Analytical Research of Expanding Hole in Plane of Viscoelasticity

Abstract:

A study is made of the analytical displacements and stresses during expanding hole in plane of viscoelasticity.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 also suit for the cases that spherical tensor has the characteristic of viscoelasticity.The method is applied to the problem of HKelvin viscoelastic model.Comparison of displacements of varying velocities shows that the displacement changs gently if radius varies slowly,but the displacenment becoms large in the end.