- Derive the stress and displacement formulations of elasticity theory for linear isotropic elastic materials, and explain the relation between the various elastic moduli.
- Apply various solution strategies (e.g. based on Navier equations, Airy stress function, superposition) to solve a broad class of static and wave phenomena in linear elasticity, more specifically to find stress and displacement distributions.
- Perform variational analysis to resolve the deformation of beams and plates, and use energetic arguments to assess their mechanical stability.
- Read and understand research articles that involve interaction between fluids and deformable bodies, and place the work in the context of theoretical frameworks.
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Many fluid flows exhibit interactions with deformable, elastic boundaries. Examples range from flexing of airplane wings to wetting of soft contact lenses by a tear film. The objective of this course is to provide an introduction to the basics principles of elasticity theory, viewed from a fluid mechanical perspective. We first derive the Navier equations and various solution strategies to classical problems in elasticity, such as Hertz contacts, cracks and surface waves. We then develop a variational formalism to discuss beam mechanics and buckling, and discuss several elastic instabilities. After these basics, we address a selected set of contemporary problems bordering fluid physics and elasticity
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