Nonlinear analysis of the simply supported spherical shells made of a compressible rubber-like material under the effect of an apical load

In this study; nonlinear analysis of the simply supported spherical shells, made of a compressible rubber-like (hyperelastic and isotropic in the unstrained state) material under the effect of an apical load, is presented. The problem is nonlinear both physically and geometrically. Because the closed form solution of the corresponding algebraical and differential equations is not possible, numerical methods are used. The corresponding differential equations are converted to algebraic equations via the finite difference method and the obtained algebraical equations are solved numerically by using the Newton-Raphson method. Polyurethane is chosen among the compressible, rubber-like materials and the effects of height, thickness and a material constant belonging to polyurethane on force-deflection behaviour and the buckling load of the simply supported, spherical shells subjected to an apical load are inspected. Keywords: Compressible material, polyurethane, spherical shells, finite difference method, Newton-Raphson method, nonlinear analysis.