High Order Rectangular Shallow Shell Finite Element

by T. Y. Yang, (A.M.ASCE), Assoc. Prof.; School of Aeronautics, Astronautics, and Engrg. Sci., Purdue Univ., West Lafayette, IN,

Serial Information: Journal of the Engineering Mechanics Division, 1973, Vol. 99, Issue 1, Pg. 157-181

Document Type: Journal Paper


The stiffness matrix for a high order shallow shell finite element is presented explicitly. The element is of rectangular plan and possesses three constant radii of curvature: two principal ones and a twist one. Each of the three displacement functions is assumed as the product of one-dimensional, first-order Hermite interpolation formulas. An eigenvalue analysis performed on the element stiffness matrix shows that the six rigid-body displacements are included. Convergence studies are carried out for a cylindrical shell, a translational shell with two constant principal radii of curvature, and a hyperbolic paraboloidal shell with a constant twist radius of curvature. Excellent agreements are found when comparing the present results with the alternative series and finite difference solutions. A review of the previously developed shell finite elements shows that the present element is highly efficient in terms of convergence rate or computational effort.

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

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