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两类基于局部标架梁单元的闭锁缓解方法

汤惠颖 张志娟 刘铖 刘绍奎

汤惠颖, 张志娟, 刘铖, 刘绍奎. 两类基于局部标架梁单元的闭锁缓解方法[J]. 力学学报, 2021, 53(2): 482-495. doi: 10.6052/0459-1879-20-274
引用本文: 汤惠颖, 张志娟, 刘铖, 刘绍奎. 两类基于局部标架梁单元的闭锁缓解方法[J]. 力学学报, 2021, 53(2): 482-495. doi: 10.6052/0459-1879-20-274
Tang Huiying, Zhang Zhijuan, Liu Cheng, Liu Shaokui. LOCKING ALLEVIATION TECHNIQUES OF TWO TYPES OF BEAM ELEMENTS BASED ON THE LOCAL FRAME FORMULATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(2): 482-495. doi: 10.6052/0459-1879-20-274
Citation: Tang Huiying, Zhang Zhijuan, Liu Cheng, Liu Shaokui. LOCKING ALLEVIATION TECHNIQUES OF TWO TYPES OF BEAM ELEMENTS BASED ON THE LOCAL FRAME FORMULATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(2): 482-495. doi: 10.6052/0459-1879-20-274

两类基于局部标架梁单元的闭锁缓解方法

doi: 10.6052/0459-1879-20-274
基金项目: 1) 国家自然科学基金(12072026);国家自然科学基金(11832005);国家自然科学基金(11672034);十三五民用航天项目资助.
详细信息
    作者简介:

    2) 刘铖, 副教授, 主要研究方向: 柔性多体系统动力学建模与计算; 非线性有限元方法等. E-mail: liucheng_bit@aliyun.com

    通讯作者:

    刘铖

  • 中图分类号: O313.7

LOCKING ALLEVIATION TECHNIQUES OF TWO TYPES OF BEAM ELEMENTS BASED ON THE LOCAL FRAME FORMULATION

  • 摘要: 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.

     

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出版历程
  • 收稿日期:  2020-08-07
  • 刊出日期:  2021-02-10

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