Logarithmic singular stress field in a semi-infinite plate consisting of two edge-bonded wedges subjected to surface tractions

Abstract

In order to take the logarithmic stress singularity into account, this paper presents a new method for analysis of the singular stress field at the vertex of a composite wedge. A condition is derived for stress singularities of a form r ^λ-1 (log r)^mas ϒ→0, where m is zero or a positive integer. The method is used to analyze the logarithmic singular stress field in a semi-infinite plate consisting of two edge-bonded wedges. The results of analysis show that the logarithmic singularities in the stress field may be of order (log r)², (log r)¹ or (log r)⁰, depending on the combination of materials and the vertex angle of the wedges. It is also found that the surface tractions are necessary for production of the logarithmic singular stress field. For particular tractions, the terms with the highest order of the power of log ϒ may vanish from the expression of the stress field.