Doubly Curved Membrane Shell Finite Element

The formulation and testing of a high-order doubly curved membrane shell finite element is presented. Specialized for application to shells of revolution, the element is defined by lines of principal curvature and allows a third-order mapping of the meridian. The in-plane displacement assumptions are complete bicubic. The functions are represented by products of one-dimensional first-order Hermite interpolation functions. The transverse displacement assumption is bilinear. Mixed displacement derivatives are condensed from the element stiffness matrix forming an element with 28 degrees-of-freedom. An eigenvalue analysis performed on the element stiffness matrix indicates that three rigid body modes are implicitly included. These three rigid body modes, the two in-plane translations and the rotation about the shell normal, are sufficient to produce excellent convergence characteristics in analyzing membrane shells, regardless of the shell's Gaussian curvature.