Stiffness Analysis of Sheet Metal Shells under Concentrated Loads

The objective of this paper is to study the applicability of the finite element method in calculating both small and large deflections of sheet metal shells subject to concentrated loads in the elastic range. In the small deflection case, three types of elements - the Hsieh-Clough-Tocher triangular plate element, the Felippa quadrilateral plate element, and the Dupuis triangular shell element - are used to calculate the stiffness of two simple panels (a sectional circular cylinder and a paraboloid) and a spherical cap. The calculated results show that all three elements give solutions converging to the exact shell solutions. Using meshes of 300-500 degrees of freedom, the errors of the finite element results relative to the exact values are about 5% or less. For the spherical cap, existing experimental data is also included in the comparison study.

For large deflections, load-displacement curves of the spherical cap are computed for deflections up to three shell thicknesses using the Dupuis element. Measured data show that the departure of the load-displacement curve from the linear extrapolation based on its initial slope is substantial for deflections greater than one shell thickness (40% or more reduction in load). Using meshes of several hundred degrees of freedom for a quarter of the cap and several load increment sizes, the calculated results compare reasonably well with measured data both in trend and in magnitude.