The action of a stamp on an elastic anisotropic half-space: PMM vol. 34, n≗1, 1970, pp. 172–178

Abstract

Studies dealing with the problem of action of a stamp on an isotropic or transversely isotropic half-space under the condition that the boundary of the half-space is a plane of elastic symmetry and that the stamp presses in the-direction of the axis of elastic symmetry and has axisymmetric shape are generally known. However, only isolated papers ll, 51 or none at all are devoted to the action of a stamp on an anisotropic halfspace in the more general case of anisotropy or the case of transversely isotropic body under the condition that the boundary of the half-space is not a plane of elastic symmetry. It is shown below that the pressure distribution for a stamp with circular or elliptical plan form remains the same when the stamp acts on an anisotropic (orthotropic) halfspace as it was for its action on an isotropic half-space. The method is based on the construction of a complex loading function corresponding to the given loading. Formulas are presented for the impression of stamps of different shapes for the orthotropic body and the transversely isotropic medium. In the last case it was assumed that the boundary plane contains the axis of elastic symmetry. The case of off-center action of the compression force is examined. Through construction and utilization of the complex loading function the possibility of expanding the method to the case of an isotropic medium is indicated.