SURFACE EFFECT IN AN ELASTIC CYLINDER WITH RING FIBERS UNDER ROTATION WHEN FREE LANDING

  • V. M. Akhundov National Metallurgical Academy of Ukraine
  • M. M. Kostrova National Metallurgical Academy of Ukraine
  • I. Yu. Naumova National Metallurgical Academy of Ukraine
Keywords: piecewise homogeneous cylinder, annular fibers, centrifugal forces, large deformations, finite difference method

Abstract

We investigated the near-surface effect in an elastic cylinder made of a matrix and ring fibers under the influence of inertial forces of rotation around its axis of symmetry during free landing. Fibers of a square cross section are arranged in a cylinder matrix according to a square packing scheme. The cylinder was formally considered as an assembly of ring elements. The annular elements are square rings of matrix material, including annular square fibers as their reinforcing core.

Geometric and physical equations and equilibrium equations were used in the nonlinear theory of elasticity to describe the deformation of the piecewise-uniform cylinder under consideration. A feature of the problem being solved is the effect on the centrifugal forces acting on the matrix and the fibers of changes in the distances from their material points to the axis of rotation of the cylinder.

The first-order derivatives of the sought quantities with respect to the axial and radial coordinates in the equations of the problem were approximated using finite-difference relations of the second order of accuracy. Together with the boundary conditions and the conditions of joint deformation of the matrix and fibers, a system of nonlinear equations is formed with respect to the main sought quantities at the nodal points of the two-dimensional region. This system of equations was solved on the basis of the discrete Newton method. The uniqueness of the solution of the boundary value problem was ensured by continuing the solution with respect to the angular velocity of rotation of the cylinder.

Under conditions of large deformations of the components of a cylindrical body, a near-surface effect in it was considered, which manifests itself in a substantially non-periodic deformation of the ring elements of the body adjacent to its internal and external surfaces. As a criterion for the non-periodic deformation of the ring elements, the upper face of the difference between the deformation components of the same name on the oppositely located bounding surfaces of the element was used. Using this criterion, the depth of the near-surface effect was determined near the inner and outer surfaces of the cylinder at its final rotation speed. The effect was revealed on the pattern of stress distribution in characteristic sections of the body.

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Published
2020-03-02
How to Cite
Akhundov, V. M., Kostrova, M. M., & Naumova, I. Y. (2020). SURFACE EFFECT IN AN ELASTIC CYLINDER WITH RING FIBERS UNDER ROTATION WHEN FREE LANDING. Bulletin of Zaporizhzhia National University. Physical and Mathematical Sciences, (2), 4-20. Retrieved from http://journalsofznu.zp.ua/index.php/phys-math/article/view/219