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 formO(r -λ) asr → 0 are established and further conditions are derived for singularities of the formO(r -λ lnr) asr → 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 theN-material wedge are presented.
Résumé
Ce papier examine le coin composé, linéaire et élastique, en deux dimensions, pour déterminer les contraintes singulières à son sommet. On va considérer la rangée totale des conditions aux limites du coin, et les conditions correspondantes dans le coin. On se sert de la séparation des variables de la fonction de contrainte d'Airy, pour déterminer les conditions usuelles sur le déterminant pour les singularités de la formeO(r -λ) quandr → 0, et on dérive des conditions additionnelles pour les singularités de la formeO(r -λ lnr) quandr → 0. L'ordre du déterminant impliqué dans ces conditions dépend du nombre des matériaux dans le coin. D'abord on propose deux méthodes systématiques de développer le déterminant du coin deN-matériaux.
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Dempsey, J.P., Sinclair, G.B. On the stress singularities in the plane elasticity of the composite wedge. J Elasticity 9, 373–391 (1979). https://doi.org/10.1007/BF00044615
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DOI: https://doi.org/10.1007/BF00044615