Introduction to Continuum Mechanics (MAGIC090)
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This course is part of the MAGIC core.
This course covers the mathematics and physics underlying continuum mechanics. Emphasis will be on elsasticity and fluid dynamics. The course begins with an in depth review and formulation of vectors and tensors in arbitrary coordinate systems. We then discuss Eulerian (fixed coordinate) and Lagrangian (moving coordinate) descriptions of motion. The lectures will then cover basic principles of elasticity, including stress and strain tensors, Hooke's law, and the Poisson ratio. Load paths and averaging processes for heterogeneous materials will also be considered. The course will move to fluid flows, covering Navier-Stokes equations, and some examples of non-Newtonian fluids.
Autumn 2017 (Monday, October 9 to Friday, December 15)
Vector Calculus, Linear Algebra, Newtonian Dynamics
1. Vectors and tensors. Coordinate transformations 2. Metrics. Derivatives of vectors and tensors 3. Deformation: Eulerian and Lagrangian descriptions of motion 4. Stress and strain tensors 5. Linear equilibrium elasticity theory 6. Fluid flow 7. Non-Newtonian fluids
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