MECHANICS OF STRUCTURES
Academic year and teacher
If you can't find the course description that you're looking for in the above list,
please see the following instructions >>
- Versione italiana
- Academic year
- 2016/2017
- Teacher
- ANTONIO MICHELE TRALLI
- Credits
- 9
- Curriculum
- COSTRUZIONI
- Didactic period
- Secondo Semestre
- SSD
- ICAR/08
Training objectives
- The goal of the course is the knowledge and the application of theoretical models, with particular interest to 2D elements, both with flat and curved middle surface, in- and out-of-plane loaded. 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 the 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
- Basic knowledge of structural mechanics concepts
Course programme
- Plane stress and plane strain states: closed form solutions for some problems of technical interest via Airy function.
2D panels in-plane loaded: reinforced concrete, steel, masonry. Thick tubes. Circular holes in steel plates in traction. Force at a point of an indefinitely extended solid (Boussinesq problem). Limits of applicability of 1D elements: Eulero and Timoshenko formulations for beams. Plates (out-of-plane loads).
Elementary concepts, geometric and kinematic models.
Mindlin-Reissner plates and Love-Kirchhoff plates, constitutive relations obtained through energetic formulations. Field problem for Kirchhoff-Love plates, Kirchhoff shear, boundary conditions on displacements and rotations, Lagrange equation, solutions in terms of Fourier expansion for rectangular plates. Reinforced concrete slabs. Circular plates axi-symmetrically loaded, closed form and approximated solutions for cases of technical interest.
Cupolas, equilibrium equations, membrane theory for axi-symmetric loads. Solutions in cases of particular interest, spherical cupolas subjected to self weight, hydrostatic pressure.
Bending local effects for axi-symmetric actions (shear, moments) on the boundary of tubes with infinite length, method of elastic coefficients.
Numerical methods: numerical methods for structural analyses in the linear elastic range. Ritz Method. Introduction to the Finite Element Method. Convergence and error estimations. Triangular, Lagrangian and isoparametric finite elements (serendipity). Finite elements for plane stress, plane strain and axi-symmetric problems. Computational aspects. Judgments about the goodness of the solution. Problems with C1 continuity, Mindlin-Reissner plate elements, "locking" problem, Love-Kirchhoff plate elements. Didactic methods
- Theoretical/practical lessons.
Learning assessment procedures
- The examination consists of a practical part and an oral part.
The practical part relies on the solution of some examples by means of a finite element code of structural problems with both elastic and elasto-plastic constitutive laws.
The exercises have to be documented and must receive a positive feedback from the teacher before the student is allowed to carry out the oral examination.
The second part of the xamination is oral. It concerns all the arguments of the program, such as the theoretical derivaton of the equilibrium equations of 2D structures, the theory of plasticity, the finite elements methods and, in general, the whole program. Reference texts
- 1) Leone Corradi Dall'Acqua, Meccanica delle strutture, vol. 2-3, McGraw Hill.
2)Belluzzi O., Scienza delle costruzioni, vol. 3, Zanichelli
3)Szabò B., Babuska I., Finite element analysis, John Wiley & Sons.
4)Pozzati P., Teoria e tecnica delle strutture, UTET
5)Thimoshenko S., Goodier J.N., Theory of elasticity, McGraw Hill.
6)Thimoshenko S., Woinowsky-Krieger, Theory of plates & shells, McGraw Hill.
7)Leonhardt F., Monning E., C.a & c.a.p. calcolo di progetto e tecniche costruttive, vol 1, ed di Scienza e Tecnica.
