接触碰撞动力学的多变量选取方法

在柔性多体的接触碰撞动力学问题中,多变量方法基于附加约束的接触模型,将柔性体的变形用不同变量来描述：接触局部区域的变形用有限元节点坐标描述,非接触局部区域的变形用模态坐标描述,兼顾了计算精度和效率. 将该方法推广到三维空间碰撞问题,对两柔性杆纵向碰撞过程进行动力学仿真,数值结果与实验结果吻合良好,验证了该方法的有效性. 针对柔性体各自区域的变量如何选取的问题,研究了节点取法、模态阶数以及材料参数对计算结果精度的影响,寻找到合理的多变量选取方法,保证精度的同时使自由度得到最大程度的缩减.     

柔性多体动力学的共旋坐标法

共旋坐标法作为柔性多体动力学的建模方法已经有数十年的发展历程.作为解决大转动小应变问题的可靠方法,共旋坐标法建模简单,意义明确,并且能借用现有的有限元理论,求解时效率高,精度好.因此柔性多体动力学中,共旋坐标法不仅在非线性分析中有良好的表现,在工程实际中也有较好的应用潜力.柔性多体系统动力学中的大变形问题大多涉及梁、板壳等柔性结构,有大量的大转动小应变问题需要解决.本文对采用共旋坐标法来分析梁、板壳类结构的研究中存在的若干关键问题进行了相关的讨论,如有限转动理论、局部坐标系的定义、单元类型和相应的动力学问题等.比较了各种方法的优势与局限,并且展望了共旋坐标法的发展趋势.     

柔性梁刚柔耦合碰撞动力学及变形传播研究

运用柔性多体系统刚柔耦合动力学理论,研究了作大范围回转运动柔性梁的碰撞动力学问题.考虑柔性梁的横向变形,以及横向变形引起的纵向缩短项即非线性耦合变形项.采用基于Hertz接触理论及非线性阻尼理论的非线性弹簧阻尼模型来求解碰撞过程中产生的碰撞力,运用第二类拉格朗日方程建立了系统的刚柔耦合碰撞动力学方程.编制仿真软件进行动力学仿真计算,得到了碰撞力和系统动力学响应,对比分析了不同动力学模型对系统动力学响应的影响.同时研究了碰撞导致的柔性梁横向变形传播的波动特性.     

薄板的多变量小波有限元分析

基于区间B样条小波和广义变分原理,提出了多变量小波有限元法,构造了一种新的薄板多变量小波有限单元.由广义变分原理推导结构的多变量有限元列式,区间B样条小波尺度函数作为插值函数构造的多变量小波有限元法中,广义应力和应变被作为独立变量进行插值,避免了传统方法中应力应变求解的微分运算,减小了计算误差.区间B样条小波良好的数值...     

两类基于局部标架梁单元的闭锁缓解方法

对于大转动、大变形柔性体的刚柔耦合动力学问题,基于李群SE(3)局部标架(local frame formulation, LFF)的建模方法能够规避刚体运动带来的几何非线性问题,离散数值模型中广义质量矩阵与切线刚度矩阵满足刚体变换的不变性,可明显地提高柔性多体系统动力学问题的计算效率. 有限元方法中,闭锁问题是导致单元收敛性能低下的主要原因, 例如梁单元的剪切以及泊松闭锁.多变量变分原理是缓解梁、板/壳单元闭锁的有效手段. 该方法不仅离散位移场,同时离散应力场或应变场, 可提高应力与应变的计算精度. 本文基于上述局部标架,研究几类梁单元的闭锁处理方法, 包括几何精确梁(geometrically exact beam formulation, GEBF)与绝对节点坐标(absolute nodal coordinate formulation, ANCF)梁单元. 其中, 采用Hu-Washizu三场变分原理缓解几何精确梁单元中的剪切闭锁,采用应变分解法缓解基于局部标架的ANCF全参数梁单元中的泊松闭锁. 数值算例表明,局部标架的梁单元在描述高转速或大变形柔性多体系统时,可消除刚体运动带来的几何非线性, 极大地减少系统质量矩阵和刚度矩阵的更新次数.缓解闭锁后的几类局部标架梁单元收敛性均得到了明显提升.      

冲击载荷下柔性储液罐动态响应数值模拟及规律分析

针对柔性材料大变形、非线性等特点,对柔性储液罐的冲击响应规律进行研究,依据实验结果,采用ALE有限元方法对冲击情况下柔性罐状储液容器及其中流体的动态响应进行了数值模拟.所得结果与实验结果具有较好的一致性.在此基础上,深入分析了空投高度、装水量等对柔性储液罐动态响应的影响规律.重点关注了表面一些关键部位的变形和应力变化情...     

基于绝对节点坐标法的弹性线方法研究

相比于浮动坐标系法,绝对节点坐标法(absolute nodal coordinate formulation, ANCF)在处理柔性体非线性大变形问题上具有显著优势, ANCF将单元节点坐标定义在全局坐标系下,采用斜率矢量代替节点转角坐标,具有常数质量阵,不存在科氏离心力等优点,然而弹性力阵为非线性项,其求解将比较耗时且占用资源.据此,在弹性力求解方法中,引入弹性线方法 (elastic line method, ELM),该方法将格林–拉格朗日应变张量定义在中心线上,采用曲率公式来定义弯曲应变,转角公式来定义扭转应变.同时采用有限元法对三维柔性梁位移场进行离散,求解梁单元常数质量阵、广义刚度阵、广义力阵,进而得到单元的动力学方程,通过转换矩阵得到三维梁的动力学方程.接着从理论上指出连续介质力学方法 (continuum mechanics method, CMM)和弹性线方法在求解弹性力上的不同点,并编制动力学仿真软件.最后分别采用连续介质力学方法和弹性线方法对柔性单摆以及履带式车辆的动力学问题进行仿真分析,结果表明:弹性线方法能在保证精度的前提下有效提高计算效率.     

基于绝对节点坐标法的弹性线方法研究

相比于浮动坐标系法, 绝对节点坐标法(absolute nodal coordinateformulation, ANCF)在处理柔性体非线性大变形问题上具有显著优势,ANCF将单元节点坐标定义在全局坐标系下,采用斜率矢量代替节点转角坐标, 具有常数质量阵,不存在科氏离心力等优点, 然而弹性力阵为非线性项,其求解将比较耗时且占用资源. 据此, 在弹性力求解方法中,引入弹性线方法(elastic line method, ELM),该方法将格林--拉格朗日应变张量定义在中心线上,采用曲率公式来定义弯曲应变, 转角公式来定义扭转应变.同时采用有限元法对三维柔性梁位移场进行离散,求解梁单元常数质量阵、广义刚度阵、广义力阵,进而得到单元的动力学方程, 通过转换矩阵得到三维梁的动力学方程.接着从理论上指出连续介质力学方法(continuum mechanics method,CMM)和弹性线方法在求解弹性力上的不同点, 并编制动力学仿真软件.最后分别采用连续介质力学方法和弹性线方法对柔性单摆以及履带式车辆的动力学问题进行仿真分析,结果表明:弹性线方法能在保证精度的前提下有效提高计算效率.      

基于能量等效原理的应变局部化分析:Ⅱ.有限元解法

以非局部塑性理论为基础,应用状态空间理论,通过局部和非局部两个状态空间的塑性能量耗散率等效原理,提出了一种求解应变局部化问题的新方法,以得到与网格无关的数值解.针对二维问题的屈服函数和流动法则导出了求解非局部内变量的一般方程,并提出了在有限元环境中求解应变局部化问题的应力更新算法.为了验证所提出的方法,对1个一维拉杆和3个二维平面应变加载试件进行了有限元分析.数值结果表明,塑性应变的分布和载荷-位移曲线都随着网格的变小而稳定地收敛,应变局部化区域的尺寸只与材料内尺度有关,而对有限元网格的大小不敏感.对于一维问题,当有限元网格尺寸减小时,数值解收敛于解析解.对于二维剪切带局部化问题,数值解随着网格尺寸的减小而稳定地向唯一解收敛.当网格尺寸减小时,剪切带的宽度和方向基本上没有变化.而且得到的塑性应变分布和网格变形是平滑的.这说明,所提方法可以克服经典连续介质力学模型导致的网格相关性问题,从而获得具有物理意义的客观解.此模型只需要单元之间的位移插值函数具有C~0连续性,因而容易在现有的有限元程序中实现而无需对程序作大的修改.     

无粘结预应力混凝土板火灾行为的非线性分析

火灾试验研究表明,火灾下无粘结预应力混凝土受弯构件的变形非常大,其中转动也很大,尤其是单面受火的板,是典型的材料非线性、几何非线性问题。如何对其进行精确、高效地求解是值得关注的问题。而基于S-R分解原理的更新拖带坐标有限元法有诸多优点:有利于跟踪变形物体中各点的变形;保证单元的质量守恒;在有限元增量法求解时,还可以避免对坐标的修正;而且将转动作为一个独立的自由度,提高了求解效率。在升温过程中,虽然预应力钢筋的应力处处相等,但其各点的温度不同,导致各点的温度应变、蠕变、塑性应变均不同。预应力筋必然产生滑移。本文采用该方法对火灾下无粘结预应力钢筋混凝土板进行编程分析。通过实际算例验证该算法的可靠性,该方法求解效率高,精度也比较好。     

Partition method and experimental validation for impact dynamics of flexible multibody system

The impact problem of a flexible multibody system is a non-smooth, high-transient, and strong-nonlinear dynamic process with variable boundary. How to model the contact/impact process accurately and efficiently is one of the main difficulties in many engineering applications. The numerical approaches being used widely in impact analysis are mainly from two fields: multibody system dynamics (MBS) and computational solid mechanics (CSM). Approaches based on MBS provide a more efficient yet less accurate analysis of the contact/impact problems, while approaches based on CSM are well suited for particularly high accuracy needs, yet require very high computational effort. To bridge the gap between accuracy and efficiency in the dynamic simulation of a flexible multibody system with contacts/impacts, a partition method is presented considering that the contact body is divided into two parts, an impact region and a non-impact region. The impact region is modeled using the finite element method to guarantee the local accuracy, while the non-impact region is modeled using the modal reduction approach to raise the global efficiency. A three-dimensional rod-plate impact experiment is designed and performed to validate the numerical results. The principle for how to partition the contact bodies is proposed: the maximum radius of the impact region can be estimated by an analytical method, and the modal truncation orders of the non-impact region can be estimated by the highest frequency of the signal measured. The simulation results using the presented method are in good agreement with the experimental results. It shows that this method is an effective formulation considering both accuracy and efficiency. Moreover, a more complicated multibody impact problem of a crank slider mechanism is investigated to strengthen this conclusion.     

Comparison of linear spring and nonlinear FEM methods in dynamic coupled analysis of floating structure and mooring system

This paper compares the dynamic coupled behavior of floating structure and mooring system in time domain using two numerical methods for the mooring lines such as the linear spring method and the nonlinear FEM (Finite Element Method). In the linear spring method, hydrodynamic coefficients and forces on the floating body are calculated using BEM (Boundary Element Method) and the time domain equation is derived using convolution. The coupled solution is obtained by simply adding the pre-determined spring constants of the mooring lines into the floating body equation. In FEM, the minimum energy principle is applied to formulate the nonlinear dynamic equation of the mooring system with a discrete numerical model. The ground contact model and Morison formula for drag forces are also included in the formulation. The coupled solution is obtained by iteratively solving the floating body equation and the FEM equation of the mooring system. Two example structures such as weathervane ship and semi-submersible structure are analyzed using linear spring and nonlinear FEM methods and the difference of those two methods are presented. By analyzing the cases with or without surge-pitch or sway-roll coupling stiffness of mooring lines in the linear spring method, the effect of coupling stiffness of the mooring system is also discussed.     

A new subregion mesh method for the investigation of the elastic-plastic impact in flexible multibody systems

Impact processes between flexible bodies often lead to local stress concentration and wave propagation of high frequency. Therefore, the modeling of flexible multi-body systems involving impact should consider the local plastic deformation and the strict requirements of the spa-tial discretization. Owing to the nonlinearity of the stiffness matrix, the reduction of the element number is extremely important. For the contact-impact problem, since different regions have different requirements regarding the element size, a new subregion mesh method is proposed to reduce the number of the unnecessary elements. A dynamic model for flexible multibody systems with elastic-plastic contact impact is established based on a floating frame of reference formulation and complete Lagrange incremental nonlin-ear finite-element method to investigate the effect of the elastic-plastic deformation as well as spatial discretization. Experiments on the impact between two bodies are carried out to validate the correctness of the elastic-plastic model. The proposed formulation is applied to a slider-crank system with elastic-plastic impact.     

刚体撞水非线性响应的边界元分析

考虑了非线性性液面条件液面条件,采用边界元法,始终撞水物体和水看成一个耦合系统,并作为一个冲击／接触问题处理。在自由注面的处理上,采用逐步迭代方法,使其始终满足液面的非线性条件,最终使自由液面达到一满足非线性条件的稳定值。而在撞水力的求解上,亦采用与自由液面相关的逐步迭代逼近方法,求取其稳定值。文中最后给出了几种不同情况下二维圆柱刚体撞水的计算实例,结果有力表明记叙虎法的可靠性和有效性。     

控制棒驱动机构步跃提升碰撞的动力学建模

控制棒驱动机构(CRDM)在步跃提升时,钩爪部件会与承压壳体上的提升磁极发生面面碰撞。本文基于混合坐标法建立控制棒驱动机构有限元离散的刚-柔耦合动力学方程,用罚函数法计算了钩爪部件与承压壳体之间的碰撞力和应力分布情况。结果表明,刚柔耦合多体方法在仿真小变形碰撞时可以提高计算效率,同时又能达到与有限元方法同等的精度。进一步对碰撞模型不同区域的网格疏密和尺寸大小做了定量分析,得到了降低有限元网格数量的方法,可为工程中碰撞模型的网格划分提供参考。     

大范围运动细长柔性空间结构动力学特性分析

自由-自由边界无约束状态的细长柔性空间结构大范围运动时的动力学特性对整体结构运动分析和运动控制系统设计具有极其重要的作用。通过浮动坐标系建立结构的运动学关系;借助假设模态法对结构变形进行变量分离;利用Lagrange’s方程建立了结构的刚柔耦合振动方程;再通过Rayleigh-Ritz法,以无大范围运动时的振型函数作为基本解组,得到了大范围运动影响下的结构振动特征方程,求解该方程得到了结构频率和振型。通过几组数值算例的对比分析,指出了非耦合模型和耦合模型下结构频率及振型之间的差异。     

Contact-impact formulation for multi-body systems using component mode synthesis

The efficiency and accuracy are two most concerned issues in the modeling and simulation of multi-body systems involving contact and impact. This paper proposed a formulation based on the component mode synthesis method for planar contact problems of flexible multi-body systems. A flexible body is divided into two parts： a contact zone and an un-contact zone. For the un-contact zone, by using the fixed-interface substructure method as reference, a few low-order modal coordinates are used to replace the nodal coordinates of the nodes, and meanwhile, the nodal coordinates of the local impact region are kept unchanged, therefore the total degrees of freedom （DOFs） are greatly cut down and the computational cost of the simulation is significantly reduced. By using additional constraint method, the impact constraint equations and kinematic constraint equations are derived, and the Lagrange equations of the first kind of flexible multi-body system are obtained. The impact of an elastic beam with a fixed half disk is simulated to verify the efficiency and accuracy of this method.