Orthotropic Model Plate under Shear-Bending

Abstract:

The aim of this paper is to analyse the behaviour of various shear deformation laminated plate theories previously proposed by Reissner [1] , Reddy [2] and Touratier [3]. The accuracy of those theories is compared on two problems laminates for which an analytical solution has been given by Timoshenko for isotropic and Lekhniski for anisotropic plate. Retaining the best model among those compared, interlaminar continuity conditions have been taken into account in this best response for laminates and show how important these interlaminar conditions are to improve accuracy by comparison with the finite element solution. Models which have been introduced are two-dimensional ones and imply the three standard generalized displacements associated with shear-bending. Studies limited to symmetric and orthotropic plates. Finally, an analysis of edge effects has been conducted for a circular symmetric orthotropic clamped plate. Edge effects have been observed with refined shear deformation theories but not with the first-order shear deformation theory due to Reissner.

• Periodical: Advanced Materials Research (Volume 423)
• Pages: 166-176
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.423.166
• Online since: December 2011
• Authors: Moussa Karama
• Keywords: Composite, Edge Effects, Experimental Simulation, Finite Difference, Finite Element Analysis (FEA)

References

[1] E. Reissner, Reflections on the theory of elastic plates, Appl. Mech. Rev., Vol. 38, n°11, pp.1453-1464, (1985).

[2] J.N. Reddy, A simple higher-order theory of laminated composite plate, J. Appl. Mech. 745-752, (1984).

[3] M. Touratier, An efficiant standard plate theory, Int. J. Engng. Sci., vol. 29, n°8, 901-916, (1991).

[4] M. Karama, Idlbi A. and Touratier M., An evaluation of the edge solution for a higher-order plate theory, Composite Structures, 25, 1995, 495-502.

DOI: 10.1016/0263-8223(93)90197-x

[5] R. Schmidt, A refined nonlinear theory of plate with transverse shear deformation, industrial Mathematics 27(1) 23-38, (1977).

[6] G. Jemielita, Technical theory of plates with moderate thickness, Engng. Trans. 23, 483-499, (1975).

[7] N.J. Pagano, Exact solutions for rectangular bidirectional composites and sandwich plates, J. Comp. Mater. 4, 20-34, (1970).

DOI: 10.1016/0010-4361(70)90076-5

[8] N.J. Pagano and S.J. Hatfield, Elastic behaviour of multilayered bidirectional composites, AIAA Journal, Technical notes Vol. 10 n°7, pp.931-933, (1972).

DOI: 10.2514/3.50249

[9] A. Béakou & M. Touratier, "A Rectangular finite element for analyzing composite multilayered shallow shells in statics, vibration and buckling, Int. J. Num. Meth. Engng, Vol. 36, 627- 653, (1993).

DOI: 10.1002/nme.1620360406

[10] E. Reissner, The effect of transverse shear deformation on the bending of elastic plates, J. Appl. Mech., A69-A77, (1945).

DOI: 10.1115/1.4009435

[11] L. Bollé Contribution au problème linéaire de flexion d'une plaque élastique, Bulletin technique Suisse Romande, Part 1, 2, 73, 281-285 and 293-298, (1947).

[12] H. Hencky, Über die Berucksichtigung der Schubverzerrung in ebenen Platten, Ing. Arch. 16, 72-76, (1947).

DOI: 10.1007/bf00534518

[13] Y.S. Uflyang, The propagation of waves in the transverse vibrations of bars and plates, Prikl. Mat. Mech., 12, 287, in Russian, (1980).

[14] S. Vlachoutsis, Shear correction factors for plates and shells, Int. J. for Numer. Meth. In. Engng., vol. 33, 1537-1552, (1992).

DOI: 10.1002/nme.1620330712

[15] Mistou, S., Karama, M., Lorrain, B. and Faye J.P., Analysis of sandwich composite beams with a new transverse shear continuity model, Int. Journal of Sandwich Structures and Materials, volume 1, April 1999, 96-110.

DOI: 10.1177/109963629900100201