On the issue of variable stiffness plates stability
Strength and thermal conditions of flying vehicles
Аuthors
^{1}^{*}, ^{2}^{**}1. Sukhoi Civil Aircraft Company, SCAC, 26, Leninskaya Sloboda str, Moscow, 115280, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А80, GSP3, 125993, Russia
*email: ap.erkov@yandex.ru
**email: a_dudchenko@mail.ru
Abstract
The article considers the problem of stability of the three types of variable stiffness plates: with the thickness stepped changing, thickness continuous linear changing, and with thickness combined changing (with the areas of both constant and continuously variable thickness). The plates are loaded with a compressive force, uniformly distributed over the two opposite edges. The force is applied in the median plane of plates. The boundary conditions are as follows: hinged joints over all four sides of the plate. Plates from isotropic materials and from laminated composites were considered. Three types of plates from isotropic material, and the plate from laminated composite with the stepped thickness changing were considered.
To study the stability of plates of variable stiffness the Ritz method was used. Analytical calculations were performed with the Maple math package. It was assumed that before plates were buckled, the stresses were in the elastic zone and were not exposed to destruction.
The results of analytical calculations were compared with the results obtained by the finite element method (MSC.Nastran / MSC.Patran). For each type of plate, three geometry options were calculated, and for the plate made of laminated composite material, three options for layups were considered additionally. In the case of an isotropic material, the maximum error compared with the results obtained in MSC.Nastran / MSC.Patran was not more than 7%. In the case of laminated composite plate, the error was not more than 9%.
In general, the accuracy of the applied method depends on two main factors:

The correctness of the approximating function of the deflection. The approximating function should satisfy the geometrical boundary conditions;

The number of the series terms accounted for. The convergence of the problem, in most cases, is the better the more series terms are accounted for.
The results of the work can be employed in the design of thinwalled structures, namely, to evaluate the stability of the thinwalled plates in areas of varying thickness.
Keywords:
buckling of the plates, variable stiffness plates, Ritz method, critical force, variable stiffness plates, composite platesReferences

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