On the stress singularities in the plane elasticity of the composite wedge

Abstract

This paper examines the composite, two-dimensional, linear elastic wedge for singular stresses at its vertex. A full range of wedge boundary and matching conditions is considered. Using separation of variables on the Airy stress function, the usual determinant conditions for singularities of the form O(r -x) as r --~ 0 are established and further conditions are derived for singularities of the form O(r -x In r) as r ~ 0.The order of the determinant involved in these conditions depends upon the number of materials comprising the wedge. Two systematic methods of expanding the determinant for the N-material wedge are presented. RESUMECe papier examine le coin compos~, lin~aire et 61astique, en deux dimensions, pour d6terminer les contraintes singuli~res ~ son sommet. On va consid6rer la rang6e totale des conditions aux limites du coin, et les conditions correspondantes dans le coin. On se sert de la s6paration des variables de la fonction de contrainte d'Airy, pour d6terminer les conditions usuelles sur le d~terminant pour les singularit6s de la forme O(r -x) quand r ~ 0, et on d~rive des conditions additionnelles pour les singularit6s de la forme O(r -x In r) quand r--~ 0. L'ordre du d6terminant impliqu~ dans ces conditions d6pend du nombre des mat6riaux dans le coin. D'abord on propose deux m6thodes syst6matiques de d~velopper le d6terminant du coin de N-mat~riaux.

Generalized plane strain thermoelastic deformation of laminated anisotropic thick plates

“…D da 1 dp 1 dD dp 1 a 1 0X 13 Dempsey and Sinclair (1979) have proved the existence of a non-trivial solution for a 1 and da 1 adp 1 of Eqs.…”

Singularity parameter determination in adhesively bonded lap joints for use in failure criteria

“…Considering homogeneous linear elastic materials, perfect adhesion between the material wedges, homogeneous boundary conditions (at external faces) and plane states (plane stress, plane strain or generalized plane strain), at the present moment there is enough information and efficient analytical and computational tools for the evaluation of accurate values of λ k , see Dempsey and Sinclair [18,19], Pageau et al [20], Ting [21], Manti et al [22] and Poonsawat et al [23,24] among others. In this work a semianalytical tool, developed by the authors, Barroso et al [25], is employed.…”

Cylindrical Bending of Laminated Plates with Distributed and Segmented Piezoelectric Actuators/Sensors

“…(9) and (17) for a 1 and da 1 / d p 1 has been discussed by Yang et al 29 and Dempsey and Sinclair. 30 Yang et al 29 have shown that a nontrivial solution exists for a 1 and da 1 / d p 1 . Therefore, the general solution is u u´=…”