Abstract
This paper evaluates the equivalent transverse shear and in-plane moduli of honeycomb cellular structures. The derivation is based upon a two scale method for the homogenization of periodic media. The equivalent two dimensional constitutive equations are evaluated analytically in terms of their geometry and material properties. The present results compare well with some of the existing analytical results obtained by conventional approaches and show the errors of some of the earlier results. The present method is a systemetic and rational technique for the homogenization of periodically inhomogeneous media. It allows us to derive the equivalent mechanical properties of honeybombs systemetically for the analysis and design of cellular structures of honeycomb. The structural efficiency of honeycombs will also be discussed.
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References
AllenH. G. 1969: Analysis and design of structural sandwich panels. London, Pergamon Press
Bensoussan, A.; Lions, J. L.; Papanicolaou, G. 1978: Asymptotic analysis for periodic structures. North Holland
ChangC. C.; EbciogluI. K. 1961: Effect of cell geometry on the shear modulus and on density of sandwich panel cores. Trans. ASME, Series D, 83: 513–518
EvansK. E. 1991: The design of doubly curved sandwich panels with honeycomb cores. Composite Structures, 17: 95–111
GibsonL. J.; AshbyM. F.; SchajerG. S.; RobertsonC. J. 1982: The mechanics of two-dimensional cellular materials. Proc. R. Soc. Lond. A 382: 25–42
KelseyS.; GellatlyR. A.; ClarkB. W. 1958: The shear modulus of foil honeycomb cores. Aircraft Engineering 30: 294–302
MeiC. C.; AuriaultJ. L. 1989: Mechanics of heterogeneous porous media with several spatial scales. Proc. R. Soc. Lond. A 426: 319–423
PenzienJ.; DidrikssonT 1964: Effective shear modulus of honeycomb cellular ctructure. AIAA J. 2: 531–535
ShiG.; AtluriS. N. 1989: Static and dynamic analysis of steel frames with nonlinear flexible connections. Int. J. Num Meth. Eng. 28: 2635–2650
Shi, G.; Tong, P. 1994: Equivalent transverse shear stiffness of honeycomb cores, to appear in Solids & Structures
TongP.; MeiC. C 1992: Mechanics of composites of multiple scales. Computational Mechanics 9: 195–210
VinsonJ. R.; SierakowskiR. L. 1990: The behavior of structures composed of composite materials. Boston, Kluwer Academic
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Communicated by S. N. Atluri, 20 July 1994
This work was supported by the GRC of Hong Kong Under Grant No. HKUST 019/91
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Shi, G., Tong, P. The derivation of equivalent constitutive equations of honeycomb structures by a two scale method. Computational Mechanics 15, 395–407 (1995). https://doi.org/10.1007/BF00350354
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DOI: https://doi.org/10.1007/BF00350354