# by osama mohammed elmardi Deflection of Rectangular Laminated Composite Plates using Dynamic Relaxation Method

(osama mohammed elmardi suleiman khayal) #1

A Dynamic relaxation (DR) program based on􀀃finite differences has been
developed for small and 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. Dynamic Relaxation (DR) method is
presented for the geometrically linear and nonlinear laterally loaded, rectangular
laminated plates. The analysis uses the Mindlin plate theory with first order shear
deformation theory (FSDT) which accounts for transverse shear deformation. A
computer program has been compiled using a FORTRAN program. The convergence
and accuracy of the DR solutions for elastic small and large deflection response are
established by comparison with various exact and approximate solutions. New
numerical results are generated for uniformly loaded square laminated plates which
serve to quantify the effects of shear deformation, material anisotropy, fiber
orientation, and coupling between bending and stretching.
It was found that linear analysis seriously over-predicts deflections of plates.
The shear deflection depends greatly on a number of factors such as length/ thickness
ratio, degree of anisotropy and number of layers. It was also found that coupling
between bending and stretching can increase or decrease the bending stiffness of a
laminate depending on whether it is positive or negative.
It was also found that: The convergence and accuracy of the DR solution is
dependent on several factors including boundary conditions, mesh size and type,
fictitious densities, damping coefficients, time increment and applied load. Also, the
DR large deflection program using uniform finite differences meshes can be
employed in the analysis of different thicknesses for isotropic, orthotropic or
laminated plates under uniform loads. All the comparison results for simply
supported (SS􀀘) edge conditions showed that deflection is almost dependent on the
direction of the applied load or the arrangement of the layers978-3-330-33164-8.pdf (9.4% u)