Dimensionless parameters in the theory of reinforced shells

In this paper a variant of the dimensionless parameters for a wide range of shell structures is proposed. For shallow shells of have a rectangular form, the dimensionless parameters are used for a long time, as for the general form of shells; there is no single form of dimensionless ratios for each type of shell, because Lame parameters differ not only in values, but also in dimensions. Therefore, the work shows the dimensionless relations for deformations, stresses, forces, moments and functional of total potential energy of deformation. The relations consider geometric nonlinearity, transverse shifts, orthotropy of material and the introduction of ribs on the structural anisotropy of the method in accordance with their shear and torsional rigidity. The authors show a further approach to solving the strength and stability tasks of different types of shells in the dimensionless parameters. Some methods for solving nonlinear problems of stability do not look quite correct, when using the dimensional parameters (e.g., a technique, based on the method of continuation of solution for the best parameter). In dimensionless parameters, all calculations are beyond doubt. The calculations of some shell structures are provided in dimensionless and dimensional parameters and their consistency is shown. The proposed approach allows one to obtain values for the calculation of a series of such shells, which is more convenient to optimize the choice of design parameters. We have examined some of the differences in critical loads, obtained in dimensionless and dimensional solution of the problem.