Premium
Semi infinite Orthotropic Cantilevered Strips and the Foundations of Plate Theories
Author(s) -
Lin Yihan,
Wan Frederic Y. M.
Publication year - 1990
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1990823217
Subject(s) - mathematics , orthotropic material , mathematical analysis , boundary value problem , kernel (algebra) , fredholm integral equation , cantilever , integral equation , cauchy distribution , scalar (mathematics) , gravitational singularity , cauchy's integral formula , strips , cauchy problem , geometry , initial value problem , structural engineering , pure mathematics , algorithm , finite element method , engineering
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.