Mechanics of Continua

Abstract

Mechanics of Elastic Media and Hydrodynamics: Strain and stress tensor, field equations, equilibrium, waves and oscillations. Dynamics of fluids, Euler and Navier-Stokes equations, Bernoulli equation, vortices, waves, potential flows; viscous fluids, Reynolds number, Stokes drag, boundary layers, instabilities, turbulence.

Objective

Knowledge of the essential concepts and methods of theoretical mechanics of elastic media and hydrodynamics. Consolidation through examples and solution of exercise problems.

Content

Introduction to the concepts and methods of theoretical mechanics of elastic media and hyrdodynamics: relation between strain and stress tensor, balance equations, field equations of elastic media, elastostatics, waves and oscillations, lattice dislocations and plastic deformation. Dynamics of fluida, Euler equations of ideal fluida, Navier-Stokes equations of real fluids, Bernoulli equations, vortex theorems of Thomson and Helmholtz, dynamics of vortices, oscillation and waves in fluida, surface waves, two-dimensional potential flow, circulation, Magnus force, theorems of Kutta and Zhukovski, flow around profiles (cylinder, platte, aerofoil), Kutta condition. Incompressible viscos fluida, Reynolds number, Hagen-Poisseuille flow, Stokes law, Prandtl's boundary layer, Couette flow and Taylor instability. Turbulence, instability of laminary flows, Reynolds number, development of turbulence, Kolmogorov scaling.

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