TY  - BOOK
AU  - Desai,Y.M.
AU  - Eldho,T.L.
AU  - Shah,A.H.
TI  - Finite Element Method with Applications in Engineering
SN  - 9789332500839
U1  - 620.00151 23
KW  - Electronic books
N1  - Cover -- Contents -- Preface -- Acknowledgements -- Authors Profile -- Chapter 1: Introduction -- 1.1 Introductory Remarks -- 1.2 Mathematical Modelling of Engineering Problems -- 1.3 Type of Governing Equations -- 1.3.1 Initial and Boundary Conditions -- 1.4 Solution Methodologies -- 1.4.1 Analytical Method -- 1.4.2 Physical Method -- 1.4.3 Computational Method -- 1.5 Numerical Modelling -- 1.6 Pre-Processing and Post-Processing -- 1.7 Scope of the Book -- 1.8 Highlights of the Book -- 1.9 How to Use the Book? -- 1.10 Closing Remarks -- References and Further Reading -- Chapter 2: Approximate Methods of Analysis -- 2.1 Introduction -- 2.2 Aproximating Methods -- 2.3 Method of Weighted Residuals -- 2.3.1 Method of Point Collocation -- 2.3.2 Method of Collocation by Sub-Regions -- 2.3.3 Method of Least Squares -- 2.3.4 Galerkin's Method -- 2.4 Rayleigh-Ritz Method -- 2.4.1 Relation Between FEM and Rayleigh-Ritz Method -- 2.5 Further Numerical Examples -- 2.6 Closing Remarks -- Exercise Problems -- References and Further Reading -- Chapter 3: Finite Element Method-An Introduction -- 3.1 General -- 3.2 What is FEM? -- 3.3 How Does FEM Work? -- 3.4 A Brief History of FEM -- 3.5 FEM Applications -- 3.6 Merits and Demerits of FEM -- 3.7 Closing Remarks -- Exercise Problems -- References and Further Reading -- Chapter 4: Different Approaches in FEM -- 4.1 Introduction -- 4.2 General Steps of FEM -- 4.3 Different Approaches Used in FEM -- 4.3.1 Direct Approach -- 4.3.2 Variational Approach -- 4.3.3 Energy Approach -- 4.3.4 Weighted Residual Approach -- 4.4 Closing Remarks -- Exercise Problems -- References and Further Reading -- Chapter 5: Finite Elements and Interpolation Functions -- 5.1 Introduction -- 5.2 Interpolation Functions -- 5.2.1 One-Independent Spatial Variable -- 5.2.2 Two-Independent Spatial Variables; 5.2.3 Three-Independent Spatial Variables -- 5.3 One-Dimensional Elements -- 5.3.1 Line Element: Linear Interpolation Function -- 5.3.2 Quadratic Interpolation Function -- 5.3.3 Cubic Interpolation Function -- 5.3.4 Lagrangian Form of Interpolation Function -- 5.3.5 Further Higher Order Elements in One-Dimension -- 5.4 Two-Dimensional Elements -- 5.4.1 Triangular Element: Linear Interpolation Function in Cartesian Co-ordinates -- 5.4.2 Triangular Element-Area Co-ordinates -- 5.4.3 Integration Formula for Triangular Elements -- 5.4.4 Triangular Element-Quadratic Function -- 5.4.5 Triangular Element-Cubic Interpolation Function -- 5.4.6 Two-Dimensional Rectangular Elements -- 5.4.7 Rectangular Elements-Lagrangian Form in Natural and Cartesian Co-ordinates -- 5.4.8 Isoparametric Elements -- 5.4.9 Lagrangian Interpolation Functions for Two-Dimensional Elements -- 5.4.10 Two-Dimensional Serendipity Elements -- 5.5 Three-Dimensional Elements -- 5.5.1 Tetrahedral Elements -- 5.5.2 Tetrahedral Elements: Quadratic Interpolation Function -- 5.5.3 Tetrahedral Elements: Cubic Interpolation Function -- 5.5.4 Three-Dimensional Elements-Prismatic Elements -- 5.5.5 Three-Dimensional Elements in Local Co-ordinates -- 5.5.6 Three-Dimensional Serendipity Elements -- 5.6 Closing Remarks -- Exercise Problems -- References and Further Reading -- Chapter 6: One-Dimensional Finite Element Analysis -- 6.1 Introduction -- 6.2 Linear Spring -- 6.2.1 Expressions for Equivalent Spring Constant and Nodal Forces -- 6.3 Truss Element -- 6.3.1 Plane Truss -- 6.3.2 Element Equations by Minimizing Potential Energy -- 6.3.3 Local and Global Element Equations for a Bar in the X-Y Plane -- 6.3.4 Computation of Stress for a Bar in the X-Y Plane -- 6.4 Space Truss -- 6.5 One-Dimensional Torsion of a Circular Shaft -- 6.6 One-Dimensional Steady State Heat Conduction; 6.7 One-Dimensional Flow Through Porous Media -- 6.8 One-Dimensional Ideal Fluid Flow Through Pipes (Inviscid Fluid Flow) -- 6.10 Analyses of Plane Frames and Grids -- 6.10.1 Plane Frame Analysis -- 6.10.2 Grid Analysis -- 6.9 Beam Element -- 6.9.1 Review of Beam Theory -- 6.9.2 Finite Element Formulation of a Beam Element -- 6.9.3 Illustrative Examples -- 6.11 Further One-Dimensional Applications -- 6.11.1 Flow Network Analysis -- 6.11.2 Electrical Network Analysis -- 6.12 Summary of Element Matrices for One-Dimensional Finite Elements -- 6.13 Closing Remarks -- Exercise Problems -- References and Further Reading -- Chapter 7: Two-Dimensional Finite Element Analysis -- 7.1 Introduction -- 7.2 Two-Dimensional Flow Through Porous Media (Seepage Flow) -- 7.2.1 Step-by-step Formulation for the CST Element for Two-dimensional Confined Seepage Analysis -- 7.3 Two-Dimensional Stress Analysis -- 7.3.1 Review of Theory of Elasticity -- 7.3.2 Application of Three-Dimensional Equations for Two-Dimensional Analysis -- 7.3.3 CST Element for Plane Stress and Plane Strain Analyses -- 7.3.4 Triangular Element for Axi-symmetric Analysis -- 7.3.5 Some Remarks on Triangular Elements -- 7.3.6 Four-Node Rectangular Element for Plane Problems -- 7.4 Iso-Parametric Formulation -- 7.4.1 Two-Node Iso-Parametric Line Element (Bar Element) -- 7.4.2 Four-Node Iso-Parametric Element for Plane Problems (Quadrilateral Element) -- 7.5 Finite Element Solution of Partial Differential Equations by Method of Weighted Residual -- 7.5.1 G overning Equations and Boundary Conditions -- 7.5.2 FEM Formulation -- 7.6 FEM Formulation Based on Variational Principle -- 7.7 Finite Element Solution of Stokes Flow Equations -- 7.7.1 Problem Statement -- 7.7.2 FEM Solution -- 7.8 Illustrative Examples -- 7.9 Closing Remarks -- Exercise Problems -- References and Further Reading; Chapter 8: Three-Dimensional Finite Element Analysis -- 8.1 Introduction -- 8.2 Axi-Symmetric Solids -- 8.2.1 Determination of the Fourier Coefficients -- 8.2.2 Isoparametric Finite Element Formulations -- 8.3 Eight-Node Isoparametric Element for Three-Dimensional Stress Analysis -- 8.4 Closing Remarks -- Exercise Problems -- References and Further Reading -- Chapter 9: Computer Implementation of FEM -- 9.1 General -- 9.2 Use of Symmetry and Anti-Symmetry Conditions in Reducing a Problem -- 9.3 Static Condensation -- 9.3.1 Applications of Static Condensation -- 9.3.2 Static Condensation Procedure -- 9.4 Computer Implementation of FEM-sfeap -- 9.5 Storage Schemes for Global Structural Stiffness Matrix -- 9.6 Application of Boundary Conditions -- 9.7 Closing Remarks -- Exercise Problems -- References and Further Reading -- Chapter 10: Further Applications of Finite Element Method -- 10.1 Introduction -- 10.2 Finite Element Analysis of Plates -- 10.2.1 Introduction -- 10.2.2 Review of Plate Theories -- 10.2.3 Finite Element Formulations -- 10.3 Dynamics with Finite Element Method -- 10.3.1 Introduction -- 10.3.2 Governing Equations -- 10.3.3 Mode Superposition Method -- 10.3.4 Direct Time Integration Method -- 10.4 Non-Linear Analysis -- 10.4.1 Finite Element Formulation for Non-Linear Analysis -- 10.4.2 Solution of Non-Linear Equations -- 10.4.3 Illustrative Examples -- 10.5 Groundwater Flow and Contaminant Transport Modelling -- 10.5.1 Introduction -- 10.5.2 Governing Equations and Boundary Conditions -- 10.5.3 Finite Element Formulation -- 10.5.4 FEM Formulation for Groundwater Flow in Unconfined Aquifer -- 10.5.5 Velocity Computation within Elements -- 10.5.6 FEM Formulation for Contaminant Transport -- 10.5.7 Case Study -- 10.6 Hydrodynamics Simulation of Shallow Water Flow -- 10.6.1 Introduction; 10.6.2 Governing Equations and Boundary Conditions -- 10.6.3 Finite Element Formulation -- 10.6.3 Case Study -- 10.7 FEM-Software and Web Resources -- 10.7.1 Introduction -- 10.7.2 FEM in Structural Engineering -- 10.7.3 FEM in Geotechnical Engineering -- 10.7.4 FEM in Fluid Mechanics -- 10.7.5 FEM in Thermal and Automobile Engineering -- 10.7.6 FEM in Physics -- 10.7.7 Multi-Field FEM Software -- 10.7.8 FEM in Other Fields -- 10.8 Concluding Remarks -- References and Further Reading -- Appendix A: Review of Matrix Algebra and Matrix Calculus -- Appendix B: Elements of Calculus of Variations -- Appendix C: Example Illustrating Use of Galerkin's Method -- Appendix D: Review of Gauss Quadrature Procedure for Numerical Integration -- Appendix E: User's Manual For the Simplified Finite Element Analysis Program (sfeap) -- Appendix F: Graphical Interface For the Simplified Finite Element Analysis Program (sfeap) -- Appendix G: Computer Programs for One-Dimensional and Two-Dimensional Problems -- Index
N2  - Finite Element Method with Applications in Engineering presents a practical understanding of the finite element method with a variety of engineering applications that will aid students, teachers, practicing engineers and researchers. It begins with an introduction to the mathematical modeling of engineering problems and approximate methods of analysis. It then introduces the different approaches in FEM such as direct approach, principle of virtual work, variational principle and method of weighted residual. Finally, the applications of FEM to real-world problems are presented in 1D, 2D and 3D for structural analysis, heat and mass transfer, geo-mechanical, fluid flow and other problems. Suitable for engineering students and professionals
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