On indentation of heterogeneous strip

Abstract

This paper presents a method for constructing approximate solutions to the problem of parabolic stamp indentation into heterogeneous elastic strip tightly engaged with the non-deformable base. The proposed method is based on the variational formulation of the problem and involves simplification of the potential energy functional through hypothesis of displacement fields introduction. Auxiliary problem of the action of a concentrated load on the boundary of an inhomogeneous strip is solved using the variational Lagrange principle. A system of two second order differential equations with variable coefficients with respect to the displacement vector components on the upper bound of the strip is obtained. Solution of the contact problem of parabolic stamp indentation into heterogeneous elastic strip in the case when the elasticity moduli depend only on the transverse coordinate is obtained. The characteristic relations such as "force - size of the contact area", "indentation - size of the contact area" and the stress distribution in the contact zone for some different laws of heterogeneity are plotted.