Non-linear Static Modeling of Moderately Thick Functionally Graded Plate Using Dynamic Relaxation Method

Document Type : Persian

Authors

1 Assistant Professor, Shahid Beheshti University, Tehran, Iran.

2 PhD Student, Shahid Beheshti University, Tehran, Iran.

Abstract

In this paper, nonlinear static analysis of moderately thick plate made of functionally graded materials subjected to mechanical transverse loading is carried out using dynamic relaxation method. Mindlin first order shear deformation theory is employed to consider thick plate. Discretized equations are extracted for geometrically nonlinear behavior analysis.Loading Conditions and boundary conditions of the plate are uniformly distributed transverse load and simply supported at the four edges of the thick plate, respectively. In order to generalize the obtained results, the equations are solved by applying dynamic relaxation method based on central finite deference discretization in the non-dimensional form. The effects of problem parameters such as gradient constant of the functionally graded material and the side to thickness ratio of plate on the results are investigated. According to the obtained results, the need of including elastic large deflection and applying the theory which considers the effects of plate thickness on the plate bending response and also finally the need of employing dynamic relaxation solution method despite the non-linear terms resulted from large deflection of the functionally graded thick plate are discussed.

Keywords

References

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[13] Yang J., Shen H.S., Non-linear analysis of functionally graded plates under transverse and in-plane loads, International Journal of Non-linear Mechanics, vol. 38, 2003, pp. 467-482.
[14]  Ghannad Pour S.A.M., Alinia M.M., Large deflection behavior of functionally graded plates under pressure loads, Composite Structures, 75, 2006, pp. 67-71.
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[17] Otter J.R.H., Day A.S., Tidal flow computations, The Engineer, 209, 1960, pp. 177-182.
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[19] Otter J.R.H., Computations for prestressed concrete reactor pressure vessels using dynamic relaxation, Nuclear Structural Engineering, vol. 1, 1965, pp. 61-75.
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[21] Falahatgar S.R., Salehi M., Dynamic relaxation nonlinear viscoelastic analysis of annular sector composite plate, Journal of Composite Materials, vol. 43, 2009, pp. 257-275.
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