Finite-Element Analysis of Thin Shells

by G. A. Wempner,
John T. Oden,
D. A. Kross,

Serial Information: Journal of the Engineering Mechanics Division, 1968, Vol. 94, Issue 6, Pg. 1273-1294

Document Type: Journal Paper


Equations describing small deformations of thin shells of arbitrary shape are written in terms of the displacements of the middle surface and rotation of the normals to the middle surface. The theory accounts for transverse shear deformations. By then using simple bilinear approximations of the displacement and rotation fields within finite elements of the shell, a consistent discrete model is obtained; the model provides complete interelement compatibility, and applies to the analysis of thin shells of arbitrary shape. A discrete equivalent of the Kirchhoff hypothesis is then introduced, which greatly improves convergence rates, and which forces the finite element model to convergence to the continuous Kirchhoff model. Numerical examples are included.

Subject Headings: Finite element method | Arbitration | Displacement (mechanics) | Rotation | Shear deformation | Convergence (mathematics) | Transverse shear | Approximation methods

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