Errors of approximate analytical solutions for pressurized toroidal shells

This dataset is presented for the paper "Curved pipes subjected to mechanochemical corrosion under pressure: Analytical and numerical estimates of the lifetime". AUTHORS: A. Ilyin, Y. Pronina. Saint-Petersburg State University Corresponding E-MAIL: [e-mail] A linearly elastic toroidal shell with mean toroidal radius R, inner radius ri and outer radius ro loaded with internal pi and external po pressures (pi ≥ 0 and po ≥ 0) is considered. The dataset contains the values of the relative error in circumferential stresses calculated by the approximate analytical "thin-shell" (eq.(8) of this paper) and "thick-shell" (eq.(9)-(10) of this paper) solutions compared to Finite element modeling (FEM) results, for the inner and outer surfaces at the torus intrados. For the "thin-shell" solution the graphical representation of the current dataset is presented in Figure 7(a) for the inner surface and in Figure 7(b) for the outer surface of the toroidal shell. For the "thick-shell" solution the graphical representation of the current dataset is presented in Figure 8(a) and Figure 8(b) for the inner and outer surfaces, correspondingly. The values of the error are calculated using the following formula: Error = (S^{an} - S^{FEM})/S^{FEM} * 100%where:S^{an} -- circumferential stress obtained by the approximate analytical solution (eq.(8) - eq.(10)),S^{FEM} -- circumferential stress obtained by the Finite element modeling (FEM). NOTATIONS: ro -- outer radius of the toroidal shell;ri -- inner radius of the toroidal shell;R -- mean radius of the toroidal shell;h -- relative thickness of the toroidal shell ( h = (ro - ri) / 2 );Error_Inner_Thin -- relative error of the "thin-shell” solution (eq. 8) compared to the FEM for the inner surface (Figure 7 (a)), in percent;Error_Outer_Thin -- relative error of the "thin-shell” solution (eq. 8) compared to the FEM for the outer surface (Figure 7 (b)), in percent;Error_Inner_Thick -- relative error of the modified Kornecki solution (eq. 10) compared to the FEM for the inner surface (Figure 8 (a)), in percent;Error_Outer_Thick -- relative error of the modified Kornecki solution (eq. 9) compared to the FEM for the outer surface (Figure 8 (b)), in percent.