Bending Analysis of Thick Rectangular Plates with Various Boundary Conditions Using Extended Kantorovich Method

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

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Bending Analysis of Mindlin Plates by Extended Kantorovich Method

Journal of Engineering Mechanics ◽

10.1061/(asce)0733-9399(1998)124:12(1339) ◽

1998 ◽

Vol 124 (12) ◽

pp. 1339-1345 ◽

Cited By ~ 28

Author(s):

Si Yuan ◽

Yan Jin ◽

Fred W. Williams

Keyword(s):

Kantorovich Method ◽

Bending Analysis ◽

Extended Kantorovich Method

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Vibration of Stiffened Rectangular Plates

Journal of the Royal Aeronautical Society ◽

10.1017/s0368393100078652 ◽

1963 ◽

Vol 67 (629) ◽

pp. 305-307 ◽

Cited By ~ 2

Author(s):

S. Mahalingam

Keyword(s):

Boundary Conditions ◽

Present Note ◽

Ritz Method ◽

Arbitrary Parameter ◽

Rectangular Plates ◽

Various Boundary Conditions ◽

Beam Function ◽

Rayleigh Method ◽

The Given ◽

Free Edges

The free flexural vibrations of rectangular plates with various boundary conditions have been considered by Warburton. The natural frequencies were calculated by the Rayleigh method, the mode assumed being the product of the characteristic beam functions for the given boundary conditions. Comparison with experimental results shows that the method gives reasonably good approximations. The present note describes a method of obtaining the approximately equivalent characteristic beam functions to enable Warburton's method to be extended to plates having one or more stiffeners parallel to an edge. As a numerical example expressions for the frequencies are derived for a plate, simply supported along two opposite edges, and having a central stiffener parallel to the other two free edges. The results are compared with those given in a recent note by Kirk, who solved the same problem by the Rayleigh-Ritz method, using a mode with one arbitrary parameter. In the case of the fundamental frequency of the unstiffened plate, the characteristic beam function in a direction perpendicular to the free edges is simply a constant, and the solution is less accurate than that given by the Rayleigh-Ritz method. However, numerical analysis of a square plate shows that above a certain stiffener depth the characteristic beam function method is more accurate than the Rayleigh-Ritz method. The two methods are also compared for the 2/2 mode.

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