A Model for a Two-Layered Plate with Interfacial Slip
In this paper we derive a model for a two-layered plate in which slip can occur at the interface. We assume that a “glue” layer of negligible thickness bonds the two adjoining surfaces in such a way that the restoring force created by the glue is proportional to the amount of slippage. Within each plate the assumptions of Timoshenko beam theory (namely, that the straight filaments orthogonal to each center sheet at equilibrium remain straight during deformation) are applied and the equations of motion are derived through the principle of virtual work. We relate the resulting system to the Mindlin-Timoshenko-Reissner plate system and also to the Kirchhoff plate system by singular perturbations involving passing the shear stiffness parameter and the glue strength parameter to infinity.
1991 Mathematics Subject Classification73K10 73K20
Key words and phrasesMulti-layer plate Mindlin plate Reissner plate
Unable to display preview. Download preview PDF.
- [La]Lagnese, J.E.: Boundary Stabilization of Thin Plates,series “SIAM Studies in Applied Mathematics” SIAM, Philadelphia 1989.Google Scholar
- [LL]Lagnese, J.E. and Lions, J.-L.: Modelling Analysis and Control of Thin Plates,collection:“Recherches en Mathématiques Appliquées”, RMA 6, Springer-Verlag, New York, 1989.Google Scholar
- [Li]Lions, J.-L.: Equations Différentielles OpérationnellesetProblèmes auxLimites,Grundlehren B III, Springer-Verlag, Berlin 1961.Google Scholar
- [Ti]Timoshenko, S., Young, D.H., Weaver, W.: Vibration problems in engineering,New York Wiley, 1974.,Google Scholar