Solving the mixed type axisymmetric problems for anisotropic bodies with mass forces

Аuthors

Ivanychev D. A.

Lipetsk State Technical University, 30, Moskovskaya str., Lipetsk, 398600, Russia

e-mail: Lsivdmal@mail.ru

Abstract

A technique for solving the mixed axisymmetric problems for the bodies bounded by the coaxial rotating surfaces from transversal-isotropic material being under the impact of mass forces was developed in this work.

Its basis is a notion of the internal and boundary states, conjugated by the isomorphism, which allows establishing one-to-one correspondence between the elements of these spaces. The internal state includes the stress tensor components, deformation tensor components and displacement vector. The boundary state includes the forces and movements at the boundary, as well as 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 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 on the method of creating basic displacement vectors. The orthogonalization of the state spaces is performed. Finally, the desired state detecting is reduced to solving an infinite system of algebraic equations regarding the Fourier coefficients.

The article presents the solution of the problem with mixed boundary conditions for a cylinder. The material is a transversely isotropic siltstone with the anisotropy axis coinciding with the geometric axis of symmetry. Mass forces, imitating centrifugal inertial forces, act on the cylinder. Mechanical characteristics have an analytical polynomial character. The article presents the explicit and indirect signs of problem solution convergence, and graphical visualization of the results.

Keywords:

the method of boundary states, main mixed task, mass forces, transversely isotropic cylinder, axisymmetric problems

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