Methods of calculation of ribbed plates for strength and stability
The desire to increase the reliability of structures forces engineers and designers not only to turn to new materials, in particular composite materials, but also to the introduction of additional reinforcing elements that do not significantly affect the change in the weight of the structure. As such effective means is the use of stiffeners, which have become widespread in engineering practice. The foundations of analytical methods of structural mechanics applied to the problems of calculating ribbed plates and shells were laid by Russian scientists S.P. Timoshenko, I.G. Bubnov, P.F. Papkovich, V.V. Novozhilov, A.I. Birger. Currently, many scientists are also engaged in the calculation of ribbed plates and shells for strength and stability. In this paper, two analytical methods for calculating ribbed plates supported by a cross system of stiffeners are proposed: a method for calculating strength in determining the stress-strain state and a method for calculating stability in determining the critical load. The calculation of the stress-strain state and stability of the structures under consideration is associated with significant mathematical difficulties that an engineer can currently overcome with the help of modern mathematical packages. In this paper, the technique of strength analysis of the stress-strain state of a ribbed plate is implemented in the Mathcad package, and the stability problem is successfully solved in the Maple package. The calculation of the strength and stability of ribbed plates reinforced with ribs placed crosswise or parallel to one of the sides of the plate is considered. The proposed computational mathematical model is based on the replacement of the original ribbed plate with an equivalent flat isotropic plate. The stiffness characteristics of the equivalent plate are calculated taking into account the contribution of the reinforcing elements of the ribbed plate. It is assumed that the thin-walled structure is supported by a sufficiently large number of ribs located at a sufficiently small distance from each other, which allows their "smearing" relative to the median surface of the plate.Control examples of calculation according to the proposed methods are given. The results of analytical calculations are in good agreement with the results of numerical analysis performed by the finite element method in the MSC.Nastran/Patran package.The proposed methods will allow the engineer at the stage of preliminary calculation and design of the structure to identify the features of its stress-strain state, such as stress concentration sites where it is necessary to reduce the size of the finite element grid during the refinement calculation in industrial packages of finite element analysis.