The Number of Members of the Double Trigonometric Series for the Stress-Strain State of Shallow Shells Assessment

The general theory of shallow shells based on a mixed solution method was developed by V.Z. Vlasov in 1944 and is actively used in our time. However, this theory is approximate and it cannot be developed into an exact theory because it is built on certain assumptions. This article presents some thoughts for clarifying the calculation results of the stress- strain state of shallow translation shells with constant curvatures using Fourier double trigonometric series. One additional equilibrium equation of all forces for a whole simply supported shell was used. The condition obtained in the article will help to refine the necessary number of members of Fourier double trigonometric series required to receive reliable results in the calculation of shallow translation shells with constant curvatures. It has been determined for the first time that the required number of series members for obtaining the necessary accuracy of the parameters of the stress-strain state of a translation shell depends on its geometric dimensions, thickness and the Poisson coefficient of its material. © 2022 American Institute of Physics Inc.. All rights reserved.