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 aims to deepen the concepts and tools to interpret and understand the mechanical and the thermal behavior of structures, with a particular focus on the modern computational aspects. In such a context the course is oriented to show how the Finite Element Method works, its limits and all the related limits.
As for the contents, these are divided into four parts:
The first part offers a brief review of the main topics of the theory of elasticity and an indepth study of the methods of solving structural problems using a matrix method. This part of the course constitutes a simple and nice introduction to the Finite Element Method (FEM).
In the second part, the theory of elasticity is extended to 2D and 3D problems, with attention devoted both to closedform solutions and to the classic numerical formulations of the FEM method; to nonlinear materials; time dependent problems and fatigue problems.
In the third part, the study of the thermal effects and the related thermomechanical coupling is explored
In the fourth part some application examples are presented.
The approach is therefore oriented to provide an organic view of the mechanical and thermomechanical behavior of the materials, with attention specifically dedicated both to the solutions in closedform, and to the classic numerical formulations of the FEM method, deepening the specific aspects 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 subproblems and use, on a casebycase basis, the appropriate mathematical tools that have been provided.
The course is specifically oriented to the development of the ability to study complex structural problems, with possible thermomechanical coupling. The student will, therefore, be able to face both simple and complex problems in the right perspective.
The fundamental notions on the mechanical and thermal behavior of structures and on the corresponding interpretative models will be acquired. These concepts will then be used to model structural behavior and evaluate safety.
The result is achieved by developing the ability to frame a complex problem, break it down into simple subproblems and use, on a casebycase 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.
The course constitutes an extension to various levels of the basic knowledge related to the Mechanics of Solids, acquired in the context of courses in Mechanics of Materials / Structural Mechanics, or similar ones.
In teaching, extensive use is made of mathematical concepts and methods. Therefore, the knowledge of the topics of the courses of Mathematics (study of functions and calculation of derivatives and integrals, matrix calculation and eigenvalue / eigenvector problems), Geometry (basic concepts of analytical geometry) and Physics (basic concepts of kinematics and statics of the rigid body) is required.
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, MohrCoulomb 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 SN 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.
PART 1  INTRODUCTION TO THE COURSE AND REVIEW OF THE ELASTIC PROBLEM
Introduction and preliminary notions:
Introduction to the course: presentation, bibliographical references, rules, and methods of examination.
Review of the elastic problem
Deformations, stresses, elastic stressstrain relation; yielding criterions of Tresca, and Von Mises; solution of hyperstatic problems with the forces method.
PART 2  EXTENSIONS OF THE ELASTIC PROBLEM
Elastic 1D problems
Axial stiffness of a structural element; bending and shear stiffnesses; the matrix method of plane frames. Similarities with the FEM formulation of the Beam element.
Elastic 2D problems
Plane states of stress and strain: formulation in Cartesian and polar coordinates: closedform solutions and FEM formulation/review. Plates and shells: formulation in Cartesian and polar coordinates: closed solutions and FEM formulation/review. Modeling of pressure vessels.
3D elastic problems
Formulation/review of FEM modeling.
Nonlinearity of materials
Tensile tests and numerical modeling of fragile and ductile materials. Iterative methods for the solution of nonlinear problems and timedependent problems.
Fatigue
Fatigue resistance  Phenomenology and characteristic parameters, Wöhler curve, fatigue limit. Haigh diagram and SN diagram.
PART 3  THERMOMECHANICAL PROBLEMS
Review of the basic thermomechanical formulation and FEM discretization. Effect of temperature on the mechanical properties of materials. Thermomechanical coupling.
PART 4  APPLICATIONS AND CODES
Use of the FEAP program for the solution of various test cases. Seminar on industrial applications of the ANSYS program.


Lessons will take place in the classroom. Some exercises will take place in the classroom, some will be assigned as homeworks.
Lectures and exercises will take place in the classroom. Some exercises will be assigned as homeworks. For each one, a small report is then required.
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, McGrawHill, 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
Books for review of the basic knowledge
Carpinteri A. (2018) Structural Mechanics Fundamentals, CRC Press.
Carpinteri A. (2017) Advanced Structural Mechanics, CRC Press.
Italian version of the two texts listed above:
Carpinteri, A. (1995) Scienza delle Costruzioni, vol. 1, Bologna, Pitagora Editrice.
Carpinteri, A. (1992) Scienza delle Costruzioni, vol. 2, Bologna, Pitagora Editrice.
The course topics are treated in small specific sections of the texts listed below. Small parts will be provided and all these books are available in the library.
Zavarise G. (2009) Introduction to the Finite Element Method – notes.
Balfour, J.A.D. (1992) Computer analysis of structural frameworks  Blackwell Scientific Publications; 2nd ed.
Oñate, E. (2009) Structural Analysis with the Finite Element Method, vol. 1, Berlin, Springer.
Oñate, E. (2013) Structural Analysis with the Finite Element Method, vol. 2, Berlin, Springer.
Ameen, M. (2014) Computational Elasticity  Revised version, Oxford, Alpha Science International Ltd.
Zienkiewicz, O.C., Taylor, R.L. (2000) The Finite Element Method  Vol. 1, 5th ed., Oxford, ButterworthHeinemann.
Zienkiewicz, O.C., Taylor, R.L. (2000) The Finite Element Method  Vol. 2, 5th ed., Oxford, ButterworthHeinemann.
Vullo V.(2016) Circular Cylinders and Pressure Vessels Stress Analysis and Design, Springer.
Ottosen N.S., Petersson H. (1992) Introduction to the Finite Element Method, Prentice Hall.
Logan, D.L. (2012) A First Course in the Finite Element Method, 5th ed., Boston, Cengage Learning.
Bathe, K.J. (2014) Finite Element Procedures, 2nd ed., Watertown, K.J. Bathe.
Campbell F.C. (2008) Elements of Metallurgy and Engineering Alloys, ASM International.
Slides; Dispense; Esercizi; Esercizi risolti;
Lecture slides; Lecture notes; Exercises; Exercise with solutions ;
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 preestablished 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.
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 preestablished 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.
EXAM MODE:
Homework reports provided some days before the written test, written test in the classroom, oral test in the classroom.
In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.