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Programme & Unit Catalogues

MA40049: Elasticity

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Masters UG & PG (FHEQ level 7)
Period: Semester 2
Assessment: EX 100%
Supplementary Assessment: MA40049 Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this unit you must take MA40065
Description: Aims:
To provide an introduction to the mathematical modelling of the behaviour of elastic materials.

Learning Outcomes:
Students should be able to derive the governing equations of the theory of elasticity and be able to solve simple problems.

Skills:
Problem Solving T/F A
Written and Spoken Communication F (solutions to exercise sheets, problem classes)

Content:
Revision: Kinematics of deformation, stress analysis, global balance laws, boundary conditions. Further topics will be chosen from the following:
Constitutive laws: Properties of real materials; constitutive law for isotropic elasticity, Lame moduli; field equations of elasticity; Young's modulus, Poisson's ratio. 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. Some simple problems of elastostatics: Expansion of a spherical shell, bulk modulus; deformation of a block under gravity; elementary bending solution.
Elastodynamics: Basic equations and general solutions; plane waves in unbounded media, simple reflection problems; surface waves.
Programme availability:

MA40049 is Compulsory on the following programmes:

Department of Physics
• USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 4

MA40049 is Optional on the following programmes:

Department of Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
• USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
• USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• TSMA-AFM09 : MSc Mathematical Sciences (Full-time)
• TSMA-APM09 : MSc Mathematical Sciences (Part-time)
• TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time)
• TSMA-AWM14 : MSc Modern Applications of Mathematics (Full-time incorporating placement)
• TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time)
Department of Physics
• USXX-AFB03 : BSc (hons) Mathematics and Physics (Full-time) - Year 3
• USXX-AKB04 : BSc (hons) Mathematics and Physics with Placement (Full-time with Thick Sandwich Placement) - Year 4
• USXX-AAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4

Notes:
* This unit catalogue is applicable for the 2013/4 academic year only. Students continuing their studies into 2014/15 and beyond should not assume that this unit will be available in future years in the format displayed here for 2013/14.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.