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Scheda Riassuntiva
Anno Accademico 2018/2019
Tipo incarico Dottorato
Insegnamento 053535 - ADVANCED TOPICS IN THE FINITE ELEMENT METHOD FOR STRUCTURAL ANALYSIS
Docente Perego Umberto
Cfu 5.00 Tipo insegnamento Monodisciplinare

Corso di Dottorato Da (compreso) A (escluso) Insegnamento
MI (1384) - INGEGNERIA STRUTTURALE, SISMICA, GEOTECNICA / STRUCTURAL SEISMIC AND GEOTECHNICAL ENGINEERINGAZZZZ053535 - ADVANCED TOPICS IN THE FINITE ELEMENT METHOD FOR STRUCTURAL ANALYSIS

Programma dettagliato e risultati di apprendimento attesi

Well posedness and stability in linear elasticity finite element models.
Recap of finite elements basics.
Introduction to the problem of locking. Incompressible elasticity and volumetric locking. Shear locking.
Mixed formulations (HU-Washizu principle and alternative multi-filed forms).
Reduced and selective integration techniques and equivalence with mixed methods.
Spurious modes (hourglass).

Nonlinear finite element modelling.
An introduction to non-linear FE analyses; iterative (Newton-Raphson) and incremental/iterative techniques.
Example problems with geometrical nonlinearity (but small strains): cables and cable-nets.
Example problems with material nonlinearity: nonlinear elastic bars.
FE elastoplastic analysis; plasticity models in 1D and 3D (von Mises, isotropic hardening); tangent elastoplastic operators; finite-step problem and return mapping algorithm; incremental finite element procedure; examples.

Contact modeling.
Contact problems in continuum mechanics. Normal contact between elastic solids (Hertzian theory). Non-Hertzian contact between elastic solids. Normal contact between inelastic solids. Tangential loading and inelastic contact. Dynamic effects and impact. Energy balance.
Formulation of contact equations for finite elements. Contact interface equations. Friction models. Weak forms: Lagrangian, penalty and augmented Lagrangian formulation for implicit time integration.
Penalty formulation in explicit time integration.
Common difficulties in contact problems. Poorly defined surfaces, adjust initial body position, contact noise, overconstraint.

Finite element modelling of large deformation problems
Nonlinear continuum mechanics: analysis of motion and deformation gradient; Green-Lagrange and rate of deformation tensors; pull-back and push-forward operations; measures of stress through Cauchy, nominal, first and second Piola-Kirchhoff tensors; conservation laws.
Updated and Total Lagrangian approaches governing equations, strong/weak forms. Total Lagrangian approach: finite element formulation. Implicit time integration procedures.

Explicit dynamics finite element analyses.
Explicit dynamics approach to the finite element solution of nonlinear problems. Explicit vs. implicit time integration.
Unconditional vs. conditional stability and time step size. CFL condition.
The central difference method. Accuracy of the central difference method.
Mesh size and mesh smoothing techniques.
Mass lumping. Mass scaling vs. selective mass scaling in explicit dynamics.

Expected skills to be gained.
The main purpose of the course is to provide the students with basic information on these topics, so that they could use advanced finite element commercial codes with an adequate level of competence, taking advantage of the many advanced features that are usually available in these codes.


Note Sulla Modalità di valutazione

The exam will consist of a written test with questions on the subjects presented during the lectures and covered by the  provided material.
The date of the exam will be agreed with the students at the end of the course.


Intervallo di svolgimento dell'attività didattica
Data inizio
Data termine

Calendario testuale dell'attività didattica
  Time Teacher Content
Tuesday,
Nov 13
14:15-16:15 Cremonesi Recap of finite element basics
Thursday,
Nov 15
10:15-12:15
14:15-16:15
Cremonesi Well posedness and stability in linear elasticity finite element models
Tuesday,
Nov 20
11:15-13:15
15:15-17:15
Novati Nonlinear finite element modelling 
Friday,
Nov 23
9:15-12:15 Mariani Finite element modelling of large deformation problems - Part 1
Monday,
Nov 26
14:15-17:15 Mariani Finite element modelling of large deformation problems - Part 2
Tuesday,
Nov 27
10:15-12:15
14:15-16:15
Perego Explicit dynamics finite element analyses.
Friday,
Nov 30
9:15-13:15
14:15-16:15
Ghisi Contact modeling
Introduction to the use of the finite element code Abaqus

Bibliografia
Risorsa bibliografica facoltativaBathe, K.-J., Finite Element Procedures, Editore: Prentice-Hall, Anno edizione: 1996
Risorsa bibliografica facoltativaBelytschko, T. Liu, W.K., Moran, B. and Elkhodary, K., Nonlinear Finite Elements for Continua and Structures, 2nd edition, Editore: Wiley, Anno edizione: 2015
Risorsa bibliografica facoltativaBenson, D.J., Explicit Finite Element Methods for Large Deformation Problems in Solid Mechanics. In Encyclopedia of Computational Mechanics (eds E. Stein, R. de Borst and T. J. Hughes), Editore: Wiley, Anno edizione: 2007
Risorsa bibliografica facoltativaBonnet, M., Frangi, A. and Rey C., The finite Element Method in Solid Mechanics, Editore: McGraw-Hill, Anno edizione: 2014
Risorsa bibliografica facoltativaHughes, T.J.R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Editore: Prentice-Hall, Anno edizione: 1987
Risorsa bibliografica facoltativaJohnson, K.L., Contact Mechanics, Editore: Cambridge University Press, Anno edizione: 1985
Risorsa bibliografica facoltativaKim, M.H., Introduction to Nonlinear Finite Element Analysis, Editore: Springer-Verlag, Anno edizione: 2015
Risorsa bibliografica facoltativaLaursen, T.A., Computational Contact and Impact Mechanics, Editore: Springer-Verlag, Anno edizione: 2003
Risorsa bibliografica facoltativaWriggers, P. and Zavarise, G., Computational Contact Mechanics. In Encyclopedia of Computational Mechanics (eds E. Stein, R. de Borst and T. J. Hughes), Editore: Wiley, Anno edizione: 2004

Mix Forme Didattiche
Tipo Forma Didattica Ore didattiche
lezione
24.0
esercitazione
0.0
laboratorio informatico
2.0
laboratorio sperimentale
0.0
progetto
0.0
laboratorio di progetto
0.0

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese

Note Docente
The course will be taught in collaboration with dr. Massimiliano Cremonesi, prof. Aldo Ghisi, prof. Stafano Mariani and prof. Giorgio Novati.
schedaincarico v. 1.6.5 / 1.6.5
Area Servizi ICT
03/12/2020