Doubly Curved Membrane Shell Finite Element

by Carl S. Gran, Research Asst.; School of Aeronautical Engrg., Purdue Univ., West Lafayette, Ind.,
T. Y. Yang, Prof. and Assoc. Head; School of Aeronautical and Astronautical Engrg., Purdue Univ., West Lafayette, Ind.,

Serial Information: Journal of the Engineering Mechanics Division, 1979, Vol. 105, Issue 4, Pg. 567-584

Document Type: Journal Paper


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.

Subject Headings: Curvature | Membranes | Displacement (mechanics) | Finite element method | Stiffening | Matrix (mathematics) | Rigid body dynamics | Mapping

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