Deflection of Laminated Composite Plates Using Dynamic Relaxation Method

“

A Dynamic relaxation (DR) program based on finite differences has been developed for large 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, meshes size, fictitious densities and applied load. 2. The DR large deflection program using uniform finite differences meshes can be employed with confidence in the analysis of moderately thick and flat isotropic, orthotropic or laminated plates under uniform loads. 3. The DR program can be used with the same confidence to generate small deflection results. 4. The 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. 5. 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. At the other hand 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.

”