Teacher's notes available on MOODLE (http://e-l.unifi.it/course/view.php?id=2884)
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Learning Objectives
Knowledge acquired:
The continuum model, Basic equations of mechanics. Statics and dynamics of fluids and solids. Constitutive equations and models. Case studies
Competence acquired:
To understand a mathematical model related to the physics of continuous bodies
Skills acquired (at the end of the course):
To analyse models more suitable to describe particular physical processes.
Prerequisites
Courses to be used as requirements (required and/or recommended)
Linear algebra, vector and tensor spaces, ordinary and partial differential equations at standard level, tensor algebra , spectral theorem, Cayley-Hamilton theorem, polar decomposition theorem, differential operators in Cartesian, cylindrical and spherical coordinates.
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 225
Hours reserved to private study and other individual formative activities: 153
Hours for lectures: 72
Further information
Attendance of lectures, practice and lab:
Not mandatory
Teaching tools:
None
Office hours:
Contact the professor by e-mail for appointments
Contact:
Attendance of lectures, practice and lab:
Not mandatory
Teaching tools: sometimes slides or video projection of didactic movies
Office hours:
Contact the professor by e-mail for appointments
Contact:
Viale Morgagni, 67/a - 50134 Firenze
Phone: 055 2752434
Fax: 055 2751452
E-mail: fabio.rosso@unifi.it
fabio.rosso@math.unifi.it
Other contact:
viale Morgagni 67/a
3296509381
Type of Assessment
Oral examination based on a technical discussion over selected topics of the course with the aim of clarify the level of understanding reached by the student compared with what expected as explained above
Course program
Fundamentals of Continuum Mechanics, kinematics, deformation analysis, small deformations, rigid deformations, motion, current lines and streamlines, local analysis of Eulerian velocity field, transport theorem, dynamics, mass conservation, contact forces, stress analysis (Cauchy theorem), linear momentum equation, angular momentum equation, Euler equation, non-inertial frames, rotating reference frames, Rossby number, constitutive equations, constitutive principles, Piola-Kirchhoff tensor, ideal and Newtonian incompressible fluids, compressible fluids, linear elastic bodies, viscous nonlinear fluids, apparent viscosity, Bingham model, linear viscoelasticity, energy balance equation, acoustic waves, thermodynamics of reversible processes, perfect gases, thermodynamic constraints on Cauchy stress and heat flux, Navier-Stokes equations, fluid equilibrium, Earth atmosphere, barotropic gases, vorticity in ideal fluids, Beltrami equation, Bernoulli theorem, Kelvin circulation theorem, Helmholtz theorems, irrotational flows of an ideal incompressible fluid, potential ideal flows, plane ideal flows, stability theory for viscous fluids, energy stability, variational method for stability, linear stability approach and eigenvalue comparison, linearization principle.
Case studies: seismic waves, the obstacle problem for an elastic membrane, the Bénard problem, lubrication theory, flow in porous media, aerodynamic boundary layer, the Stefan problem, reaction-diffusion problems.