BASIC STRESS-STRAIN STATE OF A MULTILAYER SYMMETRIC CIRCULAR ARCH UNDER THE ACTION OF NORMAL FORCES IN THE MIDDLE SECTION. REPORT 2. ARCHES OF SMALL CURVATURE

Abstract

Circular arches are common elements of construction and machine building structures. They can be both individual components and reinforcing elements of thin-walled casings. An important case of arches defor-mation is the symmetrical folding in its own plane surface under the action of concentrated force. The re-sistance of homogeneous isotropic arches is sufficiently investigated. However, the mechanics of multilayer arches deformation is studied considerably less, which creates additional obstacles to introducing such ele-ments in designing practice. The purpose of this work is a theoretical study of the basic stress-strain state (SSS) of a symmetrically fixed multilayer arch under the action of concentrated normal force in the middle section by developing the analytical solution of the corresponding problem. The second part of the article deals with developing a simplified solution of the problem obtained by using plane section hypothesis, which eliminates the effect of displacement deformation and transversal compression on other components of the SSS. Considering the accuracy, such a solution ranks below the complete solution obtained in the first part of the article, which takes into account the whole complex of elastic characteristics of layer materials, but it is much simpler to implement. Using the developed simplified solution, this made it possible to obtain com-plete ratios for unknown static and kinematic parameters (unknown constants) for solid and hinged arches in the middle section that have different types of end fixation. To test and approbate the obtained theoretical ratios, a long three-layer arch of small curvature (the ratio of the mean radius to the section height is 30) was calculated. The results of determining the arch deflection with different types of end fixations, obtained by using simplified and complete solutions, as well as by the final element method, are presented. A brief analysis of accuracy of the simplified solution in case of changes in the stiffness of outer and middle layers is made. The developed solution enables to determine stress condition of long symmetrical composite arch ele-ments and small curvature rings with accuracy accepted for practice. However, the reliable determining of displacements with its application has certain limitations, the precise identification of which requires further research.