The regular packing of fibres in three dimensions

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 454, Issue 1975, 1998, Pages 1889-1909

  Parkhouse, J G ^a,c   Kelly, A ^b  

^a UNIVERSITY OF SURREY   (United Kingdom)

^b CHURCHILL COLLEGE   (United Kingdom)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Composite materials; Fibres; Packing density; Penrose tiling

Indexed keywords

EID: 0011747016     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1998.0239     Document Type: Article

References (17)

1. Andersson, S. & O'Kecfe, M. 1977 Body-centred cubic cylinder packing and the garnet structure. Nature 267, 605-606.
2. Christensen, R. M. 1979 Mechanics of composite materials, p. 213. New York: Wiley.
3. Christensen, R. M. 1987 Sufficient symmetry conditions for isotropy of the elastic moduli tensor. Trans. ASME J. Appl. Mech. 54, 772-777.
4. Delneste, L. & Ferez, B. 1983 An inelastic finite element model of 4-d carbon-carbon composites. AIAA J. 21, 1143-1149.
5. Dow, N. F., Rosen, B. W., Shu, L. S. & Zweben, C. H. 1967 Design criteria and concepts for fibrous composites. Final Report, NASA Contract NASw-1377.
6. Gibson, A. G. & Ward, I, M. 1980 High stiffness polymers by die-drawing. Polymer Sci. Engng 20, 1229-1235.
7. Grünbaum, B. & Shephard, G. C. 1987 Tilings and patterns. New York: W. H. Freeman.
8. Hancox, N. L. 1977 Comparison of the mechanical properties of CFRP made from round and non-round carbon fibres. Fibre Sci. Tech. 10, 179-193.
9. Kelly, A. 1973 Composites with brittle matrices. In Frontiers in materials science (ed. L. E. Muir & C. Steen), pp. 335-364. New York: Marcel Dekker.
10. Kelly, A. & Groves, G. W. 1970 Crystallography and crystal defects, p. 163. London: Longman. Lidin, S., Jacob, M. & Andersson, S. 1995 A mathematical analysis of rod packings. J. Solid State Chem. 114, 36-41.
11. Maistre, M. 1980 Three-dimensional multi-dimensional structure. US Patent 4, 219-597.
12. O'Keefe, M. & Andersson, S. 1977 Rod packings and crystal chemistry. Acta Crystallogr. A 330, 914-923.
13. Parkhouse, J. G. 1984 Structuring: a process of material dilution. In Proc. 3rd Int. Conf. on Space Structures (ed. H. Nooshin). New York: Elsevier.
14. Parkhouse, J. G. & Kelly, A. 1995 The random packing of fibres in three directions. Proc. R. Soc. Land. A 451, 737-746.
15. Penrose, R. 1974 The role of aesthetics in pure and applied mathematical research. Bull. Inst. Math. Appl. 10, 266-271.
16. Rosen, B. W. & Shu, L. S. 1971 On some symmetry conditions for three-dimensional fibrous composites. J. Comp. Mat. 5, 279-282.
17. Tarnopols'kii, Y. M., Zhigun, I. G. & Polyakov, V. A. 1992 Spatially reinforced composites. Lancaster: Technomic.