Buckling of coating shell with permissible surface deflection

Abstract

It is known that the initial imperfections of the shape of the surface of the shell (defects during manufacture) affect the magnitude of the critical load. The analysis of experimental results of shell experiments showed that at an amplitude of imperfection which equal to the thickness of the shell, the critical load decreases by almost four times.

The solution of the problem of buckling of elastic shell to explain the differences between the theoretical and experimental data is made using the method of initial imperfections. According to this method, instead of the set of all initial defects of the shell, the initial equivalent deflection from the ideal form W₀^е is introduced.

To detect the minimum edge critical load of a double positive curvature shallow shell, a form of imperfection on the plan of the shell was identified as a circular localized dent.

The system of differential nonlinear equations in displacements is given to a system of algebraic nonlinear equations using the finite difference method.

The position of the local limited dent on the shell plan is determined by the points of the finite-difference grid, which coincide with the centers of the dent (i, j). The minimum dimensions of the dent on the shell plan depend on the distance between the nodes of the finite-difference grid and are assigned so that the number of nodes in the direction of the coordinate axes X (Y) is at least three in the middle of the dent. In the knots that got into the dent, geometry deviations of the denture shell from the mid-surface of the shell are determined and used as input data during the formation of a solving system of equations.

A numerical experiment is performed for a symmetric dent placement on a shell plan (shell center: i=7, j=7). Fixing of a square shell of a positive curvature on all four sides is hinged.

An overview of the studies of built shell coatings shows that it is necessary to improve the methods of their construction and to introduce limitations on defects obtained as a result of construction. The results of a numerical experiment for determining the stability of a shell of a positive curvature with initial imperfections indicate the influence of these imperfections for different curvatures and the different location of imperfections.