Exact solutions of elastic Kirchhoff plates are available only for spe- cial geometries, loadings and kinematic boundary constraints. An effective solution procedure, based on an analogy between functionally graded orthotropic Saint- Venant beams under torsion and inhomogeneous isotropic Kirchhoff plates, with no kinematic boundary constraints, is proposed. The result extends the one con- tributed in (Acta Mech, 224(12), 2955-2964 (2013)) for the special case of homoge- neous Saint-Venant beams under torsion. Closed-form solutions for displacement, bending-twisting moment and curvature fields of an elliptic plate, corresponding to a functionally graded orthotropic beam, are evaluated. A new benchmark for computational mechanics is thus provided.
Analogies between Kirchhoff plates and functionally graded Saint-Venant beams under torsion / Barretta, Raffaele; Luciano, R.. - In: CONTINUUM MECHANICS AND THERMODYNAMICS. - ISSN 0935-1175. - 27:(2015), pp. 499-505. [10.1007/s00161-014-0385-2]
Analogies between Kirchhoff plates and functionally graded Saint-Venant beams under torsion
BARRETTA, RAFFAELE;
2015
Abstract
Exact solutions of elastic Kirchhoff plates are available only for spe- cial geometries, loadings and kinematic boundary constraints. An effective solution procedure, based on an analogy between functionally graded orthotropic Saint- Venant beams under torsion and inhomogeneous isotropic Kirchhoff plates, with no kinematic boundary constraints, is proposed. The result extends the one con- tributed in (Acta Mech, 224(12), 2955-2964 (2013)) for the special case of homoge- neous Saint-Venant beams under torsion. Closed-form solutions for displacement, bending-twisting moment and curvature fields of an elliptic plate, corresponding to a functionally graded orthotropic beam, are evaluated. A new benchmark for computational mechanics is thus provided.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
