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...     

求解大柔度梁/绳索的ANCF单元及隐式迭代格式

为模拟大柔度梁/绳索结构的变形和大范围运动,基于绝对节点坐标方法ANCF(Absolute nodal coordi-nate formulation)和HHT(Hilber-Hughes-Taylor)积分方法,建立了ANCF单元的隐式动力学迭代格式.得到了简洁的节点等效力向量,且进一步导出了切线刚度矩阵的全部公式,...     

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.

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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.

     

JC本构参数反求中的自适应微型遗传算法

提出自适应微型遗传算法,使种群的交叉和变异概率可以根据适应度的大小自我调节,该算法经过了测试函数的测试。本文以JC(Johnson-Cook)本构模型描述的高导无氧铜材料为例,集成运用该算法和有限元方法来反求JC动态本构参数。结果表明,该方法提高了收敛速度和搜索效率,能够快速地获取参数。     

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。     

用无单元法求解河道水流运动方程

本文通过引入滑动最小二乘法和有限差分法,得到水动力学无单元计算法并应用于复杂边界的河道水流运动方程,实际计算表明,该方法精度高,速度快,稳定性也较好。     

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.

     

Adaptive mesh refinement‐enhanced local DFD method and its application to solve Navier–Stokes equations

Recently, the domain‐free discretization (DFD) method was presented to efficiently solve problems with complex geometries without introducing the coordinate transformation. In order to exploit the high performance of the DFD method, in this paper, the local DFD method with the use of Cartesian mesh is presented, where the physical domain is covered by a Cartesian mesh and the local DFD method is applied for numerical discretization. In order to further improve the efficiency of the solver, the newly developed solution‐based adaptive mesh refinement (AMR) technique is also introduced. The proposed methods are then applied to the simulation of natural convection in concentric annuli between a square outer cylinder and a circular inner cylinder. Numerical experiments show that the present numerical results agree very well with available data in the literature, and AMR‐enhanced local DFD method is an effective tool for the computation of flow problems. Copyright © 2005 John Wiley & Sons, Ltd.     

改进的HLLC方法及其在Baer-Nunziato模型中的应用

波速估计对HLLC方法的计算影响较大,如果取值过小,则不能抓住波系特征;如果取值过大,则会引入较大的粘性。如何确定波速已有大量的研究,但是每种方法都有一定的适用范围。本文提出一种可避免估计波速的HLLC方法,并应用于两相流Baer-Nunziato模型模拟。本文方法与三种经典的波速估计方法进行比较,针对几类典型的B-N模型初值问题,不同的波速估计方法模拟能力差异较大,而本文方法可以自动确定适当的波速,因此得到较好的模拟结果。     

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。     

应用于弹性问题的重心有限元法

摘要：通过几何的方法构造了在任意多边形上的具有重心型格式的平均值插值函数,并利用Galerkin法提出了应用于弹性问题的重心有限元法。重心有限元法的插值函数在多边形单元间是协调的,能够方便的施加本质边界条件。重心有限元法的插值函数对于不同边数的多边形单元具有统一的表达形式,编程实现简便易行,能够方便的应用于复杂几何区域的求解。通过重心有限元法分别进行了小片试验、悬臂梁和复合材料的有效模量的数值模拟。小片试验的计算精度达到了机器精度;悬臂梁的计算结果与解析解的吻合程度较高;复合材料的有效模量的数值模拟结果与传统有限元和解析解吻合得较好,变化趋势合理。     

Stability analysis method considering non-parallelism: EPSE method and its application

The e-N method is widely used in transition prediction. The amplitude growth rate used in the e-N method is usually provided by the linear stability theory (LST) based on the local parallel hypothesis. Considering the non-parallelism effect, the parabolized stability equation (PSE) method lacks local characteristic of stability analysis. In this paper, a local stability analysis method considering non-parallelism is proposed, termed as EPSE since it may be considered as an expansion of the PSE method. The EPSE considers variation of the shape function in the streamwise direction. Its local characteristic is convenient for stability analysis. This paper uses the EPSE in a strong non-parallel flow and mode exchange problem. The results agree well with the PSE and the direct numerical simulation (DNS). In addition, it is found that the growth rate is related to the normalized method in the non-parallel flow. Different results can be obtained using different normalized methods. Therefore, the normalized method must be consistent.     

Mixed hybrid penalty finite element method and its application

The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner——one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u∈H³ with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.     

防波堤基础的爆炸处理方法及应用

采用了爆炸法处理地基的新方法:它包括堤端推进爆填、边坡拓宽爆填、加抛密实爆夯、边坡整理爆夯等方法。通过玉环坎门防波堤工程中的应用、观察和比较,表明此方法能够比较彻底地置换淤泥层,夯实堆石体,形成符合设计要求的各部位尺寸及深度。     

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。