THREE-DIMENSIONAL FINITE ELEMENT SIMULATION OF TOTAL KNEE JOINT IN GAIT CYCLE

Based on CT scanning pictures from a volunteer＇s knee joint, a three-dimensional finite element model of the healthy human knee joint is constructed including complete femur, tibia, fibular, patellar and the main cartilage and ligaments. This model was validated using experimental and numerical results obtained from other authors. The pressure distribution of contact surfaces of knee joint are calculated and analyzed under the load action of ‘heel strike＇, ‘single limb stance＇ and ‘toe-off＇. The results of the gait cycle are that the contact areas of medial cartilage are larger than that of lateral cartilage; the contact force and contact areas would grow larger with the load increasing; the pressure of lateral meniscus is steady, relative to the significant variation of peak pressure in medial meniscus; and the peak value of contact pressure on all components are usually found at about 4570 of the gait cycle.     

空投鱼雷入水载荷

为了研究空投鱼雷的入水过程,首先分析入水过程中的受力情况进行数值计算;然后使用数值模拟软件Msc.Dytran建立鱼雷入水的有限元模型,计算入水过程中雷体所遭受的冲击压力及其在冲击面上的分布情况,并对不同入水速度和角度下冲击压力峰值、不同头部形状冲击压力峰值特点及鱼雷入水弹道做了分析与讨论,结果表明:鱼雷入水速度和入水角度会对鱼雷壳体所受载荷产生重要影响,研究结果可为预测鱼雷入水冲击载荷提供参考。     

含摩擦与碰撞平面多刚体系统动力学线性互补算法

基于接触力学理论和线性互补问题的算法, 给出了一种含接触、碰撞以及库伦干摩擦, 同时具有理想定常约束(铰链约束) 和非定常约束(驱动约束) 的平面多刚体系统动力学的建模与数值计算方法. 将系统中的每个物体视为刚体, 但考虑物体接触点的局部变形, 将物体间的法向接触力表示成嵌入量与嵌入速度的非线性函数,其切向摩擦力采用库伦干摩擦模型. 利用摩擦余量和接触点的切向加速度等概念, 给出了摩擦定律的互补关系式; 并利用事件驱动法, 将接触点的黏滞-滑移状态切换的判断及黏滞状态下摩擦力的计算问题转化成线性互补问题的求解. 利用第一类拉格朗日方程和鲍姆加藤约束稳定化方法建立了系统的动力学方程, 由此可降低约束的漂移, 并可求解该系统的运动、法向接触力和切向摩擦力, 还可以求解理想铰链约束力和驱动约束力. 最后以一个类似夯机的平面多刚体系统为例, 分析了其动力学特性, 并说明了相关算法的有效性.      

人工膝关节置换中的生物力学研究进展

膝关节是人全身最大最复杂的关节, 它的任何一个主要组成部分的损坏都会引起膝关节的反常运动, 久之软骨和半月板发生磨损、变性而形成骨性关节病, 从而影响人的日常生活. 通常采用的方法是进行膝关节矫形或置换, 对严重病变的膝关节, 则采用全膝置换手术.随着人工膝关节置换成为非常普遍的外科手术, 与膝关节假体相关的研究也越来越多的被人所关注. 从生物力学角度对人工膝关节假体的类型和材料、假体生物力学性能的理论和实验研究、骨重建的理论模型、骨整合的理论和实验、与理论和实验相关的有限元分析模型等几个主要方面进行了详尽的综述. 同时, 指出了人工膝关节置换和目前研究中存在的问题,并对其未来的发展方向进行了一定的预测.      

黏弹性人工边界等效荷载计算的改进方法

黏弹性人工边界在场地地震反应和结构-地基动力相互作用等问题的计算中已得到了广泛的应用.地震波在黏弹性人工边界中的输入是通过将地震波转化为作用于人工边界处的等效载荷来实现的.计算等效节点载荷的常规方法默认边界节点对应区域内的应力为均布力,但实际上该节点对应区域内的应力分布通常是不均匀的.本文在有限元方法结合黏弹性局部人工边界的显式时域波动方法的基础上,建立了无限域散射问题地震波等效载荷计算的一种改进方法.该方法采用细化网格与应力积分相结合的方法计算人工边界等效节点力,有效地降低了人工边界上等效节点力的计算误差.以不同角度入射地震波的二维算例为例,算例给出的波场位移云图和节点位移时程曲线验证了本文方法的有效性,其计算精度与网格尺寸和地震波入射角度密切相关,且网格越小、入射角度越小,计算精度越高.对于相同的网格尺寸,本文采用方法的计算精度明显高于常规方法,尤其是对于斜入射问题优势更为明显.     

考虑接触应力非线性分布的接触力元模式及其验证分析

在作者提出的非连续变形计算力学模型中,采用接触力元模型描述多体接触界面上的接触特性.由于这种模型中假定接触应力沿接触界面为线性分布,从而得到的接触界面应力分布往往出现跳跃等非光滑性特征,该文对此进行了改进,采用具有高阶光滑性的非线性函数建立了能够考虑界面上接触应力非线性分布的接触力元模式,以期合理地揭示多体系统中界面的接触特性.对某一典型算例进行了数值计算,通过与大型通用非线性有限元结构分析软件ABASQUS的计算结果对比,验证了所建议计算模型的合理性与有效性.两种方法计算得到的界面接触对上的接触力基本相同;而由于采用的应力分布模式的假定不同,接触应力有所差别,由于在该文计算模型中接触对上的接触应力是按照未知量直接求得的,因此按照所建议的非线性接触力元模式所得到的接触应力更为合理.     

EFFECTS OF 2-TUNNEL AND 3-TUNNEL FIXATION ON BIOMECHANICS OF TIBIOFEMORAL JOINT

基于正常膝关节4个屈曲角度(0°, 25°, 60°, 80°)下的磁共振(MR)图像数据, 建立正常/两隧道固定/三隧道固定内侧半月板移植术后的胫股关节模型. 对各屈曲角度下的4种模型分别施加单一轴向压载和压扭组合载荷进行有限元仿真, 得到各模型在2种载荷作用下的应力及位移分布. 提取关节软骨、半月板表面的等效应力以及半月板的最大位移进行对比分析, 得到内侧半月板移植术后两/三隧道固定对胫股关节中软骨及半月板的影响. 总体上讲内侧半月板移植中的三隧道固定要优于双隧道固定, 更利于胫股关节恢复正常的应力特性.     

MEASUREMENT OF ADHESION FORCES IN AIR WITH THE VIBRATION METHOD

The vibration method represents a practical method for the measurement of adhesion forces and adhesion force distributions. This method causes sinusoidally altemating stresses and yields detachment and contact forces between particles and substrate of the same order of magnitude. Alternating contact forces of the vibration method can cause an adhesion force intensification through flattening of asperities. The measuring principle of the vibration method and the analysis of experimental results are described in the article. Normal adhesion forces (pull-off forces) are measured using the vibration method and the colloidal probe technique. The results of both methods show good agreement for small particle sizes. The influence of the detachment force direction is shown by comparing tangential and normal adhesion forces measured using particle reentrainment in a turbulent air flow and the vibration method, respectively. The surface roughness of the substrate and the relative humidity are shown to significantly influence the measured adhesion forces. For the calculation of the adhesion forces, an approach by Rabinovich was combined with approximations of plastic micro asperity flattening. The Rabinovich approach accounts for roughness effects on the van der Waals force by incorporating the rms roughness of the interacting surfaces. rms-values of the particles and substrates were measured with atomic force microscopy at different scanning areas.     

Development of a planar multibody model of the human knee joint

The aim of this work is to develop a dynamic model for the biological human knee joint. The model is formulated in the framework of multibody systems methodologies, as a system of two bodies, the femur and the tibia. For the purpose of describing the formulation, the relative motion of the tibia with respect to the femur is considered. Due to their higher stiffness compared to that of the articular cartilages, the femur and tibia are considered as rigid bodies. The femur and tibia cartilages are considered to be deformable structures with specific material characteristics. The rotation and gliding motions of the tibia relative to the femur cannot be modeled with any conventional kinematic joint, but rather in terms of the action of the knee ligaments and potential contact between the bones. Based on medical imaging techniques, the femur and tibia profiles in the sagittal plane are extracted and used to define the interface geometric conditions for contact. When a contact is detected, a continuous nonlinear contact force law is applied which calculates the contact forces developed at the interface as a function of the relative indentation between the two bodies. The four basic cruciate and collateral ligaments present in the knee are also taken into account in the proposed knee joint model, which are modeled as nonlinear elastic springs. The forces produced in the ligaments, together with the contact forces, are introduced into the system’s equations of motion as external forces. In addition, an external force is applied on the center of mass of the tibia, in order to actuate the system mimicking a normal gait motion. Finally, numerical results obtained from computational simulations are used to address the assumptions and procedures adopted in this study.     

多体系统动力学中关节效应模型的研究进展

在一般的多体系统动力学研究中认为运动关节是理想运动副. 然而,实际中的运动关节不仅含有间隙与摩擦,还有间隙引起的关节元素之间的接触碰撞、局部变形和磨损. 多体系统动力学中的关节效应不仅引起了系统的振动和噪声,减小了系统的可靠性和寿命,而且损失了系统的精度和稳定性. 为此,对近十几年多体系统动力学中关节效应的研究进行了详细分析,总结了关节效应中间隙运动学模型、接触力模型与磨损模型在多体系统动力学中的建模过程. 其中,着重分析了多体系统动力学中关节磨损效应的研究进展,并对常用的Reye'shypothesis 和Archard 磨损模型进行了比较,详细地分析了Archard 磨损模型的演变形式以及主要磨损参数(接触应力,接触面积和滑移距离),特别分析了关键磨损参数接触应力的建模方法,解释了基于Winkler 弹性基础理论在求解接触应力时遇到的困难. 另外,介绍了4 种间隙运动副(转动副、移动副、圆柱副和球面副) 的运动学模型. 分析了考虑关节磨损多体系统动力学模型的一般建模方法,并以平面五杆机构为例说明了其建模过程.最后,简要地展望了多体系统动力学中关节效应模型的发展趋势以及应用前景.      

含摩擦滑移铰平面多刚体系统动力学的数值算法

基于LuGre摩擦模型和线性互补问题(LCP)的数值算法,给出了具有双边约束含摩擦滑移铰平面多体系统动力学的数值算法.首先,根据滑移铰的特点,当间隙充分小时,将其视为双边约束,给出了滑移铰中滑道作用于滑块上的法向接触力的互补关系;LuGre摩擦模型能有效地描述机械系统中的黏滞与滑移运动,将该模型用于描述滑块与滑道间的摩擦力.其次,结合Baumgarte约束稳定化方法,应用第一类Lagrange方程,建立了该多体系统的动力学方程,给出了Lagrange乘子与滑移铰中作用于滑块上的法向接触力的关系式.然后,将滑块与滑道间多种接触状态的判断以及作用于滑块上的法向接触力的计算转换为线性互补问题的求解,并用常微分方程的数值算法求解该多体系统的动力学方程.最后,通过数值仿真算例揭示了滑移铰中滑块的黏滞与滑移现象,以及滑块在滑道内的多种接触状态;另外,在文中分别采用Coulomb干摩擦模型和LuGre摩擦模型,对算例中的某些工况进行了数值仿真,并且分别用本文方法得到的数值仿真结果与已有方法得到的数值仿真结果对比,表明了本文给出的方法的有效性.      

前交叉韧带损伤的继发性生物力学影响

前交叉韧带(anterior cruciate ligament, ACL)损伤往往会导致半月板及周边韧带的继发性损伤. 由于离体实验和临床研究的局限性,损伤的机理仍未得到清晰的认识. 基于核磁共振断层扫面图像重建了一个比较完整和精确的膝关节三维有限元模型. 采用文献报道的解剖测量数据对关节的解剖尺寸进行了检验,证明模型在几何上比较准确. 并且对文献报道的膝关节实验作了模拟,得出的计算结果与实验比较吻合,证明模型能够在一定程度上再现膝关节真实的运动情况. 然后利用该模型对ACL损伤前后的膝关节进行模拟,分别在屈膝0$^\circ$和30$^\circ$的姿态下对胫骨施加前后方向和竖直方向的载荷. 结果表明, ACL的损伤改变了关节组织上的应力分布:内侧半月板后段的应力显著增加;外侧半月板、后交叉韧带以及侧副韧带上的应力改变程度则取决于载荷的类型和屈膝的角度. 该研究有助于认识ACL损伤之后周边组织的继发性损伤现象,并对容易诱发损伤的高危动作进行分析和预防,对研究ACL的损伤和治疗具有重要的意义.      

人工膝关节模拟试验机及其生物摩擦学性能评价研究进展

人工膝关节生物摩擦学模拟试验是在设计和制造阶段评价人工膝关节假体的主要方法.本文介绍了球面接触型、假体力和运动直接控制型及膝关节肌肉力重建型3类人工膝关节模拟试验机及其对应生物摩擦学研究现状,讨论了3类人工膝关节生物摩擦学试验的要求和特点,详细说明了现有人工膝关节生物摩擦学试验和测试标准,指出今后还需增加动物活体试验方式,扩大模拟人体运动测量范围,并应加强多因素同时作用下人工膝关节磨损机理研究,制定统一的人工膝关节生物摩擦学试验标准.     

A SIMULATION OF THE TURBULENCE RESPONSE OF HEAT EXCHANGER TUBES IN LATTICE-BAR SUPPORTS

Tube failures due to excessive flow-induced vibrations are a major concern with regards to the operation of heat exchangers in nuclear power and chemical process plants. Among the possible excitation mechanisms, turbulence-induced forces have a persistent effect and thus are an important factor in determining the long-term reliability of heat exchangers. Impact forces which occur when tube/support collisions take place play a vital role in determining tube wear. To address this issue, a tube/support interaction model was implemented in an in-house finite element program and validated against three published examples. Pseudo-forces in conjunction with modal superposition were utilized in solving the nonlinear equations of motion of loose tubes in lattice-bar supports. Time-domain simulations of the nonlinear response of the tube are presented to determine the effect of various tube and support parameters on the vibratory characteristics of the systems. Special attention was paid to the effect of increased clearance on the response of tubes in lattice-bar supports. The tube response, impact force and contact ratio were analysed and represented in dimensionless form. The dimensionless parameters developed proved effective in collapsing the data pertaining to different flow velocities over single curves. These are useful in identifying the roles of several key variables in altering tube dynamics. Moreover, these parameters may also be used to scale the results to account for differences in geometrical and material properties.     

Analysis of kinematic data and determination of ground reaction force of foot in slow squat

In the present paper, the ground reaction force (GRF) acting on foot in slow squat was determined through a force measuring system, and at the same time, the kinematic data of human squat were obtained by analyzing the photographed image sequences. According to the height and body weight, six healthy volunteers were selected, three men in one group and the other three women in another group, and the fundamental parameters of subjects were recorded, including body weight, height and age, etc. Based on the anatomy characteristics, some markers were placed on the right side of joints. While the subject squatted at slow speed on the force platform, the ground reaction forces on the forefoot and heel for each foot were obtained through calibrated force platform. The analysis results show that the reaction force on heel is greater than that on forefoot, and double feet have nearly constant force. Moreover, from processing and analyzing the synchronously photographed image sequences in squat, the kinematic data of human squat were acquired, including mainly the curves of angle, angular velocity and angular acceleration varied with time for knee, hip and ankle joints in a sagittal plane. The obtained results can offer instructive reference for photographing and analyzing the movements of human bodies, diagnosing some diseases, and establishing in the future appropriate mathematical models for the human motion.     

DYNAMIC MODELING AND ANALYSIS OF THE LOWER LIMB PROSTHESIS WITH FOUR-BAR LINKAGE PROSTHETIC KNEE$^{\bf 1)}$

相比于单轴式膝关节,四连杆膝关节具有更好的仿生特性和运动安全性,因而在下肢假肢研究中得到广泛关注. 本研究以一款四连杆膝关节被动假肢为研究对象,主要关注足-地交互作用力以及膝关节单边接触力等强非线性因素对下肢假肢步态的影响. 为此,采用 Kelvin-Voigt 模型和库伦模型描述足-地接触力和摩擦力,并采用 Kelvin-Voigt 模型描述膝关节单边接触力,从而基于第一类拉格朗日方程建立假肢动力学模型. 本研究以步态实验测得的髋关节运动数据为模型的驱动信号,针对假肢的步态特征进行了数值分析. 计算结果显示,当膝关节液压阻尼器的刚度较小时,强非线性作用力会使假肢产生显著的亚谐波响应,进而导致步态周期失谐. 进一步研究发现,提胯行为能够避免步态周期失谐,这也为残疾人行走时的提胯等代偿行为提供了一种新的力学解释. 为了评价假肢步态与健康人实测步态的一致性,本研究进一步定义了步态相关系数并分析了膝关节液压阻尼器刚度、阻尼参数对相关系数的影响. 结果表明,通过合理的刚度、阻尼参数设计,两者步态的相关系数可达到 0.9 以上,这为四连杆膝关节被动假肢进一步优化提供了理论支撑.     

ACL单束/双束重建对多屈曲角位姿的胫股关节力学特性影响

进行膝关节的轴移仿真, 在证实了单例个体膝关节的重建模型能反映不同重建术后膝关节力学特性有效性的基础上, 应用SONATA MAESTRO 1.5T扫描得到的屈曲角位姿为0°/25°/60°/80° 的膝关节MRI图像数据, 建立了对应屈曲角的正常/ACL(anterior cruciate ligament)单束/双束重建胫股关节3D模型, 通过对该系列关节模型施加轴向压力与压扭载荷, 来分析多屈曲角度位姿的ACL单束/双束重建法对胫股关节软骨、半月板和韧带应力分布影响及韧带张力特性影响. 结果表明: (1) ACL单束/双束重建关节的软骨与半月板上的应力分布改变跟屈曲角度相关, 某些角度位姿下软骨应力分布改变显著; (2) 单束重建关节的软骨和半月板上的最大等效应力有较明显的增大, 最大增幅达40%左右; 双束重建关节在各屈曲角位姿下软骨和半月板上的最大等效应力值更接近于正常关节; (3) ACL单束重建虽降低了PCL(posterior cruciate ligament)的最大等效应力值, 却使高屈曲角位姿的内侧/外侧副韧带等效应力明显增大; 双束重建后MCL(medial collateral ligament)上的最大等效应力随屈曲角的变化明显, 但LCL(lateral collateral ligament)和PCL的最大等效应力随屈曲角度的变化趋势与正常关节相一致性; (4) 单束/双束重建后MCL上平均张力要高于另外两条韧带, 而双束重建的韧带张力特性比单束重建更接近于正常关节. 总之, 综合ACL重建后软骨、半月板和3条韧带随屈曲角度的等效应力分布、张力变化等多种特性表明: ACL双束重建的胫股关节力学特性比单束重建更接近于正常关节, 且无论ACL单束还是双束重建, 都引起术后关节软骨与韧带上应力分布变化与等效应力峰值增大, 这将是诱发术后关节慢性退变与膝关节并发症的根源.     

井筒中电缆磨损风险评估技术

生产管柱下入时受复杂井眼轨迹影响,电缆磨损失效等情况时有发生,造成不必要的返工,影响作业成本与时效.针对这种情况,建立了井下生产管柱受力有限元分析模型,并采用间隙单元处理接触非线性问题,用以准确地分析井筒中生产管柱与井壁接触力大小及具体接触位置.通过定量评估不同井周处电缆磨损风险,并结合钻井平台的艏向,确定电缆最佳安放位置,使电缆在井下尽量避开管柱与井壁接触较为密集的位置,降低磨损风险.现场应用表明本评估方法可靠,能够为现场电缆安放提供参考.     

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

考虑等效曲率的超二次曲面单元非线性接触模型

基于连续函数包络的超二次曲面单元可有效地描述自然界和工业生产中的非球体颗粒形态, 并通过非线性迭代方法精确计算单元间的接触力. 对于具有复杂几何形态的超二次曲面单元, 线性接触模型不能准确地计算不同接触模式下的作用力. 考虑超二次曲面单元相互作用时不同颗粒形状及表面曲率的影响, 本文发展了相应的非线性黏弹性接触模型. 该模型将不同接触模式下的法向刚度和黏滞力统一表述为单元间局部接触点处等效曲率半径的函数; 切向接触作用则借鉴基于Mohr-Coulomb摩擦定律的球体单元非线性接触模型的计算方法. 为检验超二次曲面单元接触模型的可靠性, 对球形颗粒间的法向碰撞、椭球体颗粒间的斜冲击过程、圆柱体的静态堆积和椭球体的动态卸料过程进行离散元模拟, 并与有限元数值结果及试验结果进行对比验证. 计算表明, 考虑接触点处等效曲率半径的超二次曲面非线性接触模型可准确地计算单元间的接触碰撞作用, 并合理地反映非球形颗粒体系的运动规律. 在此基础上进一步分析了不同长宽比和表面尖锐度对卸料过程中颗粒流动特性的影响, 为非球形颗粒材料的流动特性分析提供了一种有效的离散元方法.