Postgraduate Course: The Finite Element Method (PGEE11046)
|School||School of Engineering
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Not available to visiting students
|Summary||The finite element method is an indispensable tool for engineers in all disciplines. This course introduces students to the fundamental theory of the finite element method as a general tool for numerically solving differential equations for a wide range of engineering problems. Field problems described by the Laplace, and Poisson equations are presented first and all steps of the FE formulation are described. Specific applications in heat transfer are demonstrated. The application of the method to elasticity problems is then developed from fundamental principles. Specific classes of problems are then discussed based on abstractions and idealisations of 3D solids, such as plane stress and strain, Euler-Bernoulli and Timoshenko beams and Kirchoff and Mindlin-Reissner plates and shells. Special topics such as multiple constraints and substructuring are introduced.
L2 Recap of the direct stiffness method
L3-L4: Approximation and weighted residuals
L5-L6: Rayleigh-Ritz (variational) methods
L7-L8: Heat transfer and general Poisson problems
L9-L10: Poisson problems in two and three dimensions
L11-L12: Elastostatics and thermal stress analysis
L13-L14: Static condensation and multi-freedom constraints
L15-L16: Beam and plate bending
This is a postgraduate level finite element course which builds on the introductory course "FEM for Solids and Structures". The subject is approached in a more general sense in a relatively more mathematical framework. Many topics from the rich FEM literature are presented preferring breadth over depth. The course is primarily intended for MSc students and those undergraduates who are fascinated by the subject and would like to pursue higher degrees in the field of computational mechanics.
Accreditation of Higher Education Programmes Learning Outcomes: SM2m, SM5m, EA1b, EA2, G1 (Definite); EA3m, P4 (Possible)
Entry Requirements (not applicable to Visiting Students)
|| Students MUST have passed:
||Other requirements|| None
Course Delivery Information
|Not being delivered|
On completion of this course, the student will be able to:
- Produce FEM based numerical discretisations of mathematical descriptions (differential equations) of simple problems in continuum mechanics;
- Use FEM for solving simple steady and transient field problems using a standard software package;
- Use FEM to produce a reliable prediction of displacements and stresses in linear elastic bodies of relevance to engineering practice using a standard software package;
- Make a critical assessment of FEM calculations.
J. N. Reddy, An Introduction to the Finite Element Method, 3rd ed., McGraw-Hill, 2005
E. G. Thompson, Introduction to the Finite Element Method - Theory, Programming and Applications, John Wiley and Sons, 2004.
O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method Set, 7th ed., Butterworth-Heinemann, 2013.
K. J. Bathe, Finite Element Procedures, Prentice Hall, 1996.
|Graduate Attributes and Skills
||Application of Mathematical concepts, Computer Modelling skills, Interpreting design problems.
|Keywords||Numerical methods,computational mechanics
|Course organiser||Dr Stefanos Papanicolopulos
Tel: (0131 6)50 7214
|Course secretary||Miss Margaret Robertson
Tel: (0131 6)50 5565