In this paper a general procedure for a rational derivation of plate theories is proposed. The methodology is based on the conjecture that plate theories can be carried out from the three-dimensional elasticity by imposing suitable constraints on the strain and stress fields. The powerful Lagrange multipliers theory is adopted to derive the variational principles, based on the Hu-Washizu functional, governing the constrained elasticity problems. Both the first-order shear deformation plate theory, and the higher-order Lo-Christensen-Wu plate theory are derived. The governing equations are recovered, and the reactive fields, arising as a consequence of the imposed constraints, are carried out. When these reactive fields are taken into account, the equilibrium, congruence, and constitutive equations turn out to be exactly satisfied.

Bisegna, P., Sacco, E. (1997). A rational deduction of plate theories from the three-dimensional linear elasticity. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 77(5), 349-366 [10.1002/zamm.19970770509].

A rational deduction of plate theories from the three-dimensional linear elasticity

BISEGNA, PAOLO;
1997-01-01

Abstract

In this paper a general procedure for a rational derivation of plate theories is proposed. The methodology is based on the conjecture that plate theories can be carried out from the three-dimensional elasticity by imposing suitable constraints on the strain and stress fields. The powerful Lagrange multipliers theory is adopted to derive the variational principles, based on the Hu-Washizu functional, governing the constrained elasticity problems. Both the first-order shear deformation plate theory, and the higher-order Lo-Christensen-Wu plate theory are derived. The governing equations are recovered, and the reactive fields, arising as a consequence of the imposed constraints, are carried out. When these reactive fields are taken into account, the equilibrium, congruence, and constitutive equations turn out to be exactly satisfied.
1997
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore ICAR/08 - SCIENZA DELLE COSTRUZIONI
English
Con Impact Factor ISI
Plate theory; internal constraint; elasticity
Bisegna, P., Sacco, E. (1997). A rational deduction of plate theories from the three-dimensional linear elasticity. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 77(5), 349-366 [10.1002/zamm.19970770509].
Bisegna, P; Sacco, E
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/23568
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