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Specifications of Finite Element Method

Book Details

  • ISBN 978-93-83733-85-9
  • English
  • 2015
  • Paper Back
  • -


  • 1. Introduction
    Introduction, Discretizations, Matrix Algebra, Banded Symmetric Matrix and Bandwidth, Stiffness Matrix, Two Force Member Elements, Coordinate Transformation, General Steps of FEM, Linear Spring as a Finite Element, Truss, Solved Examples, Review Questions
    2. 1- Dimensional Finite Element Analysis 
    Introduction, Heat Conduction in Uniform Bar, Basis of Structural Mechanics, Equations of Equilibrium, Strains, The Strain Tensor, The Stress Tensor, Linear Constitutive Equations , Principle of Minimum Potential Energy, Generic Form of Finite Element Equations, The Linear Bar Finite Element, The Quadratic Bar Element, Concept of Shape Functions, Solved Examples, Review Questions
    3. Various Finite Element Methods 
    Introduction, Variational Formulation, Ritz Method, Developing Elemental Equations by Ritz Method, Galerkin Method, Developing Elemental Equations by Galerkin Method, Least Square Method, Collocation Method, Sub Domain Methods, Completeness and Compatibility, Steady State Heat Conduction, Elemental Equations for a Two-noded Element, Application of Boundary Conditions, Solved Examples, Review Questions
    4. 2-Dimensional Finite Element Analysis
    Introduction, Approximation of Geometry and Field Variable, FEM Formulation, Plane Stress and Strain, Shape Function, Numerical Integration, Isoparametric Formulation of 1-D Bar Elements, Solved Examples, Review Questions
    5. Higher Order Elements in FEM
    Introduction, Langrange’s Interpolation Formula for One and Two Independent Variables Convergence, Continuity, Mesh Generation, Static Condensation, Element Mass Matrix in Dynamic Analysis, Applications of the Finite Element Method, Advantages of the Finite Element Method, Review Questions