Effect of Compressibility on Nonlinear Buckling of Simply Supported Polyurethane Spherical Shells Subjected to an Apical Load

Abstract

In this study, the effect of compressibility on the nonlinear buckling of the simply supported polyurethane spherical shells subjected to an apical concentrated load is presented. The problem is strongly nonlinear both physically and geometrically. Since the closed form solution of the corresponding algebraical and differential equations is not possible, numerical methods are used unavoidably. The governing equations of the problem are converted to algebraical difference equations via the finite difference method and the obtained algebraical equations are solved numerically by using the Newton-Raphson method. Several numerical experiments corresponding to the various values of a thickness parameter, a depth parameter and a material constant related with the compressibility of polyurethane are performed and the force-apex deflection curves are drawn. Concluding remarks pertaining to the effect of the variation of the material constant related with the compressibility on the buckling loads and buckling deflections of the simply supported polyurethane spherical shells, subjected to an apical load, with various thicknesses and depths are presented.