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Nowadays, availability, durability, reliability, weight and strength, as the most important factors in optimum engineering design, are responsible for the widespread application of plates in the industry. Buckling in the elastic or elastoplastic regim is one of the phenomena that can be occurred in the axial compressive loading. Using Galerkin method on the basis of trigonometric shape functions, the elastoplastic dynamic buckling of a thin rectangular plate with different boundary conditions subjected to compression exponetiail pulse functions is investigated in this paper. 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 the equilibrium, stability and dynamic elastoplastic buckling equations are derived. Ramberg-Osgood stress-strain model is used to describe the elastoplastic material property of plate. The effects of symmetrical and asymmetrical boundary conditions, geometrical parameters of plate, force pulse amplitude, 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. The resistance against deformation for plate with clamped boundary condition is more than plate with simply supported boundary condition. Consequently, the adjacent points to clamped boundary condition have a lower velocity field than adjacent points to simply supported boundary condition.

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When a dynamic load passes a control volume of material as a shock wave, passing this wave through the control volume could cause different phases such as elastic and plastic. From the microscopic view, during phase change, material flow would be taken in control volume which includes mass, heat, energy, and momentum transport. Phase change in material causes a material discontinuity in the control volume. During the phase change process, mass, heat, energy, momentum transport and etc will occur and the equations governing these phenomena are called transport equations. In this article, for the first time, the governing equations of elastoplastic behavior of beam under dynamic load are extracted by using mass, energy and momentum transport equations. Using transport equations with non-physical variables in integral form will cause in employing discontinuity conditions in governing equations and eliminates the discontinuity condition. These equations are also used in continuously modeling of beam elastoplastic behavior under dynamic loading and a continuous model is presented. Finite element method is used to solve the transport equation with non-physical variable. Finally, the time history of stress, strain and velocity wave propagation along beam are presented in elastic and elastoplastic phases

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In this paper, the elastoplastic response of copper, steel and aluminum circular plates with clamped boundary conditions subjected to underwater explosion loading is investigated. Cavitation is a phenomenon that can be occurred for plates in the process of underwater explosion forming. The total pressure of the explosion becomes zero at the cavitation time, so that the governing equations of motion time will be different before and fter the cavitation. As a result, in terms of analysis and design, the cavitation time is significant in studying the behavior of a circular plate at underwater explosive loading. By appling the energy method and based on Hamilton principle and variation method the equations of motion of an underwater circular plate subjected to explosive loading are derived. Then, in order to obtain the forced response of the circular plate, the exact free vibration solution is derived to calculate the mode shapes. Then, the velocity and generated stress of plate during cavitation time are calculated and compared with the yield stress plates. Using this method, one can distinguish the cavitation with in the elastic or plastic regimes. By recognizing the time of cavitation in the range of elastic or plastic, the displacement and velocity field of plate are determined in duration of explosive loading. Results show that the cavitation time is on the order of microsecond. Depending on amount of charge mass and stand-off, the cavitation time may be occurred in elastic or plastic regime.