Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-08T03:24:16.906Z Has data issue: false hasContentIssue false

Finite Elements for Curved Sandwich Beams

Published online by Cambridge University Press:  07 June 2016

P J Holt
Affiliation:
Department of Aeronautical Engineering, University of Bristol
J P H Webber
Affiliation:
Department of Aeronautical Engineering, University of Bristol
Get access

Summary

The formulation of curved finite elements to represent a two-dimensional circular sandwich ring with honeycomb core and laminated faces is investigated. Assumed stress hybrid and equilibrium methods are found to be easier to employ in this case than the displacement approach. Using these methods, an element stiffness matrix is developed. The approximations of membrane faces and an infinite core normal stiffness are then used to develop simpler elements. Test cases show that these assumptions may become invalid, but that they are adequate for most practical cases where the core thickness to radius ratio and the face thickness to core thickness ratio are both low.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 Webber, J P H Governing equations for thick sandwich shells with honeycomb cores and laminated faces. Aeronautical Quarterly, Vol XXV, p 271, November 1974.Google Scholar
2 Reissner, E Small bending and stretching of sandwich-type shells. NACA Report 975, 1950.Google Scholar
3 de Veubeke, B Fraeijs Displacement and equilibrium models in the finite element method, pp 147197 of Stress Analysis (Edited by Zienkiewicz, O C and Holister, G S) Wiley, 1965.Google Scholar
4 Pian, T H H Derivation of element stiffness matrices by assumed stress distributions. AIAA Journal, Vol 2, pp 13331336, 1964.CrossRefGoogle Scholar
5 Reissner, E A new derivation of the equations for the deformation of elastic shells. American Journal of Mathematics, Vol 63, p 177, January 1941.Google Scholar
6 Love, A E H The Mathematical Theory of Elasticity. Fourth Edition, Cambridge University Press, 1927.Google Scholar
7 Koiter, W T A consistent first approximation in the general theory of thin elastic shells, p 12 of Theory of Thin Elastic Shells. First IUTAM Symposium (Edited by Koiter, W T). North-Holland, Amsterdam, 1960.Google Scholar
8 Sanders, J L An improved first approximation theory for thin shells. NASA Technical Report R-24, 1959.Google Scholar
9 Pian, T H H Mau, S T Some recent studies in assumed stress hybrid models. In Adavances in Computational Methods in Structural Mechanics and Design. Second US Japan Seminar on Matrix Methods of Structural Analysis and Design. (Edited by Oden, J T et al). University of Alabama in Huntsville Press, 1972.Google Scholar
10 Pearce, T R A Webber, J P H Experimental buckling loads of sandwich panels with carbon fibre faceplates. Aeronautical Quarterly, Vol XXIV, p 295, November 1973.Google Scholar
11 Morris, A J A deficiency in current finite elements for thin shell applications. International Journal of Solids and Structures, Vol 9, pp 331346, 1973.Google Scholar
12 Morley, L S D Analysis of developable shells with special reference to the finite element method and circular cylinders. Phil Trans Roy Soc, Series A, Vol 281, pp 113170, February 1976.Google Scholar