A parametric study on geometrically nonlinear analysis of initially imperfect shallow spherical shells

Abstract

Geometrically nonlinear analysis of initially imperfect shallow spherical shells under uniformly distributed axisymmetrical load is investigated in this computational study. The thickness of the shell is considered to be uniform and the material is assumed to be isotropic. The numerical treatment of the nonlinear fundamental shallow spherical shell equations is carried out by the finite difference method and the Newton-Raphson method. The influence of the parameters (Poisson's ratio, parameters of thickness, depth and initial imperfection) on the critical load, the value and the location of the maximum displacement components and the maximum stress resultants is examined by various numerical experiments each of which is made for two distinct types of supports along the edge: clamped and simply supported. Despite the dominant role of the nonlinearity, some general statements are obtained and the influence of the parameters is highlighted.