Using Somigiliana's formula, the general solutions and hypersingular integral equations for a three-dimensional impermeable crack problem in an infinite transversely isotropic piezoelectric solid under mechanical and electrical loads are given.

As the cracks lie in one side of the bimaterial plane,the problem is reduced with finite-part integral conceptions to a set of hypersingular integral equations,in which the unknown functions are the displacement discontinuities on the crack surfaces.

In this paper, the problem of an arbitrarily shaped planar crack which is perpendicular to the interface of bimaterial and loaded by interior normal pressure is studied by means of the method of hypersingular integral equation in three dimensional fracture mechanics.

To simplify the calculations of wheel-rail contact force and governing equations,a surface crack problem in a semi-infinite space was reduced to solving a set of hyper-singular integral equations with displacement jumps as unknown functions.

A radial crack in an elastic plane with a circular inclusion is investigated by use of a hyper-singular integral equation method.

Based on the fundamental solution of the elastic mechanics on the half-plane body with free boundary,and using Bitt s low, the stress-displacement relation, Hooke s low, and the stress boundary condition of the crack, the hyper-singular integral equations to describe this problem was \{derived\}; through suitable integral transforms, we established the correspondi.

Then,this crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations.

Using Kelvin s solutions and the concepts of finite-part integral,a set of hypersingular integral equations to solve the inclusion problems in two dimension elasticity is derived,and its numerical method is then proposed by combining the finite-part integral method with the boundary element method.

Using the concepts and method of finite-part integrals, the hypersingular integral equations of a plane crack loaded by arbitrary loads is proved exactly.

Starting rigorously from the three-dimensional theory of transversely isotropic elasticity, this paper presents exactly solutions of displacement jumps, singular stress fields and stress intensities factor near the front edge of mode I penny-shaped crack in transversely isotropic materials with the use of hypersingular integral equation method.