Structural Analysis of Variable Stiffness Laminated Plates Using First-Order Shear Deformation Theory

Constant and variable stiffness strategies have been developed to design a composite laminate. With the former, each layer is designed with straight fibers that have the highest stiffness and strength in the fiber direction. With the latter, on the other hand, the stiffness can change within each layer by placing the fibers along a curvilinear fiber path. A variable stiffness design results in improved structural performance, as well as opens up opportunities to search for trade-off among structural properties. During the manufacture of a variable stiffness design with Automated Fiber Placement, certain defects in the form of gaps and overlaps could appear within the laminate and affect the laminate performance. In this study, we use the first-order shear deformation theory to assess the effect of transverse shear stresses on the critical buckling load, free and forced vibration of a variable stiffness laminate with embedded defects, an issue so far rarely examined in literature. The governing differential equations for the static analysis are first derived. A semi-analytic solution is then obtained using the hybrid Fourier-Galerkin method and the numeric time integration technique. The eigenvalue analysis is also conducted to determine the fundamental frequency and critical buckling load of the plate. It is found that the behavior of a variable stiffness plate is much more affected by the shear stresses than a constant stiffness plate. Ignoring the effect of transverse shear stresses results in 34% error in the predicted buckling load of a variable stiffness laminate with overlaps and a length-to-thickness ratio of 10.