LEARNING OUTCOMES

The aim of the module is to supply advanced concepts and related solution techniques to analyze the mechanical behavior of 3D and 2D structures to form the basis for their structural design under the elastic regime. elastic regime.

AIMS AND LEARNING OUTCOMES

The attendance and active participation in the proposed training activities (frontal lessons and exercises) 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 continuum models for deformable solids and of structural models for plates;

analyze the equilibrium configurations of bending elastic plates loaded in and out of their plane;

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

determine quantitatively the critical loads for plates uniformly compressed.

TEACHING METHODS

The module provides 60 hours of frontal lessons in the classroom.

The presentation of theoretical contents (40 hours) alternates with exercises and applicative examples (20 hours). The aim is to encourage learning and discussion employing the appropriate technical termonilogy for structural engineering. The exercises solved have the same characteristics of those proposed during the exam.

Transversal skills in terms of communication and independent learning ability will be also acquired doing exercises with the teacher.

SYLLABUS/CONTENT

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

Solid mechanics (30 hours):

reminders of statics and kinematics of a continuum (Cauchy continuum; stress and strain vectors and tensors; equilibrium and compatibility equations; virtual work theorem); elastic constitutive equations (theory of elasticity; general theorems; limit of elasticity; failure criteria for yielding of ductile materials); linear elastic problem (governing equations; uniqueness of solution; formulations in terms of displacements or stresses; methods of solution; plane stress and plane strain).

Theory of plates (15 hours):

Kirchhoff and Mindlin-Reissner plate theories; statics and kinematics; equilibrium, compatibility and elastic constitutive equations; stress distributions; Germain-Lagrange equation and related semi-analytical techniques of solution; buckling of plates uniformly compressed.

Finite element method (15 hours):

kinematics and statics of a finite element; discrete model and assembly procedure; local and global stiffness matrices and equivalent node load vectors; solution procedure of a numerical model; conditions of accuracy.

RECOMMENDED READING/BIBLIOGRAPHY

Additional exercises, as well as other helpful teaching materials, will be available in the web classroom. The related solutions will not be available: students are encouraged to show and discuss their solutions with the teacher in order to check that the correct approach is followed.

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.