Using of explicit time-central difference method for numerical simulation of dynamic behavior of elasto-plastic flexible reinforced plates

Abstract

Based on the step-wise algorithm involving central finite differences in time, a mathematical model is developed for elastic-plastic deformation of cross-reinforced plates with isotropic hardening materials of components of the composition, which at discrete points in time allows obtaining the solution of elasto-plastic problems by the explicit scheme. In Karman’s approximation, the initial-boundary value problem is formulated for the dynamic behavior of flexible, reinforced in their own plane, plates. Their weakened resistance to the transverse shear is taken into account. With one approach, the resolving equations are obtained that correspond to two variants of the Timoshenko theory. The explicit “cross” scheme was constructed for the numerical integration of the initial-boundary-value problem consistent with the incremental algorithm used to simulate the elastic-plastic behavior of reinforced medium. The calculations of the dynamic behavior are performed for elastic-plastic cylindrical bending of different reinforced fiberglass rectangular elongated plates. It is shown that the structure of the reinforcement significantly affects the elastic-plastic dynamic behavior of such structures. It has been found that the classical theory of plates is as a rule, unacceptable for carrying out the required calculations (except for very thin plates), and the first version of the Timoshenko theory gives reasonable results only in cases of relatively thin structures reinforced of low modulus fibers. It is recommended to use the second variant of the Timoshenko theory for calculation of the elastic-plastic behavior of reinforced plates, as more accurate.