Study Of Elastic-Plastic Sub-impact Of Flexible Beam

The problem of elastic-plastic impact of flexible beam has always been an issue of concern. However, it is still lack of study for the problem of elastic-plastic sub-impact of flexible beam. The physical behavior of elastic-plastic sub-impact is quite complex due to propagation of elastic-plastic stress wave, identification of variable contact topology and transfer of the impact system’s motion state. In this thesis, local elastic-plastic contact deformation model is presented to account for the multiple impact-contact deformations, the rigid plastic method and finite difference method are developed to investigate the sub-impact phenomenon of several typical flexible beam impact systems.The main research contents are shown as follows:(1) By the use of a uniaxial compression elastic-plastic contact deformation model, a rigid plastic method is developed to account for rigid plastic sub-impact of impact system such as a rigid mass impacting on simply support beam or free-free beam. The conversion conditions and motion equations of three motion states of the beam are obtained. The creterion for the start time of contact phase and separation phase which transits alternately is also presented through displacement boundary conditions. Due to it overcomes the shortage of tradition method that is using stick assumption to predict local deformation and impact force, the rigid plastic method can reasonably predict sub-impact phenomenon and main impact characteristics.(2) Based on Rayleigh theory of beam, a so-called MCIS method is obtained by incorporating the uniaxial compression elastic-plastic contact modal and finite difference method to investigate the problem of elastic-plastic sub-impact of flexible beam. It considers the elastic effect of material, the process of multiple impacts as well as the process of multiple separations. The effect of propagation of stress wave and strain hardening on the response of elastic-plastic sub-impact is also studied by MCIS method.(3) By employing the overstress model, the effect of strain rate on local contact deformation and beam dynamic behavior is considered. A local elastic-viscoplastic uniaxial compression deformation model is presented to account for the multiple impact-contact deformations. Incorporating the finite difference method and the local elastic viscoplastic deformation model, a so-called MEVP method is presented. By the use of MEVP method, a new result of local non-cylindrical surface indentation is found.(4) The MCIS method and MEVP method are applied to the problem of elastic-plastic sub-impact and elastic viscoplastic sub-impact of flexible beam, respectively. The MEVP solutions and MEVP solutions are compared with those solved by finite element method, rigid plastic method and experimental measurement, respectively. The comparisons illustrate that the proposed two methods are reasonable, while rigid-plastic method has shortcomings in predicting the sub-impact response.(5) The impact processes of three typical impact system, a simply support beam struck by a rigid mass, a free-free beam struck by a rigid mass and a simply support beam struck by a rigid mass are studied, respectively. It is found that the whole impact process consists of obvious process of sub-imacts which have obvious regional characteristics in distribution. Multiple sub-impacts result in more complicated deformation response. By Comparsion with the first impact, the impact energy, impact impulse and impact force of subsequent sub-impacts can not be neglected. Therefore the process of sub-impacts has a major role in physical behavior of whole impact process.(6) Different from traditional knowledge, the sub-impact will cause the traveling plastic hinge to move back and forth. Moreover, the sub-impact can change the deformation mode of the beam. The first impact zone breaks the steady state of deformation and motion of the beam and causes the beam undergos accelerated motion and plastic deformation again.(7) The sub-impact forms the intermittent type of impact energy transfer and most of impact energy is transferred by the subsequent sub-impacts. Besides, increase in mass and relative velocity of the rigid project makes the sub-impact effect more important.(8) Boundary constraint effect and material characteristics (strain hardening effect and strain rate effect) have significant effect on sub-impacts physical behavior which involved duration of impact process, number and strength of sub-impacts, impact stress, impact deformation and etc.