A Model for a Two-Layered Plate with Interfacial Slip

  • Scott W. Hansen
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 118)


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 Classification

73K10 73K20 

Key words and phrases

Multi-layer plate Mindlin plate Reissner plate 


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Copyright information

© Springer Basel AG 1994

Authors and Affiliations

  • Scott W. Hansen
    • 1
  1. 1.Department of MathematicsIowa State UniversityAmesUSA

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