( english version )
Advanced structural mechanics A ( 5 CFU )
Prof. Sabrina Vantadori
          E-mail. sabrina.vantadori@unipr.it

Finalità
To present basic concepts and tools for structural design, with reference to the theory of one-dimensional structures (beams) and two-dimensional structures (plates).

Programma
Beam theory.
Plane beams with straight axis: kinematic model (Euler-Bernoulli hypothesis and Timoshenko hypothesis), static variables, equilibrium conditions, elastic behaviour. Plane beams with curved axis.

Torsion of open-section thin-walled beams.
Introduction to non-uniform torsion. Theory of sectorial areas: kinematic model (Vlasov hypothesis), static variables, equilibrium conditions, elastic behaviour.

Plane stress and plane strain states.
Stress function or Airy function. Plane stress state for a solid of revolution: Airy function in polar coordinates; axisymmetric loading (example of a thick-walled cylinder submitted to internal or external pressure).

Bending of plates.
Membrane and flexural problem. Kinematic model for bending of plates (Kirchhoff hypothesis and Mindlin-Reissner hypothesis). Static variables. Equilibrium conditions. Boundary conditions. Formulation of the problem in cylindrical coordinates. Elastic behaviour. Equation of Sophie Germain-Lagrange for Kirchhoff plates. Axisymmetric plates. Examples of solutions: circular axisymmetric plate, rectangular plate (Navier solution and Levy solution). Finite difference method: approximate solutions for rectangular plates.

Shells of revolution.
Geometrical and loading characteristics. Membrane and bending generalized stresses. Membrane regime: equilibrium equations, examples. Bending regime for a cylindrical shell: comparison with the problem of a beam on elastic foundation (Winkler’s constraints). Bending regime for spherical and conical shells.

Attività d'esercitazione
Theory supported by exercises.

Modalità d'esame
Oral examination

Propedeuticità
Analisi A-B, Analisi C, Geometria, Meccanica Razionale, Scienza delle Costruzioni A (Structural Mechanics A), Scienza delle Costruzioni B (Structural Mechanics B).

Testi consigliati
R. BALDACCI: “Scienza delle Costruzioni”, Vol. 2, UTET, Torino, 1983.
O. BELLUZZI: “Scienza delle Costruzioni”, Vol. 3. Zanichelli, Bologna, 1967.
A. CARPINTERI: "Scienza delle Costruzioni", Vol. 1, Ed. Pitagora, Bologna, 1992.
L. CORRADI DELL’ACQUA: “Meccanica delle strutture”, Voll. 1 e 2, McGraw-Hill, Milano, 1995.
E. GIANGRECO: “Teoria e tecnica delle costruzioni”, Vol. 3, Liguori Editore, Napoli, 1969.
S.P. TIMOSHENKO – S. WOINOWSKY-KRIEGER: “Theory of plates and shells”, McGraw-Hill, New York, 1970.

 
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