The course aims to deepen the concepts and tools for interpreting and understanding the mechanical behavior of structures. As for the contents, these are divided into four parts: The first theme concerns a review of the salient elements of the theory of elasticity. In the second part the theory of elasticity is extended to 2D problems, nonlinear materials and fatigue problems. The third part explores the dependence of the mechanical behavior of materials in the presence of thermal effects. The fourth part deals with some application examples. The approach is therefore oriented to provide an organic view of the mechanical and thermomechanical behavior of the materials, deepening then the particularizations in its various application fields.

The course is specifically oriented to the development of the ability to study structural problems of a complex nature and with possible thermomechanical coupling. The student will therefore be able to deal with both simple and complex problems in the right perspective. The fundamental notions on the mechanical and thermal behavior of the structures and on the corresponding interpretative models will be acquired. These concepts will then be used to model the structural behavior and evaluate its safety. The result is achieved by developing the ability to frame a complex problem, break it down into simple sub-problems and use, on a case-by-case basis, the appropriate mathematical tools that have been provided.

Mathematical concepts and methods are widely used in teaching. Therefore, knowledge of mathematical analysis, matrix calculation and linear algebra is required. The knowledge of the differential geometry of curves and surfaces is also useful. Furthermore, the contents of the Physics and Fundamentals of Structural Mechanics, or similar courses are preparatory.

PART 1 - COURSE INTRODUCTION AND REVISITING OF THE ELASTIC PROBLEM Introduction and preliminary notions: • Introduction to the course: presentation, bibliographical references, rules and methods of examination. Revisitingof the elastic problem: • Deformations, stresses, elasticity law. • Elasticity theorems, elastic constants. Strength of materials • Rankine, Tresca, Mohr-Coulomb and Von Mises criterions. PART 2 - EXTENSIONS OF ELASTIC PROBLEM 2D Elastic problems • Axisymmetric plates. Axisymmetric shells. Nonlinear materials • Tensile testing of brittle and ductile materials. • Failure modeling for brittle and ductile materials. • Static safety factor. • Creep, fatigue notch factor, stress concentration factor. Fatigue • Fatigue strength - Phenomenology and characteristic parameters, Wöhler curve, fatigue limit. • Haigh diagram and S-N diagrams. • Effect of load type, size, surface finishing and presence of notch effects. • Safety factor in fatigue. • Stress in presence of cycles of variable amplitude, multiaxial fatigue. PART 3 - THERMOMECHANICS • Revisiting of basic thermomechanics and FEM discretization. • Effect of temperature on mechanical properties of materials. • Thermomechanical coupling. PART 4 - APPLICATIONS & CODES • Vessels subject to pressure. • Edge effects.

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Lessons will take place in the classroom. Some exercises will take place in the classroom, some will be assigned as homeworks.

A. Carpinteri, Scienza delle costruzioni, Vol. 1, 2a ed., Pitagora Editrice, Bologna, 1995 A. Carpinteri, Scienza delle costruzioni, Vol. 2, 2a ed., Pitagora Editrice, Bologna, 1993 L. Corradi Dell’Acqua, Meccanica delle Strutture, Vol. 3, McGraw-Hill, New York, 2003 F.P. Beer, E. Russel Johnston Jr., J.T. DeWolf, D.F. Mazurek, Mechanics of Materials, 7th ed., Mc Graw Hill, 2015

Slides; Dispense; Esercizi; Esercizi risolti;

Modalità di esame: Prova scritta (in aula); Prova orale obbligatoria; Elaborato scritto individuale;

Exam: Written test; Compulsory oral exam; Individual essay;

... The exam aims to evaluate the level of knowledge of the topics of the program, and the ability to use theoretical concepts for the solution of application test cases. The exam consists of a written test and, upon passing this, a subsequent oral test. Access to the oral test is subject to the positive evaluation of the homework reports. The written test (lasting 2 hours and 20 minutes) consists of three exercises, specifically aimed at verifying the achieved knowledge in both the theoretical and application fields. The test is passed with an overall score of at least 18, and the achievement of a pre-established minimum score for each exercise. During the writing it is not possible to consult texts, notes, and communication tools of any kind. The results of the written test are communicated on the web page of the course, together with the date on which the students can check the corrections and ask for any clarifications. The oral exam is aimed at verifying the level of learning of theoretical concepts of the whole course, and typically consists of 3 questions. To access the oral exam, the reports of the homeworks are required (at least 5 days in advance). The reports are examined by the teacher, who can ask for any clarifications during the oral exam. In the case of serious errors, prior to the oral exam, a resubmission of the reports may be required. In the context of the oral test, in case of doubtful cases, clarifications may also be requested regarding the written test. The final evaluation is proportional to the correctness, completeness and relative complexity of the written test (which accounts for 45%), the homework reports (which accounts for 15%) and the oral test (which accounts for 40%) ). The mark with honors is assigned based on an excellent assessment achieved in the written test, and the ability to critically analyze the results proven by the homeworks and the oral test. Onsite EXAM MODE:: Homework reports provided some days before the written test, written test in the classroom, oral test in the classroom.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.