Engineering Transactions, 43, 1-2, pp. 225-244, 1995

Finite Element Model for 3-D Analysis of Composite Plates

M. Lefik
Łódź University of Technology, Łódź
Poland

Homogenization theory is applied to the elastic analysis of plate composed of many layers parallel to the middle plane of the plate. The cross-section of each stratum has its own, complex structure. We analyse first the microstructure of the plate to define the local perturbation of a global mean behaviour, due to nonhomogeneity. We describe this perturbation using first order terms in the asymptotic expansion of displacements in the power series of the small parameter. We use this description in the derivation of a plate-type element for the analysis of plates with multiple, parallel layers. In the kinematics defining the global behaviour of the plate, additional degree of freedom is included. We quote the formula for the stiffness matrix of an equivalenet homogeneous plate element. The computational process is then illustrated by an example.

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References

J. ABOUDI, Mechanics of composite materials, Elsevier, Amsterdam 1991.

A. BENSOUSSAN, J.-L. LIONS and G. PAPANICOLAU, Asymptotic analysis for periodic structures, North Holland, Amsterdam 1976.

D. CAILLERIE, Homogenization of periodic media, tissued composite materials, Course: Mechanics of Composites, Theory and Computer Simulation, Technical University of Łódź, Poland 1991.

G. DHATT and G. TOUZOT, The finite element method displayed, J. Wiley and Sons, Chichester 1984.

H. DUMONTET, Homogenisation et effets de bords dans les materiaux composites, These de Doctorat d'Etat, L'Université Pierre et Marie Curie Paris 6.

M. LEFIK and B.A. SCHREFLER, Homogenized material coefficients for SD elastic analysis of superconducting coils, [in:] New Advances in Computational Structural Mechanics, [Eds.] P. LADEVEZE and O.C. ZIENKIEWICZ, Elsevier Science Publishers B.V., 1992.

M. LEFIK and B.A. SCHREFLER, SD finite element analysis of composite beams with parallel fibres based on the homogenization theory, Computational Mech., 14, 1, 2-15, 1994.

M. LEFIK and B.A. SCHREFLER, Application of the homogenization method to the analysis of superconducting coils, Fusion Engng. and Design, 24, 231-255, 1994.

E. SANCHEZ-PALENCIA, Non-homogeneous media and vibration theory, Springer Verlag, Berlin 1980.

O.C. ZIENKIEWICZ and R.L. TAYLOR, The finite element method, McGraw-Hill, London 1989.




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