考虑刚-柔-热耦合的板结构多体系统的动力学建模

对热载荷作用下中心刚体与大变形薄板多体系统的动力学建模问题进行研究.基于Kirchhoff假设,从格林应变和曲率与绝对位移的非线性关系式出发,推导了非线性广义弹性力阵,用绝对节点坐标法建立了大变形矩形薄板的有限元离散的动力学变分方程.为了考虑刚体姿态运动、弹性变形和温度变化的相互耦合作用,推导了热流密度与绝对节点坐标之间的关系式.引入系统的运动学约束方程,建立了中心刚体-矩形板多体系统的考虑刚-柔-热耦合的热传导方程和带拉格朗日乘子的第一类拉格朗日动力学方程.为了有效地提高计算效率,将改进的中心差分法和广义-α法相结合,求解热传导方程和动力学方程,差分后的方程通过牛顿迭代法耦合求解.对刚-柔耦合和刚-柔-热三者耦合两种模型的仿真结果进行比较表明,刚体运动对温度梯度和热变形的影响显著.此外,本文建模方法考虑了几何非线性项,因此也考虑了热膨胀引起的轴向变形对横向变形的影响.     

基于拉格朗日描述的罐车内液体晃动模拟

基于拉格朗日描述的柔性多体系统动力学理论,采用绝对节点坐标有限元方法描述液体大变形运动,开展铁路液罐车内液体晃动模拟研究.本方法能够模拟液体自由表面的连续性变化,并适用于研究具有复杂外形容器的内部液体晃动问题.基于流体力学牛顿体基础理论,推导液体粘性方程和满足体积不可压缩的条件方程;采用基于绝对节点坐标方法描述的实体单元进行液体网格划分;采用罚函数方法描述液体与罐体之间的接触关系,组建液体-罐体耦合多体系统动力学方程.仿真计算液罐车内液体的横向和纵向晃动行为,发现液体自由表面形状呈非线性变化,不同断面处的高度和形状不同.     

中心刚体-柔性梁刚柔耦合动力学模型降阶研究

有限单元法被广泛的采用来描述柔性体的弹性变形,然而有限元节点坐标数目庞大,将会给动力学方程求解带来巨大的计算负担.如何降低柔性体的自由度,是当前柔性多体系统动力学研究的一个重要命题.本文以中心刚体-柔性梁系统为例,采用Krylov方法和模态方法进行降价.然后分别采用有限元全模型、Krylov降阶模型和模态降阶模型,对中心刚体-柔性梁进行刚-柔耦合动力学仿真.仿真结果表明,与采用模态降阶方法相比,采用Krylov模型降阶方法只需要较低的自由度,就可以得到与采用有限元方法完全一致的结果.说明Krylov模型降阶方法能够有效的用于柔性多体系统的模型降价研究.     

多体系统中规则柔性板的离散建模方法研究

把柔性梁的离散坐标法有限段法扩展到规则柔性板中,视柔性板为带关节柔性(刚度、阻尼)的多刚体系统,详细阐述了离散坐标法的基本思想、理论依据,采用牛顿欧拉方法建立了动力学方程.借助通用有限元软件和动力学仿真程序验证了离散坐标法可以解决具有几何非线性变形的规则柔性板构件的多体系统动力学问题.     

柔性航天器动力学建模及模型降阶研究

针对柔性航天器振动影响飞行器姿态稳定性和精度.为了解决上述问题,提出了多柔体航天器的动力学建模.首先,根据工程实现的假设振型法,采用拟坐标拉格朗日方程,推导出带有刚体模态的二阶系统刚柔耦合动力学模型,其中,为了减少模型计算量,通过坐标变换将刚体模态和柔性模态解耦,利用一种刚体模态解耦的二阶不稳定系统的模型降阶方法,并对航天器多柔体系统动力学方程进行了仿真分析,结果飞行姿态稳定,满足了精度要求,表明了动力学建模与模型降阶法的有效性和正确性.     

绝对节点坐标法下斜率不连续问题处理方法讨论

Shabana提出的绝对节点坐标法,引入节点斜率坐标作为节点自由度描述转动.对于由梁板壳及块体组成的组合结构,在结构节点处相交单元的节点斜率自由度不连续,这给组合结构的建模和分析带来特殊的困难.本文讨论了文献中研究斜率不连续问题时的处理办法.在简要介绍绝对节点坐标法后,详细地讨论了经典折梁算例和截面呈阶梯变化的直梁算例中斜率不连续问题.对这两个算例,本文采用约束函数法和现有文献中的转换坐标方法,计算了在结构节点处相交杆件的轴向应变,对比这些数值结果,本文指出现有文献中的转换坐标办法,忽视了斜率自由度和转角自由度的差别,从而不能正确给出斜率不连续处相交杆件的轴向应变,需要进一步研究.     

变拓扑柔性多体系统接触碰撞动力学研究

在实际工程领域中存在着大量接触碰撞等非连续动力学问题,现有的解决柔性多体系统连续动力学过程的建模理论与方法,已经无法解决或无法很好解决这些问题.本文基于变拓扑思想,提出了附加接触约束的柔性多体系统碰撞动力学建模理论；通过设计柔性圆柱杆接触碰撞实验,验证了所提出附加约束接触碰撞模型的有效性；针对柔性多体系统全局动力学仿真面临时间和空间的多尺度问题,提出多变量的离散方法,从而提高了柔性多体系统非连续动力学的仿真效率.     

考虑热效应的复合材料多体系统动力学研究

研究离心力和温度变化引起的附加弯曲变形对复合材料柔性多体系统振动特性的影响．从本构关系和非线性应变与位移关系式出发,用虚功原理和有限单元法建立了复合材料柔性梁的动力学变分方程,在此基础上建立了复合材料柔性多体系统的动力学方程．对曲柄-连杆-滑块机构的数值仿真表明,对于非对称的复合材料梁,各层弹性模量和热膨胀系数的差异会引起附加弯曲变形,从而影响系统的振动特性．     

高超声速折叠翼展开动力学研究

折叠翼飞行器在飞行过程中通过机翼的展开与折叠,来满足不同飞行任务时的最优飞行性能.在飞行过程中,折叠翼能够顺利展开并安全锁定是折叠翼飞行器顺利完成任务的根本原因之一.因此,针对高超声速折叠翼被动展开过程,研究其精确动力学建模与仿真,优化系统参数与飞行姿态,使得折叠翼展开锁定后的冲击响应满足结构要求.首先,采用绝对节点坐标法建立柔性折叠翼的柔性多体系统动力学模型,采用活塞理论建立气动力模型,从而形成折叠翼的柔-流耦合动力学模型,并采用广义a算法求解.其次,研究被动展开扭杆参数、阻力扭簧参数与飞行姿态等对高超声速折叠翼被动展开动态过程的影响,优化系统参数,有效降低展开锁定后的冲击响应.     

新型三角形弹簧质点模型及弹簧参数确定

针对任意单元形状和材料参数,通过引入附加节点和附加弹簧建立了一种三角形弹簧质点模型.首先给出弹簧刚度参数及附加节点坐标的解析公式,以实现有限元模型和弹簧质点模型三角形单元刚度矩阵的精确相等;然后考虑弹簧质点模型中可能出现的负刚度弹簧,进一步完善了弹簧质点模型形变计算方法.基于平面柔性体的数值模拟结果表明,文中提出的弹簧质点模型和形变计算方法精度好、效率高,且更具通用性.     

Flexible Multibody Systems Models Using Composite Materials Components

The use of a multibody methodology to describe the large motion of complex systems that experience structural deformations enables to represent the complete system motion, the relative kinematics between the components involved, the deformation of the structural members and the inertia coupling between the large rigid body motion and the system elastodynamics. In this work, the flexible multibody dynamics formulations of complex models are extended to include elastic components made of composite materials, which may be laminated and anisotropic. The deformation of any structural member must be elastic and linear, when described in a coordinate frame fixed to one or more material points of its domain, regardless of the complexity of its geometry. To achieve the proposed flexible multibody formulation, a finite element model for each flexible body is used. For the beam composite material elements, the sections properties are found using an asymptotic procedure that involves a two-dimensional finite element analysis of their cross-section. The equations of motion of the flexible multibody system are solved using an augmented Lagrangian formulation and the accelerations and velocities are integrated in time using a multi-step multi-order integration algorithm based on the Gear method.     

A Deformation Field for Euler–Bernoulli Beams with Applications to Flexible Multibody Dynamics

The deformation field commonly used for Euler–Bernoulli beamsin structural dynamics is investigated to determine its suitability foruse in flexible multibody dynamics. It is found that the traditionaldeformation field fails to produce an elastic rotation matrix that iscomplete to second-order in the deformation variables. A completesecond-order deformation field is proposed along with the equationsneeded to incorporate the beam model into a graph-theoretic formulationfor flexible multibody dynamics [1]. This beam modeland formulation have been implemented in a symbolic computer programcalled DynaFlex that can use Taylor, Chebyshev, or Legendrepolynomials as the basis functions in a Rayleigh–Ritz discretizationof the beam's deformation variables. To demonstrate the effects of the proposed second-order deformationfield on the response of a flexible multibody system,two examples are presented.     

A formal procedure and invariants of a transition from conventional finite elements to the absolute nodal coordinate formulation

In this paper, finite elements based on the absolute nodal coordinate formulation (ANCF) are studied. The formulation has been developed by various authors for the dynamical simulation of large-displacement and large-rotation problems in flexible multibody dynamics. This study introduces a procedure to track the general geometrical properties of ANCF elements back to their prototypes in the conventional finite-element method (FEM), which deals with small-displacement problems. In this study, it is shown that each known ANCF element can be derived from a conventional FEM using a universal transform. Moreover, some important static and dynamic properties of the elements in small-displacement problems are automatically preserved. In the past, the authors of each newly proposed ANCF element have made unnecessary efforts to show the consistency of the above mentioned properties.     

Developments of multibody system dynamics: computer simulations and experiments

It is an exceptional success when multibody dynamics researchers Multibody System Dynamics journal one of the most highly ranked journals in the last 10 years. In the inaugural issue, Professor Schiehlen wrote an interesting article explaining the roots and perspectives of multibody system dynamics. Professor Shabana also wrote an interesting article to review developments in flexible multibody dynamics. The application possibilities of multibody system dynamics have grown wider and deeper, with many application examples being introduced with multibody techniques in the past 10 years. In this paper, the development of multibody dynamics is briefly reviewed and several applications of multibody dynamics are described according to the author’s research results. Simulation examples are compared to physical experiments, which show reasonableness and accuracy of the multibody formulation applied to real problems. Computer simulations using the absolute nodal coordinate formulation (ANCF) were also compared to physical experiments; therefore, the validity of ANCF for large-displacement and large-deformation problems was shown. Physical experiments for large deformation problems include beam, plate, chain, and strip. Other research topics currently being carried out in the author’s laboratory are also briefly explained. Commemorative Contribution.     

Validation of flexible multibody dynamics beam formulations using benchmark problems

As the need to model flexibility arose in multibody dynamics, the floating frame of reference formulation was developed, but this approach can yield inaccurate results when elastic displacements becomes large. While the use of three-dimensional finite element formulations overcomes this problem, the associated computational cost is overwhelming. Consequently, beam models, which are one-dimensional approximations of three-dimensional elasticity, have become the workhorse of many flexible multibody dynamics codes. Numerous beam formulations have been proposed, such as the geometrically exact beam formulation or the absolute nodal coordinate formulation, to name just two. New solution strategies have been investigated as well, including the intrinsic beam formulation or the DAE approach. This paper provides a systematic comparison of these various approaches, which will be assessed by comparing their predictions for four benchmark problems. The first problem is the Princeton beam experiment, a study of the static large displacement and rotation behavior of a simple cantilevered beam under a gravity tip load. The second problem, the four-bar mechanism, focuses on a flexible mechanism involving beams and revolute joints. The third problem investigates the behavior of a beam bent in its plane of greatest flexural rigidity, resulting in lateral buckling when a critical value of the transverse load is reached. The last problem investigates the dynamic stability of a rotating shaft. The predictions of eight independent codes are compared for these four benchmark problems and are found to be in close agreement with each other and with experimental measurements, when available.     

Absolute nodal coordinate plane beam formulation for multibody systems dynamics

A new plane beam dynamic formulation for constrained multibody system dynamics is developed. Flexible multibody system dynamics includes rigid body dynamics and superimposed vibratory motions. The complexity of mechanical system dynamics originates from rotational kinematics, but the natural coordinate formulation does not use rotational coordinates, so that simple dynamic formulation is possible. These methods use only translational coordinates and simple algebraic constraints. A new formulation for plane flexible multibody systems are developed utilizing the curvature of a beam and point masses. Using absolute nodal coordinates, a constant mass matrix is obtained and the elastic force becomes a nonlinear function of the nodal coordinates. In this formulation, no infinitesimal or finite rotation assumptions are used and no assumption on the magnitude of the element rotations is made. The distributed body mass and applied forces are lumped to the point masses. Closed loop mechanical systems consisting of elastic beams can be modeled without constraints since the loop closure constraints can be substituted as beam longitudinal elasticity. A curved beam is modeled automatically. Several numerical examples are presented to show the effectiveness of this method.     

First order sensitivity analysis of flexible multibody systems using absolute nodal coordinate formulation

Design sensitivity analysis of flexible multibody systems is important in optimizing the performance of mechanical systems. The choice of coordinates to describe the motion of multibody systems has a great influence on the efficiency and accuracy of both the dynamic and sensitivity analysis. In the flexible multibody system dynamics, both the floating frame of reference formulation (FFRF) and absolute nodal coordinate formulation (ANCF) are frequently utilized to describe flexibility, however, only the former has been used in design sensitivity analysis. In this article, ANCF, which has been recently developed and focuses on modeling of beams and plates in large deformation problems, is extended into design sensitivity analysis of flexible multibody systems. The Motion equations of a constrained flexible multibody system are expressed as a set of index-3 differential algebraic equations (DAEs), in which the element elastic forces are defined using nonlinear strain-displacement relations. Both the direct differentiation method and adjoint variable method are performed to do sensitivity analysis and the related dynamic and sensitivity equations are integrated with HHT-I3 algorithm. In this paper, a new method to deduce system sensitivity equations is proposed. With this approach, the system sensitivity equations are constructed by assembling the element sensitivity equations with the help of invariant matrices, which results in the advantage that the complex symbolic differentiation of the dynamic equations is avoided when the flexible multibody system model is changed. Besides that, the dynamic and sensitivity equations formed with the proposed method can be efficiently integrated using HHT-I3 method, which makes the efficiency of the direct differentiation method comparable to that of the adjoint variable method when the number of design variables is not extremely large. All these improvements greatly enhance the application value of the direct differentiation method in the engineering optimization of the ANCF-based flexible multibody systems.     

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.