Dynamic Investigation On Elasto-Plastic Multi-Body System

In this dissertation, rigid-flexible coupling dynamic performance of elasto-plastic multi-body system undergoing large overall motion is investigated. The material of each flexible component is assumed to be elastic-perfectly plastic.In chapter one,the previous research on the dynamics for elasto-plastic multi-body system is summarized, and the objectives of this dissertation are put forward.In chapter two,rigid-flexible coupling dynamics for elasto-plastic beam undergoing large overall motion is investigated. Taking into account of nonlinear constitutive relation and nonlinear strain-displacement relationship, dynamic variational equations for elasto-plastic beam are established using virtual work principle and absolute nodal coordinate formulation. Exact expression of curvature is used in order to get accurate results, and finite element method is used for discretization, and then dynamic equations for elasto-plastic beam system undergoing large overall motion are established. Comparison of the simulation results obtained by the present method and those obtained by Ansys software verifies the correctness of the present formulation. Furthermore, comparison of the simulation results obtained by the present method and those obtained by approximate method based on modal assumption approach is used to clarify the applicability of the approximate method. Simulations of a single pendulum and a double pendulum under gravity show that plastic strain leads to the slow recovery of the transverse and longitudinal deformation of the beam. Furthermore, plastic strain leads to the decay of the amplitude of the transverse and longitudinal vibration near the average deformation. It is shown that in case of large deformation, plastic strain significantly affects the angular velocity of the pendulum. In addition, the study also shows that for an elasto-plastic beam, the results are difficult to converge in case that the curvature is approximated, while the results are stable in case that the curvature takes exact expression.In chapter three, dynamic performance for a two-dimensional elasto-plastic plate undergoing large overall motion is investigated. Based on V.Mises yield condition and flow rule, dynamics variational equations for a two-dimensional elasto-plastic plate are established using virtual work principle and absolute nodal coordinate formulation. In the numerical calculation, we store plastic strain of each time step in the global array to achieve the iteration of plastic strain. Simulation of a two-dimensional elasto-plastic plate with lumped mass in the middle under driving constraint shows that when the angular acceleration is large enough, plastic strains occur in local area. In case that the driving constraint is released, it is shown that the plastic strain leads to the decrease of the amplitude of the angular velocity. Applied with driving constraint, the growing of total energy of the elasto-plastic material is much slower than the elastic material. In case that the driving constraint is released, the total energy of the elastic material stays the same, while the total energy of elasto-plastic material decreases. In addition, for some special area on the structure which is stress concentration, with large bending moment or close to constraint point, plastic strain easily occurs and increases quickly, which should be considered in engineering design.In chapter four, dynamic performance for a three-dimensional elasto-plastic plate undergoing large overall motion is investigated. Based on V.Mises yield condition and flow rule, dynamics variational equations for a three-dimensional elasto-plastic plate are established using virtual work principle and absolute nodal coordinate formulation. Simulations of a three-dimensional elasto-plastic plate under gravity and driving constraint show that when the acceleration is large enough, plastic strains occur in local area. It shows that the plastic strain leads to the slow recovery of the transverse deformation and the decrease of the increase amplitude of the total energy.