Analytical Research of Expanding Hole in Plane of Viscoelasticity

Abstract:

Analytical displacements and stresses during expanding hole in plane of viscoelasticity are studied in this paper. According to the basic equations, Laplace transform is introduced to deduce the differential equation of displacement in Laplace space. General expression of displacement and stresses in Laplace space is derived firstly. For stress boundary problem, inverse transforming of above stresses solutions, undetermined function in the solutions can be determined by boundary conditions, and final expressions of stresses and displacement are obtained. The solutions have no restrictive condition of volume incompressible, and are also suit for the cases that spherical tensor have the characteristic of viscoelasticity. The application of the method is given to the problem of H-Kelvin viscoelastic model. Comparison of displacement of different varying velocity shows that displacement is changed gently if radius varied slowly, but displacenmet is larger in end varying time.