INDENTATION OF AN ANNULAR PUNCH INTO AN ELASTIC LAYER WITH A THIN REINFORCING COATING

The three-dimensional nonaxisymmetric contact problem of elasticity on the indentation of a punch occupying an annular domain into a layer is considered. The layer lies on a rigid base and is reinforced by a thin coating over the upper boundary. It is assumed that the stiffness of the coating is much larger than the stiffness of the layer. Thus, the stress-strain state of the layer can be modeled by the Melan coating equations (three-dimensional analogue). The algorithm of constructing an effective approximate solution of the integral equation of this problem is developed. The method is based on Galerkinʹs procedure combined with the addition theorems for the Bessel functions. These theorems permit one to represent the coefficients of linear algebraic systems in the form of single integrals which are convenient for numerical calculations. In the particular case of the axisymmetric problem, this method leads to familiar results [1].