Year
2020
Units
4.5
Contact
1 x 120-minute lecture weekly
1 x 240-minute project work fortnightly
Enrolment not permitted
1 of MATH4701, MATH7701 has been successfully completed
Assumed knowledge
Basic knowledge of vectors, tensors and matrices; differential and partial differential equations; solid mechanics; scientific programming skills. Students undertaking the one year honours programs should check to make sure they have the appropriate background from their undergraduate degree/s.
Topic description
Fundamental concepts and mathematical background. Variational principles and general procedure of the finite element analysis; standard element shape functions. Formulation of one- and two-dimensional problems. Vector and tensor analysis. Computer program development. Introduction to some advanced finite element modelling, such as mixed and penalty methods; transient problems; isoparametric finite elements; grid generation; adaptive mesh refinement; applications to computational solid and fluid dynamics using software such as MSC Nastran and Ansys.
Educational aims
The topic aims to ensure that the students have a basic understanding of the following:

  1. Variational formulation of boundary value problems
  2. Discretisation of the problem
  3. Choosing basis functions
  4. Assembling the matrix form of the problem
  5. Solving a sparse matrix
  6. Applications of software such as MSC Nastran and Ansys
Expected learning outcomes
At the completion of this topic, students are expected to be able to:

  1. Understand the fundamental mathematical and physical basis of FEM
  2. Establish FEM models from practical problems and deal with boundary conditions along with external forces
  3. Use computer programs to solve prototype problems using FEM
  4. Describe the limitations of standard FEM for complex systems and anticipate the advanced techniques that can be applied