First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
MATHEMATICAL ENGINEERING
Course unit
CONTINUUM MECHANICS (MOD. A)
INP5070522, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
MATHEMATICAL ENGINEERING (Ord. 2017)
IN2191, Degree course structure A.Y. 2017/18, A.Y. 2017/18
N0
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Degree course track MATHEMATICAL MODELLING FOR ENGINEERING AND SCIENCE [001PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination CONTINUUM MECHANICS (MOD. A)
Department of reference Department of Civil, Environmental and Architectural Engineering
Mandatory attendance No
Language of instruction English
Branch PADOVA

Lecturers
Teacher in charge FRANCO CARDIN MAT/07

Integrated course for this unit
Course unit code Course unit name Teacher in charge
INP5070520 MATHEMATICAL PHYSICS (C.I.) FRANCO CARDIN

Mutuating
Course unit code Course unit name Teacher in charge Degree course code
SC01111314 PHYSICAL-MATHEMATICAL MODELS FRANCO CARDIN SC1159

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/07 Mathematical Physics 6.0

Mode of delivery (when and how)
Period Annual
Year 1st Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Practice 3.0 24 51.0 No turn
Lecture 3.0 24 51.0 No turn

Calendar
Start of activities 02/10/2017
End of activities 15/06/2018

Syllabus

Common characteristics of the Integrated Course unit

Prerequisites: None
Target skills and knowledge: Objective
Introduce the students to mathematical tools in continuum mechanics and dynamical systems.
Outcomes
A student who has met the objectives of the course will have a basic knowledge of :
• advanced topics in the mathematical description of continuous mechanics
• fundamentals of ODEs and dynamical systems
Examination methods: Final examination based on: Written and oral examination.
Assessment criteria: Critical knowledge of the course topics. Ability to present the studied material. Discussion of the student project.

Specific characteristics of the Module

Course unit contents: 1. Kinematics of Continuous systems, spatial and material representation.
2. Mass conservation principle. Balance and Conservation laws
3. Cauchy tetrahedron theorem.
4. Principle of virtual works in continuum mechanics. Balance law and the first
cardinal equation.
5. Material description of the stress tensor.Work-Energy Theorem. Constitutive
equations and the principle of material indifference.
6. Ideal elastic fluids. Navier-Stokes, Vorticity.
7. Hagen-Poiseuille flow, plane motion of Navier-Stokes fluids, Bernoulli Theorem.
8. Elementary Meteorology: Cyclones and Anticyclones.
9. Variational formulation of classical field theories: hyper-elasticity and linear
elasticity.
10. Principles of thermodynamics. Legendre transformation and thermodynamic
potentials. First principle of thermodynamics for continuum systems. Balance
laws and the first principle. The second principle in the Clausius-Duhem
formulation. Balance laws and the second principle. Theorem of Clausius-
Duhem. Thermoelastic materials.
11. Wave propagation. The method of characteristics: linear and quasi-linear
theories. Singularities. Nonlinear theory and the Hamilton-Jacobi equation.
Wave propagation in systems of conservation laws. Weak discontinuities,
Hugoniot-Hadamard. Sound speed. High frequency asymptotic waves. Shock
waves. Rankine-Hugoniot.
12. Fourier series and applications.
Planned learning activities and teaching methods: lectures and tutorials
Additional notes about suggested reading: See the book:
F. Cardin & M. Favretti, Modelli Fisico Matematici, CLEUP 2014 (2^ edizione)
Textbooks (and optional supplementary readings)
  • F. Cardin & M. Favretti, Modelli Fisico Matematici. --: CLEUP, 2014. (2^ edizione) Cerca nel catalogo