Servizi per la didattica

PORTALE DELLA DIDATTICA

02MNINE

A.A. 2020/21

Course Language

Inglese

Course degree

Master of science-level of the Bologna process in Mechanical Engineering - Torino

Course structure

Teaching | Hours |
---|---|

Lezioni | 40 |

Esercitazioni in aula | 20 |

Teachers

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
---|---|---|---|---|---|---|---|

Zavarise Giorgio | Professore Ordinario | ICAR/08 | 40 | 20 | 0 | 0 | 1 |

Teaching assistant

Context

SSD | CFU | Activities | Area context |
---|---|---|---|

ICAR/08 | 6 | D - A scelta dello studente | A scelta dello studente |

2020/21

The subject aims to deepen the concepts and tools to interpret and understand the mechanical behavior of the structures, in order to evaluate their safety. The main subject is the theory of elasticity and its applications in engineering. The approach is therefore oriented to provide an organic view of the theory of elasticity, then deepening the particularizations in its various fields of application.
As for the contents, they are divided into three parts. In the first one the concepts related to the theory of elasticity are recalled and deepened. In the second its applications are deepened in the study of mono- and bi-dimensional problems;. In the third part some special issues in the nonlinear field are addressed.

The subject aims to deepen the concepts and tools to interpret and understand the mechanical behavior of the structures, in order to evaluate their safety. The main subject is the theory of elasticity and its applications in engineering. The approach is therefore oriented to provide an organic view of the theory of elasticity, then deepening the particularizations in its various fields of application.
As for the contents, they are divided into three parts. In the first one the concepts related to the theory of elasticity are recalled and deepened. In the second its applications are deepened in the study of mono- and bi-dimensional problems;. In the third part some special issues in the nonlinear field are addressed.

The subject is specifically oriented towards the construction of a global view of the elastic problem, in order to face both simple and complex problems in the right perspective.
The student will acquire ground knowledge on the mechanical behavior of the structures and familiarity with the corresponding interpretative models used to understand the structural answer and evaluate its safety. This 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 knowledge and skills acquired will be applied to the solution of problems that translate into a quantitative form the assessments of structural safety and response.

The subject is specifically oriented towards the construction of a global view of the elastic problem, in order to face both simple and complex problems in the right perspective.
The student will acquire ground knowledge on the mechanical behavior of the structures and familiarity with the corresponding interpretative models used to understand the structural answer and evaluate its safety. This 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 knowledge and skills acquired will be applied to the solution of problems that translate into a quantitative form the assessments of structural safety and response.

In teaching, mathematical concepts and methods are widely used; therefore knowledge of mathematical analysis, matrix calculus and linear algebra is required. The knowledge of the differential geometry of curves and surfaces is also useful.
The contents of the course of Fundamentals of Structural Mechanics, or similar courses, are preparatory.

The subject 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 ONE - REVIEW
Introduction and preliminary notions:
• Introduction to the course: presentation, bibliographical references, rules and methods of examination.
• General framework of the structural problem: concept of equilibrium, constraint, structural response and collapse mechanisms. Overview of numerical modeling. Notes on the construction of the structural model.
Classification of structures:
• Kinematics and statics of beam systems, classification of structures by kinematic analysis.
Determination of constraint reactions:
• Computation of constraint reactions of isostatic structures using the Virtual Works Principle (PLV).
Elasticity theory:
• Deformations, stresses, elasticity law, elasticity theorems.
PART TWO - INSIGHTS AND EXTENSIONS
Particularizations of the elasticity problem:
• De Saint Venant's problem: Tension, bending, torsion, shear. Composed cases.
• Practical application of the beam theory: the elastic line, fundamental cases, composition of rotations and displacements.
• Symmetry and antimetry of structures: outline, advantages, determination of constraint conditions at the symmetry line.
• Solution of hyperstatic structures: theoretical bases and applications of the force method.
• The elastic problem in Cartesian and polar coordinates: plane stress state, plane strain state, applications of the Airy function, problems in polarsymmetry.
PART THREE - NONLINEAR PROBLEMS
Nonlinearity of materials:
• Introduction: ductile materials and brittle materials, elastoplastic constitutive laws, behavior of sections in ideally plastic material, bending moment of complete plasticization.
• Ultimate load fundamental theorems: statically admissible and kinematically sufficient load multipliers. Collapse multiplier. Static theorem and cinematic theorem.
Instability of equilibrium:
• Premises: introduction and general concepts.
• Concentrated elasticity systems: one-degree of freedom systems: bifurcation, post-critical behavior. Systems with two or more degrees of freedom: critical loads and critical deformations.
• Elastic structures: Euler critical load, critical stress. Instability of beams elastically constrained. Flexion-torsional instability in high beams.
Mechanics of contact between solids:
• One-dimensional systems: introduction, the Penalty method, the Lagrange Multipliers method.
• Two-dimensional systems: construction of the Node-To-Segment contact element.

PART ONE - REVIEW
Introduction and preliminary notions:
• Introduction to the course: presentation, bibliographical references, rules and methods of examination.
• General framework of the structural problem: concept of equilibrium, constraint, structural response and collapse mechanisms. Overview of numerical modeling. Notes on the construction of the structural model.
Classification of structures:
• Kinematics and statics of beam systems, classification of structures by kinematic analysis.
Determination of constraint reactions:
• Computation of constraint reactions of isostatic structures using the Virtual Works Principle (PLV).
Elasticity theory:
• Deformations, stresses, elasticity law, elasticity theorems.
PART TWO - INSIGHTS AND EXTENSIONS
Particularizations of the elasticity problem:
• De Saint Venant's problem: Tension, bending, torsion, shear. Composed cases.
• Practical application of the beam theory: the elastic line, fundamental cases, composition of rotations and displacements.
• Symmetry and antimetry of structures: outline, advantages, determination of constraint conditions at the symmetry line.
• Solution of hyperstatic structures: theoretical bases and applications of the force method.
• The elastic problem in Cartesian and polar coordinates: plane stress state, plane strain state, applications of the Airy function, problems in polarsymmetry.
PART THREE - NONLINEAR PROBLEMS
Nonlinearity of materials:
• Introduction: ductile materials and brittle materials, elastoplastic constitutive laws, behavior of sections in ideally plastic material, bending moment of complete plasticization.
• Ultimate load fundamental theorems: statically admissible and kinematically sufficient load multipliers. Collapse multiplier. Static theorem and cinematic theorem.
Instability of equilibrium:
• Premises: introduction and general concepts.
• Concentrated elasticity systems: one-degree of freedom systems: bifurcation, post-critical behavior. Systems with two or more degrees of freedom: critical loads and critical deformations.
• Elastic structures: Euler critical load, critical stress. Instability of beams elastically constrained. Flexion-torsional instability in high beams.
Mechanics of contact between solids:
• One-dimensional systems: introduction, the Penalty method, the Lagrange Multipliers method.
• Two-dimensional systems: construction of the Node-To-Segment contact element.

Lessons are held in the classroom with classic methods.

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 subject 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.

The exam aims to evaluate the level of learning of the various topics of the program, and the ability to use the theoretical concepts for solving practical case tests.
The exam consists of a written test and, after passing this, a subsequent oral exam.
The written test consists of three exercises, specifically aimed at verifying the learning in the practical field. 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 consists of 3 questions. In case of doubtful cases, clarifications may be requested regarding the written test.
The final evaluation, expressed in thirtieths, is proportional to the correctness, completeness and relative complexity of the two tests.
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 exam are communicated on the teaching portal, together with the date on which the students can view the test correction and ask questions.
Remote exam mode:
Written exam with webcam surveillance of the teachers, oral exam with Virtual Classroom or Skype.

The exam aims to evaluate the level of learning of the various topics of the program and the ability to use the theoretical concepts for solving practical case tests. The exam consists of a written test and, after passing this, a subsequent oral test.
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.
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 subject , 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 50%) 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.

The exam aims to evaluate the level of learning of the various topics of the program, and the ability to use the theoretical concepts for solving practical case tests.
The exam consists of a written test and, after passing this, a subsequent oral exam.
The written test consists of three exercises, specifically aimed at verifying the learning in the practical field. 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 consists of 3 questions. In case of doubtful cases, clarifications may be requested regarding the written test.
The final evaluation, expressed in thirtieths, is proportional to the correctness, completeness and relative complexity of the two tests.
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 exam are communicated on the teaching portal, together with the date on which the students can view the test correction and ask questions.
Exam with classical methods:
Written test in the classroom, oral test in the classroom.

The exam aims to evaluate the level of learning of the various topics of the program, and the ability to use the theoretical concepts for solving practical case tests. The exam consists of a written test and, after passing this, a subsequent oral test.
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.
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 50%) 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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Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY