements
137
4.3 Higher Order Elements in Terms of Natural Coordinates
138
4.4 Higher Order Elements in Terms of Classical Interpolation Polynomials
147
4.5 One-Dimensional Elements Using Classical Interpolation Polynomials
151
4.6 Two-Dimensional (Rectangular) Elements Using Classical Interpolation Polynomials
152
4.7 Continuity Conditions
154
4.8 Comparative Study of Elements
156
4.9 Isoparametric Elements
157
4.10 Numerical Integration
165
References
168
Problems
169
Chapter 5. Derivation of Element Matrices and Vectors
174
5.1 Introduction
175
5.2 Variational Approach
175
5.3 Solution of Equilibrium Problems Using Variational (Rayleigh-Ritz) Method
180
5.4 Solution of Eigenvalue Problems Using Variational (Rayleigh-Ritz) Method
184
5.5 Solution of Propagation Problems Using Variational (Rayleigh-Ritz) Method
185
5.6 Equivalence of Finite Element and Variational (Rayleigh-Ritz) Methods
186
5.7 Derivation of Finite Element Equations Using Variational (Rayleigh-Ritz) Approach
186
5.8 Weighted Residual Approach
192
5.9 Solution of Eigenvalue Problems Using Weighted Residual Method
199
5.10 Solution of Propagation Problems Using Weighted Residual Method
200
5.11 Derivation of Finite Element Equations Using Weighted Residual (Galerkin) Approach
201
5.12 Derivation of Finite Element Equations Using Weighted Residual (Least Squares) Approach
204
5.13 Strong and Weak Form Formulations
206
References
208
Problems
209
Chapter 6. Assembly of Element Matrices and Vectors and Derivation of System Equations
216
6.1 Coordinate Transformation
216
6.2 Assemblage of Element Equations
221
6.3 Incorporation of Boundary Conditions
228
6.4 Penalty Method
236
6.5 Multipoint Constraints—Penalty Method
240
6.6 Symmetry Conditions—Penalty Method
243
6.7 Rigid Elements
245
References
249
Problems
249
Chapter 7. Numerical Solution of Finite Element Equations
258
7.1 Introduction
258
7.2 Solution of Equilibrium Problems
259
7.3 Solution of Eigenvalue Problems
268
7.4 Solution of Propagation Problems
279
7.5 Parallel Processing in Finite Element Analysis
285
References
286
Problems
287
Part 3: Application to Solid Mechanics Problems
292
Chapter 8. Basic Equations and Solution Procedure
294
8.1 Introduction
294
8.2 Basic Equations of Solid Mechanics
294
8.3 Formulations of Solid and Structural Mechanics
311
8.4 Formulation of Finite Element Equations (Static Analysis)
316
8.5 Nature of Finite Element Solutions
320
References
321
Problems
321
Chapter 9. Analysis of Trusses, Beams, and Frames
328
9.1 Introduction
328
9.2 Space Truss Element
329
9.3 Beam Element
340
9.4 Space Frame Element
345
9.5 Characteristics of Stiffness Matrices
355
References
356
Problems
357
Chapter 10. Analysis of Plates
372
10.1 Introduction
372
10.2 Triangular Membrane Element
373
10.3 Numerical Results with Membrane Element
384
10.4 Quadratic Triangle Element
386
10.5 Rectangular Plate Element (In-plane Forces)
389
10.6 Bending Behavior of Plates
393
10.7 Finite Element Analysis of Plates in Bending
396
10.8 Triangular Plate Bending Element
396
10.9 Numerical Results with Bending Elements
400
10.10 Analysis of Three-Dimensional Structures Using Plate Elements
403
References
406
Problems
406
Chapter 11. Analysis of Three-Dimensional Problems
418
11.1 Introduction
418
11.2 Tetrahedron Element
418
11.3 Hexahedron Element
426
11.4 Analysis of Solids of Revolution
430
References
438
Problems
439
Chapter 12. Dynamic Analysis
444
12.1 Dynamic Equations of Motion
444
12.2 Consistent and Lumped Mass Matrices
447
12.3 Consistent Mass Matrices in a Global Coordinate System
456
12.4 Free Vibration Analysis
457
12.5 Dynamic Response Using Finite Element Method
469
12.6 Nonconservative Stability and Flutter Problems
477
12.7 Substructures Method
478
References
479
Problems
479
Part 4: Application to Heat Transfer Problems
488
Chapter 13. Formulation and Solution Procedure
490
13.1 Introduction
490
13.2 Basic Equations of Heat Transfer
490
13.3 Governing Equation for Three-Dimensional Bodies
492
13.4 Statement of the Problem
496
13.5 Derivation of Finite Element Equations
497
References
501
Problems
501
Chapter 14. One-Dimensional Problems
506
14.1 Introduction
506
14.2 Straight Uniform Fin Analysis
506
14.3 Convection Loss from End Surface of Fin
509
14.3 Tapered Fin Analysis
513
14.4 Analysis of Uniform Fins Using Quadratic Elements
516
14.5 Unsteady State Problems
519
14.6 Heat Transfer Problems with Radiation
524
References
528
Problems
528
Chapter 15. Two-Dimensional Problems
534
15.1 Introduction
534
15.2 Solution
534
15.3 Unsteady State Problems
543
References
543
Problems
543
Chapter 16. Three-Dimensional Problems
548
16.1 Introduction
548
16.2 Axisymmetric Problems
548
16.3 Three-Dimensional Heat Transfer Problems
553
16.4 Unsteady State Problems
558
References
559
Problems
559
Part 5: Application to Fluid Mechanics Problems
564
Chapter 17. Basic Equations of Fluid Mechanics
566
17.1 Introduction
566
17.2 Basic Characteristics of Fluids
566
17.3 Methods of Describing the Motion of a Fluid
567
17.4 Continuity Equation
568
17.5 Equations of Motion or Momentum Equations
569
17.6 Energy, State, and Viscosity Equations
573
17.7 Solution Procedure
574
17.8 Inviscid Fluid Flow
576
17.9 Irrotational Flow
577
17.10 Velocity Potential
578
17.11 Stream Function
579
17.12 Bernoulli Equation
581
References
583
Problems
583
Chapter 18. Inviscid and Incompressible Flows
588
18.1 Introduction
588
18.2 Potential Function Formulation
590
18.3 Finite Element Solution Using the Galerkin Approach
590
18.4 Stream Function Formulation
601
References
603
Problems
603
Chapter 19. Viscous and Non-Newtonian Flows
608
19.1 Introduction
608
19.2 Stream Function Formulation (Using Variational Approach)
609
19.3 Velocity–Pressure Formulation (Using Galerkin Approach)
613
19.4 Solution of Navier–Stokes Equations
615
19.5 Stream Function–Vorticity Formulation
617
19.6 Flow of Non-Newtonian Fluids
619
19.7 Other Developments
624
References
625
Problems
625
Part 6: Solution and Applications of Quasi-Harmonic Equations
628
Chapter 20. Solution of Quasi-Harmonic Equations
630
20.1 Introduction
630
20.2 Finite Element Equations for Steady-State Problems
632
20.3 Solution of Poisson’s Equation
632
20.4 Transient Field Problems
639
References
641
Problems
641
Part 7: ABAQUS and ANSYS Software and MATLAB® Programs for Finite Element Analysis
646
Chapter 21. Finite Element Analysis Using ABAQUS
648
21.1 Introduction
648
21.2 Examples
649
Problems
679
Chapter 22. Finite Element Analysis Using ANSYS
680
22.1 Introduction
680
22.2 GUI Layout in ANSYS
681
22.3 Terminology
681
22.4 Finite Element Discretization
682
22.5 System of Units
684
22.6 Stages in Solution
684
Problems
698
Chapter 23. MATLAB Programs for Finite Element Analysis
700
23.1 Solution of Linear System of Equations Using Choleski Method
701
23.2 Incorporation of Boundary Conditions
703
23.3 Analysis of Space Trusses
704
23.4 Analysis of Plates Subjected to In-plane Loads Using CST Elements
708
23.5 Analysis of Three-Dimensional Structures Using CST Elements
711
23.6 Temperature Distribution in One-Dimensional Fins
714
23.7 Temperature Distribution in One-Dimensional Fins Including Radiation Heat Transfer
715
23.8 Two-Dimensional Heat Transfer Analysis
716
23.9 Confined Fluid Flow around a Cylinder Using Potential Function Approach
718
23.10 Torsion Analysis of Shafts
719
Problems
720
Appendix: Green-Gauss Theorem (Integration by Parts in Two and Three Dimensions)
722
Index
724
All prices incl. VAT