Deflection of Rectangular Laminated Composite Plates using Dynamic Relaxation Method

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 SS4 edge conditions showed that deflection is almost dependent on the direction of the applied load or the arrangement of the layers
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