Analytical models for the penetration of semi-infinite targets by rigid,deformable and erosive long rods

A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.

The effects of compressibility and strength on penetration of long rod and jet

The approximate compressible model is adopted to study the effects of strength and compressibility on the penetration by WHA long rod and copper jet into semi-infinite target in detail. For WHA rod penetrating PMMA at 2 km/s <V <5 km/s, the compressibility has a significant effect on the penetration efficiency. We clarify how compressibility affects the penetration efficiency by changing the stagnation pressures of the rod and target. For WHA rod penetrating 4340 Steel and 6061-T6 Al at 2 km/s < V < 10 km/s, the effect of strength is strong and the effect of compressibility is negligible at lower impact velocity, whilst the effect of strength is weak and the effect of compressibility becomes stronger at higher impact velocity. For the copper jet penetrating 4030 Steel, 6061-T6 Al and PMMA. the virtual origin model is adopted, and the compressibility and strength are implicitly considered by the linear relation between the penetration velocity and impact velocity. The effects of compressibility and target resistance on penetration efficiency are studied. The results show that the target resistance has a significant effect on the penetration efficiency. Howver PMMA is much more compressible than copper and the huge difference of compressibility has a significant effect on the penetration by hypervelocity copper jet into PMMA.

Microstructural observations on the terminal penetration of long rod projectile

Present study focuses on the terminal penetration of tungsten heavy alloy(WHA) long rod penetrator impacted against armour steel at an impact velocity of 1600 m/s. The residual penetrator and armour steel target recovered after the ballistic test have been characterized using optical microscope, scanning electron microscope(SEM) and electron probe micro analyzer(EPMA). Metallurgical changes in target steel and WHA remnant have been analysed. Large shear stresses and shear localization have resulted in local failure and formation of erosion products. Severe plastic deformation acts as precursor for formation of adiabatic shear band(ASB) induced cracks in target steel. Recovered WHA penetrator remnant also exhibits severe plastic deformation forming localized shear bands, ASB induced cracks and shock induced cracks.

The break-up tendency of long rod projectiles

A model for the tendency of fragmentation of a long rod projectile subjected to armour components in add-on armours such as reactive armour and active protection systems is presented. The model is based on studies of the interaction between a cylindrical streamlined projectile and moving thin plates(backwards moving like the front plate in a reactive armour panel and forwards moving like the rear plate in a reactive armour panel).The assumption behind the model is that the sliding force, with velocity vslidebetween the projectile and the plate, gives rise to a transverse velocity vtransof the projectile segment it passes, which will deflect the projectile segment. This deflection is assumed to be a major reason for the fractures that can emerge along the projectile. The velocity, geometry and material of the projectile and the plate are of importance for the fragmentation of the projectile and the dimensionless parameterδ? = v trans vslideexpresses how these parameters influence the break-up tendency. Experiments and simulations have verified that the identifiedδ?-parameter predicts an increased amount of fragmentation of the projectile with increasing value of this parameter.

Laterally pre-compressed SiC tiles against long rod impact

A combined experimental and computational study was carried out to investigate ballistic performance of laterally preload compressed SiC tile against long rod impact. A 100 x 100 by 20 mm thick SiC tile was pushed into a 5 mm thick steel frame at high temperature of 430 ℃ so that after cool down to room temperature, the lateral preload compressive stress was developed in the SiC tiles. Depth of penetration tests of the SiC tiles with and without pre-stress were performed, where tungsten alloy long rods at a nominal velocity of 1240 m/s were launched to hit the SiC tiles backed by the steel blocks. Compared with the SiC tiles without any pre-stress, the pre-compressed SiC tiles were found to reduce significantly the residual penetration in the backing block. Simulations were carried out using the LS-dyna hydrocode,taking account of preload stress. The simulations showed that the lateral preload compression strengthened the intact SiC tiles and dwell occurred in the early penetration stage, eroding the striking long rod efficiently.

A three-stage model for the perforation of finite metallic plates by long rods at high velocities

A three-stage theoretical model is presented herein to predict the perforation of a thick metallic plate struck normally by a long rod at high velocities. The model is suggested on the basis of the assumption that the perforation of a thick metallic plate by a long rod can be divided into three stages:(1) initial penetration;(2) plug formation and (3) plug slipping and separation. Various analytical equations are derived which can be employed to predict the ballistic limit, residual velocity and residual length of the long rod. It is demonstrated that the present model predictions are in good agreement with available experimental results for the perforation of finite steel targets struck normally by steel as well as tungsten alloy long rods at high velocities. It is also demonstrated that the dynamic maximum shear stress of a plate material has strong effect on plug formation and plug thickness which, in turn, exerts considerable influence on the residual velocities and lengths of a long rod at impact velocities just above the ballistic limit.

Predicting the penetration of long rods into semi-infinite metallic targets

Analytical equations are presented herein to predict the penetration of semi-infinite metallic targets struck normally by long rods at high velocities for Yp<S where Yp is the rod strength and S is the static target resistance.The equations are derived based on energy balance method.It is assumed that the kinetic energy loss of a long rod is related to the energy dissipated by the plastic deformations in the target,the energy consumed by the long-rod penetrator itself and the energy carried by the eroded rod debris.Secondary penetration is also examined in the present paper due to the fact that the eroded rod debris forms a tube which can penetrate the target further if the density of the rod is greater than that of the target and the impact velocity is high enough.The present analytical equation is found to be in good agreement with the experimental data for a wide range of impact velocities.

Alekseevskii-Tate revisited:An extension to the modified hydrodynamic theory of long rod penetration

The modified hydrodynamic theory of long rod penetration into semi-infinite targets was established independently by Alek-seevskii and Tate over forty years ago and since then many investigators contributed much to the development of the high speed penetration mechanics.However,in all the models proposed so far,the target resistance Rt is not well defined and usually determined by adjusting it until the predicted depth of penetration comes to an agreement with experimental data.In this paper,assumptions are first made about particle velocity and pressure profiles together with response regions in the target and then an extension is made to the modified hydrodynamic theory of long rod penetration into semi-infinite targets,in which Rt has explicit form and is dependent on penetration velocity as well as thermo-mechanical properties of target material.The present model is compared with long rod penetration tests for different material combinations.It transpires that the present model predictions are in good agreement with the experimental data and numerical simulations in terms of penetration depth although many assumptions and simplifications are introduced into the paper.

Analytical model for cratering of semi-infinite metallic targets by long rod penetrators

Analytical model is presented herein to predict the diameter of crater in semi-infinite metallic targets struck by a long rod penetrator. Based on the observation that two mechanisms such as mushrooming and cavitation are involved in cavity expansion by a long rod penetrator, the model is constructed by using the laws of conservation of mass, momentum, energy, together with the u-v relationship of the newly suggested 1D theory of long rod penetration (see Lan and Wen, Sci China Tech Sci, 2010, 53(5): 1364–1373). It is demonstrated that the model predictions are in good agreement with available experimental data and numerical simulations obtained for the combinations of penetrator and target made of different materials.

Long-rod penetration:the transition zone between rigid and hydrodynamic penetration modes

Long-rod penetration in a wide range ol" velocity means that the initial impact velocity varies in a range from tens of meters per second to several kilometers per second.The long rods maintain rigid state when the impact velocity is low,the nose of rod deforms and even is blunted when the velocity gets higher,and the nose erodes and fails to lead to the consumption of long projectile when the velocity is very high clue to instantaneous high pressure.That is,from low velocity to high velocity,the projectile undergoes rigid rods,deforming non-erosive rods,and erosive rods.Because of the complicated changes of the projectile,no well-established theoretical model and numerical simulation have been used to study the transition zone.Based on the analysis of penetration behavior in the transition zone,a phenomenological model to describe target resistance and a formula to calculate penetration depth in transition zone are proposed,and a method to obtain the boundary velocity of transition zone is determined.A combined theoretical analysis model for three response regions is built by analyzing the characteristics in these regions.The penetration depth predicted by this combined model is in good agreement with experimental result.

Approximate solutions of the Alekseevskii–Tate model of long-rod penetration

The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.

Analysis Model on Penetration Depth of Concrete by Eroding Long-Rod Projectiles

Mass loss should be considered while calculating the penetration depth of concrete by eroding long-rod projectiles of high velocity.The penetration process is divided into two phases：eroding phase and rigid phase.During eroding phase,a model to predict the penetration depth is established on the assumption that there is a chipping region in the bottom of crater.During rigid phase,Forrestal formula is adopted to calculate the penetration depth.Using this model,the depth of concrete penetration by a tungsten alloy long-rod projectile is calculated.When the critical eroding velocity is between 950 m/s and 1 000 m/s,the result is in good agreement with the experimental data.

Perturbation of symmetries for super-long elastic slender rods

This paper analyses perturbations of Noether symmetry, Lie symmetry, and form invariance for super-long elastic slender rod systems. Criterion and structure equations of the symmetries after disturbance are proposed. Considering perturbation of all infinitesimal generators, three types of adiabatic invariants induced by perturbation of symmetries for the system are obtained.

Structure properties and Noether symmetries for super-long elastic slender rod

DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff＇s analogue technique and presents the Noether symmetries of the model by using the method of infinitesimal transformation. Baaed on Kirchhoff＇s analogue it analyses the generalized Hamilton canonical equations. The infinitesimal transfornaationa with rcspect to the radial coordinnte, the gonarnlizod coordinates, and the Cluasi-momenta of 5he model are introduced. The Noether gymmetries and conserved qugntities of the model are obtained.

长寿期小型棒控压水堆控制棒方案研究

小型棒控压水堆舍弃了可溶硼,并高度依赖控制棒与可燃毒物棒控制堆芯的反应性。为研究控制棒对堆芯关键性能的影响,本文以核动力破冰船用KLT-40模型为对象,以轴向功率偏移、堆芯寿期、燃料利用率与径向功率峰因子为指标,开展长寿期小型棒控压水堆控制棒布置与动作策略设计分析。首先,基于OpenMC程序开发带棒燃耗程序;其次,比较堆芯带控制棒与无控制棒运行时的堆芯寿期等指标;最后,分析不同动作策略对轴向功率偏移等指标的影响。结果表明:控制棒将堆芯寿期从590 EFPDs(等效满功率天,Effective full power days)延长至650~698 EFPDs;低价值棒组优先动作策略使轴向功率偏移程度由−0.69与+0.80分别下降至−0.29与+0.52。因此,要准确计算长寿期压水堆寿期必须采用带控制棒燃耗计算策略,并且通过合理的动作策略能够有效减小控制棒带来的轴向功率偏移。

Wf/Zr基复合材料长杆弹在不同速度下的头形转变规律

目的预测金属玻璃复合材料长杆弹在不同撞击速度下的侵彻/穿甲性能,为优化弹体撞击速度和弹体头部形状等提供理论指导。方法结合相关侵彻试验,基于细观有限元建模及修正的热力耦合本构模型,开展了钨纤维增强金属玻璃复合材料长杆弹在不同速度下侵彻钢靶的有限元模拟,分析了不同速度下复合材料弹体破坏模式的差异,讨论了撞击速度对复合材料弹体头部形状变化影响规律及其内在机理。结果低速撞击条件下,复合材料长杆弹体头部的钨纤维发生剧烈的屈曲弯折变形,弯折钨纤维堆积在头部,形成较厚的“边缘层”,且存在1~2条剪切带,弹体头部表现为“细长尖卵”形状;随着撞击速度逐渐增加,弹体头部钨纤维的弯折变形程度逐渐有所降低,“边缘层”厚度也有所减小,且外侧钨纤维开始发生屈曲回流,头形逐渐转变为“短粗尖卵”形状,且尖锐程度随撞击速度增加而降低;在高速撞击条件下,弹体头部“边缘层”显著变薄,同时最外侧钨纤维发生屈曲回流,弹体头部表现为“扁平”形状。结论撞击速度对复合材料弹体的头部变形及破坏特征具有重要影响。随着速度增加,复合材料弹体头部形状逐渐从“细长尖卵”转变到“短粗尖卵”,最后变为“扁平”。

基于CNN-LSTM混合神经网络的卷烟滤棒质量预测

为了在卷烟生产数据中挖掘出滤棒生产过程的有效信息,解决各批次产品质量检测困难的问题,结合卷积神经网络的特征提取能力与长短期记忆网络处理时序数据的有效性,提出了基于CNN-LSTM混合神经网络的卷烟滤棒质量预测模型。该模型通过卷积层提取输入数据的局部特征,然后在LSTM层中捕捉特征之间的时序关系,分层结构使其具有同时处理不同时间维度信息的能力,从而提升了预测精度。将滤棒的质量定义为圆周值与吸阻值两个物理量,利用卷烟厂6万余条实时生产数据进行模型训练和预测,结果表明:以平均绝对百分误差(MAPE)作为评价标准,圆周指标预测误差为0.078%,吸阻指标预测误差为1.42%,对比各类传统机器学习方法,CNN-LSTM混合神经网络表现出了更高的精确性。该方法可为快速准确地预测卷烟滤棒质量提供技术支持,提升烟草工业的自动化水平。

长螺杆加强型胶合木梁柱节点力学性能

胶合木梁柱螺栓钢填板节点由于抗弯刚度较低,在结构设计中通常被视为铰接。提出了一种长螺杆加强型胶合木梁柱节点,为无支撑或剪力墙的中高层木结构体系中提供较好的刚性连接。设计并加工了3组不同长螺杆直径的节点试件,通过单调加载和往复加载试验探究了节点的抗弯刚度、抗弯承载力、破坏模式及耗能性能。通过ABAQUS有限元软件建立了节点力学模型,模拟结果与试验结果较为吻合,并基于该模型开展了参数分析。结果表明:该节点具有较高的抗弯刚度与抗弯承载力,经过合理构造后节点损伤主要集中在长螺杆,而长螺杆在破坏后易于更换,可提高节点韧性与使用寿命。参数分析结果表明,转动刚度与长螺杆直径及力臂呈正相关。基于试验与模拟的结果,提出了该类节点抗弯刚度及抗弯承载力的计算方法,为其在实际工程中的设计与应用提供参考。

重庆龙兴足球场超限结构设计

重庆龙兴足球场主体结构采用设置少量剪力墙的框架结构,屋盖钢结构采用悬挑平面桁架+上下弦稳定支撑+立面单层网格结构。为了研究结构设计的难点,采用了SPASCAD⁃PMSA、MIDAS Gen(Ver.2019)和SAP2000设计软件分别对结构进行多遇地震下的抗震性能分析。采用了SAUSAGE、SAP2000软件对结构进行设防、罕遇地震下的抗震性能分析。采用了ANSYS软件对钢屋盖整体稳定进行分析,采用了ABAQUS软件对节点受力性能进行分析。结果表明:结构具有较好的抗震能力和抗连续倒塌能力,结构设计安全、合理、经济。

经皮微创脊柱后路钉棒系统固定治疗胸腰椎骨折近远期效果观察

目的:观察胸腰椎骨折患者接受经皮微创脊柱后路钉棒系统固定治疗的近远期疗效。方法:选择2018年2月-2022年1月我院70例胸腰椎骨折患者作为研究对象,根据随机数字表法分为对照组和观察组,每组35例。对照组采用常规切开椎弓根内固定治疗,观察组采用经皮微创脊柱后路钉棒系统固定治疗,对比2组各项手术指标、术后恢复情况及并发症发生率。结果:术后观察组患者的手术时间、术中出血量、住院时间、术后引流量、术后负重时间、骨折愈合时间均优于对照组,差异均有统计学意义(P<0.05)。术前2组患者的伤椎后凸Cobb角、伤椎前缘高度比值、伤椎后缘高度比值差异无统计学意义(P>0.05),术后3个月及术后1年伤椎后凸Cobb角均降低,伤椎前缘高度比值、伤椎后缘高度均升高,观察组变化比对照组更明显,差异有统计学意义(P<0.05)。术前2组患者ODI、Harris评分、VAS评分差异无统计学意义(P>0.05)。术后7dVAS评分降低,术后3个月及术后1年ODI评分降低,Harris评分升高,观察组变化比对照组更明显,差异有统计学意义(P<0.05)。观察组术后并发症发生率为5.71%,低于对照组的25.71%,差异有统计学意义(P<0.05)。结论:胸腰椎骨折患者接受经皮微创脊柱后路钉棒系统固定治疗,近期疗效和远期疗效均能得到有效保障,对于促进患者腰椎指标及功能改善、缓解疼痛程度及减少并发症发生率均具有显著效果。