Basic Stress-Strain State of a Multilayer Circular Ring under the Action of Mutually Opposite Normal Forces / Основное напряженно-деформированное состояние многослойного кругового кольца под действием взаимно противоположных нормальных сил
Loading...
Date
2019-03
Authors
Ковальчук, Станіслав Богданович
Горик, Олексій Володимирович
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
Closed circular rings are widely used in engineering structures both as individual parts and as reinforcing elements of thin-walled structures. One of the important cases of the load of such elements is tension-compression by mutually opposite forces acting along one diameter. For homogeneous isotropic rings, exact solutions of this plane problem are known, and various applied calculation methods are developed. At the same time, for composite and, in particular, multilayer rings, this problem is studied much worse. The purpose of this work is to develop an analytical solution of the problem of tension-compression of a composite ring with an arbitrary number of orthotropic layers with mutually opposite normal forces acting in the plane of the ring along one diameter. Using the symmetry of the problem, its solution comes to the auxiliary problem of determining the stress-strain state (SSS) of a half ring separated on loaded sections with corresponding static and kinematic conditions at the ends. The SSS of such an element, with the exception of small areas near the ends, is similar to the SSS of a circular multilayer bar with loads on the ends. This allowed us to use the exact solution of the theory of elasticity obtained by the authors for the problem of bending a multilayer circular bar with a load on the ends to develop the solution of the problem under consideration. The relations obtained in this way correspond to the exact solution of the problem for the greater part of the ring and close to the points of application of the load, give a simplified description of the SSS without local distortion near the concentrated force. This enables to determine the main SSS of multilayer rings with different sizes of the inner and outer radius, however, the solution loses its meaning for a solid disk or a disk with a small hole in the center. For thin multilayer rings made of materials that hardly respond to lateral shear and compression, a simplified solution obtained using the plane-sections hypothesis is proposed. To demonstrate the possibilities and approbation of the solutions obtained, the results of determining the SSS of a four-layer ring with the ratio of the mean radius to the height of the cross section equal to 1.75 as well as the results of additional calculations with an increase in the specified ratio to 5.5 and 10.5 are presented.
Keywords
многослойное кольцо, ортотропный слой, сосредоточенная сила, напряжения, перемещения, multilayer ring, orthotropic layer, concentrated force, stress, displacement