CODE 66265 2023/2024 5 cfu anno 1 INGEGNERIA CIVILE 10799 (LM-23) - GENOVA ICAR/08 English GENOVA 2° Semester AULAWEB

## 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.

## AIMS AND CONTENT

### AIMS AND LEARNING 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.

### PREREQUISITES

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.

### TEACHING METHODS

Lectures and laboratory sessions using the finite element code ANSYS.

### SYLLABUS/CONTENT

ment 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.

• 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

## TEACHERS AND EXAM BOARD

### Exam Board

ROBERTA MASSABO' (President)

STEFANO VOZZELLA

ILARIA MONETTO (President Substitute)

## LESSONS

### LESSONS START

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

### Class schedule

The timetable for this course is available here: Portale EasyAcademy

## EXAMS

### EXAM DESCRIPTION

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