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Finite elements for honeycomb sandwich plates and shells

Part 1: Formulation of stiffness and consistent load matrices*

Published online by Cambridge University Press:  04 July 2016

P. J. Holt
Affiliation:
Formerly British Aerospace Aircraft Group, Weybridge-Bristol Division, now CEGB, Berkeley, Gloucestershire
J. P. H. Webber
Affiliation:
Formerly British Aerospace Aircraft Group, Weybridge-Bristol Division, now CEGB, Berkeley, Gloucestershire

Extract

The honeycomb sandwich type of construction in plate and shell shapes is playing an increasing role in aerospace structures where structural efficiency is important. In some applications, such as wing or control surface trailing edges, the core is of non-constant thickness, and in others, such as engine thrust reverser buckets, the shell shape is doubly curved. Faceplates are commonly manufactured from aluminium, stainless steel or other metals, but the use of anisotropic materials, such as carbon fibre reinforced plastics (CFRP) can be expected to increase in the future.

In finite element analysis, as in analytical work, sandwich plates and shells have received far less attention than thin plates and shells. However, elements have been developed specifically for sandwich plates by Barnard, Cook and Bartelds and Ottens. Of these, only the latter allows a non-constant core thickness. Evidently, such elements could be used in a facet shell representation. Only two general (as opposed to axisymmetric) curved elements specifically formulated to deal with sandwich shells seem to have appeared in the literature. Both are subject to deficiencies as noted for thin shells by Morris, and Webber discusses certain geometrical errors in the doubly curved element of Reference 5. Furthermore, both are of limited practical application. It may be concluded, therefore, that there is a need for a honeycomb sandwich shell element which is easy to use and accurate while being capable of modelling the full range of materials and shapes found in practical structures. To this end, a family of elements for use in the linear elastic finite element method is formulated. They are of general doubly curved shape and can be used to approximate thick and thin shells of positive, zero and negative Gaussian curvature in a simple and straightforward manner. They also include anisotropic faces and non-constant core thickness. Degrees of freedom are limited to three displacements at each node, and this allows mixing with other element types.

Type
Technical Notes
Copyright
Copyright © Royal Aeronautical Society 1980 

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Footnotes

*

Part 2 will be published in the May issue of The Aeronautical Journal

References

1. Barnard, A. J.A Sandwich Plate Finite Element’ in the Mathematics of Finite Elements and Applications, Whiteman, J. R. (ed), Academic Press, London, 1973.Google Scholar
2. Cook, R. D. Two Hybrid Elements for Analysis of Thick, Thin and Sandwich Plates. Int. J. Num. Meth. Eng., Vol 5, p 277, 1972.Google Scholar
3. Bartelds, G. and Ottens, H. H. Finite Element Analysis of Sandwich Panels. Proc. IUTAM Symp. on High Speed Computing of Elastic Structures, 1, p 357, 1971.Google Scholar
4. Monforton, G. R. and Schmit, L. A. Finite Element Analysis of Sandwich Plates and Cylindrical Shells with Laminated Faces. Proc. 2nd. Conf. Matrix Meth. Struct. Mechs., AFFDL-TR-68-150, p 573, 1968.Google Scholar
5. Ahmed, K. M. Static and Dynamic Analysis of Sandwich Structures by the Method of Finite Elements. J. Sound Vib., Vol 18, No 1, p 75, 1971.Google Scholar
6. Morris, A. J. A Deficiency in Current Finite Elements for Thin Shell Application. Int. J. Solids Structs., Vol 9, p 331, 1973.Google Scholar
7. 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
8. Holt, P. J. and Webber, J. P. H. Finite Elements for Curved Sandwich Beams. Aeronautical Quarterly, Vol XXVIII, p 123, May, 1977.Google Scholar
9. Plantema, F. J. Sandwich Construction. Wiley, 1966.Google Scholar
10. Pearce, T. R. A. and Webber, J. P. H. Buckling of Sandwich Panels with Laminated Face Plates. Aeronautical Quarterly, Vol 23, pp 148160, May 1972.Google Scholar
11. Pearce, T. R. A. and Webber, J. P. H. Experimental Buckling Loads of Sandwich Panels with Carbon Fibre Face Plates. Aeronautical Quarterly, Vol 24, pp 295312, November 1973.Google Scholar
12. Ashton, J. E., Halpin, J. C. and Petit, P. H. Primer on Composite Materials: Analysis. Technomic, 1969.Google Scholar
13. Zienkiewicz, O. C. The Finite Element Method, Third Edition, McGraw Hill, 1977.Google Scholar
14. Reissner, E. Small Bending and Stretching of Sandwich-type Shells. NACA Report 975, 1948.Google Scholar
15. Ahmad, S., Irons, B. M. and Zienkiewicz, O. C. Analysis of Thick and Thin Shell Structures by Curved Elements. Int. J. Num. Meth. Eng., 2, p 419, 1970.Google Scholar
16. Zienkiewicz, O. C., Too, J. and Taylor, R. L. Reduced Integration Technique in General Analysis of Plates and Shells. Int. J. Num. Meth. Eng., 3, p 275, 1971.Google Scholar
17. Washizu, K. Variational Methods in Elasticity and Plasticity. Pergamon Press, London, 1968.Google Scholar
18. Love, A. E. H. The Mathematical Theory of Elasticity. Fourth Edition, Cambridge University Press, 1927.Google Scholar
19. Wang, C. T. Applied Elasticity. McGraw Hill, 1953.Google Scholar