Identification of the mechanical characteristics of composite materials from experimental data of shells of revolution

Abstract

A method is developed for determining the mechanical characteristics of the layer of a shell of revolution made by winding along the geodesic lines. The functions describing the nonlinear elastic behavior of the material are found by analyzing the data obtained from experiments. The equations for unknown parameters and conditions of their solvability in a particular case are obtained.In experimental determination of the mechanical characteristics of some composite materiRIA (CM), such as tapes and rovings, certain technical problems may arise because of small sizes of specimens in the direction perpendicular to the reinforcement. Moreover, these characteristics can be different for each product, which is associated, for example, with influence of the technological factors as well as operating conditions within a particular structure on the properties of materials. Some methods make it possible to determine the mechanical properties of composite materials by analyzing the data obtained from the tests on multilayered specimens (see, for example, [1][2][3][4]). Indirectly, they take into account the technological factors of producing the material, dependence of the properties of CM on the methods of forming the structure, as well as its operating conditions, and allow us to overcome these technical difficulties..In [3,4], methods were described for determining the mechanical characteristics of band-type CMs based on the analysis of experiments carried out on cylindrical shells. A necessary requirement was the availability of at least two cylindrical shells with different winding angles. In this study, a similar method is developed for the case where the specimen is a shell of revolution made by winding a nonlinearly elastic tape along the geodesic lines. This allows us to obtain linear algebraic equations for the mechanical characteristics of a CM by analyzing the experimental data for only one shell per one loading cycle.Let a shell of revolution be formed by windlng tapes and rovings, at an angle ~P(n) (n = 1,...,2N) to the meridian along the geodesic lines. In what follows, all the parameters referring to the nth layer will be put in parentheses. For simplicity, we consider the axisymmetrical problem of a shell subjected to internal premure.Since the shells are thln-walled, we assume that the stress state is plane. We use the following notation: O~ is the geographic coordinate system, N= and N v are the tangential forces acting along the meridian and the parallel, respectively, q is the normal internal pressure, P is the resultant of the loads acting on the part of the shell located above the parallel circle of radius r, while r I is the radius of the base circle, r s is the radius of the cap, h~ ) is the thickness of the nth layer on the base circle, and ~(i n) is the angle between the meridian Kazan State Architecture and Civil Engineering Academy, Tatarstau, Russia. Trn-~l~ted from Mekhanika