Orthotropic thermoelasticity problem of symmetrical heat flow disturbed by three coplanar cracks

Abstract

This article presents a study on the plane thermoelasticity problem of an infinite orthotropic plate split by three coplanar cracks under the action of symmetrical heat flow. Using the technique of Fourier transforms, the related four-part mixed boundary value problems are reduced to two kinds of quadruple integral equations with cosine and sine kernels which are solved by use of finite Hilbert transformation. Closed form solutions to the temperature, thermal displacements and thermal stresses on the crack surfaces, and especially, the thermal stress intensity factors at crack tips are obtained for the case of uniform heat flow. The known solutions to the orthotropic thermoelasticity problem of uniform heat flow disturbed by a pair of coplanar cracks or a central planar crack can be deduced from the above results in a straightforward manner, including the solution of thermal stress intensity factors for the corresponding thermoelasticity problem with two collinear cracks which is another form of the solution, equivalent to that of series expressions obtained by the authors in a previous paper, but much simpler. It is found that extremely large magnitudes of stress singularity may occur as the distance between two adjacent cracks approaches zero.