CONTINUUM MECHANICS
Stampa
Enrollment year
2019/2020
Academic year
2019/2020
Regulations
DM270
Academic discipline
ICAR/01 (HYDRAULICS)
Department
DEPARTMENT OF CIVIL ENGINEERING AND ARCHITECTURE
Course
CIVIL ENGINEERING FOR MITIGATION OF RISK FROM NATURAL HAZARDS
Curriculum
Hydrogeological risk assessment and mitigation
Year of study
Period
1st semester (23/09/2019 - 16/10/2019)
ECTS
6
Lesson hours
51 lesson hours
Language
English
Activity type
ORAL TEST
Teacher
MANENTI SAURO (titolare) - 6 ECTS
Prerequisites
Basics of vector, matrix and tensor algebra.
Mathematical foundations.
Integral theorems (Stokes and Gauss).
Learning outcomes
The course will provide the fundamental theoretical concepts and mathematical tools for the analysis and modelling of relevant problems in the hydraulic engineering field.
The students will be able to carry out computer analysis of basic engineering problems related to fluid mechanics.
Course contents
Review of mathematical foundations: vector and tensor algebra; coordinate systems; Stokes theorem and Gauss theorem.

Analysis of stress: the continuum concept; Cauchy stress principle; stress tensor; principal stresses; Mohr circles; deviator and spherical stress tensors.

Deformation and strain: Lagrangian and Eulerian description; small deformation theory; strain tensor; principal strains; spherical and deviator strain tensors; plane strain; compatibility equations; velocity gradient tensor; rate of deformation tensor; vorticity tensor.

Fundamental laws of continuum mechanics: mass conservation - continuity equation; Reynolds transport theorem; linear momentum conservation; angular momentum conservation; energy conservation.

Constitutive equations: generalized Hooke’s law. Newtonian fluid. Navier-Stokes equations.

Special cases: perfect fluid; Euler and Bernoulli equations. Laplace equation. Kelvin theorem.

Viscosity and applications to engineering problems: viscosity of Newtonian fluids; Newton's law of viscosity. Flow curve. Common non-Newtonian rheological models. Experimental measurement of fluid viscosity.
Teaching methods
=
Reccomended or required readings
R. Aris "Vectors, tensors, and the basic equations of fluid mechanics" Dover pub.

W. Prager "Introduction to mechanics of continua" Ginn and Co. 1961

P.C. Chou & N.J. Pagano "Elasticity, tensor, dyadic, and engineering approaches"
Dover pub.

Wilkinson W.L., Non-Newtonian fluids. 1960 Pergamon Press.

Liu, G-R. and Liu, M.B. Smoothed Particle Hydrodynamics: a meshfree particle method. World Scientic, 2003.
Assessment methods
The final examination will consist of an oral discussion, with the possibility for each student to carry out in-depth analysis about a peculiar topic within the course contents
Further information
Lecture notes can be downloaded from the course page on the platform KIRO (https://elearning2.unipv.it/ingegneria/)
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