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Scheda Riassuntiva
Anno Accademico 2017/2018
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 097725 - MATHEMATICAL AND PHYSICAL MODELING IN ENGINEERING [C.I.]
Docente Ciarletta Pasquale , Vianello Maurizio Stefano
Cfu 10.00 Tipo insegnamento Corso Integrato

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento
Ing Ind - Inf (Mag.)(ord. 270) - BV (478) NUCLEAR ENGINEERING - INGEGNERIA NUCLEARE*AZZZZ097725 - MATHEMATICAL AND PHYSICAL MODELING IN ENGINEERING [C.I.]
Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA*AZZZZ097725 - MATHEMATICAL AND PHYSICAL MODELING IN ENGINEERING [C.I.]
Ing Ind - Inf (Mag.)(ord. 270) - MI (491) MATERIALS ENGINEERING AND NANOTECHNOLOGY - INGEGNERIA DEI MATERIALI E DELLE NANOTECNOLOGIE*AZZZZ097725 - MATHEMATICAL AND PHYSICAL MODELING IN ENGINEERING [C.I.]

Programma dettagliato e risultati di apprendimento attesi

 

Asymptotic Analysis. Classification of singular points in ordinary differential equations. Regular singular points: Fuchs-Frobenius theory. Irregular singular points: dominant balance method. Introduction to regular and singular perturbation theory. Asymptotic matching.

Asymptotic regimes. Dimensionless Analysis: Buckingham theorem. Examples of dimensionless number in rheology. Boundary layer theory. Matching conditions: Van Dyke rule and intermediate variable method. Applications of Erdelyi theorem. WKB approximation.

Bifurcations and hydrodynamic instability. Fixed points and their linear stability analysis. Geometrical theory of bifurcation points. Multiple scale expansion and its application to nonlinear oscillators. Introduction to hydrodycamic instability problems.

Elastic instability. Basic notions of variation calculus. Elastic functionals and Euler-Lagrange equations. Applications of weakly nonlinear analysis in linear elastic problems. The methods of incremental elastic deformation in nonlinear elasticity. Derivation of incremental equations. Global and local stability. Application to the hyperelastic half-space.

Reminder about Continuum Mechanics: Cauchy stress tensor and balance equations.

Finite Elasticity: Piola transformation for vector and tensor fields. Piola stress tensor. Motion equations in a material form. Finite elasticity. Frame-indifference and isotropy. Representation theorm for the constitutive law for isotropic bodies. Strain energy. Stress power. Internal constraints. Strain energies of Blatz-Ko, Mooney-Rivlin, Ogden, Neo-Hookean, Gent. Linearization of finite elasticity. Elasticity tensor. Isotropy. Navier equations. Plane waves. General coordinates in continuum mechanics.

Thermoelasticity: Free energy and constitutive relations. Linear thermoelasticity and Fourier's law. Mechanics of surfaces. Surface vector fields. Covariant derivation. First and second fundamental form. Curvatures. Surface stresses.

 


Note Sulla Modalità di valutazione

A written exam, followed by an oral part.

Information provided by the Teachers at the beginning of the Course.


Bibliografia
Risorsa bibliografica facoltativaTommaso Ruggeri, Introduzione alla termomeccanica dei continui, Editore: Monduzzi Editore, Anno edizione: 2007
Risorsa bibliografica facoltativaC.M. Bender and S.A. Orszag, Advanced mathematical methods for scientists and engineers
Risorsa bibliografica facoltativaA. Erdelyi, Asymptotic expansions
Risorsa bibliografica facoltativaPeter Chadwick, Continuum Mechanics. Concise Theory and Problems, Editore: Dover, Anno edizione: 1976
Risorsa bibliografica facoltativaLecture Notes provided by Teachers
Note:

The teachers might place lecture notes in the Beep area of the Course.


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Mix Forme Didattiche
Tipo Forma Didattica Ore didattiche
lezione
60.0
esercitazione
40.0
laboratorio informatico
0.0
laboratorio sperimentale
0.0
progetto
0.0
laboratorio di progetto
0.0

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schedaincarico v. 1.6.9 / 1.6.9
Area Servizi ICT
29/01/2022