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考虑非线性本构的非刚性折纸结构动力学建模与分析

袁婷婷 任昆明 方雨桥 刘锦阳

袁婷婷, 任昆明, 方雨桥, 刘锦阳. 考虑非线性本构的非刚性折纸结构动力学建模与分析. 力学学报, 2022, 54(9): 1-15 doi: 10.6052/0459-1879-22-176
引用本文: 袁婷婷, 任昆明, 方雨桥, 刘锦阳. 考虑非线性本构的非刚性折纸结构动力学建模与分析. 力学学报, 2022, 54(9): 1-15 doi: 10.6052/0459-1879-22-176
Yuan Tingting, Ren Kunming, Fang Yuqiao, Liu Jinyang. Dynamic modeling and analysis for non-rigid origami structure considering nonlinear constitutive relation. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 1-15 doi: 10.6052/0459-1879-22-176
Citation: Yuan Tingting, Ren Kunming, Fang Yuqiao, Liu Jinyang. Dynamic modeling and analysis for non-rigid origami structure considering nonlinear constitutive relation. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 1-15 doi: 10.6052/0459-1879-22-176

考虑非线性本构的非刚性折纸结构动力学建模与分析

doi: 10.6052/0459-1879-22-176
基金项目: 国家自然科学基金资助项目(11932001, 11772186)
详细信息
    作者简介:

    刘锦阳, 教授, 主要研究方向: 柔性多体系统动力学、航天器动力学、接触碰撞动力学. E-mail: liujy@sjtu.edu.cn

  • 中图分类号: O313.7

DYNAMIC MODELING AND ANALYSIS FOR NON-RIGID ORIGAMI STRUCTURE CONSIDERING NONLINEAR CONSTITUTIVE RELATION

  • 摘要: 折纸结构因其大收纳比、高可控性、可重构、制造装配简单以及设计多样等优势, 在航天、生物医学、建筑、机器人、材料科学等工程领域有着广阔的应用前景. 随着折纸结构的工程应用越来越广泛, 针对低刚度折纸结构的动力学研究愈加重要. 本文将非刚性折纸结构等效为带卷簧的空间桁架结构, 建立了一种通用的杆–链动力学模型. 考虑材料的几何非线性, 采用基于Ogden超弹性本构的杆单元来模拟折痕和虚拟折痕, 可适用于作大范围运动并具有大变形的折纸结构. 引入非线性卷簧来体现折痕的抗弯作用, 相较于传统的卷簧本构模型, 本文提出的改进的非线性卷簧本构模型具有更强的通用性和鲁棒性, 能够有效避免接触碰撞动力学中折叠面的穿透. 基于虚功原理, 建立了考虑阻尼效应的非刚性折纸多体系统的动力学方程, 并采用变步长的广义-α 法求解. 最后, 对三种经典折叠形式的非刚性折纸结构进行动力学仿真, 验证了本文提出的杆–链动力学模型的准确性和高效性. 通过施加虚拟折痕和修正初始构型, 有效解决了刚性折纸模型中展开和收拢过程的锁定问题. 与刚性折纸模型相比, 杆–链动力学模型具有更好的数值模拟通用性, 并能够给出具有大变形张紧构型. 在此基础上, 揭示了非刚性折纸结构复杂的动力学行为, 并对多稳态、瞬态动力学和波动力学特性进行分析.

     

  • 图  1  杆–链模型示意图

    Figure  1.  The bar-and-hinge model

    图  2  卷簧单元示意图

    Figure  2.  Rotational spring element

    图  3  非线性卷簧单元的本构模型: 力矩与二面角的关系

    Figure  3.  Nonlinear constitutive model of rotational spring: Dihedral angle θ versus moment M

    图  4  单菱形折叠示意图

    Figure  4.  A rhombus fold

    图  5  单菱形折叠: 折叠角与外力的关系图

    Figure  5.  A rhombus fold: Fext versus θ

    图  6  叶内折叠的折痕分布

    Figure  6.  Crease pattern of leaf-in origami

    图  7  叶内折叠添加虚拟折痕的方式

    Figure  7.  Methods of adding virtual creases in leaf-in origami

    图  8  I, II, III方式下叶内折叠展开过程的奇异构型

    Figure  8.  Singular configuration of leaf-in origami during the deployment in I, II, III cases

    图  9  叶内折叠展开和收拢过程中Az坐标时域图

    Figure  9.  Time history of z coordinate of point A of leaf-in origami during unfolding and folding process

    图  10  叶内折叠: (a)初始构型; (b) 1/8模型卷簧分布

    Figure  10.  Leaf-in origami: (a) Initial configuration and (b) spring patter in 1/8 model

    图  11  叶内折叠: 刚性与非刚性折纸模型展开过程构型图

    Figure  11.  Leaf-in origami: Configuration of the rigid and non-rigid origami models during the deployment

    图  12  叶内折叠: Az坐标的 (a)位置; (b)速度; (c)加速度时域图

    Figure  12.  Leaf-in origami: Time histories of z coordinate of point A of (a) position, (b) velocity and (c) acceleration

    图  13  叶内折叠: 点A, E, F, G (图10) z坐标时域图

    Figure  13.  Leaf-in origami: Time history of z coordinate of points A, E, F, G (see Fig. 10)

    图  14  Kresling折叠: (a)折痕分布; 柱状结构: (b)主视图, (c)俯视图

    Figure  14.  Kresling origami: (a) crease pattern. Columnar structure: (b) front view and (c) top view

    图  15  Kresling折叠: 不同多边形下, (a)势能曲线; (b)力–位移曲线

    Figure  15.  Kresling origami: (a) Potential energy curve and (b) force-displacement curve in different shapes

    图  16  Kresling折叠: 不同多边形中特殊点处(见图15(b))构型图

    Figure  16.  Kresling origami: Configuration of special points (see Fig. 15(b)) in different shapes

    图  17  正十边形Kresling折纸结构

    Figure  17.  Kresling origami structure in regular decagon

    图  18  正十边形Kresling折叠: (a) z坐标时域图; (b) 不同卷簧本构模型中特殊点处(见图18(a))的构型图

    Figure  18.  Regular decagon Kresling origami: Time histories of (a) z coordinate; (b) configuration of special points (see Fig. 18(a)) in different rotational spring constitutive models

    图  19  正十边形Kresling折叠: 应变能云图

    Figure  19.  Regular decagon Kresling origami: Strain energy cloud map

    图  20  正十边形Kresling法向支座反力FN时域图

    Figure  20.  Time history of the normal support reaction force FN of the regular decagon Kresling origami

    图  21  多链Kresling折纸结构波动力学

    Figure  21.  Wave dynamics of multi-chain Kresling origami structure

    图  22  多链Kresling折纸结构的应变–构型图

    Figure  22.  Strain-configuration of multi-chain Kresling origami structure

    图  23  多链Kresling折纸结构应变波传播的时空图

    Figure  23.  Space-time of strain wave propagation in multi-chain Kresling origami structure

    图  24  多链Kresling折纸结构: 不同单元的应变时间历程图

    Figure  24.  Multi-chain Kresling origami structure: Strain versus time curves in different unites

    图  25  多链Kresling折纸结构的能量–时间曲线

    Figure  25.  Energy-time curves of multi-chain Kresling origami structure

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  • 收稿日期:  2022-04-26
  • 录用日期:  2022-06-20
  • 网络出版日期:  2022-06-21

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