Goldenweiser Asymptotic Form for Strength Analysis of the Spherical Tank

Authors: Vinogradov Yu.I., Georgievskiy V.P., Konstantinov M.V. Published: 19.06.2015
Published in issue: #3(102)/2015  

DOI: 10.18698/0236-3941-2015-3-119-133

Category: Mechanics | Chapter: Mechanics of Deformable Solid Body  
Keywords: spherical shell, asymptotic model of deflection, error

The paper considers an elementary model of the isotropic spherical shell deformation, which was developed by A.L. Goldenweiser. The model is known as an asymptotic model since it proves to determine the real phenomenon more precise if its shell is thinner. There is still no quantitative assessment of this statement. The deflected mode of the shell is analyzed considering variations in both its relative thickness and the external boundary loading condition. The analysis was carried out using both the asymptotic model and the reference model featuring an error due to the assumptions proposed by Kirchhoff. The analysis results of the two models were compared with each other. Asymptotic model limits are found judging the error estimates of the local loading type. These limits can help to choose an appropriate mathematical model for the spherical tank strength calculation.


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