The stress-strain state of ribbed shell structures
The paper presents an analysis of the stress-strain state of shallow shell structures of double curvature, reinforced from the concave side by a various number of stiffeners. Mindlin–Reissner shell deformation theory is used, which accounts for geometrical nonlinearity and transverse shears, as well as for discrete introduction of stiffeners with contact between the stiffener and the shell along the strip. The mathematical model is written in the form of a functional of full potential deformation energy. The algorithm of the analysis is based on the application of the Ritz method to the functional, which is used for reducing the problem to a system of nonlinear algebraic equations. The resulting system is solved by the parameter continuation method. Structural variations that are considered in the paper are fastened with fixed-pin joints along the contour and are subject to external uniformly distributed transverse loading. The values of stresses, forces, and moments in the stiffeners and in the shell skin are obtained and analyzed. Specific features of their distribution are revealed. All values are given in dimensionless parameters. It is shown that accounting for the contact of the stiffener with the shell skin along the strip allows one to investigate the stress-strain state in the stiffeners, which are not possible using delta functions with the introduction of stiffeners along the line.