OVERVIEW

The course aim is to introduce the mechanics of solids by the formulation of the field equations for the linear elastic boundary value problem. A collection of solutions is presented in detail referring to plane problems and bidimensional theories for plates and shells. Moreover, the course provides the basic knowledge of the finite elements method useful to determine numerical approximate solutions. Some problems of practical interest are also formulated and solved.

AIMS AND CONTENT

LEARNING OUTCOMES

The course provides the theoretical development of the mechanics of solids and structures with sufficient rigor to give students a good foundation for the determination of solutions to a broad class of problems of engineering interest. The primary goal is to formulate models, develope solutions and understand the results. 

AIMS AND LEARNING OUTCOMES

The attendance and active participation in the proposed training activities together with the individual study will allow the student to:

recognize physical problems of structural engineering which can be solved through the analysis of 3D and 2D structures;

know the fundamentals of structural models for plates and shells;

analyze the equilibrium configurations of 3D and 2D structures under the assumption of linearity;

know the fundamentals of the finite element method as a prerequisite for a correct employment of commercial software.

TEACHING METHODS

The module provides 54 hours of which 44 of lectures in the classroom and 10 of laboratory.

In the lectures the presentation of theoretical contents alternates with the discussion of case studies with the purpose of encouraging learning, discussion and employing the appropriate technical termonilogy for structural engineering.

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Federico Scarpa (federico.scarpa@unige.it ), the Polytechnic School's disability liaison.

SYLLABUS/CONTENT

The programme of the module includes the presentation and discussion of the following topics:

Linear Elasticity Theory. Field equations. Solution strategies for the elastic problem: analytical and numerical approaches. Collections of elastic solutions to introduce structural theories.

Plane strain and plane stress problems.  Stress formulation with Airy funtion. Polynomial solutions. Polar formulation. Lamé problem. Plates with hole. Radial plane solutions.

Bidimensional structural theories.  Kirchhoff Love theory for plates: membrane and bending theories. Field equations and boundary conditions. Navier and Levy solution methods. Plate effect. Mindlin-Reissner theory. Circular plates. Von Karman theory and applications. Membrane shell theory. Spherical and cylindrical shells. Examples.

Introduction to the finite elements method for numerical analyses. Variational formulation and numerical solution tecniques. Finite element method. Phases and procedures in linearity. Finite elements (1D,2D,3D). Shape functions. Stiffness matrix. Examples of linear elastic analysis with the commercial finite element code ANSYS.

RECOMMENDED READING/BIBLIOGRAPHY

Additional helpful teaching material will be available in the web classroom.

The notes taken during the lessons and the material in the web classroom are sufficient for the preparation of the exam. Anyway, the following books are suggested as supporting and deepening texts:

Nunziante L., Gambarotta L., Tralli A. (2008). Scienza delle costruzioni, McGraw-Hill, Milano.

Timoshenko S., Goodier J.N. (1951). Theory of elasticity, McGraw-Hill, New York.

Corradi dell'Acqua L.(1992). Meccanica delle strutture - Le teorie strutturali e il metodo degli elementi finiti, vol. 2, McGraw-Hill, Milano.

Timoshenko S.P., Woinowsky-Krieger S. (1959). Theory of plates and shells, McGraw-Hill, Singapore.

Timoshenko S.P., Gere J.M. (1961). Theory of elastic stability, McGraw-Hill, New York.

Felippa C.A, Introduction to Finite Element Methods, University of Colorado at Boulder, sito
web prof. Felippa (free download).

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

https://corsi.unige.it/10799/p/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The final exam of the module consists in passing an oral test after writing a technical report on the finite element analysis of a case study assigned by the teacher.

The oral test consists in an interview: the students can be required to describe case studies, concepts, theories and formulations, as well as to derive equations and prove theorems. The correctness and completeness of answers, as well as the quality of exposition, the correct use of technical terminology and critical reasoning ability will be evaluated.

ASSESSMENT METHODS

For a successfull learning, basic knowledge of mathematics, physics and mechanics of materials is required.

The details on how to prepare the exam and on the degree of deepening of each topic will be given during the lessons.

The exam aims to verify the knowledge of the theoretical bases of the module and assess the ability to apply them to general or specific cases of interest in the framework of structural engineering, as well as to derive analytical and numerical solutions to use in the design.

FURTHER INFORMATION

Students with particular needs are asked to contact the teacher at the beginning of lessons.