Elastoplastic dynamic buckling of rectangular plates subjected to impulsive loading with various boundary conditions using deformation and incremental theory of plasticity

The elastoplastic dynamic buckling of a thin rectangular plate with different boundary conditions subjected to uni- and biaxial compression sinusoidal pulse functions is investigated employing Galerkin method on the basis of trigonometric mode shape functions. The equilibrium, stability and dynamic elastoplastic buckling equations are derived based on two theories of plasticity: deformation theory of plasticity (DT) with Hencky constitutive relations and incremental theory of plasticity (IT) with Prandtl-Reuss constitutive relations. Ramberg-Osgood stress-strain model is used to describe the elastoplastic material property of plate. The effects of boundary conditions, force pulse amplitude, loading ratio and type of plasticity theory on the velocity and deflection histories of plate are investigated. According to the dynamic response of plate, the results obtained from DT are lower than those predicted through IT and the boundary conditions of rectangular plate subjected to impulsive load have a significant influence on the dynamic response of palte. The resistance against deformation for corresponding to plates with clamped boundary condition is more than those plates with simply supported boundary condition.