Finite Elements

Topics covered in the Finite Element Analysis and Applications:

• Variational Boundary Value Problems in 1-D
  • Model problem
    • Longitudinal Deformation of a bar
    • Steady State Heat conduction in a bar
  • Strong and weak formulation
  • Functional space
  • Equivalence of weak and strong form

   

• Galerkin Finite Element Method in 1-D
  • Finite element discretization
  • Trial and test function
  • Discrete weak form
  • Numerical integration
  • Stiffness matrix
  • External load work
  • Higher order finite elements
  • Error measure and convergence

   

• Galerkin Finite Element Method in 2-D (Heat Conduction)
  • Notations
    • Gradient
    • Divergence
  • Conservation of Energy
  • Weak form
  • Finite elements
    • Trial and test functions
    • Weak form discretization
    • Linear triangular elements
    • Bilinear quadrilateral elements
    • Pascal’s triangle
    • Higher order triangular and quadrilateral elements

   

• Continuum Finite Elements
  • Linearized theory of elasticity
    • Cauchy’s law
    • Equilibrium equations
    • Small strain tensor
    • Hooke’s law
    • Weak form of the equilibrium equation
    • Finite elements
      • Triangular elements
      • Quadrilateral elements
      • Tetrahedron elements
      • Eight node brick elements

 

• Structural Elements
  • Space truss
  • Euler-Bernoulli beams
  • Plate theory

 

• Solution method and stability
  • Explicit time integration method
  • Lagrange multiplier method
  • Augmented Lagrange multiplier method