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.

Information on the singular behavior at the vertex of a bi-material wedge is the objective of this paper. A summary of the necessary conditions, which depend heavily on the associated eigenvalue equation, for stress singularities of O(r -~ In r) as r --~ 0 or O(r x) as r -~ 0 is stated. The eigenvalue equations arising from a wide range of boundary and interface conditions are then provided. Bi-material wedge problems that have been subjected to singularity analyses of some generality in the literature are briefly reviewed.

No abstract

No abstract

The tendency of a laterally loaded, unilaterally constrained, rectangular plate to separate from its simple supports motivates one to consider the actual extent of contact. In the case of a square plate, an appropriately chosen finite integral transform converts the dual series equations that result from the Levy-Nadai approach to one singular integral equation which can be solved by standard methods. Being a receding contact problem, the extent of contact depends on the geometry and elastic properties of the plate only. The support reactions are integrated to confirm that total equilibrium is obtained using classical plate theory.