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.

Research on the Viscoelasticity of Polyester Mooring Lines Using the Absolute Nodal Coordinate Formulation

The taut mooring system using synthetic fiber ropes has overcome the shortcomings such as the large self-weight of the mooring lines and provides better mooring performance for the floating structures.The polyester rope has attracted much attention among numerous synthetic fiber rope materials due to its lightweight,low price,corrosion resistance,and high strength.Thus,the mooring characteristics of it are worth studying.Polyester mooring lines are flexible in deep water,when a marine structure is moored by them,the geometric nonlinearity such as large displacement,large stretch,and large bending deformation,and the material nonlinearity like viscoelastic of the polyester ropes become complex integrated problems to be studied.Considering the nonlinear phenomenon,the simulation and calculation of a polyester line were carried out by the absolute nodal coordinate formulation(ANCF)in this paper since the ANCF method has advantages in dealing with the significant deformation problems of the flexible structures.In addition,a chain mooring line was also simulated for comparison,and the results show that the polyester ropes reduce the self-weight of the mooring lines and provide sufficient mooring strength at the same time,and the nonlinear phenomenon of the polyester ropes is different from that of the chain mooring lines.

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.

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.

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.

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.

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.

基于ALE-ANCF方法的卷曲展开机构动力学建模与分析

针对含复杂的多区域接触的卷曲展开机构,该研究将其简化为带刚性转盘的变长度柔性构件,建立多体系统动力学模型,以实现高效仿真。首先,基于任意拉格朗日-欧拉描述的绝对节点坐标法对变长度梁进行建模;然后,将复杂接触问题简化为移动边界的约束关系,给出一种增删节点处理方法,有效解决了单元长度变化引起的奇异和精度问题,在此基础上建立了刚-柔耦合多体系统的动力学模型,用隐式算法实现了动力学方程的数值求解。通过滑绳和动滑轮算例验证了建模方法的有效性;最后,建立了卷曲机构充气展开系统的简化动力学模型,该模型采用任意拉格朗日-欧拉法移动网格实时跟踪卷曲机构的位置,精准捕捉移动边界点,从而高效确定接触行为。分析了气压力与黏附力对展开动力学特性的影响,通过控制黏附力分布,实现了卷曲机构的匀速展开,对工程实际具有参考价值。

基于绝对节点坐标法的架空线断线工况动力学计算

为了计算架空线断线工况下的动力学变化特性,考虑架空线的绞制几何结构及其初始构型的布置特点,以绝对节点坐标法为基础,建立了架空线单元,推导了架空线单元的质量矩阵和弹性力矩阵,给出了架空线的系统动力学方程。针对钢芯铝绞线的绞制几何结构,给出了其对应的轴向、弯曲刚度计算公式。通过仿真计算得到线缆的运动图像,设计试验验证了算法模型的可靠性。结合实际架空线初始位形和初始应力特点,对不同初始应力下的架空线断线工况动力学问题进行仿真分析,绘制了悬挂点处的受力时程曲线并对曲线进行了频谱分析,研究了初始应力对断裂架空线运动过程以及悬挂点受力的影响规律。

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。

基于绝对节点坐标法薄板结构振动特性分析

为研究柔性结构大变形问题,采用绝对节点坐标法(absolute nodal coordinate formulation,ANCF)对大变形柔性体结构进行建模。该方法由变形梯度和格林-拉格朗日应变来描述结构的运动以及变形,通过斜率矢量替代传统有限元法中的广义节点坐标,可直接用于解决结构中较复杂的大位移、大转动和大变形问题。根据绝对节点坐标法原理,研究薄板单元以及全参数板单元的振动特性,利用连续介质力学推导出单元的广义弹性力矩阵和切线刚度矩阵,由此建立板单元的动力学方程。利用MATLAB软件分别对薄板单元和全参数板单元进行自由模态分析,并将其仿真结果与ANSYS结果进行比较,同时通过牛顿迭代法验证2种板单元的收敛性。结果表明,消除厚度振荡影响的降阶薄板单元比全参数板单元有更好的精度和收敛特性,在针对模态分析的结构上,通过固有频率对比数据得出误差基本一致,从而单元的正确性得到验证,为后续研究和应用提供理论基础。

考虑径向间隙的高速旋转柔性圆锯片的振动特性分析

电圆锯是重要的林间锯割作业工具,圆锯片振动特性直接影响了电圆锯的使用寿命和安全操作。为了便于圆锯片的安装和拆卸,圆锯片通过轴孔间隙配合与刀架进行连接,这种配合方式不能使用简支或者固支边界条件进行准确的表述。在具有随动坐标系的绝对节点坐标法(absolute nodal coordinate formulation, ANCF)框架下,利用空间环扇单元建立高速柔性高速旋转柔性圆锯片模型,并引入含径向间隙的弹簧约束单元对间隙配合边界条件进行模拟,考虑旋转运动中广义离心力和克氏力,根据达朗贝尔原理建立高速旋转柔性圆锯片模型的非线性动力学微分方程。通过与其他文献进行对比,验证高速旋转柔性圆锯片模型的有效性,并分析配合间隙,旋转速度和几何形状对圆锯片振动特性和临界转速的影响。

变长度加油软管系统动力学建模及运动特性分析

空中加油过程中,软管锥套受复杂气流干扰发生飘摆运动,同时在受油机的撞击作用下可产生甩鞭现象,严重制约了空中加油的成功率及安全性。为了研究软管锥套系统的运动特性,基于绝对节点坐标方法建立变长度软管动力学模型。同时考虑软管材质的阻尼特性、加油吊舱卷盘机构的收放运动、加油过程中存在的紊流及尾涡等风场环境,根据多体系统动力学建模理论,获得软管复杂风场下加油锥套系统动力学模型。利用有限元分析软件ANSYS仿真及Simulink数值计算对软管平稳拖曳状态下锥套的下沉量进行模拟,同时将锥套平稳拖曳阻力Simulink数值结果与NASA公开数据资料进行比较,说明所提建模方法的准确性和可行性。通过数值仿真,确定了不同飞行高度/飞行速度下加油软管的稳定拖曳状态,分析了不同对接速度下软管甩鞭动力学特性,验证了不同测力反馈点对甩鞭抑制效果的影响。

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.

L形输流管道三维振动固有特性研究

输流管道在众多工程领域中发挥着输送介质的作用,其振动特性是动力学研究者关注的热点.鉴于管道形状的多样性,构建复杂构型管道的动力学模型显得尤为重要.采用绝对节点坐标法(absolute nodal coordinate formulation, ANCF)建立三维管道动力学模型,并以两端弹性支撑的L形管为例进行分析.基于广义扩展拉格朗日方程得到系统动力学方程,借助ANSYS软件对模态结果进行比较验证,并分析竖直和扭转弹簧刚度、流速、结构参数以及充液率对管道固有频率的影响规律.结果表明,增加竖直刚度和扭转弹簧刚度均会提高管道的固有频率,且竖直弹簧刚度的影响较大,低阶频率的曲线拐点早于高阶频率.增加壁厚、增大管径以及缩短管长都能显著提高管道的固有频率和临界流速.充液率的变化不会显著影响低流速时管道的固有频率,但会明显改变临界流速.研究结果可为复杂结构管道流激振动研究提供一个可靠的三维动力学模型.