The asymptotic solution of the three-dimensional problem of the theory of elasticity for plates of incompressible materials

Abstract The asymptotic form is established and recurrence formulae are derived for determining the stress—strain state of plates of incompressible materials, when the kinematic conditions are specified on the face surfaces of the plate. By combining the solution obtained with the solution of similar problems for plates of compressible materials, a solution of the boundary-value problem for a three-layer plate with an incompressible middle layer is constructed when there is complete contact between the layers. Examples are given which model, in particular, the operation of rubber—metal seismic isolators.