Why Do Shallow Caps Deflect More Than Deep Ones?

The deflection of a clamped thin shell spherical cap is evaluated by the finite element method. Elastic material properties are assumed. The ratio of the center height to the base radius of the cap is used to distinguish shallow from deep caps. Comparing the deflection of clamped shallow caps to deep ones resulted in a very interesting behavior which may contradict the intuition of some engineers. For example, the deflection of a shallow clamped cap is considerably larger than that of a sphere or hemisphere with the same radius of curvature. The causes for this behavior are discussed. Results are presented for a wide range of geometries, pressures, and material properties for design purposes.