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The Finite Element Method in Engineering.
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Engineering
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ISBN
9780080470504
-- 9780750678285
Author
RAO, Singiresu S.
Title
The Finite Element Method in Engineering.
4th ed.
Description
1 online resource (685 pages)
Contents
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.
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Engineering mathematics
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RAO, Singiresu S.
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