Dimensionless Models of Deformation of Stiffened Shell Structures

Abstract

Original Russian Text: Karpov V.V., Semenov A.A. Dimensionless models of deformation of stiffened shell structures. PNRPU Mechanics Bulletin, 2015, no. 3, pр. 74-94. This paper suggests a variant of dimensionless parameters for a wide range of shell structures. Dimensionless parameters have been used for shallow shells of rectangular planform for a long time. There is no universal form of dimensionless relations for shells of a general type, since the Lamé parameters are different for each type of shells, as far as their values and dimensions are concerned. Therefore, the work shows the dimensionless relations for strains, stresses, forces, moments and the functional of total potential energy of deformation. These relations consider geometrical nonlinearity, transverse shears, material orthotropy, as well as the introduction of ribs according to the structural anisotropy method with their shear and torsional rigidity taken into account. The authors show a further approach to solving strength and stability problems with respect to different types of shells in dimensionless parameters. Some methods intended to solve nonlinear strength problems are not quite correct, when dimensional parameters are used (for example, the methods based on the best parameter continuation method). In dimensionless parameters, all calculation are beyond doubt, as far as their correctness is concerned. The article also provides the calculations of some shell structures in dimensionless and dimensional parameters and shows their consistency. The introduction of dimensionless parameters in the course of calculation of such structures allows to obtain more comprehensive information on the stress and strain state of shells and detect strain features for a whole range of such shells. Also, this approach is suitable for optimizing the choice of structural parameters. The authors analyze some differences in critical loads that were obtained in the dimensionless and dimensional solutions of the problem. © PNRPU