Some methods for calculating stiffness properties of periodic structures. (English) Zbl 1099.74053

The paper deals with calculating effective properties of periodic structures based on the homogenization method. The case of elastic unilateral fiber composite is studied. Symmetry of the cell problem and isotropy of elastic material simplify the formulae and computation of effective elastic moduli. Formulation of the corresponding 2D cell problem, coordinate transformation and a computational example close the paper.
Reviewer: Jan Franců (Brno)


74Q15 Effective constitutive equations in solid mechanics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
74K99 Thin bodies, structures
74S30 Other numerical methods in solid mechanics (MSC2010)
Full Text: DOI EuDML


[1] J. Byström, N. Jekabsons and J. Varna: An evaluation of different models for prediction of elastic properties of woven composites. Composites: Part B 31, 2000, pp. 7-20.
[2] R. D. Cook, D. S. Malkus and M. E. Plesha: Concepts and Applications of Finite Element Analysis. J. Wiley and Sons, 1989. · Zbl 0696.73039
[3] J. Franců: Homogenization of linear elasticity equations. Apl. Mat. 27 (1982), 96-117.
[4] L. Greengard, J. Helsing: On the numerical evaluation of elastostatic fields in locally isotropic two-dimensional composites. J. Mech. Phys. Solids 46 (1998), 1441-1462. · Zbl 0955.74054
[5] J. Helsing: An integral equation method for elastostatics of periodic composites. J. Mech. Phys. Solids 43 (1995), 815-828. · Zbl 0870.73042
[6] R. Hill: Theory of mechanical properties of fibre-strengthened materials. I. Elastic behaviour. Journal of the Mechanics and Physics of Solids 12 (1964), 199-212.
[7] A. Holmbom, L. E. Persson and N. Svanstedt: A homogenization procedure for computing effective moduli and microstresses in composite materials. Composites Engineering 2 (1992), 249-259.
[8] V. V. Jikov, S. M. Kozlov and O. A. Oleinik: Homogenization of Differential Operators and Integral Functionals. Springer-Verlag, Berlin, 1994.
[9] D. Lukkassen: A new reiterated structure with optimal macroscopic behavior. SIAM J. Appl. Math. 59 (1999), 18250-1842. · Zbl 0933.35023
[10] D. Lukkassen: Some aspects of reiterated honeycombs. 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.
[11] D. Lukkassen, L.-E. Persson, P. Wall: Some engineering and mathematical aspects on the homogenization method. Composites Engineering 5 (1995), 519-531.
[12] A. Meidell: The out-of-plane shear modulus of two-component regular honeycombs with arbitrary thickness. 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.
[13] A. Meidell, P. Wall: Homogenization and design of structures with optimal macroscopic behaviour. Computer Aided Optimum Design of Structures V, S. Hernández, C. A. Brebbia (eds.), Computational Mechanics Publications, Southampton, 1997, pp. 393-402.
[14] L. E. Persson, L. Persson, N. Svanstedt and J. Wyller: The Homogenization Method: An Introduction. Studentlitteratur, Lund, 1993. · Zbl 0847.73003
[15] J. N. Reddy: Energy and Variational Methods in Applied Mechanics. J. Wiley and Sons, New York, 1984. · Zbl 0635.73017
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