Shell and Plate Analysis by Finite Elements

A doubly-curved quadrilateral shell element is described which uses the exact shell geometry in computing the stiffness matrix and consistent load vector. The element's degree-of-freedom may be transformed to and from three-dimensional coordinate systems, which enables it to be used in the analysis of branched and stiffened shells. The elimination of midside nodes through the assumption of linear variation of derivative degrees-of-freedom on the four sides reduces data input requirements considerably and, yet, does not detract from the element's performance. The element's convergence characteristics provide solutions to linear and nonlinear problems with a minimum number of elements.