Aims & Learning Objectives:
Aims: To provide an introduction to the mathematical modelling of the behaviour of solid elastic materials.
Students should be able to derive the governing equations of the theory of linear elasticity and be able to solve simple problems.
Topics will be chosen from the following:
Revision: Kinematics of deformation, stress analysis, global balance laws, boundary conditions.
Constitutive law: Properties of real materials; constitutive law for linear isotropic elasticity, Lame moduli; field equations of linear elasticity; Young's modulus, Poisson's ratio.
Some simple problems of elastostatics: Expansion of a spherical shell, bulk modulus; deformation of a block under gravity; elementary bending solution.
Linear elastostatics: Strain energy function; uniqueness theorem; Betti's reciprocal theorem, mean value theorems; variational principles, application to composite materials; torsion of cylinders, Prandtl's stress function.
Linear elastodynamics: Basic equations and general solutions; plane waves in unbounded media, simple reflection problems; surface waves.