ID:
508196
Durata (ore):
48
CFU:
6
SSD:
IDRAULICA
Anno:
2024
Dati Generali
Periodo di attività
Primo Semestre (23/09/2024 - 15/10/2024)
Syllabus
Obiettivi Formativi
The course will provide the fundamental theoretical concepts and mathematical tools for the formalization, analysis and solution of relevant problems of material continuum mechanics. They include: the fundamental mathematical relations for the analysis of stress and deformation at material point; the mathematical formulation of the conservation principles leading to the governing equations of material continua; the linear constitutive equations for the analysis of solid and fluid.
These topics, whose understanding is strengthened through the computer analysis and solution of applied engineering problems of practical interest, will provide the basis for the analysis and mitigation of natural hazards, such as flooding and landslide induced risk.
These topics, whose understanding is strengthened through the computer analysis and solution of applied engineering problems of practical interest, will provide the basis for the analysis and mitigation of natural hazards, such as flooding and landslide induced risk.
Prerequisiti
Student must have a good command of the basic concepts of integral and differential calculus for real functions. Also, the student should know the fundamentals of mechanical physics for engineers.
Metodi didattici
Lectures will be taught in English and include theoretical classes on: basics of vector, tensor and matrix algebra; fundamental concepts and governing laws of Continuum Mechanics for the dynamic analysis of solid and fluid.
Exercises will be carried out on fundamental aspects of Continuum Mechanics, as well as on the analytical/numerical solution of representative problems in the field of applied engineering. Support material will be made available, including lecture notes and Matlab scripts for exercises.
Exercises will be carried out on fundamental aspects of Continuum Mechanics, as well as on the analytical/numerical solution of representative problems in the field of applied engineering. Support material will be made available, including lecture notes and Matlab scripts for exercises.
Verifica Apprendimento
The final exam consists of an oral discussion on the theoretical topics and exercises developed within the course.
The student must demonstrate acquired capacity to: illustrate the problem (e.g., basic assumptions and input data); describe its mathematical formulation (e.g., system of partial differential equations and the physical meaning of their terms); illustrate the solution method (e.g., analytical or approximate-numerical); perform critical analysis of results (e.g., physical consistency, theoretical coherence); explore the influence on results induced by varying input parameters.
The student must demonstrate acquired capacity to: illustrate the problem (e.g., basic assumptions and input data); describe its mathematical formulation (e.g., system of partial differential equations and the physical meaning of their terms); illustrate the solution method (e.g., analytical or approximate-numerical); perform critical analysis of results (e.g., physical consistency, theoretical coherence); explore the influence on results induced by varying input parameters.
Testi
1) Aris R. "Vectors, tensors, and the basic equations of fluid mechanics" 1990 Dover pub ISBN-10: 0486661105.
2) Chou P.C. & Pagano N.J. "Elasticity, tensor, dyadic, and engineering approaches" 1992 Dover pub ISBN-13: 978-0486669588.
3) Mase G.E. “Theory and problems of Continuum Mechanics" Schaum’s Outline Series – McGraw Hill 1970.
4) Prager W. "Introduction to Mechanics of Continua" Ginn and Co. 1961.
2) Chou P.C. & Pagano N.J. "Elasticity, tensor, dyadic, and engineering approaches" 1992 Dover pub ISBN-13: 978-0486669588.
3) Mase G.E. “Theory and problems of Continuum Mechanics" Schaum’s Outline Series – McGraw Hill 1970.
4) Prager W. "Introduction to Mechanics of Continua" Ginn and Co. 1961.
Contenuti
Fundamental concepts and applications of vector, tensor and matrix algebra; coordinate systems; integral theorems of Stokes and Gauss. The continuum postulate.
Analysis of stress: Cauchy stress principle; normal and shear stress components; static equilibrium of finite continuum, static equilibrium equation and symmetry of stress tensor; deviator and spherical stress tensors. Mohr’s representation of the state of stress at a material point. Plane stress and incomplete Mohr's representation.
Local deformation and strain: material and spatial coordinate systems; displacement gradient tensor, small deformation theory, linear strain and rotation tensors; Saint-Venant compatibility equations; Lagrangian and Eulerian description of flow, material derivative; velocity gradient tensor, rate of deformation tensor and vorticity tensor.
Reynolds transport theorem. Fundamental laws of Continuum Mechanics: mass conservation principle, continuity equation; linear momentum conservation principle, Cauchy equation of motion; angular momentum conservation principle; mechanical energy conservation principle; first principle of Thermodynamics, energy equation.
Constitutive equations: generalized Hooke’s law for the linear elastic solid continuum; Newtonian fluid, Stokes assumption.
Navier-Stokes equation; Euler and Bernoulli equations; Laplace equation. Kelvin theorem.
Viscosity of Newtonian fluids: basic concepts; flow curve. Short description of non-Newtonian rheological models: apparent viscosity, shear thinning and shear thickening fluids.
Applications to relevant problems in the field of applied engineering: finite difference solution of 1D heat equation for the analysis of thermal induced stresses in massive concrete; analytical and numerical modelling of annular viscous fluid damper as a passive energy dissipation system.
Analysis of stress: Cauchy stress principle; normal and shear stress components; static equilibrium of finite continuum, static equilibrium equation and symmetry of stress tensor; deviator and spherical stress tensors. Mohr’s representation of the state of stress at a material point. Plane stress and incomplete Mohr's representation.
Local deformation and strain: material and spatial coordinate systems; displacement gradient tensor, small deformation theory, linear strain and rotation tensors; Saint-Venant compatibility equations; Lagrangian and Eulerian description of flow, material derivative; velocity gradient tensor, rate of deformation tensor and vorticity tensor.
Reynolds transport theorem. Fundamental laws of Continuum Mechanics: mass conservation principle, continuity equation; linear momentum conservation principle, Cauchy equation of motion; angular momentum conservation principle; mechanical energy conservation principle; first principle of Thermodynamics, energy equation.
Constitutive equations: generalized Hooke’s law for the linear elastic solid continuum; Newtonian fluid, Stokes assumption.
Navier-Stokes equation; Euler and Bernoulli equations; Laplace equation. Kelvin theorem.
Viscosity of Newtonian fluids: basic concepts; flow curve. Short description of non-Newtonian rheological models: apparent viscosity, shear thinning and shear thickening fluids.
Applications to relevant problems in the field of applied engineering: finite difference solution of 1D heat equation for the analysis of thermal induced stresses in massive concrete; analytical and numerical modelling of annular viscous fluid damper as a passive energy dissipation system.
Lingua Insegnamento
Inglese
Altre informazioni
Lecture notes can be downloaded from the course page on the platform KIRO
https://elearning.unipv.it
https://elearning.unipv.it
Corsi
Corsi
CIVIL ENGINEERING FOR MITIGATION OF RISK FROM NATURAL HAZARDS
Laurea Magistrale
2 anni
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