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 Author Rao, Singiresu S Title The Finite Element Method in Engineering Imprint Burlington : Elsevier Science & Technology, 2004 ©2005 Edition 4th ed Descript 1 online resource (685 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Note 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 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 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 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 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 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 Description based on publisher supplied metadata and other sources Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries Link Print version: Rao, Singiresu S. The Finite Element Method in Engineering Burlington : Elsevier Science & Technology,c2004 9780750678285 Subject Finite element method.;Engineering mathematics Electronic books Alt Author RAO, Singiresu S
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