A criterion on inclusion of stress stiffening effects in flexible multibody dynamic system simulation

This paper presents a criterion on inclusion of stress stiffening effects in dynamic simulation of flexible multibody systems. The proposed criterion examines numerically the eigenvalue variation of the total modal stiffness matrix that is a combination of the modal stress stiffness matrix and the conventional linear modal stiffness matrix prior to actual dynamic simulation. If the variation is sufficiently large for any flexible body in the multibody system, then stress stiffening effects must be included in dynamic simulation of flexible multibody systems for accurate prediction of dynamic behavior. Since the criterion uses the most general stress stiffness matrix contributed from applied and constraint reaction loads as well as from a system of 12 inertial loads, this criterion is applicable to any general flexible multibody dynamic system. Several numerical results are presented to show the effectiveness of the proposed criterion.     

Erratum to: New efficient method for dynamic modeling and simulation of flexible multibody systems moving in plane

Efficient, precise dynamic analysis for general flexible multibody systems has become a research focus in the field of flexible multibody dynamics. In this paper, the finite element method and component mode synthesis are introduced to describe the deformations of the flexible components, and the dynamic equations of flexible bodies moving in plane are deduced. By combining the discrete time transfer matrix method of multibody system with these dynamic equations of flexible component, the transfer equations and transfer matrices of flexible bodies moving in plane are developed. Finally, a high-efficient dynamic modeling method and its algorithm are presented for high-speed computation of general flexible multibody dynamics. Compared with the ordinary dynamics methods, the proposed method combines the strengths of the transfer matrix method and finite element method. It does not need the global dynamic equations of system and has the low order of system matrix and high computational efficiency. This method can be applied to solve the dynamics problems of flexible multibody systems containing irregularly shaped flexible components. It has advantages for dynamic design of complex flexible multibody systems. Formulations as well as a numerical example of a multi-rigid-flexible-body system containing irregularly shaped flexible components are given to validate the method.     

An efficient computational method for dynamic stress analysis of flexible multibody systems

This paper presents an efficient computational method of dynamic stress history calculation for a general three-dimensional flexible body by combining flexible multibody dynamic simulation and quasi-static finite element analysis (FEA). In the dynamic simulation of flexible multibody systems, flexible components can undergo nonsteady gross motion and small elastic deformation that is described with respect to the body reference frame by using the assumed mode method. D'Alembert inertia loads from the gross body motion and the elastic deformation are expressed as a combination of space-dependent and time-dependent terms that are obtained from the dynamic simulation. D'Alembert inertia loads that are associated with each unit value of the time-dependent terms are then distributed to all finite element nodes in order to compute a corresponding stress influence coefficient through quasi-static structural analyses. Total dynamic stresses due to D'Alembert inertia loads are obtained by multiplying actual magnitude of time-dependent terms with the associated stress influence coefficients. By the proposed method, it is shown that, for a general three-dimensional component, the required number of FEAs can be significantly reduced.     

New efficient method for dynamic modeling and simulation of flexible multibody systems moving in plane

Efficient, precise dynamic analysis for general flexible multibody systems has become a research focus in the field of flexible multibody dynamics. In this paper, the finite element method and component mode synthesis are introduced to describe the deformations of the flexible components, and the dynamic equations of flexible bodies moving in plane are deduced. By combining the discrete time transfer matrix method of multibody system with these dynamic equations of flexible component, the transfer equations and transfer matrices of flexible bodies moving in plane are developed. Finally, a high-efficient dynamic modeling method and its algorithm are presented for high-speed computation of general flexible multibody dynamics. Compared with the ordinary dynamics methods, the proposed method combines the strengths of the transfer matrix method and finite element method. It does not need the global dynamic equations of system and has the low order of system matrix and high computational efficiency. This method can be applied to solve the dynamics problems of flexible multibody systems containing irregularly shaped flexible components. It has advantages for dynamic design of complex flexible multibody systems. Formulations as well as a numerical example of a multi-rigid-flexible-body system containing irregularly shaped flexible components are given to validate the method.     

A general model of the dynamics of moving and rotating rods

A general and accurate model of a curved rod that roates and moves in a linear motion is presented. Any kind of motion can be dealt with. Large deformations of the rod are allowed. The inertia loads are accurate and for this reason a matrix notation is used throughout the whole derivation of these loads. Special attention is devoted in order to describe the motions at the point of attachment of the rod in cases where the rod is not moving freely in space. The equations of motion, their derivation and solution are described in detail. The capabilities of the model are presented by solving representative examples.     

Dynamic response of plate to moving loads: Structural impedance method

An algorithm based on a structural impedance approach has been developed to study the transient response of plates with arbitrary boundary conditions and subjected to moving loads. Thin plate theory is assumed for the plate model and the algorithm places no restrictions on the loading conditions. The algorithm accounts for the complete dynamic interactions between the moving loads and the plate. Therefore, the method can be applied to the general moving mass problems and to the simplified moving force and static problems. The accuracy of the algorithm is verified by comparing the results obtained from the structural impedance method (SIM), in the case of moving force solutions, with the available exact solutions and with other numerical results. The dynamic deflections obtained from the moving mass solutions are compared with available experimental results. Parametric analyses over a wide spectrum of velocities and mass ratios indicate that the inertial effect on dynamic deflections is pronounced when the vehicle is traveling at high speed.     

Numerical methods for analysis of structure and ground vibration from moving loads

An overview of the main theoretical aspects of finite-element and boundary-element modelling of the response to moving loads is given. The moving loads represent sources of noise and vibration generated by moving vehicles, and the analysis describes the propagation of the disturbances generated in soil. A finite-element time-domain analysis in convected coordinates with a simple upwind scheme is presented, including a special set of boundary conditions permitting the passage of outgoing waves in the convected coordinate system. The modification of frequency-dependent damping to convected coordinates is described, and the convected formulation of boundary elements is presented and used for illustrating the effect of ‘high-speed’ motion. Finally, a procedure for the coupling of a local finite-element model with a boundary-element model of an exterior, or open, domain is described. The paper uses recent results from the Danish research programme ‘Damping Mechanisms in Dynamics of Structures and Materials’ as a basis for a general discussion and review of the recent literature on the subject.     

Advances in the analysis of short span railway bridges for high-speed lines

The physical model based on moving constant loads is widely used for the analysis of railway bridges. Nevertheless, the moving loads model is not well suited for the study of short bridges (L⩽20–25 m) since the results it produces (displacements and accelerations) are much greater than those obtained from more sophisticated ones. In this paper two factors are analysed which are believed to have an influence in the dynamic behaviour of short bridges. These two factors are not accounted for by the moving loads model and are the following: the distribution of the loads due to the presence of the sleepers and ballast layer, and the train–bridge interaction. In order to decide on their influence several numerical simulations have been performed. The results are presented and discussed herein.     

Finite element procedures for nonlinear structures in moving coordinates. Part 1: Infinite bar under moving axial loads

This paper deals with analyzing nonlinear structures under high-speed moving loads by use of the finite element method. The stationary response of an infinite bar posed on a Winkler foundation under constant moving loads is investigated. Instead of the transient analysis, the stationary solution of this problem is obtained by solving a static system in a reference frame which moves with the load for reducing the computation cost. To overcome the difficulty due to numerical instabilities when considering very fast loads (supersonic loads), a new procedure to govern the finite element formulation in moving coordinates is proposed. Comparing numerical solutions with analytical ones shows that the proposed method is valid for all values of load speed. Last, an example of nonlinear elastic foundation is considered to outline the nonlinear effects.     

Optimization of flexible components of multibody systems via equivalent static loads

An optimization methodology that iteratively links the results of multibody dynamics and structural analysis software to an optimization method is presented to design flexible multibody systems under dynamic loading conditions. In particular, rigid multibody dynamic analysis is utilized to calculate dynamic loads of a multibody system and a structural optimization algorithm using equivalent static loads transformed from the dynamic loads are used to design the flexible components in the multibody dynamic system. The equivalent static loads, which are derived from equations of motion, are used as multiple loading conditions of linear structural optimization. A simple example is solved to verify the proposed methodology and the pelvis part of the biped humanoid, a complex multibody system which consists of many bodies and joints, is redesigned using the proposed methodology.     

Discrete element analysis of dynamic response of Timoshenko beams under moving mass

In this paper, dynamic response of Timoshenko beams under moving mass is analyzed using a numerical method called discrete element technique (DET). In DET, continuous flexible beam elements are replaced by a system of rigid bars and flexible joints. We present a DET model of Timoshenko beams under moving mass. The results of our DET model are compared with the solutions obtained by PAFEC (programs for automatic finite element calculations) for Euler–Bernoulli beams and finite difference method for Timoshenko beams. The effects of beam thickness and moving mass velocity on dynamic response of beams under moving mass are numerically studied.     

移动荷载作用下非线性基础梁内共振分析

研究了有限长弹性基础上梁在移动载荷作用下的内共振响应.建立了移动集中力激励的非线性粘弹性基础支承的有限长Euler-Bernoulli梁模型,并对非线性偏微分方程进行离散,在第三阶固有频率与第一阶固有频率成三倍关系时,采用多尺度方法导出了3:1内共振的可解性条件,研究了有无移动载荷时基础阻尼和非线性刚度对梁内共振条件下自由振动响应和受迫振动响应的影响规律.在此基础上,应用Lyapunov第一方法确定了系统的稳定性条件.     

Stiffness requirement of flexible skin for variable trailing-edge camber wing

The method for analyzing the deformation of flexible skin under the air loads was developed based on the panel method and finite element method.The deformation of flexible skin under air pressures and effects of the local deformation on the aerodynamic characteristics were discussed.Numerical results show that the flexible skin on the upper surface of trailing-edge will bubble under the air loads and the bubble has a powerful effect on the aerodynamic pressure near the surface of local deforma-tion.Then the...     

Configuration Tracking for Continuum Manipulators With Coupled Tendon Drive

Robotic control of flexible devices can enhance and simplify many medical procedures. We present a method for controlling a tendon-driven continuum manipulator by means of specifying the shape configuration. The basis for control is a linear beam configuration model that transforms beam configuration to tendon displacement by modeling internal loads of the compliant system. An essential aspect of this model is the inclusion of both the mechanical and geometrical coupling among serial articulating sections. Important capabilities of this model are the general forward kinematics and the decoupled inverse kinematics that allow for independent control of multiple sections. Tracking results are presented for a cardiac catheter with two articulating sections.      

Analytical and numerical study of the effects of an elastically-linked body on sloshing

In order to investigate the effects of an elastically-linked moving body on liquid sloshing inside a tank, an analytical formulation and a numerical approach were proposed to assess hydrodynamic loads in a partially filled rectangular tank with a body connected to the tank by springs. The analytical approach was developed based on the potential theory to calculate fluid velocity field, and the dynamics of the liquid sloshing coupled to the moving body are described as a mechanical system with two degrees of freedom. The coupling between the fluid and the moving body is given by a damping force calculated based on the body geometry and the fluid velocity field. The proposed numerical approach is based on the Moving Particle Semi-implicit (MPS) method, which is a Lagrangian particle-based method and very effective to model nonlinear hydrodynamics due to fluid–structure interaction. In the numerical approach, the rigid body is modeled as a cluster of particles and the motions are calculated considering its mass, moment of inertia, hydrodynamic loads and springs restoring forces. The elastic link between the body and tank is modeled by applying Hooke’s law. Simple cases of floating body motion were used to validate the numerical method. Finally, analytical and numerical results were compared. Despite its simplicity, the analytical approach proposed in the present work is an efficient approach to provide qualitative understanding and a first estimate of the moving body effects on the sloshing inside the tank. On the other hand, the numerical approach can provide more detailed information about the coupling phenomena, and it is an effective mean for the assessment of the reduction of the sloshing loads due to the moving body with elastic link. Finally, the effectiveness of the concept as a sloshing suppressing device is also investigated.     

Optimization of airplane wing structures under taxiing loads

A methodology is presented for the optimum design of aircraft wing structures subjected to taxiing loads. The dynamic stresses induced in the wing as the airplane accelerates or decelerates on the runway during take-off or landing are computed by considering the interaction between the landing gear and the flexible airplane structure. The procedure is capable of taking into account both the effects of discrete runway bumps and the effects of runway unevenness. A numerical step-by-step method is developed for solving the nonlinear differential equations of motion. The optimization methodology is illustrated with two examples. The first example deals with the design of the typical section (symmetric double wedge airfoil). This example is studied by using a graphical procedure mainly to understand qualitatively the behavior of wing structures under taxiing loads and also to obtain a physical insight into the nature of the optimum solution. The second example is concerned with the design of a more realistic wing structure. In this case, the problem is formulated and solved as a constrained nonlinear programming problem based on finite element modeling.     

提高柔性机器人运动状态下固有频率的一种方法

对提高柔性机器人运动状态下的固有频率进行了研究．首先分析了影响柔性机器人固有频率的因素，得出了在结构参数不变的情况下，可以通过适当调整运动参数来提高机器人固有频率的结论；然后研究了机器人的初始位形与运动参数的关系，提出了通过规划机器人的初始位形来调整运动参数从而提高机器人在运动状态下的固有频率的方法，并且给出了相应的算法；最后通过数值仿真验证了该方法的有效性．     

Moving robot’s mind of autonomous decentralized FMS and mind change control

This article describes the control of moving robots in an autonomous decentralized flexible manufacturing system (FMS) by changing the mind of the moving robot. In an autonomous decentralized flexible manufacturing system where a lot of moving robots operate, there are problems of path interference. There is an existing method which we have developed called AAA, and this is used to evade these interference problems. However, using this method, it is very difficult to grasp entirely the innumerable path interference situations that really occur. Therefore, to evade these unexpected situations flexibly, we propose a mind model, which is the complicated expression of combinations of three elements: stimulation vector, unit, and load. Even if a familiar situation happens, moving robots can make different actions when their mind is changed.     

An approach for modeling long flexible bodies with application to railroad dynamics

Considering track flexibility in railroad vehicle simulations can lead to improved results. In modeling a railroad vehicle as a multibody system, track flexibility can be incorporated by using the floating frame of reference formulation (FFRF), which describes rail deformations in terms of shape functions defined in the track body frame of reference. However, the FFRF method is subject to two serious shortcomings, namely: it uses unreal track boundary conditions to calculate shape functions and requires a large number of functions to describe deformation. These shortcomings can be circumvented by defining shape functions in the trajectory frame of reference. Based on this notion, a new form of FFRF that can be used to describe the dynamics of long bodies subjected to moving loads (cable cars, zip-lines, elevator guides, pantograph catenary mechanism, etc.) was developed here. The shape functions selected in this work are based on the steady deformation exhibited by a beam on a Winkler foundation under the action of a moving load. However, other sets of shape functions more appropriate for transient dynamics are suggested. The definition of the deformation shape functions in a frame that moves with respect to the flexible body produces new terms in the generalized inertia forces of the flexible track. The proposed approach was applied to an unsuspended wheelset traveling on a tangent track supported on an elastic foundation. The results thus obtained under variable foundation stiffness conditions are discussed and comparisons made with the case of a rigid track. The new approach is also compared with the moving mass problem as solved with the mode superposition method.     

基于多尺度空间划分与路网建模的城市移动轨迹模式挖掘

针对城市移动轨迹模式挖掘问题展开研究, 提出移动全局模式与移动过程模式相结合的挖掘方法, 即通过移动轨迹的起始位置点--终点位置点 (Origin-destination, OD点) 与移动过程序列分别进行移动全局模式与过程模式的发现. 在移动全局模式发现中, 提出了弹性多尺度空间划分方法, 避免了硬性等尺度网格划分对密集区域边缘的破坏, 同时增强了密集区域与稀疏区域的区分能力.在移动过程模式发现中, 提出了基于移动轨迹的路网拓扑关系模型构建方法, 通过路网关键位置点的探测抽取拓扑关系模型.最后基于空间划分集合与路网拓扑模型对原始 移动轨迹数据进行序列数据转换与频繁模式挖掘. 通过深圳市出租车历史 GPS 轨迹数据的实验结果表明, 该方法与现有方法相比在区域划分、数据转换等方面具有更好的性能, 同时挖掘结果语义更为丰富, 可解释性更强.