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.
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.
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.
The module provides 50 hours of frontal lessons in the classroom.
The presentation of theoretical contents alternates with the discussion of case studies. The aim is to encourage learning and discussion employing the appropriate technical termonilogy for structural engineering.
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 theory. 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. Bending effects in shells. 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 a commercial finite element code.
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).
Ricevimento: The office hours are by appointment; the email address is ilaria.monetto@unige.it
Ricevimento: They will be decided at the beginning of the course
GIUSEPPE PICCARDO (President)
ROBERTA MASSABO'
FEDERICA TUBINO
ILARIA MONETTO (President Substitute)
https://corsi.unige.it/10799/p/studenti-orario
The final exam of the module consists in passing an oral test.
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 final grade for the module will take into account the correctness and completeness of answers in the oral test, as well as the quality of exposition, the correct use of technical terminology and critical reasoning ability.
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.
Students with particular needs are asked to contact the teacher at the beginning of lessons.
