Impact-Wave Interaction Behavior Of Elastic-Plastic Beams

The elastic-plastic impact of beam-like structures is a typical impact problem.It is significantly important in science and engineering applications.It involves many complicated physical phenomena,such as local elastic-plastic contact deformation,impact-induced wave propagation and structural dynamical responses.One of its key issue is the interaction between impact and impact-induced wave.The moving boundary due to elastic-plastic waves makes its analytical solution much more difficult.Thus,the characteristics of its impact response is unknown for lack of study.It is important to obtain the types of impact responses by the detailed investigation of impact-wave interaction and a huge,intensive amount of analytical data,and then to predict impact force,contact time,impact impulse and wave effect by selecting suitable analytical methods.Such predictions is important for pre-design of impact structure and simplifying complex impact test systems.To study the impact-wave interaction and capture the impact response characterizations,a huge,intensive amount of analytical data are required.Hence,a high accuracy and high efficient numerical method is desired.In this thesis,a highly efficient hybrid numerical-analytical model,named SCFDI model,is presented with high computational accuracy.SCFDI model is the coupling of a two-dimensional finite difference model with the refined Stronge model.SCFDI model is validated by the experiments and the three-dimension finite element(FE)analysis.By the use of SCFDI model,the effects of impact parameters on impact responses and the interaction between impact and waves are studied.The impact-wave interaction characteristic diagram is obtained.It is applied to predict the type of impact response,multiple impact phenomenon and impact responses.The main research contents are shown as the followings:(1)Based on the Rayleigh's beam theory and a theoretical contact model(a refined Stronge model),a hybrid,numerical-analytical model(SCFDI model)is presented to investigate the impact response of a simply supported elastic-plastic beam subjected to impact of a sphere.SCFDI model take into account local elastic-plastic contact deformation,impact-induced wave propagation,interaction between impact and waves,and structural damping.SCFDI model is verified by the experiments.The comparison between SCFDI model and 3D finite element model shows that the presented model is highly efficient and accurate.(2)By the use of the SCFDI model,the parametric studies are carried out through a huge number of simulations to investigate the effects of impact parameters.The studies shows the damping of the structure has no effect on contact behaviors during impact.The impact force,indentation and the permanent indentation increase with the impact mass,impact velocity,radius of the sphere and beam yield strength,while the contact time is on the contrary.The loading stiffness is proportional to the radius of the sphere and the beam yield strength,but is independent upon the impact mass,impact velocity,beam size and impact location.Before the impact-induced waves are reflected and have not arrived at the impact position,the contact time is independent upon the beam sizes,the impact force is independent upon the beam length,and the impact force is dependent upon the beam width and thickness.As the impact-induced waves have arrived at the impact position,the waves will interact strongly with the impact,and cause the jumping of the energy loss and the Newton coefficient of restitution.(3)By the use of SCFDI model,the propagation of impact-induced waves,plastic hinge and interaction between impact and impact-induced waves are investigated.According the interaction between impact and impact-induced waves,the impact responses are divided into four phases,wave controlled,strong wave-impact interaction,quasi-static elastic and quasi-static inelastic phases.A mass criterion for identifying the phase of impact responses is presented according the variation of the beam recoverable energy with the mass ratio of sphere to beam.(4)By the use of SCFDI model,the characteristic diagrams of the wave-impact interaction for elastic-plastic beam impact is constructed,and a simplified criterion of strong wave-impact interaction is presented.The characteristic diagrams consist of a main diagram(Diagram ?)and two auxiliary diagrams(Diagram ? and ?).Diagram ? consists the characteristic lines of normalized contact time and energy loss factor,and can be applied to identify the phase of impact responses and to predict impact responses.Diagram ? consists the characteristic lines of normalized contact time and theoretical return time ratio,and can be applied to identify the phase of strong wave-impact interaction and to predict impact responses.Diagram ? consists the characteristic lines of normalized contact time and theoretical main wave order,and can be applied to identify the main wave arriving at the impact position,to identify the phase of impact responses and to predict impact responses.The diagrams have the function for scaling impact models,and can predict multiple-impact phenomenon.All the three diagrams include either the one for central impact or the another one for non-central impact.The diagrams and the simplified criterion are validated by 3D FE analysis.(5)By the application of the characteristic diagrams,the phases of impact responses,impact force,contact time and multi-impact have been predicted for an experimental beam impact system,a clamped beam impact system and an arch beam impact system.The predictions are validated by the experiments and 3D FE simulations.