Nonlinear bending analysis of shallow spherical shells and circular plates

Geometrically nonlinear axisymmetric bending of circular shallow spherical shells is investigated numerically. Transverse shear deformation is considered in the study. Material of the shell is assumed homogeneous and isotropic. As a special case of the shell investigated in the study the analysis of a circular plate is also presented. Clamped or simply supported shells are examined. The thickness of the shell is uniform. The influences of the conical angel, the thickness of the shell, and the parameter of loading zone on the deflection and on the stress resultants are studied. The analysis is made by means of the finite difference method. Newton-Raphson method is employed in the solution of the nonlinear algebraic equations.