Keywords: laminated plates, shear deformation, bending, specially orthotropic.

The aim of this paper is to analyse the mechanical behaviour of materials having different properties in tension and compression, using different laminated plate models, previously presented by Kirchhoff-Love [2,3], Reissner-Mindlin [4,5], and Touratier [7]. The accuracy of these theories is then compared to the results obtained by Papazoglou and Tsouvalis [1] which are based on the Reddy [6] Theory of higher order shear deformation. The study was carried out on square simply supported, multilayered, non-symmetrical, specially orthtropic laminates under uniformally distributed sinsoinadale load . Finally theses results are compared to finite element analysis.

For bi-modulus material, the different properties in tension and compression cause a shift in the neutral surface away from the geometric midplane, and symmetry at midplane no longer holds. The result of this is that bending-stretching coupling of an orthotropic type is exhibited, i.e. analogous to a two-layer cross-ply plate (one layer at 0 and the other at 90) of ordinary orthotropic material. The governing equations of composite materials could be used for bi-modulus materials except that the stress- strain relation must be of the bimoduler form.

The material model to be used as a basis for the present extension is the Weighted Compliance Matrix material model (WCM Model), presented by Jones [8,9]. The WCM model introduces weighting factors which depend on the principal stress state and which determine the percentage of the tensile and compressive properties which form the final compliance matrix. In this article, weighting factors are introduced in a little bit different way as defined by Jones [8,9].

In this study, a comparison has been made of the mechanical behaviour of bimodulus laminated plate between various analytical models and finite element analysis. Since no exact solution exists for non-symmetrical laminated plates, finite element has been taken as a reference for the comparison of different models of laminated plate.

All the analytical results of the various models have been calculated on the basis of non-continuity of shear stress on layer interfaces. Further improvement in the mechanical behaviour of the bi-modulus laminate are possible firstly by considering the continuity of the shear stresses on the layer interface of the laminate and secondly by a better definition of "Material Model" for bi-modulus material and by the accurate definition of weighting factors.

1

V.J. Papazoglou, N.G. Tsouvalis, "Mechanical Behaviour of Bimodulus Laminated Plates", Elsevier Science, Composite Structures, 17, 1-22, 1991. doi:10.1016/0263-8223(91)90057-6

2

Kirchhoff,G.J., "Uber das gleichgewicht und die bewegung einer elastischen schreitbe", Reine Angew Math, 40, 51-58, 1850.

3

Love, A.E.H., "A Treatise on the Mathematical Theory of Elasticity", Cambridge University Press, 4th ed, 1934.

4

Reissner, E., "Reflection on the theory of elastic plates", App. Mech. Rev., 38, 1453-1464, 1945.

5

Mindlin, R.D., "Influence of Rotatory Inertia and Shear on Flexural motions of isotropic elastic plates", J. App. Mech., ASME, 18, 31-38, 1951.

6

Reddy, J.N., "A simple high-order theory of laminated composite plate", J. App. Mech, 51, 745-752, 1984.

7

Touratier, M., "An Efficient Standard Plate Theory", Int. J. Egg. Sci., 29, No. 8, 901-916, 1991. doi:10.1016/0020-7225(91)90165-Y

8

Jones, R.M., "Buckling of circular cylindrical shells with different moduli in tension and compression", AIAA Journal, 9 (1), 53-61, January, 1971. doi:10.2514/3.6124

9

Jones, R.M., "tress-strain relations for materials with different moduli in tension and compression", AIAA Journal, 15 (1), 16-23, January, 1977. doi:10.2514/3.7297

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