Aims & Learning Objectives: Aims: To provide an introduction to the mathematical modelling of the behaviour of solid elastic materials.
Objectives:
Students should be able to derive the governing equations of the theory of linear elasticity and be able to solve simple problems.
Content: 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.
