MECHANICS OF STRUCTURES
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- ANDREA CHIOZZI
- Credits
- 9
- Curriculum
- COSTRUZIONI
- Didactic period
- Secondo Semestre
- SSD
- ICAR/08
Training objectives
- The goal of the course is the knowledge and practical application of theoretical models describing the behavior of 2D elastic continua, with both flat and curved middle surface, with in- and out-of-plane loading (plates and shells). General equations of elasticity are applied to the study of two-dimensional problems of engineering interest. Both rigorous analytical methods and approximate techniques are illustrated, aimed at the computation of stress and strain fields. Finally, the basis of the Finite Element method is illustrated, with emphasis on the goodness of the numerically obtained solutions.
Prerequisites
- Knowledge of the basic concepts of solid and structural mechanics.
Course programme
- Structural theories for two dimensional continua: plane strain and plane stress problems, elastic theory of thin plates (Kirchhoff-Love), kinematic assumptions, equilibrium equations, Sophie Germain-Lagrange equations for pure bending of plates, essential and natural boundary conditions, Kirchhoff shear, concentrated shear forces at corners, solutions for rectangular and axisymmetric plates, plates on an elastic foundation, membrane theory of shells of revolution, membrane theory of cylindrical shells, shperical and pointed domes, tanks, pipes.
Introduction to the finite element method: strong and weak forms for one- and two-dimensional problems, 1D and 2D interpolation, weighted residual methods (collocation, subdomain, least squares, Galerkin), the finite element method, FEM for elastic beams, FEM for 2D and 3D elasticity, FEM for plates and shells, isoparametric elements, numerical integration and Gauss quadrature.
Limit analysis of structures: elastoplastic behavior, plasticity theory (outline), hypothesis of rigid-plastic material behavior, static and kinematic theorems of limit analysis, plastic hinge model, determination of the collapse load multiplier for systems of beams. Applications.
Theory of elastic stability: stability and postcritical behavior of discrete mechanical systems with one or more degrees of freedom (outline), stability and postcritical behavior of continuum mechanical systems: beams, frames, plates and shell. Didactic methods
- Frontal teaching.
Learning assessment procedures
- The examination consists of a practical part and an oral part.
The practical part relies on the solution of several meaningful structural problems by means of a finite element code. The exercises have to be documented and must receive a positive feedback from the instructor before the student is allowed to carry out the oral examination.
The second part of the examination is oral and concerns all the topics covered by the course. Reference texts
- Lecture notes will be provided by the instructor.
Further readings:
For plane stress and plane strain problems:
- Corradi Dall'Acqua, L., Meccanica delle strutture, vol. 1, McGraw Hill, 1992.
For plates and shells:
- Thimoshenko, S., Woinowsky-Krieger, S., Theory of plates & shells, McGraw Hill, 1959.
- Flügge, W., Stresses in Shells, Springer-Verlag, 1960.
- Belluzzi, O., Scienza delle costruzioni, vol. 3, Zanichelli
For the finite element method:
- Ottosen, N., Petersson, H., Introduction to the Finite Element Method, Prentice Hall, 1992.
For the theory of elastic stability:
- Corradi Dall'Acqua, L., Meccanica delle strutture, vol. 3, McGraw Hill, 1994.
- Luongo, A., Ferretti, M., Di Nino, S., Stabilità e Biforcazione delle Strutture, Esculapio, 2022.
- Timoshenko, S., Gere, J.M., Theory of Elastic Stability, Dover.
