PRESENTAZIONE

Il modulo affronta lo studio della risposta nonlineare dei solidi e delle strutture, con particolare attenzione ai problemi di nonlinearità geometrica e materiale. Lo studio è affrontato con tecniche analitiche e numeriche mediante il metodo degli elementi finiti.  Il corso prevede varie esercitazioni in aula informatica col codice agli elementi finiti ANSYS. Il corso è insegnato in lingua italiana e in lingua inglese.

OBIETTIVI E CONTENUTI

OBIETTIVI FORMATIVI

The course provides fundamental knowledge and analytical and numerical techniques (Finite Element Method) for the evaluation of the post-elastic regime and loading capacity of structures while accounting for material and geometrical nonlinearities. Upon completion of the course participants will be able to analyze and simulate using the FE code ANSYS problems such as: large displacement collapse and buckling of structures; progressive plasticity and plastic collapse of structures; fracture of brittle materials.

OBIETTIVI FORMATIVI (DETTAGLIO) E RISULTATI DI APPRENDIMENTO

Overview: The course deals with the nonlinear response of solids and structures with focus on problems characterized by geometric and material nonlinearities. The problems are solved using analytical and numerical approaches through the finite element method. Numerical applications are presented using the finite element code ANSYS.

Outcomes: Basic knowledge to evaluate the ultimate load-bearing capacity of solids and structures using nonlinear analyses. Analytical and numerical approaches to treat material and geometrical nonlinearities.

PREREQUISITI

Basic knowledge of structural mechanics (beams, frames, trusses, plates, membranes, shells), plane problems (plane stress and plane strain), 3D elasticity; stability of beams; elastoplasticity (1D); incremental and limit analysis of beams and frames and plastic collapse.

MODALITA' DIDATTICHE

Lectures and laboratory sessions using the finite element code ANSYS.

(Lezioni in aula ed esercitazioni in aula informatica con utilizzo del codice agli elementi finiti ANSYS)

PROGRAMMA/CONTENUTO

The finite element method (brush up): the direct stiffness method (bar and MOM element and trusses), the variational formulation (bar element), plane stress and isoparametric elements and shape functions; finite element modeling.

Stability and Buckling: basic concepts and response diagrams; stability of systems with n degrees of freedom; stability of trusses and frames; Von Mises arch and snapping instability. Applications with ANSYS.   

The elasto-brittle solid (introduction to fracture mechanics): stress concentration and intensification; fracture criteria; ductile-brittle transition in the structural collapse. Applications with ANSYS.  

The elasto-plastic solid: incremental analysis and limit analysis. Applications with ANSYS

The Nonlinear Finite Element Method: the nonlinear bar element; finite element solution of nonlinear problems: geometric nonlinearities; linearized buckling; post-buckling; plasticity; constraints and contact; continua with cracks. The finite element code ANSYS, introduction and applications. 

(Richiami sul metodo degli elementi finiti: metodo diretto e formulazione variazionale degli elementi asta e isoparametrico.  La stabilità dell’equilibrio: concetti di base e diagrammi di risposta; stabilità di sistemi elastici discreti a più gradi di libertà; stabilità di sistemi di aste e travi; l’instabilità  non euleriana, l’arco ribassato. Il solido elasto-fragile e un'introduzione alla meccanica della frattura: concentrazione ed intensificazione delle tensioni; criteri di frattura; transizioni duttile-fragile nel collasso strutturale. Il continuo elasto-plastico: analisi incrementale e calcolo a rottura. Il metodo agli elementi finiti non lineare: l’asta in grandi spostamenti; analisi non lineare,  nonlinearità geometriche e del materiale; analisi di buckling linearizzato e post-critico; plasticità; analisi di continui con difetti. Applicazioni con codice ANSYS.)

TESTI/BIBLIOGRAFIA

• Felippa C.A, Introduction to Finite Element Methods, University of Colorado at Boulder, sito web prof. Felippa.
• Felippa C.A., Nonlinear Finite Element Methods, University of Colorado at Boulder, sito web prof. Felippa.
• L. Nunziante, L. Gambarotta, A. Tralli, Scienza delle costruzioni, McGraw-Hill.
• Carpinteri A., Scienza delle Costruzioni 1,2, Pitagora Editrice, Bologna.
• L. Corradi dell'Acqua, Meccanica delle strutture vol. 3, McGraw-Hill.
• Z.P. Bazant, L. Cedolin, Stability of structures, Oxford Press.
• M. Jirasek, Z. P.Bazant, Inelastic analysis of structures, Wiley.
• Carpinteri A., Meccanica della Frattura, Pitagora

DOCENTI E COMMISSIONI

Commissione d'esame

ROBERTA MASSABO' (Presidente)

ANDREA BACIGALUPO

ILARIA MONETTO (Presidente Supplente)

LEZIONI

INIZIO LEZIONI

https://corsi.unige.it/10799/p/studenti-orario

Orari delle lezioni

L'orario di questo insegnamento è consultabile all'indirizzo: Portale EasyAcademy

ESAMI

MODALITA' D'ESAME

The exam consists in :

a) a final oral exam (three-four questions, solution of simple problems and applications);

b) a written report on a take-home lab exam (solution of a nonlinear problem using the finite element code ANSYS). The report will be discussed during the oral exam.

The final oral exam may be substituted by one mid-term oral exam on the first part of the course (in the semester break) and a final orale exam on the second part of the course. he students must complete the report by September 2024 and the final exam by February 15, 2025.

The take-home lab exams may have different levels of complexity:

Lab exam B: solution of a basic problem, similar to those solved in class, presented in the tutorials on the course website or in ANSYS verification manual

Lab exam H: solution of a problem which requires the use of different techniques or different ANSYS commands or some analytical derivations for verification. This second option is reserved to students who are interested in deepening their knowledge on the solution of nonlinear problems, on the use of FEM codes or in tackling an applied problem

MODALITA' DI ACCERTAMENTO

Final grade composed of:

oral exam (50%) and take-home Lab exam (50%) 

Calendario appelli