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.

A rational deduction of plate theories from the three-dimensional linear elasticity / Bisegna, P.; Sacco, E.. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK. - ISSN 0044-2267. - 77:5(1997), pp. 349-366. [10.1002/zamm.19970770509]

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

#### 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.
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1997
A rational deduction of plate theories from the three-dimensional linear elasticity / Bisegna, P.; Sacco, E.. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK. - ISSN 0044-2267. - 77:5(1997), pp. 349-366. [10.1002/zamm.19970770509]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11588/710434`
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