A MECHANICAL ANALYSIS OF THE PROBLEM: HOW MANY TIMES CAN A SHEET OF PAPER BE FOLDED 1)

通过将纸张折叠问题简化为矩形截面简支梁在中段集中力作用下的三点弯曲问题,通过最大弯曲挠度和最小折叠载荷讨论了A4打印纸和八开报纸在普通人力作用下的最大对折次数问题。结果表明对于普通A4打印纸,一般成年人只能对折6次,最多也只能对折7 次。对于八开报纸,一般成年人能轻松对折7次,但是基本不可能对折8次。试验测试结果与理论预测结果吻合良好。     

轴向冲击载荷下薄壁折纹管的屈曲模态与吸能

在方管的基础上引入折纹结构, 利用几何关系建立折纹管的折角公式。采用LS-DYNA软件研究了6种折纹管在轴向冲击下的屈曲模态与能量吸收性能, 并与方管进行对比分析。结果表明, 折纹管在冲击载荷作用下屈曲变形过程可分为3个阶段, 初始峰值阶段、稳定渐进屈曲阶段和密实化阶段。折角是影响初始峰值载荷和平均载荷的重要因素之一, 折纹结构的引入有效的降低了初始峰值载荷, 减小了冲击力的波动幅度; 折纹管的比吸能低于方管, 但是在特定折角下, 折纹管的压缩力效率和比总体效率高于方管。     

负泊松比蜂窝材料的动力学响应及能量吸收特性

针对传统正方形蜂窝,通过用更小的双向内凹结构胞元替代原蜂窝材料的结构节点,得到了一种具有负泊松比特性的节点层级蜂窝材料模型。利用显式动力有限元方法,研究了冲击荷载作用下该负泊松比蜂窝结构的动力学响应及能量吸收特性。研究结果表明,除了冲击速度和相对密度,负泊松比蜂窝材料的动力学性能亦取决于胞元微结构。与正方形蜂窝相比,该负泊松比层级蜂窝材料的动态承载能力和能量吸收能力明显增强。在中低速冲击下,试件表现为拉胀材料明显的"颈缩"现象,并展示出负泊松比材料独特的平台应力增强效应。基于能量吸收效率方法和一维冲击波理论,给出了负泊松比蜂窝材料的密实应变和动态平台应力的经验公式,以预测该蜂窝材料的动态承载能力。本文的研究将为负泊松比多胞材料冲击动力学性能的多目标优化设计提供新的设计思路。     

Inertia effects on the progressive crushing of aluminium honeycombs under impact loading

This paper presents the test results under quasi-static and impact loadings for a series of aluminum honeycombs (3003 and 5052 alloys) of different cell sizes, showing significantly different enhancements of the crushing pressure between 3003 honeycombs and the 5052 ones. A comprehensive numerical investigation with rate insensitive constitutive laws is also performed to model the experimental results for different cell size/wall thickness/base material, which suggests that honeycomb crushing pressure enhancement under impact loading is mostly due to a structural effect.Such simulated tests provide detailed local information such as stress and strain fields (in the cell wall) during the whole crushing process of honeycombs. A larger strain (in the cell wall) under impact loading than for the quasi-static case before each successive folding of honeycombs is observed, because of the lateral inertia effect. Thus, differences of the ratios of the stress increase due to strain hardening over the yield stress between 3003 and 5052 alloys lead to the different enhancements of crushing pressure. This result illustrates that the lateral inertia effect in the successive folding of honeycombs is the main factor responsible for the enhancement of the crushing pressure under impact loading.     

Elastic buckling of honeycomb structure under out-of-plane pressure

A theoretical model and an analytical method, which are suitable for initial elastic buckling analysis of two-dimensional honeycomb structures including hexagonal honeycombs with walls of equal or unequal thickness, rectangular and triangular honeycombs etc., are developed in this paper. The results given in present paper agree well with the experimental data of hexagonal honeycombs with walls of unequal thickness.The project was supported by National Natural Science Foundation of China.     

非凸截面管与多胞方管轴向冲击能量吸收性能对比研究

研究了非凸薄壁管在轴向冲击下的能量吸收性能,并与方管以及多胞方管进行了比较分析。首先,采用显式非线性有限元分析软件ANSYS/LS-DYNA对比分析了这三类薄壁管在壁厚相同情况下的能量吸收性能。然后,在一定的材料用量限制（相同的质量）、一定的能量吸收量需求以及一定的极限峰值力要求等三种情况,比较了这三类截面薄壁管的冲击能量吸收性能。研究表明,非凸截面管在所研究的四种条件下无论在能量吸收效率还是在载荷一致性方面都远远优于方管。此外,非凸截面薄壁管在能量吸收效率方面也显著优于多胞方管,在载荷一致性方面与多胞方管相比各有优劣。     

In-plane crushing behavior and energy absorption design of composite honeycombs

Theoretical analysis and numerical simulation methods were used to study the in-plane crushing behavior of single-cell structures and regular and composite honeycombs. Square, hexagonal, and circular honeycombs were selected as honeycomb layers to establish composite honeycomb models in the form of composite structures and realize the complementary advantages of honeycombs with type I and type II structures. The effects of honeycomb layer arrangement, plastic collapse strength, relative density, and crushing velocity on the deformation mode, plateau stress, load uniformity, and energy absorption performance of the composite honeycombs were mainly considered. A semi-empirical formula for plateau stress and energy absorption rate per unit mass for the composite honeycombs was developed. The results showed that the arrangement mode of honeycomb layers is an important factor that affects their mechanical properties. Appropriately selecting the arrangement of honeycomb layers and the proportion of honeycomb layers with different structures in a composite honeycomb can effectively improve its load uniformity and control the magnitude of plateau stress and energy absorption capacity.     

井筒内受压杆管后屈曲能量法分析与实验研究

目前不少理论力学教材都涉及刚体平面运动动力学方程的教学内容,但有些教材在叙述上有许多值得商榷之处.对这一重要的基本概念,本文提出作者的思考,供理论力学教学的教师与学过此内容的学生讨论.     

基于相似材料的岩爆模型实验及其能量释放机制

岩体的卸载破坏和加载破坏有本质区别,岩爆是高地应力区地下工程开挖卸载产生的地质灾害现象.针对处于高静水压力状态下的岩体,采用松香模型实验研究径向瞬时卸载引起动力破碎型“岩爆”;通过分析动力破碎过程中的速度峰值、卸载波作用时间特征,推导了.应变能及剥落(破碎)块体动能及速度计算公式.结果表明:文中给出的速度峰值和动能计算方法是可行的,剥落(破碎)块体动能仅占可恢复应变能很小部分,大部分能量最终以不同形式耗散掉;距自由面不同距离处的卸载波作用时间大致相等,远大于卸载波的扰动时间;破碎波阵面在介质中推进速度大致为匀速,也远小于卸载波扰动速度.     

爆炸荷载下矩形板的塑性动力响应

本文采用Jones-Sawczuk控制方程,导出了脉冲荷载下矩形板最大残余挠度的简单理论计算公式,并应用该公式和动态屈服条件,计算了固支方板在爆炸荷载下的最大残余挠度值,与试验结果比较,取得了令人满意的结果。     

泡沫铝填充金属薄壁圆管侧向压缩的实验和理论

利用实验研究与理论分析相结合方法研究了泡沫铝填充金属薄壁圆管在准静态侧向压缩下的力学响应。基于能量法,建立了泡沫铝填充圆管和金属薄壁圆管在侧向均匀压缩时的瞬时侧向力、平均侧向力和总吸能的理论公式。对泡沫铝填充管与金属薄壁圆管进行了准静态侧向压缩实验,并且将实验结果与理论公式进行了对比,结果表明理论预测值与实验结果吻合较好。基于建立的理论分析模型,研究了管的几何尺寸以及泡沫铝材料的密度对结构的瞬时侧向力、平均侧向力、总吸能和比吸能的影响。结果表明,在准静态侧向压缩下,泡沫铝填充管的总吸能大于对应的金属薄壁圆管;泡沫铝填充管的侧向压缩力和总吸能随管长度、壁厚和直径的增加而增大;当填充材料泡沫铝密度增大时,填充管的总吸能与侧向压缩力均增加。     

胞元微拓扑结构对蜂窝材料面内冲击性能的影响

研究了面内冲击载荷作用下胞元微拓扑结构对蜂窝材料动态冲击性能的影响。首先,在胞元边长、厚度一致的条件下,讨论了不同形状胞元、以及胞元形状相同但排列方式不同的蜂窝材料的动态冲击性能,并给出了试件及其微结构的动态演化过程。在此基础上,讨论了胞元微观排列方式对蜂窝材料的能量吸收能力的影响。计算结果表明,除了胞元基本结构参数（边长、壁厚等）,胞元形状及排布方式也是影响蜂窝材料动态性能的重要因素。由于三角形单胞的稳定性,三角形填充蜂窝材料与四边形填充蜂窝材料相比,表现出更强的能量吸收能力。而交错排布则对应着更加均匀的变形和稳定的平台区。同时,局部拓扑结构的变化,交错排布的试件在冲击压缩的过程中表现出独特的颈缩现象。此结论将为蜂窝材料微结构的动力学优化设计提供指导和依据。     

含随机填充孔圆形蜂窝结构的面内冲击性能

研究多孔材料细观结构与宏观力学性能之间的关系, 建立具有固定相对密度的含随机固体填充孔的圆形蜂窝结构模型。在此模型的基础上具体讨论了不同孔洞填充比和冲击速度对圆形蜂窝结构变形模式、动态冲击平台应力以及能量吸收性能的影响。研究结果表明:填充孔在蜂窝变形过程中有局部牵制作用, 蜂窝材料变形模式仍为准静态模式、过渡模式、动态模式; 当变形模式为过渡模式或动态模式时, 结构的平台应力与速度的平方成线性关系, 存在明显的速度效应; 高速冲击下, 含固体填充孔的蜂窝结构单位质量吸收的能量高于规则蜂窝结构。研究结果可为蜂窝材料的研究和设计提供参考。     

A theoretical and numerical study of thin film delamination using the pull-off test

An accurate closed-form analytical solution for the strain energy release rate for a thin rectangular film loaded by a central line force using the pull-off test is derived in the presence of a tensile residual stress. The theoretical constitutive relation and the strain energy release rate agree very well with two-dimensional nonlinear finite element analysis for the entire deformation regime ranging from bending plate to stretching membrane. Fracture modes for this pull-off test are also investigated based upon the finite element analysis, offering additional insights to the interfacial delamination.     

Instantaneous Squeeze-Film Force Between a Heat Exchanger Tube and a Support Plate for Arbitrary Tube Motion

The instantaneous squeeze-film force between a heat exchanger tube and a support plate is studied. Based on a two-dimensional rectangular plate model, a short-sleeve squeeze-film model for arbitrary tube motion is developed. The instantaneous squeeze-film force is expressed in normal and tangential directions. The normal squeeze-film force consists of four nonlinear terms, the viscous, unsteady inertia, convective inertia and centripetal inertia terms. Three nonlinear terms, the viscous, unsteady inertia and Coriolis inertia terms, make up the tangential squeeze-film force. An experimental apparatus was developed in order to evaluate the theoretical models against measurements of a finite length squeeze film. A modified model based on the experimental data is obtained where the viscous terms for both directions are multiplied by the instantaneous Reynolds number. All the inertia terms are multiplied by constant coefficients. The modified model is in good agreement with most experimental cases for unsymmetrical linear motion, approximate circular motion and elliptical motion. The form of the modified model is suitable for predicting instantaneous squeeze-film forces in the simulation of heat exchanger tube vibration. Further work using different sized components and fluid properties is required in order to finalize coefficient values.     

振动挤出过程中毛细管内聚合物熔体的剪切速率分析

借助自行研制的恒速型毛细管动态流变实验研究装置,对平行叠加振动条件下聚合物熔体经毛细管的挤出过程进行了分析;不依赖现有的任何本构关系,在考虑惯性项影响的前提下,建立了振动力场下毛细管壁处聚合物熔体剪切速率的计算公式;实验测量一定振动频率和振幅下毛细管瞬时入口压力、瞬时体积流量以及体积流量与入口压力波形的相位差,通过上述公式即可求得聚合物熔体在毛细管壁处的剪切速率。     

Long-wave in-plane buckling of elastoplastic square honeycombs

In this study, two formulae derived for very long-wave in-plane buckling of elastic square honeycombs are extended and examined in the elastoplastic case. To this end, microscopic buckling and post-buckling behavior of elastoplastic square honeycombs subject to in-plane compression are numerically analyzed using a homogenization theory of the updated Lagrangian type. It is thus demonstrated that very long-wave buckling occurs just after the onset of macroscopic instability if periodic length is sufficiently long, and that plasticity can cause the localization of microscopic buckling accompanied by a significant decrease in macroscopic compressive stress. Then, the very long-wave buckling stresses computed are predicted by incorporating the effect of plasticity in the two formulae of elastic square honeycombs. It is shown that the resulting formulae are successful in predicting the very long-wave buckling stresses in the plastic range as well as in the elastic range.     

湍流能量耗散率标度律实验研究

应用粒子图像测速(PIV)系统对平板湍流边界层内流向和法向的瞬时速度进行了测量。湍流的能量耗散率由轴对称假设得到,同时在研究湍流动能耗散率标度律的过程中采用传统的统计学方法。实验结果显示,对于不同尺度上和不同法向位置湍流耗散率标度律来说,湍流耗散主要发生在小尺度上,也就是说湍动能耗散率标度律在小尺度上具有普适性。另外,根据层次结构理论假设,通过PIV实验数据对最高激发态的标度指数进行了研究,结果发现,最高激发态存在绝对标度指数,并且绝对标度律是由信号中最强耗散涨落的局部结构产生的。     

Physical mechanism of the destabilizing effect of damping in continuous non-conservative dissipative systems

The paper attempts to give a physical explanation of the mechanism behind the so-called destabilizing effect of small internal damping in the dynamic stability of Beck's column. Both internal (material) and external (viscous fluid) damping are considered. An energy equation is derived for the balance between the work done by the non-conservative ‘follower force’ and the energy dissipated by the internal and external damping forces. Evaluated at the critical load, where a flutter instability is initiated, this equation explicitly shows the influence of damping upon flutter frequency, phase angle, and vibration amplitude. The gradient of the phase angle, evaluated at the free end of the column, is found to be the ‘valve’, which controls how much work the follower force can do on the column during each period of oscillation. And a large change in this gradient with increasing—but still small—internal damping is found to be responsible for the destabilizing effect.     

胞孔构型对金属蜂窝动态力学性能的影响机理

采用ANSYS/LS-DYNA有限元研究了具有不同胞孔构型和排列方式的金属蜂窝材料在面内冲击荷载下的力学性能。在蜂窝的相对密度和冲击速度保持恒定的情况下,比较了它们的变形模式、动态承载力和能量吸收性能。结果表明,不同的胞孔构型导致在蜂窝压垮过程中胞壁的受力状态不同,从而影响蜂窝的宏观力学性能。根据胞壁的应力状态,可将蜂窝分为膜力主导蜂窝和弯曲主导蜂窝2大类。研究结果显示,蜂窝吸收的能量绝大部分转化为变形所需的内能,并且膜力主导蜂窝的内能占总能量的百分比更大。胞壁的屈曲导致膜力主导蜂窝的应力应变曲线呈现较大的波动。膜力主导蜂窝在变形过程中其胞壁会耗散更多的内能,从而比弯曲主导蜂窝具有更高的动态承载力和能量吸收能力。