ANALYSIS OF DEFORMATIONS OF AN ELASTOPROPED TUBE UNDER THE INFLUENCE OF INTERNAL PRESSURE

Abstract

The study of the deformation of soft composite structures, when their initial configuration changes significantly, re-mains one of the problems of the mechanics of composite materials. As one of these structures, we considered a long thin-walled tube of elastic layers with ring fibers of a more rigid elastic material. Pipes of this structure can be used to create flexible gas and air ducts, in order to transport substances in a spray form, to collect environmentally hazardous waste. The most common approach in the study of the bodies of a fibrous structure is based on the use of a model of a piecewise-homogeneous medium, when the matrix and fibers are considered as contacting bodies. A numerical solution of the problem according to this model of the deformation of a pipe of three layers with circular fibers of square cross section under the influence of internal pressure during large displacements and deformations is presented. The pipe was modeled as an assembly of ring elements. Such elements are square rings of a binder material, including ring fibers as their reinforcing core. The pipe design was accepted as a long cylindrical shell, which is axisymmetrically deformable under pressure, when the extreme and central sections of the ring elements move in the planes of their initial position. The boundary problem for assembling the ring elements of the shell was formulated on the basis of the equations of the nonlinear theory of elasticity for the matrix and the fibers in it. The problem was solved using the finite difference method, the first order derivatives of the main quantities with respect to the axial and radial coordinates were approximated using second-order finite-difference relations. The discrete analogue of the problem was solved on the basis of the Newton method procedure. The uniqueness of the solution of the boundary value problem was ensured by the continuation of the pressure solution in the pipe.