Keywords: large deflections, FGM, sector plates, finite element, composite, micromechanics, geometrical non-linearity.

Geometrically non-linear Finite Element analysis of Functionally Graded Material (FGM) sector plates are carried out. The use of such material properties is due to the fact that in fiber-reinforced laminated sector plates the fibers are arranged in the radial and circumferential directions. The fibers in the radial direction cause the Fiber Volume Fraction (FVF) become invariant in that direction, consequently FGM analogy is required. Such behaviour does not occur in, for example, fiber-reinforced laminated rectangular plates.

Although, FGM properties were originally developed for thermal stress analysis, but it can be applied to such composite structures as sector plates with variable FVF in the radial direction. The invariance of fiber volume fraction in the radial direction causes the composite strength become a function of sector radius. Therefore, from the micromechanical point of view, using the Rule of Mixture a relationship for the composite modulus of elasticity in the radial direction is developed. This relationship is incorporated in the ANSYS finite element code and the fibers are defined in polar coordinate system. This type of arrangement of fibers is the most optimum form of laying the fibers in the matrix. Although, manufacturing such sector plates is not so simple, nevertheless is not impossible. Cutting a sector out of a fiber-reinforced laminated rectangular plate is not an efficient way of designing a sector plate. Assuming constant stiffness in the radial direction for sector plates is studied in [1,2]. However, Figure 32.1 shows a significant variation of stiffness in both the radial and transverse directions. An FGM model for circular and annular plates is presented in [3].

In this paper a geometrically non-linear finite element analysis is carried out for a single layer fiber-reinforced composite sector plate with various sector angles and different material. The reason for choosing a single layer only is to explore the effect of variations of the mechanical properties on the response of sector plate under the uniformly distributed pressure. The boundary conditions are all-round simply supported or clamped. The results generated include deflections and stresses.

Unfortunately, it is not possible to verify the present results due to the lack of similar analysis, however, the purpose of this analysis is to present the effect of variable stiffness on the deflections and stresses, in other words, on the whole response of sector plates. However, the present results for deflections of an isotropic plate are compared with similar results and the correlations are very satisfactory. Consequently, the new results generated here are more likely to be correct than not.

1

Salehi, M., Shakeri, M. and Khorsandi, A., "Small Deflection Analysis of Fiber- Reinforced Laminated Sector Mindlin Plates", in Proceedings of the Fourth International Conference on Computational Structures Technology, B.H.V. Topping, (Editor), Civil-Comp Press, Stirling, United Kingdom, pp. 199-208, 1998. doi:10.4203/ccp.55.9.6

2

Salehi, M. and Sobhani, A.R., "Initial Flexural Failure Prediction of Fiber- Reinforced Laminated Sector Mindlin Plates", in Proceedings of the Sixth International Conference on Computational Structures Technology, B.H.V. Topping and Z. Bittnar, (Editors), Civil-Comp Press, Stirling, United Kingdom, paper 78, 2002. doi:10.4203/ccp.75.78

3

Reddy, J.N., Wang, C.M. and Kitipornchai, S. "Axisymmetric Bending of Functionally Graded Circular and Annular Plates", European Journal of Mechanics A-Solids, Vol.18, pp. 185-199, 1999. doi:10.1016/S0997-7538(99)80011-4

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