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Introduction to Finite Elements in Engineering, 3rd Edition
ISBN-10: 0-13-061591-9
ISBN-13: 978-0-13-061591-6
Published by Prentice Hall
© 2002
Pub. Date: Jan 17, 2002
Format: Cloth
Table of Contents
Preface.
1. Fundamental Concepts.
Introduction. Historical Background. Outline of Presentation. Stresses and Equilibrium. Boundary Conditions. Strain-Displacement Relations. Stress-Strain Relations. Temperature Effects. Potential Energy and Equilibrium; The Rayleigh-Ritz Method. Galerkin's Method. Saint Venant's Principle. Von Mises Stress. Computer Programs. Conclusion.
2. Matrix Algebra and Gaussian Elimination.
Matrix Algebra. Gaussian Elimination. Conjugate Gradient Method for Equation Solving.
3. One-Dimensional Problems.
Introduction. Finite Element Modeling. Coordinates and Shape Functions. The Potential-Energy Approach. The Galerkin Approach. Assembly of the Global Stiffness Matrix and Load Vector. Properties of K. The Finite Element Equations; Treatment of Boundary Conditions. Quadratic Shape Functions. Temperature Effects.
4. Trusses.
Introduction. Plane Trusses. Three-Dimensional Trusses. Assembly of Global Stiffness Matrix for the Banded and Skyline Solutions.
5. Two-Dimensional Problems Using Constant Strain Triangles.
Introduction. Finite Element Modeling. Constant-Strain Triangle (CST). Problem Modeling and Boundary Conditions. Orthotropic Materials.
6. Axisymmetric Solids Subjected to Axisymmetric Loading.
Introduction. Axisymmetric Formulation. Finite Element Modeling: Triangular Element. Problem Modeling and Boundary Conditions.
7. Two-Dimensional Isoparametric Elements and Numerical Integration.
Introduction. The Four-Node Quadrilateral. Numerical Integration. Higher Order Elements. Four-Node Quadrilateral for Axisymmetric Problems. Conjugate Gradient Implementation of the Quadrilateral Element.
8. Beams and Frames.
Introduction. Finite Element Formulation. Load Vector. Boundary Considerations. Shear Force and Bending Moment. Beams on Elastic Supports. Plane Frames. Three-Dimensional Frames. Some Comments.
9. Three-Dimensional Problems in Stress Analysis.
Introduction. Finite Element Formulation. Stress Calculations. Mesh Preparation. Hexahedral Elements and Higher Order Elements. Problem Modeling. Frontal Method for Finite Element Matrices.
10. Scalar Field Problems.
Introduction. Steady State Heat Transfer. Torsion. Potential Flow, Seepage, Electric and Magnetic Fields, and Fluid Flow in Ducts. Conclusion.
11. Dynamic Considerations.
Introduction. Formulation. Element Mass Matrices. Evaluation of Eigenvalues and Eigenvectors. Interfacing with Previous Finite Element Programs and a Program for Determining Critical Speeds of Shafts. Guyan Reduction. Rigid Body Modes. Conclusion.
12. Preprocessing and Postprocessing.
Introduction. Mesh Generation. Postprocessing. Conclusion.
Appendix.
Bibliography.
Index.
