MATH7701 Finite Element Methods

2017

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)
2k Admission into MSCMT-Master of Science (Mathematics)
2l Admission into MEMT-Master of Engineering (Materials)
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 or 2k or 2l)))

1 of ENGR7961, MATH4701 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 using software such as MSC Nastran and Ansys.

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

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.