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.

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.

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.

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.

Modeling Method and Application of Rational Finite Element Based on Absolute Nodal Coordinate Formulation

In multibody system dynamics, the absolute nodal coordinate formulation （ANCF） uses power functions as interpolating polynomials to describe the displacement field. It can get accurate results for flexible bodies that undergo large deformation and large rotation. However, the power functions are irrational representation which cannot describe the complex shapes precisely, especially for circular and conic sections. Different from the ANCF representation, the rational absolute nodal coordinate formulation （RANCF） utilizes rational basis functions to describe geometric shapes, which allows the accurate representation of complicated displacement and deformation in dynamics modeling. In this paper, the relationships between the rational surface and volume and the RANCF finite element are provided, and the generalized transformation matrices are established correspondingly. Using these transformation matrices, a new four-node three-dimensional RANCF plate element and a new eight-node three-dimensional RANCF solid element are proposed based on the RANCF. Numerical examples are given to demonstrate the applicability of the proposed elements. It is shown that the proposed elements can depict the geometric characteristics and structure configurations precisely, and lead to better convergence in comparison with the ANCF finite elements for the dynamic analysis of flexible bodies.

Coupled attitude-vibration analysis of an E-sail using absolute nodal coordinate formulation

In this study,the effects of solar wind on an electric sail(E-sail)are modeled and analyzed using an absolute nodal coordinate formulation(ANCF).First,the thrust of the charged metal tether that makes up the E-sail was analyzed and a model was established.Numerical simulations of a single metal tether were performed.Then,an overall E-sail model was established using the connection matrix,and E-sails subjected to different angular velocities were compared.Simulation results of the ANCF model and a dumbbell model were compared at different angular velocities.The results confirm that with a relatively high angular velocity,the flexible metal chain can be approximately regarded as a rigid body.However,with a small angular velocity,the flexibility of the metal chain cannot be ignored.

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。

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.

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.

构架式天线柔性动力学建模与展开精度分析

构架式可展开天线具有结构非线性强、桁架系统复杂以及运动环节多等特点,通常被视作刚体系统进行建模分析。然而多刚体动力学方法在求解复杂的连杆结构时,难以处理数量大、非线性强的铰接间隙模型,因此并不能准确还原真实的结构特性,给构架式天线的地面展开验证带来很大困难。本文建立了一套适用于该型天线的柔性多体动力学模型,通过引入微小弹性形变来消除铰链间隙对天线展开的影响,并在型面精度方面与期望的天线展开模型进行了比较说明。在确保不影响结构真实性的前提下,通过降阶、引入稳定系数等手段提高了柔性体单元计算效率。通过约束方程的设计与模块拆分求解等方法,消除结构非线性的影响。解决了针对构架式可展开天线的复杂桁架系统强非线性动力学的高精度建模问题,为构架式天线的仿真提供了技术手段。

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。

基于绝对节点坐标方法的压发装置建模与优化

研究压发装置的精确建模与产品性能优化问题.基于绝对节点坐标方法的缩减板单元对压发装置电路板进行建模,通过实验确定电路板的材料参数及支撑弹簧与触发装置的非线性刚度特性,采用非线性力–位移关系建立了支撑弹簧与触发装置力学模型,搭建了压发装置结构的精确有限元模型;设计了压发装置加载实验系统,采用实验数据验证了上述有限元模型的正确性.根据目标触发载荷范围,优化了压发装置中支撑弹簧的刚度及长度参数.数值模拟直接指导了压发装置参数设计,并已成功应用于型号研制.

大型抛物柱面天线展开动力学分析与展开过程控制

为揭示大型抛物柱面天线在轨展开过程中各部件的动力学特性,保障可展天线在轨展开过程稳定性,提出了一种基于模块组装的大型抛物柱面可展天线支撑机构动力学快速建模方法与非线性展开过程反馈控制策略。首先,基于绝对节点坐标法建立了天线可展支撑机构基本模块的动力学方程集与约束方程集。然后,通过子模块组装的方式实现对超大型支撑机构的动力学快速建模,并进一步提出逐块缩聚与递归的动力学微分方程高效求解算法。最后,基于非线性展开过程反馈控制策略实现了抛物柱面可展支撑机构该类强非线性系统的展开稳定控制。结果表明,该控制方法能显著降低可展支撑机构展开过程中的速度峰值,有效提高了大型抛物柱面天线展开过程中的展开同步性。

多体柔性机械臂的非线性能量阱被动控制研究

柔性机械臂具有质量轻、能耗低、灵敏性高等优点,近年来在航空航天、机器人、军事等高科技领域被广泛应用。针对两端铰接中间亦铰接的双柔性机械臂,将其简化为多柔体梁系统。基于绝对节点坐标法推导其质量矩阵和非线性刚度矩阵,进而建立动力学模型,并采用能量原理验证模型的正确性。之后对集中荷载作用下两端铰接多柔体梁的振动响应进行分析,使用非线性能量阱对其振动进行抑制。结果表明,非线性能量阱能对多柔体梁系统由外载荷激起的振动进行有效地抑制。此外,随着非线性能量阱质量参数的增加,系统振动幅值衰减得更快,系统的振动能量损耗更迅速。

采用绝对节点坐标法的剪式单元可展机构动力学分析

针对可展机构在工程实践中由于质量轻、柔度大、尺寸大等特点而暴露出展开精度低、控制复杂和运动失稳等问题,采用绝对节点坐标法(ANCF)从多柔体角度分析了构件柔性对剪式单元可展机构动态特性的影响。首先,基于绝对节点坐标法,提出了一种新型无闭锁平面梁单元;然后,考虑服役于太阳能帆板、伸展臂等空间机构的剪式单元可展机构的构型特点与运动条件,基于第一类拉格朗日方程建立了三单元可展机构动力学模型;最后,采用动力学模型分析了杆件柔性对可展机构动力学行为的影响。研究结果表明:所提出的新型单元在解决单元闭锁问题的同时,将计算效率提升了18.2%;构件柔性会导致不同构件间产生共振和谐振现象,影响可展机构的展开精度。该研究可为大型、超大型伸展臂的在轨展开提供理论参考。