MATH4701 Finite Element Methods

2011

4.5

1 x 2-hour lecture weekly
1 x 4-hour project work fortnightly

1 2 of MATH2701, MATH2711, MATH2014, MATH2111
1a ENGR2711 - Engineering Mathematics
1b 2 of MATH2111, MATH1141
2 Admission into GCEB-Graduate Certificate in Engineering (Biomedical)
2a Admission into GDPEB-Graduate Diploma in Engineering (Biomedical)
2b Admission into MEB-Master of Engineering (Biomedical)
2c Admission into GCEE-Graduate Certificate in Engineering (Electronics)
2d Admission into GDPEE-Graduate Diploma in Engineering (Electronics)
2e Admission into MEE-Master of Engineering (Electronics)
2f Admission into GCESI-Graduate Certificate in Engineering (Smart Instrumentation)
2g Admission into MESI-Master of Engineering (Smart Instrumentation)
2h Admission into HBIT-Bachelor of Information Technology (Honours)
2i Admission into HBSC-Bachelor of Science (Honours)
2j Admission into MSCCS-Master of Science (Computer Science)
Must Satisfy: (((1 or 1a or 1b)) or ((2 or 2a or 2b or 2c or 2d or 2e or 2f or 2g or 2h or 2i or 2j)))

ENGR7961 has been successfully completed

Basic knowledge of vectors, tensors and matrices; differential and partial differential equations; 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.

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.

The topic aims to ensure that the students understand 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. Writing a computer program for solving finite element method problems
7. Applications of Matlab

At the completion of the 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. Develop computer programs to solve prototype problems using FEM
4. Describe the limitations of standard FEM for complex systems and anticipate what advanced techniques can be applied