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MA30253: Continuum mechanics

[Page last updated: 15 October 2020]

Follow this link for further information on academic years Academic Year: 2020/1
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Honours (FHEQ level 6)
Further information on teaching periods Period:
Semester 1
Further information on unit assessment Assessment Summary: EX 100%
Further information on unit assessment Assessment Detail:
  • Examination (EX 100%)
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA20223
Description: Aims:
To describe the general theory of continuum mechanics, introduce inviscid fluid mechanics and waves.

Learning Outcomes:
Students should be able to explain the basic concepts of continuum mechanics such as stress, deformation and constitutive relations, be able to formulate balance laws.

Skills:
Numeracy T/F, A
Problem Solving T/F, A
Written Communication F (on problem sheets).

Content:
Cartesian Tensors: Orthogonal transformations, rotation of axes, transformations of components, symmetry and skew symmetry. Isotropic tensors.
Kinematics: Transformation of line elements, deformation gradient, Green strain. Linear strain measure. Displacement, velocity, velocity gradient, strain-rate and spin tensor.
Stress: Cauchy stress; relation between traction vector and stress tensor.
Global Balance Laws: Equations of motion, simple constitutive laws.
Inviscid Fluids: Particle paths and streamlines, Reynold's transport theorem, Euler's equations of motion, Bernoulli's equation. Vorticity, circulation and Kelvin's Theorem.
Irrotational incompressible flow; velocity potential, stream function in two-dimensional flow.
Further topics to be chosen from the following.
Complex potential: line sources and vortices. Method of images, Circle theorem, Blasius's Theorem. Conformal mappings, flow past a wing. Water waves, including effects of finite depth and surface tension. Dispersion, simple introduction to group velocity.
Further information on programme availabilityProgramme availability:

MA30253 is Compulsory on the following programmes:

Department of Physics
  • USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 4)
  • USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
  • USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)

MA30253 is Optional on the following programmes:

Department of Mathematical Sciences
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
  • USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
  • USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
  • USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
  • USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
  • USMA-AFB05 : BSc(Hons) Statistics (Year 3)
  • USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
  • USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
Department of Physics
  • USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
  • USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
  • USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)

Notes:

  • This unit catalogue is applicable for the 2020/21 academic year only. Students continuing their studies into 2021/22 and beyond should not assume that this unit will be available in future years in the format displayed here for 2020/21.
  • Programmes and units are subject to change 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.
  • Find out more about these and other important University terms and conditions here.