Analysis of the stability of the computational algorithm to a change in the geometric parameters of cylindrical shell structures

Abstract

This study deals with testing sustainability of a computational algorithm to a change in geometric parameters of cylindrical shell structures. A change in geometry implies the replacement of one type of a cylindrical shell (elliptic, hyperbolic, parabolic) with another so that the quantitative change (the difference in elevations) in the area under consideration is minimal. On the one hand, this test allows to assessing the correctness of the algorithm itself and is relevant for algorithms that use both numerical methods and symbolic calculations. On the other hand, it allows to evaluating the possibility of simplifying calculations by approximating a complex surface with a simpler one both in understanding the surface definition itself and in expressing its basic characteristics such as Lame coefficients and main curvatures. A mathematical model of deformations of shell structures based on the hypotheses of Timoshenko (Mindlin - Reisner) are used in the work. The model takes into account transverse shifts, geometric nonlinearity and orthotropy of the material, and its written in the form of a functional of the total potential strain energy. The calculation algorithm is built on the basis of the Ritz method to reduce the variational problem of the minimum functional to the solution of a system of nonlinear algebraic equations, and on the method of continuing the solution with the best parameter for its solution. All calculations were carried out in dimensionless parameters. Three types of cylindrical panels are calculated, and critical loads of buckling and deflection fields at subcritical and supercritical moments are obtained. It is shown that for the considered class of problems the previously proposed mathematical model and computational algorithm are resistant to changes in the geometry of the structure.