An asymptotic solution for non-linear behavior of imperfect shallow spherical shells

This paper deals with non-linear behavior of an elastically restrained shallow spherical shell with imperfections and subjected to uniform normal load by the asymptotic iteration method. An asymptotic relation between the external load and central transverse displacement (deflection) of the structure incorporating the effects of the characteristic geometrical parameter, imperfection factor and edge-restraint coefficients is formulated. The corresponding solutions resulting from the use of the second and third iteration processes are compared with each other and available data. The numerical calculations show that the second iteration is adequate for the non-linear analysis of the structure. The effects of geometrical imperfections and boundary constraint coefficients on buckling of the structures are presented graphically.