Fundamental Finite Element Analysis and Applications
with Mathematica and Matlab Computations
1. Auflage Februar 2005
720 Seiten, Hardcover
Praktikerbuch
Kurzbeschreibung
*Finite Element Analysis with Mathematica and Matlab Computations and Practical Applications is an innovative, hands-on and practical introduction to the Finite Element Method that provides a powerful tool for learning this essential analytic method.
*Support website (www.wiley.com/go/bhatti) includes complete sets of Mathematica and Matlab implementations for all examples presented in the text. Also included on the site are problems designed for self-directed labs using commercial FEA software packages ANSYS and ABAQUS.
*Offers a practical and hands-on approach while providing a solid theoretical foundation.
*Finite Element Analysis with Mathematica and Matlab Computations and Practical Applications is an innovative, hands-on and practical introduction to the Finite Element Method that provides a powerful tool for learning this essential analytic method.
*Support website (www.wiley.com/go/bhatti) includes complete sets of Mathematica and Matlab implementations for all examples presented in the text. Also included on the site are problems designed for self-directed labs using commercial FEA software packages ANSYS and ABAQUS.
*Offers a practical and hands-on approach while providing a solid theoretical foundation.
1. Finite Element Method: The Big Picture.
1.1 Discretization and Element Equations.
1.2 Assembly of Element Equations.
1.3 Boundary Conditions and Nodal Solution.
1.4 Element Solutions and Model Validity.
1.5 Solution of Linear Equations.
1.6 Multipoint Constraints.
1.7 Units.
2. Mathematical Foundation of the Finite Element Method.
2.1 Axial Deformation of Bars.
2.2 Axial Deformation of Bars Using Galerkin Method.
2.3 One Dimensional BVP Using Galerkin Method.
2.4 Rayleigh-Ritz Method.
2.5 Comments on the Galerkin & the Rayleigh-Ritz Methods.
2.6 Finite Element Form of Assumed Solutions.
2.7 Finite Element Solution of Axial Deformation Problems.
3. One Dimensional Boundary Value Problem.
3.1 Selected Applications of 1D BVP.
3.2 Finite Element Formulation for Second Order 1D BVP
3.3 Steady State Heat Conduction.
3.4 Steady State Heat Conduction and Convection.
3.5 Viscous Fluid Flow Between Parallel Plates.
3.6 Elastic Buckling of Bars.
3.7 Solution of Second Order 1D BVP.
3.8 A Closer Look at the Inter-Element Derivative Terms.
4. Trusses, Beams, and Frames.
4.1 Plane Trusses.
4.2 Space Trusses.
4.3 Temperature Changes and Initial Strains in Trusses.
4.4 Spring Elements.
4.5 Transverse Deformation of Beams.
4.6 Two Node Beam Element.
4.7 Uniform Beams Subjected to Distributed Loads.
4.8 Plane Frames.
Contents
4.9 Space Frames.
4.10 Frames in Multistory Buildings.
5. Two Dimensional Elements.
5.1 Selected Applications of the 2D BVP.
5.2 Integration by Parts in Higher Dimensions.
5.3 Finite Element Equations Using the Galerkin Method.
5.4 Rectangular Finite Elements.
5.5 Triangular Finite Elements.
6. Mapped Elements.
6.1 Integration Using Change of Variables.
6.2 Mapping Quadrilaterals Using Interpolation Functions.
6.3 Numerical Integration Using Gauss Quadrature.
6.4 Finite Element Computations Involving Mapped Elements.
Fundamental Finite Element Theory and Applications.
6.5 Complete Mathematica and Matlab Based Solutions of 2DBVP Involving Mapped.
Elements.
6.6 Triangular Elements by Collapsing Quadrilaterals.
6.7 Infinite Elements.
7. Analysis of Elastic Solids.
7.1 Fundamental Concepts in Elasticity.
7.2 Governing Differential Equations.
7.3 General Form of Finite Element Equations.
7.4 Plane Stress and Plane Strain.
7.5 Planar Finite Element Models.
8. Transient Problems.
8.1 Transient Field Problems.
8.2 Elastic Solids Subjected to Dynamic Loads.
Contents
9. p-Formulation.
9.1 p-Formpulation for Second-Order 1D BVP.
9.2 p-Formpulation for Second-Order 2D BVP.
Appendix A: Use of Commercial FEA Software.
A.1 Ansys Applications.
A.2 Optimizing Design Using Ansys.
A.3 Abaqus Applications.
Appendix B: Variational Form for Boundary Value Problems.
B.1 Basic concept of variation of a function.
B.2 Derivation of Equivalent Variational Form.
B.3 Boundary Value Problem Corresponding to a Given Functional.
Bibliography.
Index.
