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Advanced structural and thermal mechanics

01TWLND

A.A. 2020/21

Course Language

Inglese

Course degree

Master of science-level of the Bologna process in Energy And Nuclear Engineering - Torino

Course structure
Teaching Hours
Lezioni 54
Esercitazioni in aula 26
Teachers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Zavarise Giorgio Professore Ordinario ICAR/08 54 31 0 0 2
Teaching assistant
Espandi

Context
SSD CFU Activities Area context
ICAR/08
ING-IND/14
3
5
C - Affini o integrative
C - Affini o integrative
Attività formative affini o integrative
Attività formative affini o integrative
2020/21
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 behavior of structures. 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 in-depth study of the methods of solving hyperstatic structures. In the second part, the theory of elasticity is extended to 2D and 3D problems, with attention devoted both to closed-form solutions and to the classic numerical formulations of the FEM method; to nonlinear materials; to fatigue problems. In the third part, the study of the mechanical behavior of materials in the presence of thermal effects is deepened. In the fourth part some application examples are presented. The approach is therefore oriented to provide an organic view of the mechanical and thermo-mechanical behavior of the materials, with attention specifically dedicated both to the solutions in closed-form, 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 sub-problems and use, on a case-by-case 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 and 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 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.
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, 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.
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 stress-strain 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: closed-form 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. Fatigue Fatigue resistance - Phenomenology and characteristic parameters, Wöhler curve, fatigue limit. Haigh diagram and S-N diagram. Effect of the load type, size, surface finishing, and presence of notch effects. Stress concentration and fatigue notch factor. Fatigue safety factor. PART 3 - THERMOMECHANICAL PROBLEMS Review of the basic thermo-mechanical 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, 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
The course topics are treated on specific sections of the texts listed below. All these books are available in the library. Carpinteri, A. (1995) Scienza delle Costruzioni, vol. 1, Bologna, Pitagora Editrice. Carpinteri, A. (1992) Scienza delle Costruzioni, vol. 2, Bologna, Pitagora Editrice. English version of the two texts listed above: Carpinteri A. (2018) Structural Mechanics Fundamentals, CRC Press. Carpinteri A. (2017) Advanced Structural Mechanics, CRC Press. Ameen, M. (2014) Computational Elasticity - Revised version, Oxford, Alpha Science International Ltd. Oñate, E. (2013) Structural Analysis with the Finite Element Method, vol. 2, Berlin, Springer, 2013. Logan, D.L. (2012) A First Course in the Finite Element Method, 5th ed., Boston, Cengage Learning. Zienkiewicz, O.C., Taylor, R.L. (2000) The Finite Element Method - Vol. 1, 5th ed., Oxford, Butterworth-Heinemann. Bathe, K.J. (2014) Finite Element Procedures,2nd ed., Watertown, K.J. Bathe.
Modalità di esame: Prova orale obbligatoria; Elaborato scritto individuale; Prova scritta su carta con videosorveglianza dei docenti;
Assessment and grading criteriaThe 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 2.5 hours) 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 and typically consists of 3 questions. In the event of doubtful cases, clarifications may be requested regarding the written test and the homework reports. The final evaluation is proportional to the correctness, completeness and relative complexity of the written test (which accounts for 35%), the homework reports (which accounts for 15%) and the oral test (which accounts for 50%) ). Remote exam mode: Written exam with webcam surveillance of the teachers, oral exam with Virtual Classroom or Skype.
Exam: Compulsory oral exam; Individual essay; Paper-based written test with video surveillance of the teaching staff;
The exam aims to evaluate the level of knowledge of the topics of the program, and the ability to use theoretical concepts for solving practical case tests. The exam consists of a written test and, upon passing this, a subsequent oral test. The access to the oral test is subject to the positive evaluation of the homework reports. The written test (lasting 2.5 hours) consists of three exercises, specifically aimed at verifying the achieved knowledge in both the theoretical and application fields. A score is assigned to each exercise, depending on its difficulty; the sum of the three maximum scores is equal to 30. The test is considered to have been passed with the achievement of an overall score equal to or greater than 18, and the achievement of a pre-established minimum score, again depending on the difficulty, for each exercise. The oral exam is oriented to the verification of the learning level of the theoretical concepts and, usually, it consists of 3 questions. In case of doubtful situations, clarifications may be requested regarding the written test and the homework reports. During the written test it is not allowed to keep and consult documents of any kind (notebooks, books, sheets with exercises, forms ...). It is also forbidden to keep and use communication tools of any kind (cell phones, or other). 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 test corrections and ask for any clarifications. The final evaluation is proportional to the correctness, completeness and relative complexity of the written test (which accounts for 35%), the homework reports (which accounts for 15%) and the oral test (which accounts for 50%). Remote exam mode: Written exam with webcam surveillance of the teachers, oral exam with Virtual Classroom or Skype.
Modalità di esame: Prova scritta (in aula); Prova orale obbligatoria; Elaborato scritto individuale;
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 2.5 hours) 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 and typically consists of 3 questions. In the event of doubtful cases, clarifications may be requested regarding the written test and the homework reports. The final evaluation is proportional to the correctness, completeness and relative complexity of the written test (which accounts for 35%), the homework reports (which accounts for 15%) and the oral test (which accounts for 50%) ). Exam with classical methods: Written test in the classroom, oral test in the classroom.
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 solving practical case tests. The exam consists of a written test and, upon passing this, a subsequent oral test. The access to the oral test is subject to the positive evaluation of the homework reports. The written test (lasting 2.5 hours) consists of three exercises, specifically aimed at verifying the achieved knowledge in both the theoretical and application fields. A score is assigned to each exercise, depending on its difficulty; the sum of the three maximum scores is equal to 30. The test is considered to have been passed with the achievement of an overall score equal to or greater than 18, and the achievement of a pre-established minimum score, again depending on the difficulty, for each exercise. The oral exam is oriented to the verification of the learning level of the theoretical concepts and, usually, it consists of 3 questions. In case of doubtful situations, clarifications may be requested regarding the written test and the homework reports. During the written test it is not allowed to keep and consult documents of any kind (notebooks, books, sheets with exercises, forms ...). It is also forbidden to keep and use communication tools of any kind (cell phones, or other). 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 test corrections and ask for any clarifications. The final evaluation is proportional to the correctness, completeness and relative complexity of the written test (which accounts for 35%), the homework reports (which accounts for 15%) and the oral test (which accounts for 50%). Exam with classical methods: Written test in the classroom, oral test in the classroom. Remote exam mode: Written exam with webcam surveillance of the teachers, oral exam with Virtual Classroom or Skype.


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