The Strength of the Small Curvature Composite Compressed Panels at Geometrically Nonlinear Behavior

Aeronautical and Space-Rocket Engineering


Аuthors

Mitrofanov O. V.*, Toropylina E. Y.**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: oleg1mitrofanov@yandex.ru
**e-mail: toropylina.ekaterina@yandex.ru

Abstract

The article considers the small curvature cylindrical panels of the airframe design  as the smooth ones with account for the permissibility of buckling and beyond critical condition in the event of membrane and bending stresses. In this case, the panels in question may be classified as the panels of medium thickness. We will assume as well that the article tackles the initial stage of the geometrically nonlinear behavior of the panels and the wave formation realignment is not allowed.
The purpose of the article consists in substantiating the strength of the low curvature compressed composite cylindrical panels. This is a formal record of geometrically nonlinear relationships for performing verification calculations and formalization of applied techniques formalization. These techniques are being applied for conducting confirmatory analysis for minimum thicknesses determining of the orthotropic rectangular low curvature cylindrical panels under assumption of postbuckling behavior under the action of compressing strain and employing condition of the originating membrane and bending stresses sum to the limit by strength values for the composite structure by the static strength criteria.
This subject has been developing and remained relevant for several decades in terms of the composite panels calculation and design with account limitations on the static strength, stability and the static strength substantiation in case of postbuckling behavior.
This article special feature consists in considering the sum of the membrane and bending stresses in the analysis of geometrically nonlinear stress-strain state. It should be noted as well that the extreme values of the total stresses and the of the PCP position, which in general will not coincide with the PCP, are determined separately for membrane or bending stresses. The general technique for the medium thickness panels designing in a post-buckling state consists in the thicknesses determining with account for the geometrically nonlinear behavior of membrane and bending stresses. Then mathematical optimization problem is being reduced to solving a nonlinear equation with respect to panel thickness considering the eeffect of two parameters (x and y coordinates) when finding the PCP, in which maximum modulo stresses are being realized.
The authors have obtained analytical solutions that may be employed to perform confirmatory analysis of orthotropic cylindrical panels with geometrically nonlinear behavior under longitudinal compression., The applied methods for determining the minimum thicknesses of the orthotropic low curvature cylindrical panels, which should be classified as panels of medium thickness, based on the obtained solutions to geometrically nonlinear problems are proposed. Each design technique is reduced to the numerical solution of a nonlinear equation with respect to the panel thicknesses and parametric studies by the coordinates (xi, yi) to determine potentially critical points, at which stresses may reach maximum modulo values. The items of the general technique for estimating the minimum thicknesses of composite panels are formulated for the cases geometrically nonlinear behavior is acceptable considering the static strength criteria under various boundary conditions. The basic results obtained in this work are the analytical relations presented below and the proposed general algorithm for minimum thicknesses determining.

Keywords:

postbuckling behavior, orthotropic material, membrane stresses, bending stresses, small curvature cylindrical panels, compressive stresses

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