Keywords: fiber volume fraction, FGM, circular plates, sector plates, finite element, composite, micromechanics, macromechanics.

Fiber reinforced laminated circular and sector plates can replace metal circular and sector plates. Reinforcing these plates with fibers is not as straight forward as it is for rectangular plates. The best orientation of fibers in both circular and sector plates is to have the bundles of fibers placed in radial and circumferential directions. Fibers placed in radial direction causes the composite plate to have a variable fiber volume fraction. Consequently, the composite plate strength will vary with its radius.

Practically, designing and building such a plate is cumbersome, however, from the theoretical point of view, one can analyse such plates by assuming that the fibers are orientated only in radial and circumferential directions. This type of fiber orientation gives composite plate the highest strength. Composite circular and sector plates have been analysed previously in [1,2] but this aspect of the work has not been studied.

In this paper the variation of stiffness of the composite plate in the radial direction is taken into account. As the plate radius increases the fiber volume fraction decreases. Now, if the plate is designed on the bases of the fiber volume fraction at the maximum radius, then the true stiffness of the plate is not taken into account. On the other hand if the stiffness at the minimum radius is used then the strength is over- estimated which will result in plate failure well below the estimated pressure on the plate.

In Figure 33.1, the variation of the composite stiffness based on the maximum fiber volume fraction, i.e. at minimum radius, the minimum fiber volume fraction, i.e. at maximum radius, a mean value for the stiffness and a linear variation of the composite stiffness is shown. It is clear that the variations from to are very significant. Obviously, this difference becomes more apparent with increasing of the ratio of stiffness in fiber direction to that in the direction perpendicular to fiber direction ().

A finite element modeling of variable (radial and transverse), (Poisson's ratio) and (shear modulus) with respect to fiber volume fraction and plate radius is studied. The variation of these mechanical properties with respect to fiber volume fraction is compared with existing theories, the correlations are very satisfactory. The variations of the aforementioned properties with respect to plate radius are presented in this paper and their importance is in the analysis of circular, annular and sectorial plates. In conclusion it seems quite necessary to use a variable stiffness for fiber reinforced laminated circular, annular and sector plates.

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

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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