Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation

The purpose of this paper is to present formulations for beam elements based on the absolute nodal co-ordinate formulation that can be effectively and efficiently used in the case of thin structural applications. The numerically stiff behaviour resulting from shear terms in existing absolute nodal co-ordinate formulation beam elements that employ the continuum mechanics approach to formulate the elastic forces and the resulting locking phenomenon make these elements less attractive for slender stiff structures. In this investigation, additional shape functions are introduced for an existing spatial absolute nodal co-ordinate formulation beam element in order to obtain higher accuracy when the continuum mechanics approach is used to formulate the elastic forces. For thin structures where bending stiffness can be important in some applications, a lower order cable element is introduced and the performance of this cable element is evaluated by comparing it with existing formulations using several examples. Cables that experience low tension or catenary systems where bending stiffness has an effect on the wave propagation are examples in which the low order cable element can be used. The cable element, which does not have torsional stiffness, can be effectively used in many problems such as in the formulation of the sliding joints in applications such as the spatial pantograph/catenary systems. The numerical study presented in this paper shows that the use of existing implicit time integration methods enables the simulation of multibody systems with a moderate number of thin and stiff finite elements in reasonable CPU time.     

结构模态参数的子空间辨识方法

子空间状态空间系统辨识(4SID)方法是近年来出现的一种用于辨识线性振动系统动态特性的时域技术.它直接由输入/输出数据矩阵序列,通过基本的代数运算求取系统模型.本文概要地介绍了子空间系统辨识方法及其运算步骤,并应用该方法对一已知模态参数的桁架结构进行了仿真计算,得到了准确的辨识结果.     

相近参数拉索的同/异步振动特性研究

辅助索被认为是一种具有潜力的减振手段,但仅在拉索间发生异步振动时才能取得良好的效果．然而,目前对拉索同/异步振动机理尚缺乏系统研究,为此对双水平索进行了模型试验研究．试验主要关注两根不同垂跨比水平拉索跨中面内响应的相位关系．首先对模型进行不同激励频率和保持激励幅值不变下的振动测试,发现垂跨比相同时,两根索相位差基本保持一致;垂跨比不同时,两根索由同步振动转为异步振动．同时采用有限元软件模拟测试实验,其结果与实验吻合良好．为更进一步探究其机理,对试验模型进行了相同激励幅值下的扫频试验．通过对双索幅频特性和相频特性的分析,发现拉索相近参数导致共振区错位是双索存在异步振动现象的根本原因．     

汽车车架结构参数的优化设计

本文采用有限元和优化设计相结合的方法，恰当地解决了通用约束的非线性规划问题。通过对汽车车架结构特点的分析，提出了车架结构参数优化的数学模型，讨论了车架的各种约束条件，并采用混合罚函数法对实例进行了优化设计。     

基于线法的U形切口混凝土梁断裂参数研究

混凝土的断裂韧度是重要的材料参数,本文利用含U形切口的三点弯曲梁试验结合临界距离线法来获得混凝土的断裂韧度.理论推导了含断裂韧度与不同根部半径的断裂失效方程,采用有限元法计算了切口应力集中系数.根据断裂失效方程和试验中的材料几何参数,利用最小二乘法拟合计算得到混凝土材料的断裂韧度和抗拉强度.对小切口半径情形,采用双K断裂准则分析计算了混凝土起裂韧度和失稳断裂韧度,分析结果表明:临界距离线法得到的材料断裂韧度与双K断裂准则中的失稳断裂韧度吻合,同时获得相应临界距离值.     

结构形状优化与智能模型化

阻碍形状优化软件广泛应用的障碍之一是依据自然设计度量描述和建立设计模型、分析模型、优化模型以及实现三个模型之间的转换.本文称这一困难为结构形状优优设计软件的适用性.本文提出了一种方法用来动态地确定平面连续体结构形状优化过程中的边界,应用基于人工智能方法的启发式规则与技术,自动生成由设计单元法表示的几何模型,也就是将一个结构自动剖分成若干个大的四边形映射单元.这些大单元对于进一步的网络生成是必要的,同时也是向全自动计算机辅助形状优化系统前进的重要一步.     

CFRP索斜拉桥的索-浅拱模型及面内自由振动分析

论文针对斜拉桥的受力特点,基于索和浅拱的经典动力学运动方程,结合拉索与浅拱之间的耦合边界条件,并且考虑两者的几何非线性,建立了斜拉桥的多索-浅拱面内自由振动模型.将浅拱分段处理,结合索、浅拱连接处的动态平衡条件,应用分离变量法,建立多索-浅拱模型的面内自由振动理论.以双索浅拱模型为例,求解其特征值问题.同时,建立了相应的有限元模型,有限元计算结果与本文理论分析吻合良好.最后针对CFRP索斜拉桥的关键参数,基于本文的索-浅拱理论,对面内自由振动进一步研究.研究表明:浅拱的矢高在一定范围内变化,仅对某一阶频率产生影响,而其他各阶频率几乎没影响;CFRP拉索能显著改善索-浅拱组合结构的基本动力学特性.     

Influence of Geometrical Parameters on the Critical Load in Three-Dimensional Stability Problems for Rectangular Plates and Beams

Two- and three-dimensional stability problems for a rectangular plate under uniaxial compression are solved by the mesh method. It is shown that the difference between the critical loads obtained in the three- and two-dimensional problems is not greater than 5% for arbitrary fixation conditions and arbitrary length and thickness ratio of the plate     

Multi-scale Structural Modeling of Soft Tissues Mechanics and Mechanobiology

Soft tissues account for a major fraction of the body volume and mass. They are present in all non-skeletal organs, being responsible for protecting the body, maintaining internal homeostasis, and allowing for mobility. Their function in different organs is highly diverse, as are their properties which are optimally suited for their specific tasks. From a mechanical perspective, specificity of structure and properties is acquired via evolutionary adaptation of the tissue composition and multi-scale structure. In modeling tissue mechanics and mechano-biology, it is thus natural to seek the structural determinants of tissues and their evolution (the “structural approach”). Earlier models were exclusively phenomenological, based either on the general principles of non-linear continuum mechanics or alternatively, on empirical mathematical expressions that fit specific response patterns. In the late 1970’s, structural models were introduced to tissue mechanics (Lanir in J. Biomechanics 12(6): 423–436, 1979; Lanir in J. Biomechanics 16(1): 1–12, 1983). Ever since, a gradually increasing number of structural models have been developed for different types of tissues, and today, it is the method of choice (Cowin and Humphrey in J. Elasticity 61: ix–xii, 2000). The structural approach was recently extended to incorporate a mechanistic formulation of mechano-biological pathways by which tissue structures remodel during growth (Lanir in Biomech Model Mechanobiol, 14(2): 245–266, 2015). Here, the characteristic features of soft tissue structures and their constitutive modeling are reviewed. The presentation starts with a brief survey of the multi-scale and multi-phasic soft tissues structure. The global mechanical characteristics of soft tissues and of their constituents are then briefly reviewed. These two aspects form the basis for structural constitutive formulation via the multi-scale structure-function link. Based on established criteria for model validity, predictions of the formulated theory are contrasted against measured response characteristics. Using this structure-function relationship, the evolutionary pathway by which tissue structure and mechanics remodel during growth to adapt to their physiological function, is laid down. The review concludes with an account of the state of the art, the big picture, and future research challenges in tissue mechanobiological modeling.     

具有随机参数的动力系统随机地震响应分析

本文同时考虑地震输入的随机性和结构动力本数的随机性，在随机振动分析中引入随机有限元法，以单自由反动力系统为例，分析了不同参数变异性对随机结构动力响应的影响。     

起落架结构参数对飞机机轮摆振的影响

建立了飞机机轮摆振运动方程,详细研究了起落架三个重要结构参数;稳定距、支柱刚度和减摆器传动系统扭转刚度对飞机机轮摆振的影响,考虑了各参数之间的耦合作用,严格区分“轮胎型”摆振和“结构型”摆振,并分别予以研究,所得结论为新机防摆设计和现役飞机防摆维护提供了理论依据。     

基于正交性条件识别机械结构结合面参数方法的改进

本文在文献［１］所提出的基于正交性条件识别机械结构结合面阻尼参数方法的基础上，进一步提出采用正交条件式中虚部方程识别结合面动力学参数的方法。理论和算例分析表明这种改进方法能大大降低机械结构的物理参数（即质量、阻尼和刚度）矩阵和结构系统测试振型二者的误差对结合面参数识别精度的不利影响，从而使这种方法更具有可行性。     

Al基含能结构材料的Johnson-Cook本构模型及失效参数研究

利用万能实验机和Hopkinson杆装置测试了Al基含能结构材料在不同温度下的静动态力学性能,分析实验结果得到了温度效应和应变率效应对材料力学性能的影响及该合金的Johnson-Cook本构模型参数.结合二维数字图像相关(DIC)方法,研究了Al基含能结构材料的失效应变与应力三轴度及温度之间的关系,得到了该合金的Johnson-Cook失效模型参数.通过平面撞击实验获得了Al基含能结构材料粒子速度和应力波波速之间的经验线性关系和该合金的Grüneisen系数.基于实验获得的材料本构关系和状态方程参数,完成了Al基含能结构材料超高速撞击多层间隔薄钢板的数值模拟,结果表明,数值模拟中靶板的毁伤模式、破孔直径及弹坑主要散布区和实验结果吻合.     

Low-Dimensional Modeling of a Driven Cavity Flow with Two Free Parameters

By applying Proper Orthogonal Decomposition (POD) one is able to extract a limited amount of data which characterizes a flow of interest. The modes resulting from the decomposition form a basis in the phase space on which a Galerkin projection of the equations of motion can be performed. By carrying out such a procedure one obtains a low-dimensional model consisting of a reduced set of Ordinary Differential Equations (ODEs) which models the original equations. A technique called Sequential Proper Orthogonal Decomposition (SPOD) is developed to perform decompositions suitable for low-dimensional models. SPOD is capable of transforming data organized in different sets separately while still producing orthogonal modes. A low-dimensional model is constructed and used for analyzing bifurcations occurring in the flow in the lid-driven cavity with a rotating rod. The model allows one of the free parameters to appear in the inhomogeneous boundary conditions without the addition of any constraints. This is necessary because both the driving lid and the rotating rod are controlled simultaneously. Apparently, the results reported for this model are the first to be obtained for a low-dimensional model based on projections on POD modes for more than one free parameter. Received 29 October 2001 and accepted 27 August 2002 Published online 13 January 2003 Communicated by P. Hall     

基于初应力法的作大范围运动柔性梁动力学建模理论研究

研究了初应力法的作大范围运动柔性梁的建模理论.根据连续介质理论,考虑应变-位移中的非线性项,用一致质量有限元法对柔性梁进行离散,基于Jourdain速度变分原理导出定轴转动下大范围运动为自由的柔性梁刚-柔耦合动力学方程.从其刚柔耦合动力学方程出发,考虑在大范围运动已知情况下的结构动力学方程.通过引入准静态概念,把其结构动力学方程转化为准静态方程.对纵向和横向变形节点坐标进行坐标分离,解出与纵向变形相关的准静态方程,得到准静态时的纵向应力表达式,从而获得附加刚度项.并对此非惯性系下作大范围运动柔性梁的结构动力学方程进行数值仿真,对零次近似模型、一次近似模型、初应力法动力学模型的仿真结果进行分析,揭示三种模型的动力学性质的差异.     

利用地脉动试验识别楼房结构的模态参数

论述了在地脉动对结构物的环境激励条件下,进行结构物地脉动响应测量的试验原理及方法,提出了固有频率识别与振型识别的互补较正法．通过对实际楼房结构的地脉动响应测量识别结构的模态参数．识别结果表明该理论及试验方法行之有效．     

模态分析和有限元法结合识别机械结构结合面动力学参数的研究

本文探讨了一种将实验模态分析和有限元法相结合，识别机械结构结合面动力学参数的新方法，以解决大型复杂机装拆不例，难于用实验方法识别部件间结合面动力学参数的问题。用些方法识别了一台遥臂钻床的接触度和接触阻尼。     

梁的动力稳定性分析的有限元方法

提出了对梁进行动力学稳定性分析的有限元方法──给出了单元质量矩阵，抗弯刚度矩阵，几何刚度矩阵及相应的Ｍａｔｈｉｅｕ方程，通过坐标变换消除了方程的动力与静力耦合，然后说明了由这种具有参数激励耦合的多自由度系统的Ｍａｔｈｉｅｕ方程求得系统一般参数共振及组合参数共振的过渡曲线的约束参数方法与多尺度方法。最后作为算例求出了均匀简支梁受简谐轴向力作用时的过渡曲线。     

Modeling and Dynamic Analysis of Telescopic Systems of Structural Members with Clearance

The dynamic behavior of multi-section constructions with clearance during extending and retracting motion of the sections is analyzed. First, an appropriate physical modeling is introduced before next, the governing boundary value problem is derived by applying Hamilton's principle. Then, a classical discretization procedure is used to generate a coupled system of nonlinear ordinary differential equations as the corresponding truncated mathematical model. Performing appropriate simulations to be verified by results of an alternative software package and partly validated by some preliminary experiments, the vibrational behavior of the suggested type of multi-section telescoping systems can be studied in detail.     

Variational Derivative for Buckling Loads of Beams and Frames

The finite-difference method is a numerical technique for obtaining approximate solutions to differential equations. The main objective of the present study is to give a new aspect to the finite-difference method by using a variational derivative. By applying this formulation, accurate values of the buckling loads of beams and frames with various end supports are obtained. The performance of this formulation is verified by comparison with numerical examples in the literature __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 139–144, July 2005.