Linear Deflection of Laminated Composite Plates using Dynamic Relaxation Method

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A Dynamic relaxation (DR) program based on finite differences has been developed for small deflection analysis of rectangular laminated plates using first-order shear deformation theory (FSDT). The displacements are assumed linear through the thickness of the plate. A series of new results for uniformly loaded thin, moderately thick, and thick plates with simply supported edges have been presented. Finally, a series of numerical comparisons have been undertaken to demonstrate the accuracy of the DR program. These comparisons show the following:- 1. The convergence of the DR solution depends on several factors including boundary conditions, mesh size, fictitious densities and load. 2. The type of mesh used (i.e. uniform or graded mesh) may be responsible for the considerable differences in the mid – side and corner stress resultants. 3. For simply supported (SS1) edge conditions, all the comparison results confirmed that deflection depends on the direction of the applied load or the arrangement of the layers. 4. The DR small deflection program using uniform finite difference meshes can be employed with less accuracy in the analysis of moderately thick and flat isotropic, orthotropic or laminated plates under uniform loads. 5. Time increment is a very important factor for speeding convergence and controlling numerical computations. When the increment is too small, the convergence becomes tediously slow, and when it is too large, the solution becomes unstable. The proper time increment in the present study is taken as 0.8 for all boundary conditions. 6. The optimum damping coefficient is that which produces critical motion. When the damping coefficients are large, the motion is over – damped and the convergence becomes very slow. And when the coefficients are small, the motion is under – damped and can cause numerical instability. Therefore, the damping coefficients must be selected carefully to eliminate under – damping and over – damping. 7. Finer meshes reduce the discretization errors but increase the round – off errors due to a large number of calculations involved.

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