Elastic limit load prediction and equivalent cylinder proposal for circular concave shells subjected to axial compression

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The paper aims to propose an equivalent cylinder radius approach for circular cross-section concave shells under axial compression. Several buckling relations are introduced to predict critical stresses and to limit loads considering the extensive range of geometrical parameters. A detailed parametric study is conducted to reveal the influence of concavity on critical stress using geometrically nonlinear analysis (GNA). The amount of reduction in limit load of a concave shell, as a reference to an ideal case, is expressed as a function meridional curvature. An asymmetry factor is described to evaluate the change of critical stresses for longitudinally asymmetric concave shells. A similarity approach is given for the concave shells. A statistical procedure is utilized to examine the accuracy of the equations and relatively satisfactory results are achieved.