A fast and stable first-order method for simulation of flexible beams and cables

Nonlinear Dynamics - Gradient deficient beam elements (commonly known as cable elements in the literature) based on the absolute nodal coordinate formulation (ANCF) have great potential for...     

ANCF curvature continuity: application to soft and fluid materials

The continuity of the position-vector gradients at the nodal points of a finite element mesh does not always ensure the continuity of the gradients at the element interfaces. Discontinuity of the gradients at the interface not only adversely affects the quality of the simulation results, but can also lead to computer models that do not properly represent realistic physical system behaviors, particularly in the case of soft and fluid material applications. In this study, the absolute nodal coordinate formulation (ANCF) finite elements are used to define general curvature-continuity conditions that allow for eliminating or minimizing the discontinuity of the position gradients at the element interface. For the ANCF solid element, with four-node surfaces, it is shown that continuity of the gradients tangent to an arbitrary point on a surface is ensured as the result of the continuity of the gradients at the nodal points. The general ANCF continuity conditions are applicable to both reference-configuration straight and curved geometries. These conditions are formulated without the need for using the computer-aided-design knot vector and knot multiplicity, which do not account properly for the concept of system degrees of freedom. The ANCF curvature-continuity conditions are written in terms of constant geometric coefficients obtained using the matrix of position-vector gradients that defines the reference-configuration geometry. The formulation of these conditions is demonstrated using the ANCF fully parameterized three-dimensional solid and tetrahedral elements, which employ a complete set of position gradients as nodal coordinates. Numerical results are presented in order to examine the effect of applying the curvature-continuity conditions on achieving a higher degree of smoothness at the element interfaces in the case of soft and fluid materials.

     

Modelling and transient planar dynamics of suspended cables with moving mass

In this study, the 3D nonlinear equations of motion of the suspended cable with moving mass are obtained via the Hamilton principle, and its transient linear planar dynamics is investigated. Considering the quasi-static assumption, the condensed planar model accounting for the effect of the moving mass is derived, and it is then discretized by choosing the static deflection and sine series as shape functions. It is shown that this expansion shows good convergence features. The Newmark method is used to investigate the transient response. The effects of the inertia force, mass, sag and velocity of the moving mass on the transient dynamics of the suspended cable are systematically investigated. Finally, the horizontal tension of the suspended cable and the case of sequentially moving masses are examined.     

自适应Sage-Husa粒子滤波及其在组合导航中的应用

针对非线性滤波问题,提出一种新的自适应Sage-Husa粒子滤波算法。通过Sage-Husa滤波方法计算状态估值和协方差阵来获得重要性密度分布函数,充分考虑了最新量测信息的影响,并利用欧氏距离和反映量测噪声统计特性的精度因子自适应地调整粒子权值的分布,降低粒子退化程度,提高了滤波精度,适用于非线性非高斯系统模型的滤波问题。将提出的算法应用于SINS/SAR组合导航系统中,与扩展Kalman滤波和粒子滤波比较,仿真结果表明,自适应Sage-Husa粒子滤波能提高导航系统定位的解算精度,得到的东向和北向定位误差控制在?5.3m附近,其性能明显优于扩展Kalman滤波和粒子滤波。     

Finite elements and sensitivity coefficients in flexible planar linkage analysis

Summary A Kineto-Elasto-Dynamic approach, which is based on the use of finite elements, is presented for 1 d.o.f. planar mechanisms. No requirements are needed for the reference rigid mechanism time-history, which is computed in a fully dynamic way.A simple test case shows the independence of the response from the chosen reference mechanism.The frequency content of the response matches the expected frequencies of the model.

---

Sommario Viene presentato un approccio cineto-elasto-dinamico, basato su tecniche agli elementi finiti, per meccanismi piani ad 1 g.d.l. Nessuna ipotesi è richiesta per la legge del moto del meccanismo di riferimento a membri rigidi. Detta legge del moto è calcolata in maniera dinamica diretta. Un semplice caso di prova mostra l'indipendenza della risposta dalla scelta del meccanismo di riferimento. Il contenuto in frequenza della risposta corrisponde alle frequenze prevedibili per il modello.

     

Ghost-Fluid Eulerian-Lagrangian方法及其应用

考察了将独立的Euler程序和Lagrange程序通过Ghost Fluid方法结合起来以处理流固耦合问题的算法。在Euler计算步中,采用基于物质界面建立的Levelset函数对被Lagrange域覆盖的Euler网格上的物理量进行外插,同时确保界面两侧压力和法向速度连续;而在Lagrange计算步中,根据界面所在Euler网格压力确定界面各个节点的受力情况,从而确定Lagrange单元的运动与变形。应用这种方法对瞬时起爆爆轰产物作用于爆炸容器问题进行了计算分析,给出了流场演化及容器各关键位置的超压与变形情况。计算表明,对长径比为2:1的椭球封头爆炸容器最大超压及最大应变均出现在封头顶部,这与封头顶部最易破坏的实际相符。     

Nonlinear mechanics of flexible cables in space robotic arms subject to complex physical environment

A nonlinear model of a special cable in space robotic arms is developed in space environment. The mechanic effects of control cables in powerful robots can often be neglected. However, in complex space multi-physics environments, involving ultra-low temperature, radiation, and other extreme conditions of outer space, the externally mounted cables (protected by shielding layers) can induce strong nonlinear interference to robot arms; and this can induce further small-range slow rotations or oscillations of the flexible joint of robots at a specific posture, which consequently affect the precision and operation performance of end effectors. Effective mathematical models on nonlinear mechanics of strong cables under multi-physics environments and their effects on weak robots have not been well developed yet. Complex key factors, such as low gravity, nonlinear friction, and unexpected curved surface constraints, have not been extensively investigated either. In this study, considering all these key factors, a Kirchhoff nonlinear mechanical model of cables in complex space environments is developed, and a relatively improved algorithm based on a trust-region strategy is proposed for solving this nonlinear model, based on which the geometry and terminal force of the modeled robot cable can be obtained. The validity and accuracy of the proposed algorithm and theoretical calculation results are verified via experiments. The theoretical findings revealed in this study are significant to future research on the slow rotations and oscillations of weak robot joints in space exploration with robotic arms.

     

一种可观测度分析方法及在传递对准中的应用

针对卡尔曼滤波器中状态可观测度的定量分析问题,提出了一种新的可观测度分析方法。利用无系统噪声输入的动态系统初始状态的加权最小二乘估计,推导了动态系统初始状态估计误差的传递方程,将状态变量的可观测度指标定义为估计误差传递矩阵的对角线元素,从系统初始状态估计误差衰减角度定义了可观测度。推导了考虑子惯导安装矩阵的姿态观测方程,将机翼变形视为观测噪声,构建了速度加姿态匹配的传递对准模型。将可观测度分析方法应用到该传递对准模型中,结果表明:水平加速计零偏可观测度低,估计误差大,而其他状态可观测度高,估计误差小。     

基于灰色模型的混合建模预测方法及其应用

针对陀螺仪寿命预测的特点,提出了一种基于灰色模型的混合建模预测方法。为了提高一阶灰色模型GM（1,1）的建模能力,此模型引入了小波变换。首先小波变换对实测的动力调谐陀螺（DTG）漂移数据进行预处理以减少干扰噪声,接着处理后的数据被用来建立灰色模型。来自于长期测量的DTG的漂移数据的实验结果证明了文中所提混合策略的有效性。并且为了进行比较,对神经网络建模方法进行了相应的研究,结果表明当小波变换被引入到混合模型中,此基于灰色模型的混合建模预测方法具有令人满意的性能,为陀螺仪的寿命预测提供了借鉴和参考。     

基于小波变换的状态x~2改进检测算法及其应用

在惯导器件的故障检测中,针对传统的状态x2检验法无法对缓变故障持续时间进行准确判定的问题,提出一种基于小波变换的状态x2改进检测算法。该方法首先利用小波变换后的模极大值在不同尺度上的衰减速度找出信号突变点;然后将检测结果反馈给Kalman滤波器,通过引入状态修正项,修正状态误差值,使故障检测曲线能够反映缓变故障的持续时间。仿真验证表明,采用基于小波变换的状态x2检测算法较好地解决了缓变故障持续时间无法准确判定的问题,大大提高了系统故障检测的准确性。     

Experimental method of dynamic caustics and its application in fracture mechanics

The equation of static and dynamic caustics, and the formulae determining the position of crack tip and stress intensity factor are given. It is proven that for the case of low speed of crack propagation the static formula is applicable in calculation. A simple method to measure the static stress-optical constants is proposed. An Optical system which is suitable for the experiments of dynamic caustics was set-up and used to study the fracture in beam and rings with initial crack under impact loading. A series of dynamic caustics' photographs and curves showing the variations of corresponding crack lengths and dynamic stress intensity factors with time, are presented.     

参数概率灵敏度分析的神经网络方法及其应用

参数概率灵敏度分析是可靠性设计中非常重要的一项工作,它可以提供基本变量分布参数的变化引起可靠性的变化信息,为判断系统参数的重要性提供依据.本文将商用有限元计算.神经网络方法-Monte Carlo法相结合,基于这种快速响应模型的复杂结构可靠性分析方法,针对结构随机参数的概率灵敏度分析,提出一个考虑随机变量全局分散性的新...     

Effects of temperature variations on nonlinear planar free and forced oscillations at primary resonances of suspended cables

Nonlinear Dynamics - This paper is concerned with the analysis of the free and forced nonlinear vibrations of the suspended cable with thermal effects. By introducing the new thermal stressed...     

Computational method for the SPSD of dynamic systems and its application

In this paper, a new method of obtaining the stress power spectral density (SPSD) of a structure that is not through measurement but through imitative computation is presented. First, the dynamic model of a system is established. Then, considering the randomness of the load, the response spectra of the system under different random excitations and parameters are computed by numerical imitation. Last, a concept of unit load stress matrix is put forward. Based on it, the relationship between the SPSD of a structure in a system and the response spectra of the system can be obtained. In particular, the method can be used to compute the SPSD of a new type dynamic structure and to emulate dynamic fatigue life. In the process, an example of the track of a high-speed train is used to compute its SPSD, and the result is used to estimate its fatigue life and to analyze its reliability.     

Interval finite element method and its application on anti-slide stability analysis

The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements are given. The sub-interval amount is discussed and the approximate computation formula is given. At the same time, the computational precision is discussed and some measures of improving computational efficiency are given. Finally, based on sub-interval perturbed finite element method and anti-slide stability analysis method, the formula for computing the bounds of stability factor is given. It provides a basis for estimating and evaluating reasonably anti-slide stability of structures.     

A field method and its application to the theory of vibrations

The problem of integration of the differential equations of motion of a nonconservative dynamical system is replaced by an equivalent problem of finding a complete integral of a quasi-linear partial differential equation of the first order. In the second part, these complete integrals are combined with the two time scales perturbation method in the study of non-linear oscillatory motions.     

Averaging method for discrete systems and its application to control problems

We propose and justify algorithms for partial and complete averaging of systems of discrete equations and inclusions. On the basis of the averaging schemes obtained, we construct algorithms for the numerical asymptotic solution of problems of optimal control for discrete systems.Translated from Neliniini Kolyvannya, Vol. 7, No. 2, pp. 241–254, April–June, 2004.