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Programme & Unit Catalogues

## MA30253: Continuum mechanics

Owning Department/School: Department of Mathematical Sciences
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Honours (FHEQ level 6)
Period:
Semester 1
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA20223
In taking this module you cannot take MA40065
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
Programme 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: This unit catalogue is applicable for the 2018/19 academic year only. Students continuing their studies into 2019/20 and beyond should not assume that this unit will be available in future years in the format displayed here for 2018/19. 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. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.