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

LEARNING OUTCOMES

Basic knowledge to evaluate the loading capacity of structures through nonlinear analyses with special reference to problems with geometric and material nonlinearities.

TEACHING METHODS

Lectures and laboratory sessions using the finite element code ANSYS.

SYLLABUS/CONTENT

The finite element method: finite element modeling, variational formulation (bar and isoparametric elements); the nonlinear bar element; finite element solution of nonlinear problems; linearized buckling; continua with cracks. The finite element code ANSYS, introduction and applications.  

Geometric instability: post-critical response of systems with n degrees of freedom; stability of frames; non eulerian stability. Applications wih ANSYS.   

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

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

RECOMMENDED READING/BIBLIOGRAPHY

• 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

SIMONE CAFFE' (President)

ROBERTA MASSABO' (President)

HOSSEIN DARBAN

ILARIA MONETTO

LESSONS

LESSONS START

Polytechnic school calender

EXAMS

EXAM DESCRIPTION

The exam consists in one of the following:

(a) oral discussion on the topics of the course. Three-four questions, solution of simple problems and applications;
(b) written report on the solution of a problem using ANSYS (single student); oral discussion on the same topic and on the finite element method;
c) written report on the solution of a problem solved with ANSYS (single student or group of students) and oral discussion on all topics of the course. 
 

The problem to be solved using ANSYS will be decided with the student and can have different levels of complexity depending on the interest.

Exam schedule