More accurate equations of the deformation of thin plates, which are more c
onvenient for solving contact problems for bodies with coatings and contain
ing, as a special case, the equations of all known applied theories, are de
rived by an asymptotic analysis of the first fundamental problem of the the
ory of elasticity. The equations of the deformation of thin-walled elastic
bodies are classified, their qualitative correspondence to the equations of
the theory of elasticity is clarified, and the forms of the features that
arise along the shift lines of the boundary conditions in the corresponding
contact problems are established. A criterion for selecting approximate mo
dels to describe the properties of the coatings depending on the geometrica
l and mechanical characteristics of the coating and the substrate and also
on their degree of adhesion is given. (C) 1999 Elsevier Science Ltd. All ri
ghts reserved.