柔性梁弹塑性次碰撞的研究
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摘要
虽然柔性梁的弹塑性碰撞问题的研究历来受到关注,但国内外针对弹塑性次碰撞问题的研究仍然非常缺乏。由于柔性梁的弹塑性次碰撞过程涉及弹塑性应力波的传播,多变拓扑结构的识别和碰撞系统运动状态的转换,其次碰撞动态响应行为相当复杂。目前,柔性梁弹塑性次碰撞问题的研究还处于现象观测阶段,对于弹塑性次碰撞行为的发生原因及其对结构瞬态响应的影响规律,尚无完整系统的研究工作发表。本文选择简支梁和自由运动梁作为柔性梁的代表,结合能够考虑多次碰撞接触行为的弹塑性局部接触模型,完善并运用刚塑性理论方法和有限差分方法,对柔性梁的弹塑性次碰撞行为进行了一些探索性研究,并采用有限元方法和实验测试方法进行了验证。
主要研究结论如下：
(1)针对刚性质量碰撞简支梁和刚性质量碰撞自由运动梁的两个碰撞系统,基于刚塑性动力学理论和单轴压缩弹塑性局部接触模型,建立了能够用于塑性次碰撞研究的刚塑性方法,给出了塑性次碰撞过程中梁的三种运动状态的转换条件和运动方程。通过接触面上的位移边界条件,给出了交替进行的碰撞过程和分离过程开始的判断条件。该理论方法克服了传统粘附性假设对碰撞力和局部碰撞变形预测的困难,可以描述次碰撞行为,对结构的主要碰撞响应特征的预测合理。
(2)为研究柔性梁弹塑性次碰撞过程,基于Rayleigh梁理论,运用了结合单轴压缩弹塑性局部接触模型和有限差分法的MCIS方法,使之可以同时考虑弹性效应和多次碰撞接触分离过程。并利用该方法研究了弹塑性波动效应和应变强化效应对弹塑性次碰撞响应的影响。
(3)采用过应力模型,考虑局部碰撞接触变形中的材料应变率效应,提出了能够考虑多次碰撞接触行为的单轴压缩弹粘塑性局部接触变形模型。继而建立了将弹粘塑性局部接触变形模型和有限差分法相结合的MEVP方法。使之可以研究次碰撞过程中的局部接触变形和梁动力响应的应变率效应。运用该方法研究柔性粱弹粘塑性次碰撞过程的局部接触变形时,发现了局部非圆柱面压痕,有别于以前的研究成果。
(4)分别将MCIS方法和MEVP方法应用于应变率不敏感材料和应变率敏感材料的柔性梁碰撞系统,研究碰撞过程中出现的弹塑性次碰撞现象和弹粘塑性次碰撞现象,并与刚塑性理论方法、有限元方法和实验测试方法进行对比研究,表明MCIS方法和MEVP方法可以准确模拟次碰撞过程,计算结果可靠。而刚塑性方法在预测后续次碰撞力和弹性响应上存在一定的局限性。
(5)研究刚性质量碰撞简支梁,刚性质量碰撞自由运动梁和刚性球碰撞简支梁三种碰撞系统的碰撞过程,均发现了明显的次碰撞现象,且次碰撞在整个碰撞过程中的分布具有明显的分区特征。多次的次碰撞过程使梁的变形响应更为复杂。相对于首次碰撞过程,后续次碰撞过程的能量、冲量和碰撞力幅值均不可忽略,因此,次碰撞过程将对梁的碰撞物理行为产生重要影响。
(6)次碰撞会造成塑性区(铰)的往复运动。并且,次碰撞还可改变梁的变形模式,研究发现第二碰撞区的次碰撞过程,打破了梁在第一碰撞区之后在分离区形成的稳定变形和运动模式,使梁的运动和变形重新表现出瞬态响应特征。
(7)次碰撞过程改变了碰撞能量的传递方式,使碰撞能量以非连续的、间歇方式传递。大质量碰撞引起的次碰撞效应更显著,高相对碰撞速度引起的次碰撞效应更显著。
(8)梁边界约束效应和梁材料特性(应变强化效应和应变率效应)使碰撞过程的碰撞力,碰撞持续时间,次碰撞次数和强度,碰撞应力,碰撞变形等发生明显变化,显著影响了次碰撞物理行为。
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.
主要研究结论如下：
(1)针对刚性质量碰撞简支梁和刚性质量碰撞自由运动梁的两个碰撞系统,基于刚塑性动力学理论和单轴压缩弹塑性局部接触模型,建立了能够用于塑性次碰撞研究的刚塑性方法,给出了塑性次碰撞过程中梁的三种运动状态的转换条件和运动方程。通过接触面上的位移边界条件,给出了交替进行的碰撞过程和分离过程开始的判断条件。该理论方法克服了传统粘附性假设对碰撞力和局部碰撞变形预测的困难,可以描述次碰撞行为,对结构的主要碰撞响应特征的预测合理。
(2)为研究柔性梁弹塑性次碰撞过程,基于Rayleigh梁理论,运用了结合单轴压缩弹塑性局部接触模型和有限差分法的MCIS方法,使之可以同时考虑弹性效应和多次碰撞接触分离过程。并利用该方法研究了弹塑性波动效应和应变强化效应对弹塑性次碰撞响应的影响。
(3)采用过应力模型,考虑局部碰撞接触变形中的材料应变率效应,提出了能够考虑多次碰撞接触行为的单轴压缩弹粘塑性局部接触变形模型。继而建立了将弹粘塑性局部接触变形模型和有限差分法相结合的MEVP方法。使之可以研究次碰撞过程中的局部接触变形和梁动力响应的应变率效应。运用该方法研究柔性粱弹粘塑性次碰撞过程的局部接触变形时,发现了局部非圆柱面压痕,有别于以前的研究成果。
(4)分别将MCIS方法和MEVP方法应用于应变率不敏感材料和应变率敏感材料的柔性梁碰撞系统,研究碰撞过程中出现的弹塑性次碰撞现象和弹粘塑性次碰撞现象,并与刚塑性理论方法、有限元方法和实验测试方法进行对比研究,表明MCIS方法和MEVP方法可以准确模拟次碰撞过程,计算结果可靠。而刚塑性方法在预测后续次碰撞力和弹性响应上存在一定的局限性。
(5)研究刚性质量碰撞简支梁,刚性质量碰撞自由运动梁和刚性球碰撞简支梁三种碰撞系统的碰撞过程,均发现了明显的次碰撞现象,且次碰撞在整个碰撞过程中的分布具有明显的分区特征。多次的次碰撞过程使梁的变形响应更为复杂。相对于首次碰撞过程,后续次碰撞过程的能量、冲量和碰撞力幅值均不可忽略,因此,次碰撞过程将对梁的碰撞物理行为产生重要影响。
(6)次碰撞会造成塑性区(铰)的往复运动。并且,次碰撞还可改变梁的变形模式,研究发现第二碰撞区的次碰撞过程,打破了梁在第一碰撞区之后在分离区形成的稳定变形和运动模式,使梁的运动和变形重新表现出瞬态响应特征。
(7)次碰撞过程改变了碰撞能量的传递方式,使碰撞能量以非连续的、间歇方式传递。大质量碰撞引起的次碰撞效应更显著,高相对碰撞速度引起的次碰撞效应更显著。
(8)梁边界约束效应和梁材料特性(应变强化效应和应变率效应)使碰撞过程的碰撞力,碰撞持续时间,次碰撞次数和强度,碰撞应力,碰撞变形等发生明显变化,显著影响了次碰撞物理行为。
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.
引文
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