直杆的撞击屈曲及其应力波效应的实验和理论研究
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摘要
结构经受撞击作用极为广泛地存在于许多工程技术领域,如航空器的着陆、交通车辆相撞、核电设施防护、导弹拦截、结构安全与耐撞性等都会遇到撞击加载问题。撞击加载以其历史短、强度高为特征,结构受到撞击加载,变形和运动极为迅速,惯性效应必须计及。工程上常用的细杆、薄板、薄壳等柔性结构元件,其膜刚度远大于侧向弯曲刚度,在撞击载荷作用下容易由于屈曲强度不足而引起灾变性的破坏。近年来由于结构耐撞性及各种能量吸收装置研制的需要,结构在撞击加载下的动态屈曲成为固体力学中一个十分活跃的前沿研究领域。在屈曲问题研究的各个发展阶段中,细长杆总是充当着首选对象,由其发展的力学模型可以揭示深刻的物理内函。细杆经受轴向撞击的屈曲,同样在结构动力屈曲研究中具有特殊重要的地位,从某种意义上讲,它比径向动压作用下薄壳的屈曲更复杂。因为杆撞击加载是轴向应力波加载,其屈曲的发生和发展是与应力波传播相关的复杂的动力学过程。为了揭示直杆撞击屈曲的机理及其应力波传播与动力屈曲之间的联系,建立各特征量之间的定量关系,本文从实验和理论方面开展了一系列的研究工作,取得了以下重要结果。
1、借助空气动力枪,实现了杆—杆撞击加载,对两种支承条件,三种长度的理想直杆进行了轴向撞击屈曲的动力实验研究。记录了不同速度下试件特定截面两侧对称点的应变时程曲线,由时程曲线的应变幅值和分叉时间,得到了不同支承条件下撞击屈曲载荷与屈曲长度关系曲线。
2、实验结果表明:在讨论轴向应力波传播(未发生反射时)导致的动力分叉时,波阵面处可视为固定约束,撞击端的约束条件却是非常重要的。在两种不同支承条件的实验中都只记录到最低屈曲模态,而对应的
Impact events occur in a wide variety of circumstance. Clearly, impact problems are often encountered in many technologies, such as landing of air craft, the collision of vehicle, the protection of nuclear power station, the interception of the missile, the design of structural safety and crashworthiness, etc. The impact loads are characterized by short duration and high intensity. The deformation and motion of a structure subjects to impact load is extremely rapid, hence the inertial effect has to be considered. The slender columns, thin plates and shells are the structural elements often used in practical engineering. The membrane rigidity of these elements is much bigger than lateral flexural rigidity. When they subject to impact load, the disaster failure easily caused due to the insufficiency of buckling strength. In recently years, the dynamic buckling of the structures under impact load is an active subject in solid mechanics because of the needs of the structural crashworthiness and manufacturing energy absorption facilities. In each developing period on the buckling investigation, the columns are always severed as first select object, and the mechanics model developed from columns can reveal profound connotation of physics. The dynamic buckling of the columns subjected to impact load has also special position in the structural dynamic buckling, and it is, in one respect, a more complex problem than buckling of shells under radial dynamic pressure. Axial impact load is, in fact, communicated to the columns by stress wave and the occurring and growing of buckling is a complex dynamic process related to the propagation of stress wave. In order to reveal the mechanism of the impact buckling of the columns and to determine the quantitative relation between
the propagation of stress wave and the dynamic buckling, a series of studies have made experimentally and theoretically in present paper. The important results are summarized in the following several aspects:1. The bar-bar impact experiments were carried out by means of air driver. The dynamic experimental studies on the buckling of the perfect columns with two kinds of bearing conditions and with three kinds of length under axial impact were completed. The time-history curves of strain on two symmetric surfaces of columns were recorded under different velocity. The relation curves between impact buckling load and buckling length under different bearing conditions are obtained from the amplitude and bifurcation time of strain time-history.2. The experimental results show that the constraint of wave front can be regarded as fixed constraint, and the constraint conditions at the impact end is very important when the dynamic buckling induced by stress wave is discussed. The lowest buckling mode are only recorded in our experiment, corresponding buckling load is distinctly greater than the static one under the same boundary condition and same length. The dynamic critical load is about 2.23 and 2.49 times of the static one in condition of movable clamped and hinged, and the ratio of dynamic load to static one has increasing trend as the impact velocity increases.3. The constraint conditions of wave front and the equation of lateral domination on the columns subjected to axial step pressure load are derived by using Hamilton principle. The qualitative analyzing buckling dominating equation shows that the scope of dynamic parameter sets the characteristics of the solutions, and the solutions stand for buckling motion when X < 0. The dynamic buckling load and buckling mode that the impact end is clamp and movable hinge are obtained by solving twin-parameter equation with direct-spread method. The dynamic buckling load is basically consistent with the one obtained by the experiment.4. The whole traveling process of elastic and elastic-plastic wave under impact processing was analyzed by characteristics method. The regularity of stress changes at both column ends and the first separating time of the rigid body and the columns were obtained.
5. Using the energy principles and taking into account of the propagation and reflection of stress wave, the lateral disturbance equation on elastic and elastic-plastic columns was derived and power series solution was given. The critical buckling condition can be obtained from stability analysis of the solution. By numerical computation and analysis, the relationship among critical velocity and impact mass, hardening modulus, buckling time was given.6. Considering axial inertia, lateral inertia and the non-linearity of axial strain, the dynamic post-buckling dominating equations are derived. The post-buckling behavior of semi-infinite columns is analyzed by using finite difference method integrating non-linear equations with post-buckling initial conditions, which are characteristics parameter of linear bifurcation, and the load forms and the constrains conditions at impact end and so on influencing on post-buckling are discussed. The results show that the initial buckling mode grows into a series of high-order modes with the increase of the time, and the wave number of mode increases and the amplitude of mode continuously become greater in post-buckling period.
1、借助空气动力枪,实现了杆—杆撞击加载,对两种支承条件,三种长度的理想直杆进行了轴向撞击屈曲的动力实验研究。记录了不同速度下试件特定截面两侧对称点的应变时程曲线,由时程曲线的应变幅值和分叉时间,得到了不同支承条件下撞击屈曲载荷与屈曲长度关系曲线。
2、实验结果表明:在讨论轴向应力波传播(未发生反射时)导致的动力分叉时,波阵面处可视为固定约束,撞击端的约束条件却是非常重要的。在两种不同支承条件的实验中都只记录到最低屈曲模态,而对应的
Impact events occur in a wide variety of circumstance. Clearly, impact problems are often encountered in many technologies, such as landing of air craft, the collision of vehicle, the protection of nuclear power station, the interception of the missile, the design of structural safety and crashworthiness, etc. The impact loads are characterized by short duration and high intensity. The deformation and motion of a structure subjects to impact load is extremely rapid, hence the inertial effect has to be considered. The slender columns, thin plates and shells are the structural elements often used in practical engineering. The membrane rigidity of these elements is much bigger than lateral flexural rigidity. When they subject to impact load, the disaster failure easily caused due to the insufficiency of buckling strength. In recently years, the dynamic buckling of the structures under impact load is an active subject in solid mechanics because of the needs of the structural crashworthiness and manufacturing energy absorption facilities. In each developing period on the buckling investigation, the columns are always severed as first select object, and the mechanics model developed from columns can reveal profound connotation of physics. The dynamic buckling of the columns subjected to impact load has also special position in the structural dynamic buckling, and it is, in one respect, a more complex problem than buckling of shells under radial dynamic pressure. Axial impact load is, in fact, communicated to the columns by stress wave and the occurring and growing of buckling is a complex dynamic process related to the propagation of stress wave. In order to reveal the mechanism of the impact buckling of the columns and to determine the quantitative relation between
the propagation of stress wave and the dynamic buckling, a series of studies have made experimentally and theoretically in present paper. The important results are summarized in the following several aspects:1. The bar-bar impact experiments were carried out by means of air driver. The dynamic experimental studies on the buckling of the perfect columns with two kinds of bearing conditions and with three kinds of length under axial impact were completed. The time-history curves of strain on two symmetric surfaces of columns were recorded under different velocity. The relation curves between impact buckling load and buckling length under different bearing conditions are obtained from the amplitude and bifurcation time of strain time-history.2. The experimental results show that the constraint of wave front can be regarded as fixed constraint, and the constraint conditions at the impact end is very important when the dynamic buckling induced by stress wave is discussed. The lowest buckling mode are only recorded in our experiment, corresponding buckling load is distinctly greater than the static one under the same boundary condition and same length. The dynamic critical load is about 2.23 and 2.49 times of the static one in condition of movable clamped and hinged, and the ratio of dynamic load to static one has increasing trend as the impact velocity increases.3. The constraint conditions of wave front and the equation of lateral domination on the columns subjected to axial step pressure load are derived by using Hamilton principle. The qualitative analyzing buckling dominating equation shows that the scope of dynamic parameter sets the characteristics of the solutions, and the solutions stand for buckling motion when X < 0. The dynamic buckling load and buckling mode that the impact end is clamp and movable hinge are obtained by solving twin-parameter equation with direct-spread method. The dynamic buckling load is basically consistent with the one obtained by the experiment.4. The whole traveling process of elastic and elastic-plastic wave under impact processing was analyzed by characteristics method. The regularity of stress changes at both column ends and the first separating time of the rigid body and the columns were obtained.
5. Using the energy principles and taking into account of the propagation and reflection of stress wave, the lateral disturbance equation on elastic and elastic-plastic columns was derived and power series solution was given. The critical buckling condition can be obtained from stability analysis of the solution. By numerical computation and analysis, the relationship among critical velocity and impact mass, hardening modulus, buckling time was given.6. Considering axial inertia, lateral inertia and the non-linearity of axial strain, the dynamic post-buckling dominating equations are derived. The post-buckling behavior of semi-infinite columns is analyzed by using finite difference method integrating non-linear equations with post-buckling initial conditions, which are characteristics parameter of linear bifurcation, and the load forms and the constrains conditions at impact end and so on influencing on post-buckling are discussed. The results show that the initial buckling mode grows into a series of high-order modes with the increase of the time, and the wave number of mode increases and the amplitude of mode continuously become greater in post-buckling period.
引文
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