Transient Response of Strain Rate Dependent Composite Plates Using Finite Difference Method

In the present work, the response of laminated composite plate under dynamic loading is investigated using a macro-mechanical approach by use of a finite difference model which accounts for geometric nonlinearity and strain rate effects. Coupled nonlinear equations of motion of a laminated plate based on classical laminated plate theory (CLPT) and first-order shear deformation laminated plate theory (FSDT) are derived and reduced to nonlinear ordinary differential equations in time domain by finite difference approximations for displacements. Newmark time integration scheme in association with Newton-Raphson iteration method is applied to solve the system of nonlinear equations. Sudden material property degradation rules are modified to account for strain rate effects. A progressive damage model is developed based on the modified material property degradation rules and Hashin-type failure criteria and added to a finite difference model. The model is implemented into a computer code in Mathematica 6. The model is validated by comparison of the present results with those are available in the literature. The effects of transverse shear strain are studied by comparison of the results obtained using CLPT and FSDT. In order to investigate the strain rate effects, a clamped Glass/Epoxy composite plate subjected to a triangular load is considered. Results for static model, in which the mechanical properties are constant and dynamic model which has strain rate dependent mechanical properties are compared for various stacking sequences and load magnitudes. The results show that the deflections are overestimated by static model and the difference between static and dynamic models results increases with the magnitude of load. Furthermore, the variation trend of maximum displacement with stacking sequence is the same for both material models.