Large Deflection of Shallow Paraboloid Shells

Based on the well-known Marguerre's theory of shallow shells, a study is made of large deflection of rectangular paraboloid shells caused by transverse loads. Using the Ritz procedure, load deflection curves have been computed for a variety of shells of clamped edges and for a particular class of transverse loads. The transverse loads are so prescribed that they contain as limiting cases the uniform pressure load and the concentrated load at the shell apex. Results are presented graphically that depict the effect of the shell rise to thickness ratio, of the load distribution, and of the shell's cross curvature ratio on the load-deflection curves. Numerical experiment indicates that the present scheme is satisfactory only for relatively small shell rise to thickness ratios.