# NON LINEAR ANALYSIS OF STRUCTURES

iten
Code
66265
2021/2022
CREDITS
5 credits during the 1st year of 10799 CIVIL ENGINEERING (LM-23) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
ICAR/08
LANGUAGE
English
TEACHING LOCATION
GENOVA (CIVIL ENGINEERING)
semester
2° Semester
Teaching materials

## 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.

TEACHING METHODS

Lectures and laboratory sessions using the finite element code ANSYS.

SYLLABUS/CONTENT

The finite element method: introduction; brush up on 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; 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.

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

• 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

Office hours: Office hours during the semester will be defined in the first week of classes. Office hours outside the semester can be requested through email: roberta.massabo@unige.it

Exam Board

ROBERTA MASSABO' (President)

STEFANO VOZZELLA

ILARIA MONETTO (President Substitute)

## LESSONS

TEACHING METHODS

Lectures and laboratory sessions using the finite element code ANSYS.

Class schedule

All class schedules are posted on the EasyAcademy portal.

## 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 final oral exam may be substituted by two written mid-term quizzes.

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

ASSESSMENT METHODS