Asymptotic buckling analysis of imperfect shallow spherical shells on non-linear elastic foundation

An asymptotic solution is formulated for non-linear buckling of elastically restrained imperfect shallow spherical shells continuously supported on a non-linear elastic foundation. The asymptotic iteration method is introduced to result in a cubic non-linear analytical relation between the external load and central transverse displacement (deflection) of the structures incorporating the effects of geometrical imperfection, edge-restraint coefficients, moduli of foundation and characteristic geometrical parameter. The resulting expression can be used easily to evaluate the effects of these factors on buckling behaviors. Numerical examples are given, and comparisons of the available results show validity of the method suggested in the present work.