Spherical reservoirs, as objects perfect with respect to their weight, are used in spacecrafts, where thin-walled elements are joined by frames into multifunction structures. The junctions are local, which results in origination of stress concentration regions and the corresponding rigidity problems. The thin-walled elements are reinforced by frame to decrease the stresses in them. To simplify the analysis of the mathematical model of common deformation of the shell (which is a mathematical idealization of the reservoir) and the frame, the assumption that the frame axial line is inextensible is used widely (in particular, in the manual literature). The unjustified use of this assumption significantly distorts the concept of the stress-strain state. In this paper, an example of a lens-shaped structure formed as two spherical shell segments connected by a frame of square profile is used to carry out a numerical comparative analysis of the solutions with and without the inextensible frame hypothesis taken into account. The scope of the hypothesis is shown depending on the structure geometric parameters and the load location degree. The obtained results can be used to determine the stress-strain state of the thin-walled structure with an a priori prescribed error, for example, in research and experimental design of aerospace systems.
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Vinogradov, Y.I. Scope of inextensible frame hypothesis in local action analysis of spherical reservoirs. Mech. Solids 52, 342–352 (2017). https://doi.org/10.3103/S0025654417030116