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100 1  Rao, Singiresu S 
245 14 The Finite Element Method in Engineering 
250    4th ed 
264  1 Burlington :|bElsevier Science & Technology,|c2004 
264  4 |c©2005 
300    1 online resource (685 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
505 0  Front Cover -- The Finite Element Method in Engineering --
       Copyright Page -- Contents -- Preface -- Principal 
       Notation -- PART 1: INTRODUCTION -- Chapter 1. Overview of
       Finite Element Method -- 1.1 Basic Concept -- 1.2 
       Historical Background -- 1.3 General Applicability of the 
       Method -- 1.4 Engineering Applications of the Finite 
       Element Method -- 1.5 General Description of the Finite 
       Element Method -- 1.6 Comparison of Finite Element Method 
       with Other Methods of Analysis -- 1.7 Finite Element 
       Program Packages -- References -- Problems -- PART 2: 
       BASIC PROCEDURE -- Chapter 2. Discretization of the Domain
       -- 2.1 Introduction -- 2.2 Basic Element Shapes -- 2.3 
       Discretization Process -- 2.4 Node Numbering Scheme -- 2.5
       Automatic Mesh Generation -- References -- Problems -- 
       Chapter 3. Interpolation Models -- 3.1 Introduction -- 3.2
       Polynomial Form of Interpolation Functions -- 3.3 Simplex,
       Complex, and Multiplex Elements -- 3.4 Interpolation 
       Polynomial in Terms of Nodal Degrees of Freedom -- 3.5 
       Selection of the Order of the Interpolation Polynomial -- 
       3.6 Convergence Requirements -- 3.7 Linear Interpolation 
       Polynomials in Terms of Global Coordinates -- 3.8 
       Interpolation Polynomials for Vector Quantities -- 3.9 
       Linear Interpolation Polynomials in Terms of Local 
       Coordinates -- References -- Problems -- Chapter 4. Higher
       Order and Isoparametric Elements -- 4.1 Introduction -- 
       4.2 Higher Order One-Dimensional Elements -- 4.3 Higher 
       Order Elements in Terms of Natural Coordinates -- 4.4 
       Higher Order Elements in Terms of Classical Interpolation 
       Polynomials -- 4.5 One-Dimensional Elements Using 
       Classical Interpolation Polynomials -- 4.6 Two-Dimensional
       (Rectangular) Elements Using Classical Interpolation 
       Polynomials -- 4.7 Continuity Conditions -- 4.8 
       Comparative Study of Elements -- 4.9 Isoparametric 
       Elements -- 4.10 Numerical Integration -- References 
505 8  Problems -- Chapter 5. Derivation of Element Matrices and 
       Vectors -- 5.1 Introduction -- 5.2 Direct Approach -- 5.3 
       Variational Approach -- 5.4 Solution of Equilibrium 
       Problems Using Variational (Rayleigh-Ritz) Method -- 5.5 
       Solution of Eigenvalue Problems Using Variational 
       (Rayleigh-Ritz) Method -- 5.6 Solution of Propagation 
       Problems Using Variational (Rayleigh-Ritz) Method -- 5.7 
       Equivalence of Finite Element and Variational (Rayleigh-
       Ritz) Methods -- 5.8 Derivation of Finite Element 
       Equations Using Variational (Rayleigh-Ritz) Approach -- 
       5.9 Weighted Residual Approach -- 5.10 Solution of 
       Eigenvalue Problems Using Weighted Residual Method -- 5.11
       Solution of Propagation Problems Using Weighted Residual 
       Method -- 5.12 Derivation of Finite Element Equations 
       Using Weighted Residual (Galerkin) Approach -- 5.13 
       Derivation of Finite Element Equations Using Weighted 
       Residual (Least Squares) Approach -- References -- 
       Problems -- Chapter 6. Assembly of Element Matrices and 
       Vectors and Derivation of System Equations -- 6.1 
       Coordinate Transformation -- 6.2 Assemblage of Element 
       Equations -- 6.3 Computer Implementation of the Assembly 
       Procedure -- 6.4 Incorporation of Boundary Conditions -- 
       6.5 Incorporation of Boundary Conditions in the Computer 
       Program -- References -- Problems -- Chapter 7. Numerical 
       Solution of Finite Element Equations -- 7.1 Introduction -
       - 7.2 Solution of Equilibrium Problems -- 7.3 Solution of 
       Eigenvalue Problems -- 7.4 Solution of Propagation 
       Problems -- 7.5 Parallel Processing in Finite Element 
       Analysis -- References -- Problems -- PART 3: APPLICATION 
       TO SOLID MECHANICS PROBLEMS -- Chapter 8. Basic Equations 
       and Solution Procedure -- 8.1 Introduction -- 8.2 Basic 
       Equations of Solid Mechanics -- 8.3 Formulations of Solid 
       and Structural Mechanics -- 8.4 Formulation of Finite 
       Element Equations (Static Analysis) -- References -- 
       Problems 
505 8  Chapter 9. Analysis of Trusses, Beams, and Frames -- 9.1 
       Introduction -- 9.2 Space Truss Element -- 9.3 Beam 
       Element -- 9.4 Space Frame Element -- 9.5 Planar Frame 
       Element -- 9.6 Computer Program for Frame Analysis -- 
       References -- Problems -- Chapter 10. Analysis of Plates -
       - 10.1 Introduction -- 10.2 Triangular Membrane Element --
       10.3 Numerical Results with Membrane Element -- 10.4 
       Computer Program for Plates under Inplane Loads -- 10.5 
       Bending Behavior of Plates -- 10.6 Finite Element Analysis
       of Plate Bending -- 10.7 Triangular Plate Bending Element 
       -- 10.8 Numerical Results with Bending Elements -- 10.9 
       Analysis of Three-Dimensional Structures Using Plate 
       Elements -- 10.10 Computer Program for Three-Dimensional 
       Structures Using Plate Elements -- References -- Problems 
       -- Chapter 11. Analysis of Three-Dimensional Problems -- 
       11.1 Introduction -- 11.2 Tetrahedron Element -- 11.3 
       Hexahedron Element -- 11.4 Analysis of Solids of 
       Revolution -- References -- Problems -- Chapter 12. 
       Dynamic Analysis -- 12.1 Dynamic Equations of Motion -- 
       12.2 Consistent and Lumped Mass Matrices -- 12.3 
       Consistent Mass Matrices in Global Coordinate System -- 
       12.4 Free Vibration Analysis -- 12.5 Computer Program for 
       Eigenvalue Analysis of Three-Dimensional Structures -- 
       12.6 Dynamic Response Using Finite Element Method -- 12.7 
       Nonconservative Stability and Flutter Problems -- 12.8 
       Substructures Method -- References -- Problems -- PART 4: 
       APPLICATION TO HEAT TRANSFER PROBLEMS -- Chapter 13. 
       Formulation and Solution Procedure -- 13.1 Introduction --
       13.2 Basic Equations of Heat Transfer -- 13.3 Governing 
       Equation for Three-Dimensional Bodies -- 13.4 Statement of
       the Problem -- 13.5 Derivation of Finite Element Equations
       -- References -- Problems -- Chapter 14. One-Dimensional 
       Problems -- 14.1 Introduction -- 14.2 Straight Uniform Fin
       Analysis 
505 8  14.3 Computer Program for One-Dimensional Problems -- 14.4
       Tapered Fin Analysis -- 14.5 Analysis of Uniform Fins 
       Using Quadratic Elements -- 14.6 Unsteady State Problems -
       - 14.7 Heat Transfer Problems with Radiation -- 14.8 
       Computer Program for Problems with Radiation -- References
       -- Problems -- Chapter 15. Two-Dimensional Problems -- 
       15.1 Introduction -- 15.2 Solution -- 15.3 Computer 
       Program -- 15.4 Unsteady State Problems -- References -- 
       Problems -- Chapter 16. Three-Dimensional Problems -- 16.1
       Introduction -- 16.2 Axisymmetric Problems -- 16.3 
       Computer Program for Axisymmetric Problems -- 16.4 Three-
       Dimensional Heat Transfer Problems -- 16.5 Unsteady State 
       Problems -- References -- Problems -- PART 5: APPLICATION 
       TO FLUID MECHANICS PROBLEMS -- Chapter 17. Basic Equations
       of Fluid Mechanics -- 17.1 Introduction -- 17.2 Basic 
       Characteristics of Fluids -- 17.3 Methods of Describing 
       the Motion of a Fluid -- 17.4 Continuity Equation -- 17.5 
       Equations of Motion or Momentum Equations -- 17.6 Energy, 
       State, and Viscosity Equations -- 17.7 Solution Procedure 
       -- 17.8 Inviscid Fluid Flow -- 17.9 Irrotational Flow -- 
       17.10 Velocity Potential -- 17.11 Stream Function -- 17.12
       Bernoulli Equation -- References -- Problems -- Chapter 
       18. Inviscid and Incompressible Flows -- 18.1 Introduction
       -- 18.2 Potential Function Formulation -- 18.3 Finite 
       Element Solution Using the Galerkin Approach -- 18.4 
       Stream Function Formulation -- 18.5 Computer Program for 
       Potential Function Approach -- References -- Problems -- 
       Chapter 19. Viscous and Non-Newtonian Flows -- 19.1 
       Introduction -- 19.2 Stream Function Formulation (Using 
       Variational Approach) -- 19.3 Velocity-Pressure 
       Formulation (Using Galerkin Approach) -- 19.4 Solution of 
       Navier-Stokes Equations -- 19.5 Stream Function-Vorticity 
       Formulation -- 19.6 Flow of Non-Newtonian Fluids -- 19.7 
       Other Developments 
505 8  References -- Problems -- PART 6: ADDITIONAL APPLICATIONS 
       -- Chapter 20. Solution of Quasi-Harmonic Equations -- 
       20.1 Introduction -- 20.2 Finite Element Equations for 
       Steady-State Problems -- 20.3 Solution of Poisson's 
       Equation -- 20.4 Computer Program for Torsion Analysis -- 
       20.5 Transient Field Problems -- References -- Problems --
       Chapter 21. Solution of Helmholtz Equation -- 21.1 
       Introduction -- 21.2 Finite Element Solution -- 21.3 
       Numerical Examples -- References -- Problems -- Chapter 
       22. Solution of Reynolds Equation -- 22.1 Hydrodynamic 
       Lubrication -- 22.2 Finite Element Solution -- 22.3 
       Numerical Examples -- References -- Problems -- Appendix 
       A. Green-Gauss Theorem -- Index 
520    Finite Element Analysis is an analytical engineering tool 
       developed in the 1960's by the Aerospace and nuclear power
       industries to find usable, approximate solutions to 
       problems with many complex variables. It is an extension 
       of derivative and integral calculus, and uses very large 
       matrix arrays and mesh diagrams to calculate stress points,
       movement of loads and forces, and other basic physical 
       behaviors. Students will find in this textbook a thorough 
       grounding of the mathematical principles underlying the 
       popular, analytical methods for setting up a finite 
       element solution based on those mathematical equations. It
       quickly bridges that knowledge to a host of real-world 
       applications--from structural design, to problems in fluid
       mechanics and thermodynamics. Professional engineers will 
       benefit from the introduction to the many useful 
       applications of finite element analysis, and will gain a 
       better understanding of its limitations and special uses. 
       New to this edition: · New sections added on the 
       assemblage of element equations, and an important new 
       comparison between finite element analysis and other 
       analytical methods…showing advantages and disadvantages 
       of each · Updated solutions manual available · Improved 
       sample and end-of-chapter problems * The only book to 
       provide a broadoverview of the underlying principles of 
       finite element analysis and where it fits into the larger 
       context of other mathematically based engineering 
       analytical tools. * New sections added on the assemblage 
       of element equations, and an important new comparison 
       between finite element analysis and other analytical 
       methods, showing the advantages and disadvantages of each.
       * New Companion website that will host usable finite 
       element programs and sample engineering problems, as well 
       as a Solutions Manual for end-of-chapter problems 
588    Description based on publisher supplied metadata and other
       sources 
590    Electronic reproduction. Ann Arbor, Michigan : ProQuest 
       Ebook Central, 2020. Available via World Wide Web. Access 
       may be limited to ProQuest Ebook Central affiliated 
       libraries 
650  0 Finite element method.;Engineering mathematics 
655  4 Electronic books 
700 1  RAO, Singiresu S 
776 08 |iPrint version:|aRao, Singiresu S.|tThe Finite Element 
       Method in Engineering|dBurlington : Elsevier Science & 
       Technology,c2004|z9780750678285 
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