Author | Kythe, Prem K. author |
---|---|
Title | An Introduction to Linear and Nonlinear Finite Element Analysis [electronic resource] : A Computational Approach / by Prem K. Kythe, Dongming Wei |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |
Connect to | http://dx.doi.org/10.1007/978-0-8176-8160-9 |
Descript | XXIII, 445 p. online resource |
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 Newtonโ 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 Greenโ Identities -- E Gaussian Quadrature -- F Gradient-Based Methods