Closed Forms for the Stresses in a Class of Orthotropic Wedges

Abstract

The Mellin transform is applied to problems of stress distribution in symmetric orthotropic wedges. Integral representations for the stresses are obtained and specialized for the fundamental problem of line loads. Asymptotic forms are obtained for the general class which gives the solution when loads are applied at the tip. A subclass of wedges is considered which satisfy a certain relationship between the opening angle and elastic constants. Closed forms for the stresses can be obtained for this subclass which is dense and therefore can be used to approximate any symmetric orthotropic wedge. As an example, numerical results are presented for a quarter-plane subjected to normal or shear loads.