Axially variable-length solid element of absolute nodal coordinate formulation

An axially variable-length solid element with eight nodes is proposed by integrating the arbitrary Lagrangian-Eulerian (ALE) formulation and the absolute nodal coordinate formulation (ANCF). In addition to the nodal positions and slopes of eight nodes, two material coordinates in the axial direction are used as the generalized coordinates. As a consequence, the nodes in the ALE-ANCF are not associated with any specific material points and the axial length of the solid element can be varied over time. These two material coordinates give rise to a variable mass matrix and an additional inertial force vector. Computationally efficient formulae of the additional inertial forces and elastic forces, as well as their Jacobians, are also derived. The dynamic equation of a flexible multibody system (FMBS) with variable-length bodies is presented. The maximum and minimum lengths of the boundary elements of an FMBS have to be appropriately defined to ensure accuracy and non-singularity when solving the dynamic equation. Three numerical examples of static and dynamic problems are given to validate the variable-length solid elements of ALE-ANCF and show their capability.

Numerical Investigation on Dynamics of the Tendon System of A TLP by Applying Absolute Nodal Coordinate Formulation

In the present study,the dynamics of the tendon system of a tension-leg platform(TLP)is investigated through the absolute nodal coordinate formulation(ANCF).Based on the energy conversion principle,the stiffness,generalized elastic force,external load and mass matrices of the element are deduced to perform the element assembling by using the finite element method.Then the motion equation of the tendon/riser is established.In this study,the TLP in the International Ship Structures Committee(ISSC)model under the first and second wave forces is considered as the case study.The simulation is performed in the MATLAB environment.Moreover,the accuracy and reliability of the programs are verified for cases of beam model with theoretical solutions.It is found that the motion response of tendons is affected by the TLP movement and environmental load,simultaneously.Then,the motion response is calculated using the SESAM software and exported as the boundary of ANCF tendons.Finally,the static and dynamic characteristics of the four tendons of ISSC TLP are analyzed systematically by the ANCF method.Performed analysis proves the effectiveness and feasibility of the ANCF method.It is concluded that the proposed method is a powerful scheme for calculating the dynamics of tendon/riser in the field of ocean engineering.

Contact dynamics of elasto-plastic thin beams simulated via absolute nodal coordinate formulation

Under the frame of multibody dynamics, the contact dynamics of elasto-plastic spatial thin beams is numerically studied by using the spatial thin beam elements of absolute nodal coordinate formulation（ANCF）. The internal force of the elasto-plastic spatial thin beam element is derived under the assumption that the plastic strain of the beam element depends only on its longitudinal deformation.A new body-fixed local coordinate system is introduced into the spatial thin beam element of ANCF for efficient contact detection in the contact dynamics simulation. The linear isotropic hardening constitutive law is used to describe the elasto-plastic deformation of beam material, and the classical return mapping algorithm is adopted to evaluate the plastic strains. A multi-zone contact approach of thin beams previously proposed by the authors is also introduced to detect the multiple contact zones of beams accurately, and the penalty method is used to compute the normal contact force of thin beams in contact. Four numerical examples are given to demonstrate the applicability and effectiveness of the proposed elasto-plastic spatial thin beam element of ANCF for flexible multibody system dynamics.

Nonlinear Absolute Nodal Coordinate Formulation of a Flexible Beam Considering Shear Effect

Nonlinear modeling of a flexible beam with large deformation was investigated. Absolute nodal cooridnate formulation is employed to describe the motion, and Lagrange equations of motion of a flexible beam are derived based on the geometric nonlinear theory. Different from the previous nonlinear formulation with Euler-Bernoulli assumption, the shear strain and transverse normal strain are taken into account. Computational example of a flexible pendulum with a tip mass is given to show the effects of the shear strain and transverse normal strain. The constant total energy verifies the correctness of the present formulation.

Planar Weak Form Quadrature Beam Elements Based on Absolute Nodal Coordinate Formulation: A Structural Mechanics Approach

A planar nonlinear weak form quadrature beam element of arbitrary number of axial nodes is proposed on the basis of the absolute nodal coordinate formulation (ANCF). Elastic forces of the element are established through geometrically exact beam theory, resulting in good consistency with classical beam theory. Two examples with strong geometrical nonlinearity are presented to verify the effec-tiveness of the formulation.

一种新开发的ANCF缆索单元

为精确模拟系浮系统中系留缆索的动力学行为,应用绝对节点坐标公式(absolute nodal coordinate formulation,ANCF),开发一种新的ANCF缆索单元。该单元考虑了缆索的层级数目、各层材料的力学性能,并通过子域划分来更好地适应材料的层间差异。其中,利用Kelvin-Voigt模型来解释内芯层的黏弹性性质,而将改进后的Yeoh模型应用于护套层当中以更好地契合材料的超弹性性能。此外,设计一种具有隐式效果的差分格式对动力学微分方程组进行数值求解。最后,通过一系列静力学与动力学数值计算证明单元的精度与收敛特性,并对比几种应用不同超弹性模型的ANCF单元,证实应用改进的Yeoh模型的ANCF单元的合理性与优越性。

基于ANCF的链型悬挂接触网找形及分析

为精准获得高速铁路接触网的初始平衡构型,基于绝对节点坐标法建立适用于不同悬挂形式接触网系统的找形模型。完成直链型悬挂接触网的找形,其中吊弦长度、接触线初始构型以及接触网静态刚度结果与参考值相比均显示了良好的一致性;完成对实际线路京津线、武广线接触网模型的找形分析,得到的各参数与参考值基本一致,且吊弦长度随承力索张力的增加;通过吊弦力系平衡建立双层迭代获取半斜链型、斜链型悬挂接触网初始平衡构型,解决其吊弦长度不易计算的问题,在动力学模型稳态下的张力结果与预设值基本相同,验证了模型的正确性与适用性;通过对比分析得到斜链型悬挂接触网具有较大的吊弦长度、定位器作用力以及较小的弹性不均匀度,可为接触网系统的工程设计、施工提供参考。

Deployment dynamics of a simplified spinning IKAROS solar sail via absolute coordinate based method

The spinning solar sail of large scale has been well developed in recent years. Such a solar sail can be considered as a rigid-flexible multibody system mainly composed of a spinning central rigid hub, a number of flexible thin tethers, sail membranes, and tip masses. A simplified interplanetary kite-craft accelerated by radiation of the Sun （IKAROS） model is established in this study by using the absolute-coordinate-based （ACB） method that combines the natural coordinate formulation （NCF） describing the central rigid hub and the absolute nodal coordinate formulation （ANCF） describing flexible parts. The initial configuration of the system in the second-stage deployment is determined through both dynamic and static analyses. The huge set of stiff equations of system dynamics is solved by using the generalized-alpha method, and thus the deployment dynamics of the system can be well understood.

基于ANCF的旋转超弹性厚壁REF振动特性分析

为了探究子午线轮胎面内振动特性,建立了旋转超弹性厚壁REF模型。并在具有随动坐标系的绝对节点坐标法(absolute nodal coordinate formulation,ANCF)框架下,提出平面内旋转环扇单元,对旋转超弹性厚壁弹性基环模型(ring on the elastic foundation,REF)进行离散。考虑到非线性本构关系和旋转运动中的广义惯性力,建立了该模型的非线性运动微分方程以及线性化运动微分方程。通过与现有文献中的试验结果进行对比,验证了上述模型的有效性,并分析了弹性基参数、环体厚度和旋转角速度对子午线轮胎固有特性的影响规律。

Dynamic Analysis and Optimal Parameter Design of FlexibleComposite Structures via Absolute Nodal Coordinate Formulation

The composite structure with the dielectric elastomer and soft materials is the main form of theactuators in soft robots. However, the theoretical model is hard to obtain due to the nonlinear large deformationof materials. In this paper, a new composite element model is established based on the absolute nodal coordinateformulation. The consistent deformation conditions at the contact interface between two thin plates are deduced.The hyperelastic constitutive model and the dielectric elastomer constitutive model are introduced for the twothin plates. Then the dynamic model is established to study the dynamic behaviors of the composite flexiblestructure with various parameters. The results show that the nonlinear deformation appears obviously whenthe flexible composite plate structure is driven by various voltages, and the warping deformation becomes moreobvious with the increase of the voltage. The width and thickness of the driven thin plate influence the stabilityof the whole structure. With the decrease of the width or thickness, the deformation of the structure is moreconsistent with obvious periodicity, and the control performance is improved. Finally, the structural parametersof the composite structures are optimized to improve the control performance based on the dynamic performance.Additionally, smaller width and thickness parameters are preferred to obtain better performance in the design offlexible actuator of soft robot.

完备化ANCF薄板单元及在钢板弹簧动力学建模中的应用

绝对节点坐标方法已在多体系统动力学研究中广泛应用,但常用来描述板壳类结构的薄板单元,由于梯度不完备而无法直接用于带有初始弯曲参考构型的柔性体变形描述.为避免全参数板单元建立车辆钢板弹簧模型时存在的严重截面闭锁问题,拟采用薄板单元用于板簧建模.为此,探索了将现有绝对节点坐标薄板单元纳入一般连续介质力学弹性力表达的方法,采用中面上单位法向量作为单元厚度方向的梯度向量,从而得到了完备化的薄板单元及其描述初始弯曲构型时消除初应变的方法.在此基础上通过定义簧片的未变形构型,在钢板弹簧中引入可控的预应力,实现对钢板弹簧装配过程的准确模拟.通过数值算例验证了本方法的正确性.建立了车辆钢板弹簧模型,通过建立在簧片上的局部坐标系实现接触点的跨单元搜索,并采用惩罚函数法和平滑化的库伦摩擦模型施加簧片间的接触力.引入参考节点的概念建立了整合车身与吊耳及其机构运动关系的刚柔耦合模型.

一种在轨可展开天线的多柔体动力学建模与计算

研究了一种考虑重力梯度的大型空间可展开天线桁架的动力学建模与计算问题.使用绝对节点坐标法和绝对节点坐标参考节点法建立了可展开结构的刚柔耦合动力学模型.利用离散方向导数构建了动力学方程的保能量动量时间积分算法,通过计算获得了含有多个模块的大型空间可展开天线在轨展开以及展开后轨道机动过程轨道-姿态-变形耦合动响应.通过数值计算结果与经典算例结果、商业软件ADAMS计算结果的对比分析验证了提出方法的正确性.

基于变长度单元ANCF的轴向伸展悬臂梁振动分析

伸展悬臂梁系统中含有刚体运动和大变形运动,属于时变刚柔耦合非线性动力学问题。采用Shabana提出的绝对节点坐标法(ANCF),建立了一种变长度的Euler-Bernoulli梁单元模型。从大变形条件下准确的曲率和Green-Lagrangian正应变出发,基于考虑惯性力的虚功原理,得到了轴向伸展悬臂梁的单元非线性动力学方程组,以及组装后的伸展悬臂梁系统的非线性动力学方程组。最后,通过算例分析了材料特性参数(弹性模量、密度)和伸展规律(匀速伸展、匀加速伸展)对伸展悬臂梁系统的末端非线性挠度响应的影响。

超大型多模块结构组装过程动力学与姿态控制

机器人在轨自主组装是未来建造超大型航天结构最具潜力的方式.超大型结构通常包含多个模块,需要机器人在柔性结构上反复进行抓捕、安装和爬行等操作.此外,组装过程中结构还受到空间环境干扰力的影响,需要经历构型的增长和参数的变化,导致其动力学行为非常复杂.为了研究机器人空间组装超大型多模块结构的过程,提出了一套轨道-姿态-结构耦合动力学、规划与控制的仿真框架.首先,采用自然坐标法和绝对节点坐标法建立主结构、空间机器人和组装模块的轨道-姿态-结构耦合动力学模型,采用Kelvin-Voigt线性弹簧阻尼模型描述机器人末端夹持机构和模块对接机构的接触碰撞.然后,对机器人进行运动规划、轨迹规划和关节轨迹跟踪控制研究.最后,采用不同的组装姿态和不同的姿态控制方案对组装过程进行动力学仿真.仿真结果表明,由于质心位置的改变和组装模块的轨道差异,主结构在组装过程中可能会出现显著的轨道漂移(取决于组装姿态).如果模块沿轨道半径方向组装到主结构,将导致组装过程长半轴和离心率出现快速增长;反之,如果模块沿轨道切向组装,长半轴和离心率基本保持不变.此外,即使采用了万有引力梯度稳定的组装姿态,仍需进行姿态控制和结构振动控制,以减小结构振动幅值,降低机器人与结构的碰撞风险,提高组装精度和组装效率.

ANCF/CRBF平面梁闭锁问题及闭锁缓解研究

本文系统地研究了基于一致旋转场列式的绝对节点坐标(ANCF consistent rotation-based formulation,ANCF/CRBF)平面梁单元的泊松闭锁问题及闭锁缓解技术.为了全面理解该类型单元的闭锁特性及明确单元的应用范围,文中首先开发了两种新的ANCF/CRBF刚性截面梁单元,新单元在ANCF全参数梁的基础上,对梯度向量施加正交矩阵约束,得到梯度与转角对时间导数之间的速度转换矩阵,从而引入转角参数.新单元节点处完全消除了泊松闭锁和剪切效应,这是与传统ANCF/CRBF刚性截面梁单元的不同之处.然后,对比分析了这三种ANCF/CRBF刚性截面梁单元泊松闭锁的特点.发现该类型单元对节点的横向梯度施加了运动学约束,导致节点处截面不能变形,无法捕捉泊松效应,但是单元内部能完全捕捉,这种不连续情况会加重单元整体的泊松闭锁问题.并且发现对单元梯度约束的越多,闭锁问题越严重.随后,分别采用两种闭锁缓解技术,弹性线方法和应变分解方法,进一步研究了单元的收敛性.最终,通过多种静力学和动力学测试研究了泊松闭锁对ANCF/CRBF平面梁单元计算精度的影响及闭锁缓解技术在该类型单元上的缓解效果.

Nonlinear formulation for flexible multibody system with large deformation

In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation.

Adaptive ANCF method and its application in planar flexible cables

In the conventional absolute nodal coordinate formulation(ANCF), the model is pre-meshed, the number,distribution and type of elements are unchangeable during the simulation. In addition, the deformations of a flexible body are space-varying and time-varying, one cannot predict when, where, and how the deformations will occur. Therefore, in order to obtain a satisfactory accuracy during the whole simulation, the model is usually densely meshed, but it will result in a loss of computational efficiency. In this study,an adaptive absolute nodal coordinate formulation(AANCF)is proposed to optimize the accuracy and efficiency of flexible dynamics. The movement features of flexible bodies are analyzed, and the conventional and adaptive ANCF methods are compared. Then the adaptive computation strategy is presented. The discretization errors come from the inability of interpolation functions of individual elements to capture the complexity of the exact solution, so the mesh can be adaptively optimized by changing the element sizes or the orders of interpolation functions during dynamic computation. Important issues of AANCF, including error estimation,mesh updating, and performance of the AANCF model, are analyzed and discussed in detail. A theoretical model of a planar AANCF cable is presented, where the strategies of dividing and merging elements are discussed. Moreover, the continuity of dynamic variables is deduced, and the mean factors that affect the continuity are obtained, which is very important for the subsequent continuity optimization. Thesimulation results indicate that the distribution of elements varies with time and space, and the elements are denser in large-deformed domains. The AANCF model improved the computational accuracy and efficiency, but the system energy is discontinuous when the elements are merged. Therefore,a continuity-optimized AANCF model is given based on the previous continuity analysis, the results show that the accuracy and continuity of energy are further improved by the continuity-optimized AANCF model.

INTEGRATION OF NON-UNIFORM RATIONAL B-SPLINES GEOMETRY AND RATIONAL ABSOLUTE NODAL COORDINATES FORMULATION FINITE ELEMENT ANALYSIS

This investigation is intended to develop a computer procedure for the integration of NURBS geometry and the rational absolute nodal coordinate formulation （RANCF） finite element analysis. A linear transformation is given that can be used to convert the NURBS curve to RANCF cable element mesh retaining the same geometry and the same degree of continuity, including the discussion of continuity control and mesh refinement. The green strain tensor is used to establish the nonlinear dynamic equations with numerical examples to demonstrate the use of the procedure in the dynamic analysis of flexible bodies.

A new absolute nodal coordinate formulation beam element with multilayer circular cross section

A systematic numerical integration method is applied to the absolute nodal coordinate formulation(ANCF)fully parameterized beam element with smooth varying and continuous cross section.Moreover,the formulation for the integration points and weight coefficients are given in the method which is used to model the multilayer beam with a circular cross section.To negate the effect of the bending stiffness for the element used to model the high-voltage electrical wire,the general continuum mechanical approach is adjusted.Additionally,the insulation cover for some particular types of the wire is described by the nearly incompressible Mooney-Rivlin material model.Finally,a static problem is presented to prove the accuracy and convergence properties of the element,and a dynamic problem of a flexible pendulum is simulated whereby the balance of the energy can be ensured.An experiment is carried out in which a wire is released as a pendulum and falls on a steel rod.The configurations of the wire are captured by a high-speed camera and compared with the simulation results.The feasibility of the wire model can therefore be demonstrated.

Geometric Nonlinear Formulation for a Rectangular Plate with Large Deformation

Absolute nodal coordinate formulation for a rectangular plate with large deformation was improved. Based on nonlinear elastic theory, a precise strain expression is used to derive the equations of motion. Both shear strain and transverse normal strain are taken into account. Different from the previous absolute nodal coordinate formulation, the absolute nodal coordinates, which describe the displacement and slope of the element nodes, are separated into three parts: the absolute nodal coordinates in X, Y and Z directions, respectively, so that the dimension of the mass, stiffness and force matrices is reduced. Furthermore, by using constant matrices, which can be calculated and saved before simulation, the nonlinear stiffness matrices can be calculated by matrix multiplication for each time step, so that the computational efficiency can be improved. Finally, simulation example of a rectangular plate with large deformation was used to verify the accuracy and efficiency of the present formulation.