In functionally graded structures, the volume fractions of two or more materials are varied continuously as a function of position along certain dimension(s) of the structure to achieve a required function. These structures are usually made from a mixture of metals and ceramics. The composition is varied from a ceramic-rich surface to a metal-rich surface, with a desired variation of the volume fractions of the two materials in between the two surfaces. With the escalating application of functionally graded materials, the attention of some of the researcher's in the field has been attracted to the investigation of the non-linear behaviour of the structures made up of these materials.

In the current paper, the application of the same FSM as that developed earlier by the authors [2] is extended to the analysis of large deflection behaviour of functionally graded plates subjected to the normal pressure loading. This task is fulfilled by defining a new strip which is called a functionally graded strip (FGS). The plate is discretized into some functionally graded strips. The material properties of the functionally graded plates are assumed to vary continuously through the thickness of the plate, according to the exponential law distribution. The plates are assumed to be simply supported out of their plane at their boundaries, where the in-plane movements are allowed to take place. The solution is obtained by the minimization of the total potential energy. The Newton-Raphson method is used to solve the resulting non-linear equilibrium equations.

The analysis of functionally graded plates is conducted for the type of ceramic and metal combination. The surface of the plate is assumed to be pure alumina (i.e. pure ceramic), while the surface of the plate is assumed to be pure aluminum (i.e. pure metal). Young's modulus and Poisson's ratio are selected as being 380 GPa and 0.3 for alumina, and 70 GPa and 0.3 for aluminum, respectively. The analysis is performed on a square plate of side mm and thickness mm. The plate is assumed to be simply supported out of its plane at its boundaries, where the in-plane movements are allowed to take place. It is also noted that for all the examples under consideration, the analyses are accomplished by utilizing the series representation in the longitudinal direction of the form sin 2, 4, 6/cos 0, 2, 4, 6/sin 1, 3 for , and , respectively. It is worth mentioning that the convergence studies with regard to the number of strips have revealed that 48 functionally graded strips are sufficient to obtain converged results. The results are presented in terms of dimensionless deflection and stress.

The analysis of the results has indicated that for a given value of pressure loading, among different plates, the plate made up of pure aluminium encounters the largest central deflection, whilst the smallest central deflection is encountered by the plate made up of pure alumina. This obviously occurs due to the fact that the former plate has the lowest Young's modulus , in contrast to the highest Young's modulus Ec of the latter plate.

The effects of material properties on the stress field and on the variation of the central deflection at a given value of normal pressure loading are determined. The results are also compared with those available in the literature, wherever possible. The good comparison of the results verifies the current large deflection FSM analysis for the case of functionally graded plates. It is observed that the values of the stresses in the case of the FGM cannot be predicted based on the stress values obtained for the two extreme cases of pure aluminium and pure alumina. For example, among all different materials under consideration, the highest level of longitudinal stress (i.e. ) is experienced in the case of the pure alumina, and the lowest level of longitudinal stress (i.e. ) is experienced in the case of the FGM.

1

Koizumi M. "FGM activities in Japan". J. Composites, 28, 1-4, 1997. doi:10.1016/S1359-8368(96)00016-9

2

Ovesy H.R., GhannadPour S.A.M. "Geometric Nonlinear Analysis of Imperfect Composite Laminated Plates, Under End Shortening and Pressure loading, Using Finite Strip Method" Accepted for publication in special issue of the composite structures (iccs/13-14 November 2005-Australia-Monash University), 2006. doi:10.1016/j.compstruct.2006.04.005

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