Numerical Analysis
 
 
Subject Code: EEM2096
Aim of Subject: To train students in the finite difference method and the finite element method, as applied to the numerical solutions of engineering problems.
Learning Outcome of Subject: At the completion of the subject, students should be able to:
  • Revise the first and second derivatives from Taylor Series expansion.
  • Solve ODE, as well as parabolic, elliptic and hyperbolic PDE using FDM.
  • Understand FEM through physical and mathematical approaches.
  • Understand the types of two-dimensional elements in FEM.
Programme Outcomes:
  • Ability to acquire and apply fundamental principles of science and engineering(60 %)
  • Capability to communicate effectively(10%)
  • Acquisition of technical competence in specialised areas of engineering discipline(10%)
  • Ability to identify, formulate and model problems and find engineering solutions based on a systems approach(10%)
  • Ability to work independently as well as with others in a team(10%)
Assessment Scheme:
  • Tutorial / Assignment - Group assignment Focus group discussion at tutorial To enhance understanding of basic concepts in lecture (20% )
  • Test Quiz - Written exam (20%)
  • Final Exam - Written exam(60% )
Teaching and Learning Activities: 50 hours (lectures and tutorials)
Credit Hours: 3
Pre-Requisite: EEM2036: Engineering Mathematics III
References:
  • M. L. James, G.M. Smith and J.C. Wolford, "Applied Numerical Methods for Digital Computation", Harper Collins, 1993.
  • L. J. Segerlind, "Applied Finite Element Analysis", John Wiley and Sons, 1984.

Subject Contents

  • Review of Taylor Series (1 hour)
    The first derivative
    The second derivative.
     
  • ODE: 1-D steady state heat conduction (5 hours)
    Derivation of the governing equation
    Solution: no heat source, uniform heat source, non-uniform heat source.
    Treatment of Neumann boundary conditions.
    Writing a computer code.
     
  • Parabolic PDE: 1-D transient heat conduction (5 hours)
    Derivation of the governing equation
    Solution using explicit method
    Stability of the explicit method
    The implicit method
    Writing a computer code.
     
  • Elliptic PDE: 2-D steady state heat conduction (4 hours)
    Solution: no heat source, heat source
    Treatment of Neumann boundary conditions.
     
  • Hyperbolic PDE: 1-D wave equation (2 hours)
    Derivation of the governing equation
    Solution.
     
  • The physical approach (4 hours)
    One-dimensional spring-force system
    Assemblage of springs
    One-dimensional, steady state heat conduction.
     
  • The mathematical approach (2 hours)
    Galerkin’s weighted residual method.
     
  • Structural problems (6 hours)
    Truss equations
    Beam equations.
     
  • Types of element (6 hours)
    Two-dimensional constant strain triangle element
    Two-dimensional linear strain triangle element.