Preface. - Notation. - 1 Introduction. - 1. 1 Historical Sketch. - 1. 2 Euler-Lagrange Equations. - 1. 3 Weak Variational Form. - 1. 4 Galerkin Method. - 1. 5. - 1. 6. - 2 One-Dimensional Shape Functions. - 2. 1 Local and Global Linear Shape Functions. - 2. 2 Local and Global Quadratic Shape Functions. - 2. 3 Parametric Coordinates. - 2. 4 Hermite Shape Functions. - 2. 5 Exercises. - 3 One-Dimensional Second-Order Equation. - 3. 1 Galerkin Finite Element Method. - 3. 2 Two Dependent Variables. - 3. 3 Exercises. - 4 One-Dimensional Fourth-Order Equation. - 4. 1 Euler-Bernoulli Beam Equation. - 4. 2 Exercises. - 5 Two-Dimensional Elements. - 5. 1 Linear Three-Node Triangular Elements. - 5. 2 Bilinear Four-Node Rectangular Elements. - 5. 3 Global Shape Functions. - 5. 4 Triangular Coordinates. - 5. 5 Shape Functions on the Sides of a Triangle. - 5. 6 Exercises. - 6 Two-Dimensional Problems. - 6. 1 Single Dependent Variable Problems. - 6. 2 Exercises. - 7 More Two-Dimensional Problems. - 7. 1 Heat Transfer. - 7. 2 Torsion. - 7. 3 Seepage. - 7. 4 Fluid Flows. - 7. 5 Exercises. - 8 Axisymmetric Heat Transfer. - 8. 1 Radial Symmetry. - 8. 2 Linear Elements. - 8. 3 Linear Elements for Heat Transfer in Fluids. - 8. 4 Nonlinear Heat Transfer. - 8. 5 Exercises. - 9 Transient Problems. - 9. 1 Classical Methods. - 9. 2 One-Dimensional Transient Problems. - 9. 3 Time-Dependent Heat Conduction. - 9. 4 Two-Dimensional Transient Problems. - 9. 5 Exercises. - 10 Single Nonlinear One-Dimensional Problems. - 10. 1 Newton' method. - 10. 2 Radiation Heat Transfer. - 10. 3 Stress Analysis of Plastic Rods. - 10. 4 Power-Law Pressure Driven Flow between Two Plates. - 10. 5 Mixing-Length Equation for Turbulent Flow in Pipes. - 10. 6 Rayleigh-Ritz and Nonlinear Gradient Methods. - 10. 7 Exercises. - 11 Plane Elasticity. - 11. 1 Stress-Strain Relations. - 11. 2 Constant-Strain Triangular Element. -11. 3 Virtual Displacement Finite Element Model. - 11. 4 Weak Form Finite Element Model. - 11. 5 Stiffness Matrix and Load Vector. - 11. 6 Exercises. - 12 Stokes Equations and Penalty Method. - 12. 1 Equality-Constrained Programs and Lagrange Multipliers. - 12. 2 Penalty Formulation for Linear Stokes Equation. - 12. 3 Penalty Linear Triangular Stokes Element. - 12. 4 Penalty Bilinear Rectangular Stokes Element. - 12. 5 Penalty Linear Triangular Power-law Stokes Element. - 12. 6 Solutions by Conjugate Gradient Methods. - 12. 7 Exercises. - 13 Vibration Analysis. - 13. 1 Hamiltonian Principle. - 13. 2 Free Axial Vibrations of an Elastic Rod. - 13. 3 Free Vibrations of a Euler Elastic Beam. - 13. 4 Free In-Plane Vibrations of an Elastic Plate. - 13. 5 Axial Vibrations of a Plastic Rod. - 13. 6 Eigenvalue Problems. - 13. 7 Exercises. - 14 Computer Codes. - 14. 1 Mathematica Codes. - 14. 2 Ansys Codes. - 14. 3 Matlab Codes. - 14. 4 Fortran Codes. - Integration Formulas. - A Special Cases. - B Temporal Approximations. - C Isoparametric Elements. - D Green' Identities. - E Gaussian Quadrature. - F Gradient-Based Methods. Language: English