On 3D problems of thermoelastostatics for transversely isotropic solids with anticracks

• The 3D anticrack problems of thermal stresses are solved.
• The thermal problems are reduced to their mechanical counterparts.
• The 2D integral governing equations for the stress jump functions are derived.
• Solutions for penny-shaped anticracks under constant thermal loads are given.

A general method is proposed for the solution of uncoupled thermoelasticity problems for a transversely isotropic space containing a rigid sheet-like inclusion (an anticrack) in the isotropy plane under some thermal actions. An analogy between the thermal anticrack problems and their mechanical counterparts is exploited and used to reduce the resulting boundary-value problems in the symmetric and antisymmetric cases to the mixed problems of potential theory. The governing boundary integral equations for a planar anticrack of arbitrary shape are obtained with the unknown stress jumps across the inclusion. As an application of the theory, complete solutions in elementary functions are given and discussed for a circular rigid disc-inclusion whose surfaces are exposed to uniform cooling temperatures or temperature gradients.