## Linear Analysis of Composite Laminated Plates Using First Order Shear Deformable Theory

Osama Mohammed Elmardi Suleiman Khayal
• Engineering and Technology Journal, November 2016, Research and Analysis Journals
• DOI: 10.18535/etj/v1i3.01

# Linear Analysis of Composite Laminated Plates Using First Order Shear Deformable Theory

Dynamic Relaxation (DR) method is presented for the analysis of geometrically linear laterally loaded, rectangular laminated plates. The analysis uses the Mindlin plate theory which accounts for transverse shear deformations. A computer program has been compiled. The convergence and accuracy of the DR solutions of isotropic, orthotropic, and laminated plates for elastic small deflection response are established by comparison with different exact and approximate solutions. The present Dynamic Relaxation (DR) method shows a good agreement with other analytical and numerical methods used in the verification scheme. It was found that: The convergence and accuracy of the DR solution is dependent on several factors which include boundary conditions, mesh size and type, fictitious densities, damping coefficients, time increment and applied load. Also, the DR small deflection program using uniform meshes can be employed in the analysis of different thicknesses for isotropic, orthotropic or laminated plates under uniform loads in a fairly good accuracy.

### Why is it important?

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 the large number of calculations involved.

### Perspectives

##### professor Osama Mohammed Elmardi Suleiman Khayal (Author)
Nile Valley University

This research paper is part of my master thesis entitled nonlinear analysis of rectangular laminated plates using dynamic relaxation technique.

http://dx.doi.org/10.18535/etj/v1i3.01

The following have contributed to this page: professor Osama Mohammed Elmardi Suleiman Khayal