MAPPING AN ELASTIC FIELD FOR AN ANISOTROPIC BODY UNDER THE CONDITIONS OF AN ASYMMETRICAL BOUNDARY PROBLEM OF ELASTICITY THEORY

The paper presents a method of mapping an elastic field for a transversely isotropic body of revolution under the conditions of the second main problem of elasticity theory in a non-axisymmetric formulation of boundary conditions. The specified displacements of boundary points depend on all the three cylindrical coordinates. The problem was solved using the boundary state method. A method for forming bases of internal and boundary states is presented. Scalar products in these spaces are assigned based on the Clapeyron theorem. Orthogonalization of state bases is performed and the desired state is expanded into a Fourier series in terms of the elements of an orthonormal basis. The coefficients of these series are quadratures. The solution of the non-axisymmetric second main problem for a circular cylinder made of rock is given. The result is presented graphically