MA30253: Continuum mechanics
Academic Year:  2020/1 
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:  EX 100% 
Supplementary Assessment: 

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, strainrate 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 twodimensional 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. 
Programme availability: NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2020 
MA30253 is Compulsory on the following programmes:Department of Physics
MA30253 is Optional on the following programmes:Department of Mathematical Sciences

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