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Department of Mathematical Sciences, Unit Catalogue 2008/09

MA40049 Linear elasticity

Credits: 6
Level: Masters
Semester: 2
Assessment: EX 100%
Before taking this unit you must take MA20010 and take MA40065

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.
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.