Exact solution of the mixed axisymmetric problem of elasticity theory for an infinite elastic layer weakened by cylindrical cavity

摘要

A study was conducted to demonstrate exact solution of the mixed axisymmetric problem of elasticity theory for an infinite elastic layer weakened by cylindrical cavity. An exact solution of the mixed axisymmetric problem of elasticity theory for an infinite elastic layer weakened by a cylindrical cavity was constructed. The faces of the layer were in contact with an absolutely rigid plate and a normal axisymmetric compressing load was applied to the cylindrical face of the cavity, while there was no tangential stresses. It was required to find the field of displacements and stresses and the problem was solved by a new method. The integral Fourier transform was applied directly to the Lamé equations in the cylindrical system of coordinates. The inhomogeneous vector boundary-value problem was formulated and a new method of constructing the matrix Green function for its solution.