Keywords: laminated plate, variable thickness, differential quadrature method, static analysis, classical plate theory, parabolic thickness variation.

In the study reported in this paper, the static analysis of specially-orthotropic laminated tapered plates is carried out employing differential quadrature method. Plates having linear and parabolic thickness variations are analyzed. Plates of simply-supported and clamped on all four edges are considered. The differential quadrature method is a numerical solution technique for the rapid solution of linear and non-linear partial differential equations introduced by Bellman and associates [1,2]. It has been employed in the solution of a variety of structural problems including the static and free vibration analysis of beams, plates and shells [3,4]. The plate considered here is assumed to be thin and the classical plate theory is used when formulating the problem. Both linear and parabolic thickness variations are considered. Simply supported and clamped boundary conditions are analyzed. The DQM is used to discretize the physical domain by converting the governing differential equation into a set of algebraic equations. The resulting set of algebraic equations is solved and the displacement and strain distributions on the plate are obtained. The displacement and strain distributions are also obtained by using the finite element software ANSYS. An agreement is found between the results obtained by using the DQM and ANSYS. The convergence is obtained rapidly with the DQM. The effects of thickness variation and stacking sequences on the displacement and strain distributions are investigated. Increasing the taper ratio increased the deformation for the linearly tapered simply-supported plates. The DQM can also be used for the thermal, buckling, and large deflection analyses of the plates. These will be the subject of future studies.

1

R. Bellman, J. Casti, "Differential quadrature and long term integration", Journal of Mathematical Analysis and Applications, 34, 235-238, 1971. doi:10.1016/0022-247X(71)90110-7

2

R. Bellman, B.G. Kashef, J. Casti, "Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations", Journal of Comput. Phys., 10, 40-52, 1972. doi:10.1016/0021-9991(72)90089-7

3

X. Wang, C.W. Bert, A.G. Striz, "Differential quadrature analysis of deflection, buckling, and free vibration of beams and rectangular plates", Computers and Structures, 48(3), 473-479, 1993. doi:10.1016/0045-7949(93)90324-7

4

C.W. Bert, M. Malik, "Free vibration analysis of thin cylindrical shells by the differential quadrature method", Journal of Pressure Vessel Technology, 118, 1-12, 1996. doi:10.1115/1.2842156

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