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