Finite Element Analysis

Syllabus

1. Overview (2 hours)
   1. History and development
   2. Mathematical modeling of the physical system
   3. Finite element method (FEM) analysis process and its steps
   4. Applications and advantages of the finite element method
2. Mathematical Background (2 hours)
   1. Vector analysis
   2. Matrix theory
   3. Differential equations
3. Direct Stiffness Method: Discrete Finite Elements (10 hours)
   1. Spring/bar element
   2. Truss element
   3. Beam element
   4. Frame element
   5. Analogous problems in one dimension
4. Continuum Problems (6 hours)
   1. Trial solution procedures
   2. Weighted residual methods
   3. Point collocation method
   4. Subdomain collocation method
   5. Least square method
   6. Galerkin method
5. One-Dimensional Elements (5 hours)
   1. Linear elements
   2. Quadratic elements
   3. Cubic elements
   4. Global, local and natural coordinates
   5. Isoparametric elements
   6. Numerical integration: Gauss-Legendre quadrature
6. Analysis of One-Dimensional Problems (10 hours)
   1. Physical examples
   2. Weak form of the differential equation
   3. Interpolation shape functions
   4. Bar under axial loading
   5. Heat transfer problems
   6. Fluid mechanics: irrotational flow
7. Two-Dimensional Heat Transfer Problem (10 hours)
   1. Rectangular elements; quadrilateral elements
   2. Steady state 2D heat flow
   3. Boundary conditions: Dirichlet, Neumann, Cauchy
   4. Divergence theorem
   5. Isoparametric mapping

Evaluation

1. Chapters 1 and 2 (4 hours): 5 marks
2. Chapter 3 (10 hours): 15 marks
3. Chapter 4 (6 hours): 10 marks
4. Chapters 5 and 6 (15 hours): 15 marks
5. Chapter 7 (10 hours): 15 marks