In this Note we present a formal scaling method that allows for the deduction from three-dimensional linearized elasticity of the equations of shearable structures such as Reissner-Mindlin's equations for plates and Timoshenko's equations for rods, as well as other models of thin structures. This method is based on the requirement that a scaled energy functional possibly including second-gradient terms stay bounded in the limit of vanishing 'thinness'.
Miara, B., PODIO GUIDUGLI, P. (2006). Une approche formelle unifiée des théories de plaques et poutres linéairement élastiques = A unified formal approach for theories of linear elastic plates and rods. COMPTES RENDUS MATHÉMATIQUE, 343(10), 675-678 [10.1016/j.crma.2006.09.035].
Une approche formelle unifiée des théories de plaques et poutres linéairement élastiques = A unified formal approach for theories of linear elastic plates and rods
PODIO GUIDUGLI, PAOLO
2006-01-01
Abstract
In this Note we present a formal scaling method that allows for the deduction from three-dimensional linearized elasticity of the equations of shearable structures such as Reissner-Mindlin's equations for plates and Timoshenko's equations for rods, as well as other models of thin structures. This method is based on the requirement that a scaled energy functional possibly including second-gradient terms stay bounded in the limit of vanishing 'thinness'.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
