The course is mainly aimed at Applied/NA postgraduates (MSc and PhD) for whom attendance is compulsory. All other students and members of staff are also most welcome to attend. The course is taught by Dr. Matthias Heil. Note that no prior knowledge of continuum mechanics will be required.
The motivation for the course is as follows: The nonlinear Navier Stokes equations of fluid mechanics are well known in their exact form and are commonly used as the starting point for any mathematical investigation. Linearisations about specific reference states can easily be obtained.
Conversely, most of the elasticity literature (and indeed the department's elasticity course MT4721) is based on linearised theories and is therefore a priori restricted to infinitesimal displacements/deformations. Attempts to extend the linearised theory to larger displacements are tedious (and error prone!) since many of the complications associated with large displacements cannot really be appreciated from the framework of a small displacement-theory. In many ways it is easier to re-derive the governing equations of continuum mechanics (without any restrictions on the magnitude of the displacements) from scratch. In this framework, linear and weakly non-linear theories appear as subset of the general theory. The lecture course will follow this approach.
The outline of the course is as follows:
This will be followed by a visit to a local pub...
If you have any questions about the lecture, please see me in my office (18.07), contact me by email ( M.Heil@maths.man.ac.uk) or catch me after the lecture.