Решение комбинированных краевых задач для анизотропных тел вращения с массовыми силами

Abstract

The aim of the work is to determine the stress-strain state of anisotropic bodies of revolution under the action of mass forces and external conditions of a physical and geometrical nature in a combined formulation. The task is ensured by the development of the method of boundary states, based on the concepts of spaces of internal and boundary states. The theory of the formation of the basis of the space of internal states, which includes displacements, deformations, stresses and mass forces, is constructed. A common basis is a combination of two bases. The first is formed for the case of plane deformation from the action of only mass forces, based on the application of the application of fundamental polynomials. Further, on its basis, according to the method of integral overlays, a basis of internal spatial states is induced. The second is the basis of internal states in the classical boundary value problem for transversely isotropic bodies. After orthogonalization of the common basis, where the inner energy of elastic deformation acts as the scalar product, the desired state is determined by a Fourier series, the coefficients of which are defined integrals. Checking the adequacy of the solution is carried out by comparing a given field of mass forces with that obtained, as well as by comparing the specified boundary conditions with the resulting solutions. Solutions of problems with different combinations of boundary conditions for a circular cylinder of rock with the corresponding conclusions are given. Presents a graphical visualization of the results.