Undergrad FEM

In this course, besides learning the mathematical theory of finite element method, the students will learn using Abaqus for linear finite element modeling.

Topics Covered in this class include:

  • Introduction to FEA
  • Introduction to Linear Algebra (vectors, matrices, eigenvalue problems etc.)
  • Stress (3-D)
  • Strain (3-D)
  •  Generalized Hooke’s Law
  • Equilibrium Equations
  • Boundary Conditions
  • Plane Stress, Plane Strain and Axisymmetry
  • One Dimensional Bar Problem (Strong Formulation, Derivation)
  • Beam Elements
  • Rigid Frame Joints
  • Approximation Solutions to Differential Equations (different methods)
  • Weak Formulation of the above problem
  • Linear Finite Elements
  • Stiffness Equation, Global Stiffness Matrix and Global Force Vector
  • Element Stiffness Matrix, Element Force Vector
  • Equivalent Nodal Forces
  • Assembly
  • Solution to Systems of Linear Equations
  • Calculation of Stress and Strain from FE solution
  • Quadratic Elements in 1D
  • Modification of the 1D bar problem to 1D heat conduction
  • Various types of elements available in 2D and 3D
  • Choice of Elements
  • Convergence considerations