Geometrically nonlinear finite element analysis of sandwich plates using normal deformation theory

The geometrically nonlinear bending and vibration behavior of soft core sandwich plates is investigated here using higher order finite element model incorporating transverse shear and normal deformation. The geometric nonlinearity, based on von Kármán’s assumption is introduced and the nonlinear governing equations of motion are derived considering in-plane and rotary inertia. The nonlinear governing equation is solved by Newton–Raphson iteration technique for the nonlinear bending problem, whereas, the harmonic balance method is employed to obtain the frequency versus amplitude relationships for the large amplitude free and forced vibration of sandwich plates. The results obtained from the normal deformation theory are compared with the results of first-order and third-order shear deformation theories. Limited parametric study is conducted to examine the influences of span-to-thickness ratio and core-to-face sheet thickness ratio of soft core sandwich plates.