绝对节点坐标方法的模型降噪研究

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (11) : 139-146.

论文

绝对节点坐标方法的模型降噪研究

张志刚1,2，周翔1,2，毛红生1,2，王胜永1，宋慧涛3

作者信息 +

Model denoising based on absolute node coordinate method

ZHANG Zhigang1,2, ZHOU Xiang1,2, MAO Hongsheng1,2, WANG Shengyong1, SONG Huitao3

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文章历史 +

摘要

绝对节点坐标方法（absolute nodal coordinate formulation, ANCF）已成功应用于大变形柔性多体系统动力学问题的建模与仿真分析，但由于节点参数多且自身包含复杂高阶模态，其系统动力学方程的刚性问题突出。目前广泛采用的隐式算法的核心步骤是通过数值阻尼滤除高频响应，但求解效率仍难以令人满意。基于在建模中滤除高频分量的思想，用一小段时间区间内的平均应力代替弹性力虚功率中的瞬时应力，推导了包含附加惯性项和附加阻尼项的绝对节点坐标单元模型降噪列式。通过调整平均应力所在时间区间长度参数即可消除系统方程的过高频率，使常规显式算法也能应用于传统刚性问题的仿真求解。数值算例表明采用绝对节点坐标单元模型降噪列式可极大降低数值仿真求解难度，在保证计算精度的同时计算效率得到大幅提升。

Abstract

Absolute nodal coordinate formulation (ANCF) is successfully applied in dynamic problems’ modeling and simulation of large deformation flexible multibody system.However, due to many node parameters and containing complex high-order modes, the system dynamic equation’s stiff problem is prominent.The core step of the existing widely used implicit algorithm is to filter high-frequency response with numerical damping, but the solving efficiency is not satisfactory.Here, based on the idea to filter high frequency components in modeling, the instantaneous stress in virtual power of elastic force was replaced by the average stress in a short time period to derive the absolute nodal coordinate element model denoising formulation containing additional inertia term and additional damping term.Through adjusting time interval length parameter of the average stress, high frequency components in the system equation could be eliminated, and the conventional explicit algorithm could be applied in simulation solving of traditional stiff problems.Numerical examples showed that the proposed absolute nodal coordinate element model denoising formulation can greatly reduce solving difficulty of numerical simulation, ensure calculation accuracy and improve calculation efficiency.
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导出引用

张志刚1,2，周翔1,2，毛红生1,2，王胜永1，宋慧涛3. 绝对节点坐标方法的模型降噪研究[J]. 振动与冲击, 2021, 40(11): 139-146

ZHANG Zhigang1,2, ZHOU Xiang1,2, MAO Hongsheng1,2, WANG Shengyong1, SONG Huitao3. Model denoising based on absolute node coordinate method[J]. Journal of Vibration and Shock, 2021, 40(11): 139-146

参考文献

［1］HOWELL L L.Compliant mechanisms［M］.New York: John Wiley and Sons, 2001.
［2］SIMO J C.A finite strain beam formulation.The three-dimensional dynamic problem.Part I［J］.Computer Methods in Applied Mechanics and Engineering, 1985, 49(1): 55-70.
［3］SIMO J C, VUQUOC L.A three-dimensional finite-strain rod model.Part II: computational aspects［J］.Computer Methods in Applied Mechanics and Engineering, 1986, 58(1): 79-116.
［4］ZUPAN E, SAJE M.Integrating rotation from angular velocity［J］.Advances in Engineering Software, 2011, 42(9): 723-733.

［5］CRISFIELD M A, JELENIC G.Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation［J］.Proceedings: Mathematical, Physical and Engineering Sciences, 1999, 455(1983): 1125-1147.
［6］SHABANA A A, YAKOUB R Y.Three dimensional absolute nodal coordinate formulation for beam elements: theory［J］.Journal of Mechanical Design, 2002, 123(4): 606-613.
［7］YAKOUB R Y, SHABANA A A.Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications［J］.Journal of Mechanical Design, 2002, 123(4): 614-621.
［8］LAN P，SHABANA A A.Integration of B-spline geometry and ANCF finite element analysis［J］.Nonlinear Dynamics，2010, 61(1/2): 193-206.
［9］兰朋，於祖庆，赵欣.Bézier和B-spline曲线的绝对节点坐标列式有限元离散方法［J］.机械工程学报，2012，48(17):128-134.
LAN Peng, YU Zuqing, ZHAO Xin.Using absolute nodal coordinate formulation elements to model Bézier and B-spline curve for finite element analysis［J］.Journal of Mechanical Engineering, 2012, 48(17): 128-134.
［10］NADA A A.Use of B-spline surface to model large-deformation continuum plates: procedure and applications［J］.Nonlinear Dynamics, 2013, 72(1/2): 243-263.
［11］袁新鼎.刚性常微分方程初值问题的数值解法［M］.北京: 科学出版社，1987.
［12］GROSSI E, SHABANA A A.Analysis of high-frequency ANCF modes: Navier-Stokes physical damping and implicit numerical integration［J］.Acta Mechanica, 2019, 230(7): 2581-2605.
［13］SHABANA A A.ANCF consistent rotation-based finite element formulation［J］.Journal of Computational and Nonlinear Dynamics, 2015, 11(1): 014502.
［14］GEAR C W.Numerical initial value problems in ordinary differential equation［M］.Englewood Cliffs: Prentice-Hall, 1971.
［15］EL-ZAHAR E R, HABIB H M, RASHIDI M M, et al.A comparison of explicit semi-analytical numerical integration methods for solving stiff ODE systems［J］.American Journal of Applied Sciences, 2015, 12(5): 304-320.
［16］NEWMARK N M.A method of computation for structural dynamics［J］.Journal of the Engineering Mechanics Division, 1959, 85(3): 67-94.

［17］WILSON E L，FARHOOMAND I，BATHE K J.Nonlinear dynamic analysis of complex structures［J］.Earthquake Engineering & Structural Dynamics，1973，1: 241-252.
［18］HILBERT H M, HUGHES T J R, TAYLOR R L.Improved numerical dissipation for time integration algorithms in structural dynamics［J］.Earthquake Engineering & Structural Dynamics, 1977, 5(3): 283-292.
［19］CHUNG J, HULBERT G M.A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method［J］.Journal of Applied Mechanics, 1993, 60(2): 371-375.

［20］GARCID D, VALVERDE J, DOMINGUEZ J.An internal damping model for the absolute nodal coordinate formulation［J］.Nonlinear Dynamics, 2005, 42(4): 347-369.
［21］ZHANG Y Q, TIAN Q, CHEN L P, et al.Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods［J］.Multibody System Dynamics, 2009, 21(3): 281-303.
［22］MOHAMED A N A, SHABANA A A.A nonlinear visco-elastic constitutive model for large rotation finite element formulations［J］.Multibody System Dynamics, 2011, 26(1): 57-79.
［23］齐朝晖，曹艳，王刚.多柔体系统数值分析的模型降噪方法［J］.力学学报，2018，50(4): 863-870.
QI Zhaohui, CAO Yan, WANG Gang.Model smoothing methods in numerical analysis of flexible multibody systems［J］.Chinese Journal of Theoretical and Applied Mechanica, 2018, 50(4): 863-870.