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MA30253: Continuum mechanics

Follow this link for further information on academic years Academic Year: 2018/9
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
In taking this module you cannot take MA40065
Further information on descriptions 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.
Before taking this module you must take MA20223
In taking this module you cannot take MA40065
Further information on programme availabilityProgramme availability:

MA30253 is Compulsory on the following programmes:

Department of Physics

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)
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: