Università di Pavia - Offerta formativa

CONTINUUM MECHANICS

Anno immatricolazione

2019/2020

Anno offerta

2019/2020

Normativa

DM270

SSD

ICAR/01 (IDRAULICA)

Dipartimento

DIPARTIMENTO DI INGEGNERIA CIVILE E ARCHITETTURA

Corso di studio

CIVIL ENGINEERING FOR MITIGATION OF RISK FROM NATURAL HAZARDS

Curriculum

Hydrogeological risk assessment and mitigation

Anno di corso

1°

Periodo didattico

Primo Semestre (23/09/2019 - 16/10/2019)

Crediti

6

Ore

51 ore di attività frontale

Lingua insegnamento

English

Tipo esame

ORALE

Docente

MANENTI SAURO (titolare) - 6 CFU

Prerequisiti

Basics of vector, matrix and tensor algebra.

Mathematical foundations.

Integral theorems (Stokes and Gauss).

Mathematical foundations.

Integral theorems (Stokes and Gauss).

Obiettivi formativi

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.

The students will be able to carry out computer analysis of basic engineering problems related to fluid mechanics.

Programma e contenuti

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.

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.

Metodi didattici

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Testi di riferimento

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.

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.

Modalità verifica apprendimento

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

Altre informazioni

Lecture notes can be downloaded from the course page on the platform KIRO (https://elearning2.unipv.it/ingegneria/)