Asymptotic solution for nonlinear buckling of orthotropic shells on elastic foundation

An asymptotic solution for nonlinear buckling of elastically restrained imperfect, orthotropic, shallow spherical shells on an elastic foundation is derived in this paper. An analytic and explicit relation between external pressure and central deflection of the shell is presented in nondimensional form using the asymptotic iteration method. The solution incorporates the effects of orthotropic and material parameters, geometric imperfection, Young's and shear moduli of foundation, and edge-restraint coefficients. An extensive parametric study is carried out for deformation and buckling of such structures. Comparisons with available data for some specific cases show that the resulting solution is accurate in computation. It also indicates that the present solution can be readily used to evaluate nonlinear deformation and buckling behavior of orthotropic, imperfect, shallow spherical shells. © 2009 by the American Institute of Aeronautics and Astronautics, Inc.