T804 study materials are
provided online via the module website. They include the following:
Block 1 introduces the background development of the finite element method with reference to some key milestone references and the context in solving field problems. The basic theory is illustrated with simple linear one-dimensional elements of structural form introducing the concepts of element and global stiffness matrices and matrix methods of solution for displacements. Also covered are key concepts such as linear and parabolic shape functions and interpolation polynomials for simple finite elements.
Block 2 concentrates on two of the main areas of use of the finite element method in the context of current engineering. The general formulation of three dimensional stress analysis equations is revised to set out the basic field problem in determining the displacements under the load conditions. Emphasis is placed on modelling issues such as boundary conditions, material properties and use of symmetry. Studies of the background theory continue in greater depth addressing the formulation of elements, their characteristic matrices and vectors for field problems, assembly and solution of the displacement and temperature equations. Further instruction in running the software is given, concentrating on modelling procedures, results processing, estimation of errors and convergence limits.
Also addressed are the properties, formulation and use of various types of element to use in two-dimensional solid mechanics problems, beams and frames. For heat transfer, studies include simple one- and two-dimensional elements, modelling a thermal rod and heat conduction through walls. Stresses due to thermal expansion will also be covered.
Section 1 is a review of the theory of mechanical vibrations, including beams, plates and mass-spring systems. Following on from Blocks 1 and 2, section 2 describes finite element method formulation of vibrating systems. Both free and forced vibrations are considered. This section will cover modal analysis, transient response analysis, harmonic response analysis and wave/sound propagation. Section 3 provides an introduction to non-linear behaviour of materials under stress, covering large deformation, buckling, material and contact non-linearity.