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.

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 - 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.

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.

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.

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.

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.