Semi infinite Orthotropic Cantilevered Strips and the Foundations of Plate Theories

Abstract

Elastostatic problems of semiinfinite orthotropic cantilevered strips with traction‐free edges and loading at infinity are reduced to the solution of a single scalar Fredholm integral equation of the first kind with a generalized Cauchy kernel. The known complex variable method for equations with a Cauchy type kernel is extended to handle the singularities in the solution for the generalized Cauchy kernel. The reduced problem lends itself to a more efficient numerical solution scheme than all existing methods. Moments of stresses at the root of the cantilever are accurately evaluated and used for the correct formulation of displacement boundary conditions for a plate theory solution (or the actual interior solution) of the elastostatics of thin flat bodies.