冲击荷载作用下轴心受压构件动力屈曲研究
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摘要
稳定理论就其性质而言属于固体力学的一个分支,随着稳定理论研究的不断深入,现今已由简单的弹性稳定理论扩展到非弹性、非线性稳定理论,荷载也由静载发展到动载。动力屈曲问题由于时间参数的引入相比静力屈曲问题要复杂得多,特别是对冲击荷载作用下的动力屈曲(冲击屈曲)问题尤甚,研究成果相对较少,对许多问题的认识尚未达成一致。有鉴于此,本文就冲击荷载作用下轴心受压构件的动力屈曲进行系统研究,涵盖了冲击分岔屈曲、应力波效应、初始缺陷(残余应力与初弯曲)、冲击荷载形式、材料损伤、板件局部动力屈曲等各个方面。材料本构关系采用线性强化模型,构件边界条件考虑简支与固定两种情况,冲击荷载以阶跃荷载为主。
本文首先对轴向应力波在构件中的传播、反射及相互作用进行系统分析,推导出适合轴心受压构件冲击屈曲分析的轴向弹、塑性应力波计算公式。其次,通过对不同边界条件理想轴心受压构件进行分析,建立动力屈曲条件,获得了动力屈曲临界荷载及相应屈曲模态,表明了动力屈曲与静力屈曲的差异。其中,应力波效应也作为一个重要参数纳入到研究范围中,对轴心受压构件的动力屈曲有重要影响。再次,通过对残余应力初始缺陷进行分析,可知残余应力的存在使构件提前进入弹塑性状态,这对构件的动力屈曲临界荷载和屈曲变形十分不利。然后,通过有限差分法对初始几何缺陷轴心受压构件的动力屈曲进行计算,并同时考虑残余应力作用,得到了一些有价值的结论。最后,就冲击荷载作用下轴心受压构件的若干问题进行了研究,重点集中在冲击荷载形式、材料损伤、板件局部动力屈曲三个方面,给出了一些相关计算方法和研究思路。
The theory of stability is one branch of solid mechanics in nature. With the theory research more deeply, the theory of stability has extended from elasticity to non-elasticity and non-linearity, and the load considered is from static to dynamic. Because of introducing the time, the problem of dynamic buckling is much more complex than static one, especially under impact load (i.e. impact buckling) which has few study findings relatively. So some viewpoints have not been consistent. Systematic study is made on dynamic buckling of axial compression member under impact load in this paper for that reasons. This study include impact bifurcation buckling, stress wave effect, initial flaws (residual stress and initial bending), form of impact load, damage of material, local dynamic buckling of plate, and so on. The constitutive relationship of material is assumed linear hardened and two boundary conditions (i.e. simple supported and fixed) are considered. Step load is the main form of impact load adopted.
First, systematic study on propagation, reflection and interaction of axial stress wave is made to deduce the calculation equation for axial elastic and plastic stress wave, which fit for analysis of impact buckling of axial compression member. Second, dynamic buckling condition is erected after analysis of perfect axial compression member with different boundary conditions, by which dynamic buckling critical load and corresponding buckling modal are obtained. These indicate the difference between dynamic buckling and static one. Stress wave effect is one important parameter considered in the study and it may have some influence on the dynamic buckling of axial compression member. Third, as one main flaw, residual stress would make the member section into elasto-plasticity in advance. This would be much disadvantage to the dynamic buckling critical load and buckling deformation. Fourth, systematic study on dynamic buckling of axial compression initial bending member through finite difference method, considered residual stress simultaneously, make some valuable conclusions. Final, some problems about axial compression member under impact load are studied, which focus on the form of impact load, damage of material, local dynamic buckling of plate. Some calculation method and research viewpoints are presented.
本文首先对轴向应力波在构件中的传播、反射及相互作用进行系统分析,推导出适合轴心受压构件冲击屈曲分析的轴向弹、塑性应力波计算公式。其次,通过对不同边界条件理想轴心受压构件进行分析,建立动力屈曲条件,获得了动力屈曲临界荷载及相应屈曲模态,表明了动力屈曲与静力屈曲的差异。其中,应力波效应也作为一个重要参数纳入到研究范围中,对轴心受压构件的动力屈曲有重要影响。再次,通过对残余应力初始缺陷进行分析,可知残余应力的存在使构件提前进入弹塑性状态,这对构件的动力屈曲临界荷载和屈曲变形十分不利。然后,通过有限差分法对初始几何缺陷轴心受压构件的动力屈曲进行计算,并同时考虑残余应力作用,得到了一些有价值的结论。最后,就冲击荷载作用下轴心受压构件的若干问题进行了研究,重点集中在冲击荷载形式、材料损伤、板件局部动力屈曲三个方面,给出了一些相关计算方法和研究思路。
The theory of stability is one branch of solid mechanics in nature. With the theory research more deeply, the theory of stability has extended from elasticity to non-elasticity and non-linearity, and the load considered is from static to dynamic. Because of introducing the time, the problem of dynamic buckling is much more complex than static one, especially under impact load (i.e. impact buckling) which has few study findings relatively. So some viewpoints have not been consistent. Systematic study is made on dynamic buckling of axial compression member under impact load in this paper for that reasons. This study include impact bifurcation buckling, stress wave effect, initial flaws (residual stress and initial bending), form of impact load, damage of material, local dynamic buckling of plate, and so on. The constitutive relationship of material is assumed linear hardened and two boundary conditions (i.e. simple supported and fixed) are considered. Step load is the main form of impact load adopted.
First, systematic study on propagation, reflection and interaction of axial stress wave is made to deduce the calculation equation for axial elastic and plastic stress wave, which fit for analysis of impact buckling of axial compression member. Second, dynamic buckling condition is erected after analysis of perfect axial compression member with different boundary conditions, by which dynamic buckling critical load and corresponding buckling modal are obtained. These indicate the difference between dynamic buckling and static one. Stress wave effect is one important parameter considered in the study and it may have some influence on the dynamic buckling of axial compression member. Third, as one main flaw, residual stress would make the member section into elasto-plasticity in advance. This would be much disadvantage to the dynamic buckling critical load and buckling deformation. Fourth, systematic study on dynamic buckling of axial compression initial bending member through finite difference method, considered residual stress simultaneously, make some valuable conclusions. Final, some problems about axial compression member under impact load are studied, which focus on the form of impact load, damage of material, local dynamic buckling of plate. Some calculation method and research viewpoints are presented.
引文
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