Mechanics of Composite Materials

, Volume 31, Issue 5, pp 493–497 | Cite as

Model of a layered plate considering nonideal contact between layers

  • V. G. Piskunov
  • A. V. Marchuk
  • S. A. Ogarkov


We propose a mathematical model for doing calculations for layered plates, allowing for both rigid and sliding contact in the presence of frictional forces between the sliding layers. The model takes into account the distribution of tangential and normal displacements across the thickness of the sliding layered stack, and also the distribution of transverse normal stresses. The strain tensor is obtained using the Cauchy relations; the stress tensor is obtained based on Hooke's law. Tne Lagrange variational principle allows us to obtain the resolvent system of differential equations and the corresponding boundary conditions. The spatial model for deformation of a layered plate has a number of special features compared with familiar models. The system of differential equations has operators no higher than second order. It is described relative to displacements on the faces of the stack. This is convenient in solving problems involving sliding of layers with and without friction.


Boundary Condition Differential Equation Mathematical Model Normal Stress Stress Tensor 
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    V. G. Piskunov, V. S. Sipetov, and Sh. Sh. Tuimetov, “Bending of a thick transversely isotropic plate with transverse loading,” Prikl. Mekh., No. 11, 21–26 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. G. Piskunov
  • A. V. Marchuk
  • S. A. Ogarkov

There are no affiliations available

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