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刘海生, 张润森, 张腾, 刘铖. 局部标架的共旋Timoshenko梁单元多体动力学数值特性分析[J]. 力学学报.
引用本文: 刘海生, 张润森, 张腾, 刘铖. 局部标架的共旋Timoshenko梁单元多体动力学数值特性分析[J]. 力学学报.
NUMERICAL ANALYSIS OF MULTIBODY DYNAMICS CHARACTERISTICS OF THE CO-ROTATIONAL TIMOSHENKO BEAM ELEMENT BASED ON THE LOCAL FRAME FORMULATION[J]. Chinese Journal of Theoretical and Applied Mechanics.
Citation: NUMERICAL ANALYSIS OF MULTIBODY DYNAMICS CHARACTERISTICS OF THE CO-ROTATIONAL TIMOSHENKO BEAM ELEMENT BASED ON THE LOCAL FRAME FORMULATION[J]. Chinese Journal of Theoretical and Applied Mechanics.

局部标架的共旋Timoshenko梁单元多体动力学数值特性分析

NUMERICAL ANALYSIS OF MULTIBODY DYNAMICS CHARACTERISTICS OF THE CO-ROTATIONAL TIMOSHENKO BEAM ELEMENT BASED ON THE LOCAL FRAME FORMULATION

  • 摘要: 多柔体系统的动力学过程不仅包含结构大范围刚体运动带来的几何非线性,也存在大变形导致的几何非线性。近年来,基于李群局部标架的建模方法(local frame of Lie group, LFLG)被验证可与各类建模方法结合,能够消除刚体运动带来的几何非线性。同时,大变形导致的几何非线性也将随着空间离散加密逐渐减弱。由此,LFLG可消除多柔体系统中部件的几何非线性,刚体与柔性体惯性力、内力及其Jacobian矩阵均满足刚体运动的不变性,可有效减少单元Jacobian矩阵更新次数。但,由于多体系统还广泛存在约束及载荷的非线性,LFLG方法在实际应用中是否能够提升系统整体的Jacobian矩阵复用效率尚未进行深入探讨。并且,多柔体系统通常采用变阶变步长时间积分策略求解动力学方程,算法阶数以及时间步长变化也将导致多体系统Jacobian变化,加剧了系统Jacobian复用难度。为客观分析LFLG方法的在实际仿真中的数值特性,本文首先以共旋坐标建模方法为例,给出了基于李群局部标架的三维Timoshenko梁单元建模方法。较于几何精确建模、绝对节点坐标等方法,该方法能够最大复用小变形有限元方法的单元算法,可降低单元开发难度;其次,搭建了LFLG方法的变阶变步长BDF(Backward Difference Formula)与变步长广义α积分器的计算流程,并针对小变形与大变形两种工况,分析单元弹性力及阻尼力几何非线性特性,对比Jacobian复用效率;最后,通过与全局标架算法对比,分析局部标架方法与全局标架建模方法的数值特性。

     

    Abstract: The flexible multibody system dynamics issues have high geometrically nonlinear, which is not only due to the large deformation of the flexible components but also caused by the extensive rigid body motion. Recently, the modeling method based on local frame of Lie group (LFLG) has been verified that it can be combined with various modeling methods to eliminate geometric nonlinearity caused by rigid body motion. At the same time, the geometric nonlinearity caused by large deformation will gradually weaken with spatial discrete encryption. Therefore, LFLG can eliminate the geometric nonlinearity of the components in the multi-flexible system, and the generalized inertial forces and internal forces as well as their Jacobian matrices are invariable under the arbitrary rigid body motion. However, due to the nonlinearity of constraints and loads in multibody systems, whether LFLG method can improve the overall Jacobian matrix reuse efficiency in practical applications is still to be discussed. In addition, the time integral strategy of variable order and variable step size is usually used to solve the dynamic equation of multibody flexible systems. The change of algorithm order and step size will also lead to Jacobian change of multibody systems, which intensifies the Jacobian reuse difficulty of the system. In order to analyze the numerical characteristics of the LFLG method objectively in practical simulation, this paper firstly presents a 3D corotational Timoshenko beam element based on the Lie group local frame, which can reuse the element algorithm of small deformation finite element method to the maximum, and reduce the difficulty of element development compared with geometrically exact beam formulation and absolute nodal coordinate formulation. Secondly, the calculation flow of Backward Difference Formula (BDF) with variable step size and order as well as generalized α integrator with variable step size of LFLG method is set up, and the geometric nonlinear characteristics of the element elastic force and damping force are analyzed for small deformation and large deformation conditions, and the Jacobian reuse efficiency is compared. Finally, the numerical characteristics of LFLG method and traditional modeling method in the global frame are analyzed.

     

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