Abstract
The aim of this paper is to give the title theory of shearable plates a precise and exact position with respect to three-dimensional linear elasticity. We assume that the Reissner-Mindlin representation of the displacement field hold in a 3-D body in the shape of a plate, and discuss how a constitutive response consistent with such a representation should be chosen. We find that the Reissner-Mindlin plate theory results from mere integration over the thickness of the equilibrium equations of a cylindrical body made of a linearly elastic material which is both transversely inextensible and transversely isotropic.
Sommario
Scopo di questo articolo è fornire una deduzione esatta, nell'ambito dell'elasticità lineare tridimensionale, della teoria delle piastre deformabili a taglio menzionata nel titolo. Ammesso che la rappresentazione di Reissner-Mindlin per il campo di spostamento valga in una regione tridimensionale a forma di piastra, si discute come scegliere la risposta costitutiva in maniera coerente con quella rappresentazione. Si trova che la teoria delle piastre di Reissner-Mindlin si ottiene per semplice integrazione sullo spessore delle equazioni di equilibrio di un corpo cilindrico che sia costituito di un materiale linearmente elastico tanto trasversalmente inestensibile che trasversalmente isotropo.
Similar content being viewed by others
References
Podio-Guidugli, P.,The Linear Theory of Elastic Plates and Shells, 1988, in preparation.
Podio-Guidugli, P.,Lezioni sulla Teoria Lineare dei Gusci Elastici Sottili, Masson Italia, Milano, 1991.
Podio-Guidugli, P., ‘An exact derivation of the thin plate equation’,J. Elasticity,22 (1989) 121–133.
Lembo, M., ‘The membranal and flexural equations of thin elastic plates deduced exactly from the three-dimensional theory’,Meccanica,24 (1989) 93–97.
Lembo, M. and Podio-Guidugli, P., ‘Dinamica lineare dei gusci elastici sottili’, pp. 121–123 ofAtti del X Congresso Nazionale di Meccanica Teorica ed Applicata (Pisa, 1990), Volume I.
Lembo, M. and Podio-Guidugli, P., ‘Plate theory as an exact consequence of three-dimensional linear elasticity’,European J. Mech., A/Solids,10 (1991) 485–516.
Podio-Guidugli, P., ‘Constraint and scaling methods to derive shell theory from three-dimensional elasticity’,Riv. Mat. Univ. Parma,16 (1990) 73–83.
Reissner, E., ‘On bending of elastic plates’,Q. Appl. Math.,5 (1945) 55–69.
Reissner, E., ‘On the theory of transverse bending of elastic plates’,Int. J. Solids Structures,12 (1946) 545–554.
Mindlin, R.D., ‘Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates’,J. Appl. Mech., (1951) 31–38.
Reissner, E., ‘Reflections on the theory of elastic plates’,Appl. Mech. Rev.,38 (1985) 1453–1464.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nardinocchi, P., Podio-Guidugli, P. The equations of Reissner-Mindlin plates obtained by the method of internal constraints. Meccanica 29, 143–157 (1994). https://doi.org/10.1007/BF01007498
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01007498