Investigating nonlinear moving load responses of FG-GPLRC skew plates using meshfree radial point interpolation method

As a first endeavor, the nonlinear response under moving load of multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) skew plates is investigated. The nonlinear kinematic relations are derived based on the higher-order shear deformation theory (HSDT) under the von K ' arm ' an nonlinear geometric assumptions. A meshfree radial point interpolation method (RPIM) is employed to derive the spatially discretized motion equations. The different boundary conditions of the multilayer FG-GPLRC skew plates are imposed by employing the mixed collocation-Lagrange multiplier method. The Newmark's time integration scheme together with the Newton-Raphson method are employed to solve the obtained nonlinear system of ordinary differential equations of motion. The fast rate of convergence and accuracy of the method are verified through different examples. Then, the influences of different GPLs distribution patterns, skew angle, load velocity and boundary conditions on the nonlinear response of the multilayer FG-GPLRC skew plates subjected to a moving load are studied. The results indicate that the dynamic magnification factor of the multilayer FG-GPLRC skew plates based on the nonlinear theory is lower than the one based on the linear theory.

Automated summary

This study investigates the nonlinear response of multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) skew plates under moving load. Nonlinear kinematic relations are derived based on higher-order shear deformation theory and von K'arm'an nonlinear geometric assumptions. A meshfree radial point interpolation method is used to discretize the motion equations. Different boundary conditions are imposed using the mixed collocation-Lagrange multiplier method. The results show that the dynamic magnification factor of the multilayer FG-GPLRC skew plates based on the nonlinear theory is lower than the one based on the linear theory.