Mathematical and Computational Modelling in Mechanics

Semester 1, 2020

Staff

- Maedeh Amirpourmolla
- John Cater
- David Dempsey (director, coordinator)

Calendar notes

Development of macroscopic models of physical systems using fundamental mathematical techniques and physical laws. Topics include vector and tensor calculus including indicial notation and integral theorems, conservation laws, control volumes and constitutive equations, continuum assumptions, isotropy and homogeneity. Possible applications include deformation, strain and stress, fluid flow, electromagnetism, reactive chemical transport, and kinetics.

Prerequisite: BIOMENG 221 or MECHENG 242, and ENGSCI 211 or 213Restriction: BIOMENG 321

## Intended learning outcomes |
## Related graduate attributes |
## Related assessments |
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The student will have knowledge of the language of mathematical and computational mechanics, including tensors, coordinate transformations and eigenvalue analysis. |
No related attributes |
Quiz 1 Mechanics Test Mechanics Assignment Exam Quiz 2 |

Kinematics, the description of motion, displacement, deformation and strain. Including Material coordinates, Spatial coordinates, motion, deformation gradient, linear approximations, homogeneous deformations, shear, stretch, rotation, rigid rotations, Polar decomposition, multiplicative decomposition, linear strain. Displacement, displacement gradient, 2D strains and rotations, strain-displacement relations, compatibility, principal strains. |
No related attributes |
Quiz 1 Mechanics Test Mechanics Assignment Exam Quiz 2 |

The stress tensor, equilibrium and the equations governing continuum mechanics. Including internal stress, traction, the stress matrix, the stress tensor, Cauchy's Law, principal stress, surface forces, body forces, equations of motion, equations of equilibrium. |
No related attributes |
Quiz 1 Mechanics Test Mechanics Assignment Exam Quiz 2 |

Static elasticity with applications in structural mechanics. Including material models, linear elasticity, linearised kinematics, isotropy, problems in linear elasticity, elastostatics, Navier's equations, plane stress, plane strain, stress function, axisymmetric problems, pressurised cylinders, rotating discs, stress concentrations. |
No related attributes |
Quiz 1 Mechanics Test Mechanics Assignment Exam Quiz 2 |

Fluid Dynamics: The student will be able to derive and manipulate the basic equations of fluid dynamics. The student will understand the meaning of the equations and variables. The students will apply the equations to solve some problems of inviscid and viscous flow including the Stokes and Navier-Stokes equations and the derivation of fundamental solutions. Describe the continuum hypothesis for fluids, explain the difference between an Eulerian and Langrangian description of a fluid flow. Define and explain total and advective acceleration. |
No related attributes |
Fluids Test Fluids Assignment Exam |

The student will be able to derive the flow field for viscous flows in simple situations, such as thin film flow down a slope, or viscous channel\pipe flow. |
No related attributes |
Fluids Test Fluids Assignment Exam |

Calculation of relatively complex irrotational flows, such as that around a circular cylinder, by superpositioning simple irrotational flow solutions, such as Point Sources, Line Vortices, Uniform Flow. Find the surface pressure using the Bernoulli equation. Integrate surface pressure components to evaluate forces. Be able to explain the Magnus Effect and D’Alembert’s Paradox. |
No related attributes |
Fluids Test Fluids Assignment Exam |

Coursework

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Exam rules

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Inclusive learning

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