Nonlinear impact response of thin imperfect laminated plates using a reduction method

Abstract

The nonlinear transient response of thin imperfect laminated plates subjected to impact loads is studied using a 48 DOF finite element based on the classical laminated plate theory. Comparison between the first-order shear deformation theory and the classical laminated plate theory is also made to study the effect of shear deformation. The modified Hertzian law by Tan and Sun is incorporated to evaluate the impact loads due to a projectile. The transient response of an example problem is obtained using both full and reduced equations of motion. A reduction method using Ritz vectors as the basis vectors is employed to reduce the size of the nonlinear problem and thus save computational effort. The resulting reduced (but still coupled) set of equations is integrated in a step-by-step fashion using the Newmark constant-average acceleration time integration scheme along with an iterative scheme for dynamic equilibrium. It is observed that geometric imperfections cause significant changes in the impact response of thin laminated plates. The reduction method used in this study was not found to be very efficient for obtaining the nonlinear impact responses. Further research is needed to develop reduction methods that are more suitable for studying nonlinear impact responses.