Monday, 11 October 2004 - 5:10 PM

This presentation is part of : Surface Stress in Nature and Technology

Exact solutions for a thick elastic plate with a thin elastic surface layer

Anthony J M Spencer, University of Nottingham, University of Nottingham, School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom

In previous papers the author and colleagues have developed a procedure for deriving exact solutions of the equations of linear elasticity for an isotropic elastic material that is inhomogeneous to the extent that the elastic moduli can depend in an arbitrary manner on a single coordinate, which here we take to be the through-thickness coordinate in a thick elastic plate. The dependence on this coordinate may be continuous, as in a functionally graded material, or discontinuous, as in a laminate. The underlying idea is that any solution of the two-dimensional classical thin plate equations can be used, by simple substitutions, to generate a family of solutions of the three-dimensional linear elasticity equations for a material with the stated inhomogeneity.

In this paper we apply this procedure to the case of a thick plate (which for simplicity we take to have uniform mechanical properties, although this is not essential) which is coated by a thin surface layer of different elastic material on one or both faces. We obtain exact three-dimensional elasticity solutions for some illustrative examples for bending and stretching of the composite plate. These give analytical expressions for the stress and deformation in both the plate and the surface layer, and also the interface tractions between the plate and the surface layer.

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