Some methods for calculating stiffness properties of periodic structures

Stein A. Berggren; Dag Lukkassen; Annette Meidell; Leon Simula

Applications of Mathematics (2003)

  • Volume: 48, Issue: 2, page 97-110
  • ISSN: 0862-7940

Abstract

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We present a general numerical method for calculating effective elastic properties of periodic structures based on the homogenization method. Some concrete numerical examples are presented.

How to cite

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Berggren, Stein A., et al. "Some methods for calculating stiffness properties of periodic structures." Applications of Mathematics 48.2 (2003): 97-110. <http://eudml.org/doc/33138>.

@article{Berggren2003,
abstract = {We present a general numerical method for calculating effective elastic properties of periodic structures based on the homogenization method. Some concrete numerical examples are presented.},
author = {Berggren, Stein A., Lukkassen, Dag, Meidell, Annette, Simula, Leon},
journal = {Applications of Mathematics},
keywords = {homogenization theory; numerical methods; effective stiffness properties; homogenization theory; computing methods; effective elastic moduli; unilateral fiber composite; symmetry of the cell problem},
language = {eng},
number = {2},
pages = {97-110},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some methods for calculating stiffness properties of periodic structures},
url = {http://eudml.org/doc/33138},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Berggren, Stein A.
AU - Lukkassen, Dag
AU - Meidell, Annette
AU - Simula, Leon
TI - Some methods for calculating stiffness properties of periodic structures
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 2
SP - 97
EP - 110
AB - We present a general numerical method for calculating effective elastic properties of periodic structures based on the homogenization method. Some concrete numerical examples are presented.
LA - eng
KW - homogenization theory; numerical methods; effective stiffness properties; homogenization theory; computing methods; effective elastic moduli; unilateral fiber composite; symmetry of the cell problem
UR - http://eudml.org/doc/33138
ER -

References

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  1. An evaluation of different models for prediction of elastic properties of woven composites, Composites: Part B 31, 2000, pp. 7–20. (2000) 
  2. Concepts and Applications of Finite Element Analysis, J.  Wiley and Sons, 1989. (1989) 
  3. Homogenization of linear elasticity equations, Apl. Mat. 27 (1982), 96–117. (1982) MR0651048
  4. 10.1016/S0022-5096(97)00041-0, J.  Mech. Phys. Solids 46 (1998), 1441–1462. (1998) MR1634000DOI10.1016/S0022-5096(97)00041-0
  5. 10.1016/0022-5096(95)00018-E, J.  Mech. Phys. Solids 43 (1995), 815–828. (1995) Zbl0870.73042MR1332235DOI10.1016/0022-5096(95)00018-E
  6. Theory of mechanical properties of fibre-strengthened materials. I. Elastic behaviour, Journal of the Mechanics and Physics of Solids 12 (1964), 199–212. (1964) MR0176652
  7. 10.1016/0961-9526(92)90008-T, Composites Engineering 2 (1992), 249–259. (1992) DOI10.1016/0961-9526(92)90008-T
  8. Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin, 1994. (1994) MR1329546
  9. 10.1137/S0036139997320081, SIAM J.  Appl. Math. 59 (1999), 18250–1842. (1999) Zbl0933.35023MR1710545DOI10.1137/S0036139997320081
  10. Some aspects of reiterated honeycombs, In: Mechanics of Composite Materials and Structures. Vol. III, C. A.  Mota Soares, C. M.  Mota Soares and M. J. M.  Freitas (eds.), NATO ASI, Troia, Portugal, 1998, pp. 399–409. (1998) 
  11. 10.1016/0961-9526(95)00025-I, Composites Engineering 5 (1995), 519–531. (1995) DOI10.1016/0961-9526(95)00025-I
  12. The out-of-plane shear modulus of two-component regular honeycombs with arbitrary thickness, In: Mechanics of Composite Materials and Structures. Vol.  III, C. A.  Mota Soares, C. M. Mota Soares and M. J. M.  Freitas (eds.), NATO ASI, Troia, Portugal, 1998, pp. 367–379. (1998) 
  13. Homogenization and design of structures with optimal macroscopic behaviour, In: Computer Aided Optimum Design of Structures V, S.  Hernández, C. A.  Brebbia (eds.), Computational Mechanics Publications, Southampton, 1997, pp. 393–402. (1997) 
  14. The Homogenization Method: An Introduction, Studentlitteratur, Lund, 1993. (1993) MR1250833
  15. Energy and Variational Methods in Applied Mechanics, J.  Wiley and Sons, New York, 1984. (1984) Zbl0635.73017

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