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.

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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。     

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.     

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。     

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。     

A discrete nonlinear stepping optimization method and its application

Most of the practical design variables should always be discrete quantity within engineering optimization design problems. To obtain the true optimization solution, a discrete optimization method must be used. In this paper, a new method called step optimization search method is presented to solve the discrete quantity mathematic programming problems. The basic idea of this method is to find out an initial feasible point and then to search the optimum point step by step in the neighbouring region of this point so as to obtain an improved new discrete point. Respectively, the new point can be taken as initial one, and the whole process can be carried out once more until the optimum solution of the problem is obtained. Some results of numerical examples of practical problems show that this new method can solve problems quickly and simply and can be applied in a lot of engineering design problems.     

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。     

并行有限元网格生成方法及其应用

大型工程数值仿真中,在前处理阶段需要生成千万甚至亿量级的网格,传统的串行网格生成方法由于内存和时间的限制,难以处理如此规模的网格。针对此问题,本文提出了一种大规模网格并行生成方法。首先基于推进波前法对几何模型进行初始体网格划分,接着利用图论理论进行区域分解,并通过表面单元恢复保持其几何精度,然后通过分裂法进行网格的并行生成。将所述方法应用到实际大型工程数值仿真前处理阶段,结果表明所述方法可以获得较好的并行效率,同时所产生的网格质量可以满足后续计算需要。     

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.     

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。     

超级有限元法及其在结构工程中的应用

本文探讨一种基于半连续半离散思想，适用于复杂结构（如高层框架、剪力墙、桁架、网架等结构系统）工程分析的超级有限元，其结构数值分析是按连续体进行，但又按单个构件进行有限元计算。这种按整体系统进行离散所获得的单元内部包含众多构件，有别于一般常见的实体有限元，称为“超级有限元”。这种方法自由度数比一般有限元法少很多，又与单元内部所含构件数多少无关，并可求取结构内每个构件的内力值。