The contact problem solution of the elasticity theory for anisotropic rotation bodies with mass forces

In this paper presents a developed method aimed to solve contact axisymmetric problems for limited bodies of revolution from transversely isotropic material which are simultaneously under the action of mass forces. The method involves the development of the energy method of boundary states, which is based on the concepts of spaces of internal and boundary states conjugated by isomorphism, which allows us to establish a one-to-one correspondence between the elements of these spaces. The internal state includes stress tensor components, deformation tensor components and displacement vector. The boundary state includes efforts and moving boundary points and mass forces. The isomorphism of the state spaces is proved, which allows finding the internal state to be reduced to the study of a boundary state that is isomorphic to it. The basis is formed based on the general solution of the boundary value problem for a transversely isotropic body of revolution and based on the method of creating basic displacement vectors while determining the state from continuous nonconservative mass forces. The orthogonalization of the state spaces is carried out, where the double internal energy of elastic deformation is used as scalar products in the space of internal states; in the space of boundary states, the work of external and mass forces is used. Finally, the problem of finding a desired state is reduced to solving an infinite system of algebraic equations regarding the Fourier coefficients. The solution of the contact problem without friction in contacting surfaces for a circular in terms of the cylinder is presented. The material of the cylinder is a transversely isotropic siltstone with the anisotropy axis coinciding with the geometric axis of symmetry. Mass forces act on the body, imitating centrifugal forces of inertia and gravity. Mechanical characteristics have analytical polynomial view. Explicit and indirect convergence patterns of the problem solving and graphical visualization of the results are presented.