Finite Element Solution for Axisymmetrical Shells

by Egor P. Popov,
Joseph Penzien,
Zung-An Lu,

Serial Information: Journal of the Engineering Mechanics Division, 1964, Vol. 90, Issue 5, Pg. 119-146

Document Type: Journal Paper


A comprehensive method of analysis of axisymmetrical thin elastic shells of revolution based on finite element approach is presented. The basic finite element, by which any axisymmetrical shell may be approximated, is a truncated conical ring. In the limiting case, such an element is replaced by a short cylinder; at the ends of a shell, shallow spherical caps are used. By using many elements, thickness variation of the shell can be approximated. The procedures are stated in matrix algebra and, in principle, are based on the displacement method of analysis. An example illustrates convergence of the proposed method. The stiffnesses of the elements are derived from the classical shell theory, the use of which assures accurate results. Two alternative methods of obtaining equivalent joint loads for distributed load acting on a shell are given. The possible extensions of the proposed method to other situations of engineering interest are examined.

Subject Headings: Finite element method | Axisymmetry | Elastic analysis | Load distribution | Load factors | Cylinders | Thickness | Matrix (mathematics)

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