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基于T样条的变网格等几何薄板动力学分析

王悦 崔雅琦 於祖庆 兰朋 陆念力

王悦, 崔雅琦, 於祖庆, 兰朋, 陆念力. 基于T样条的变网格等几何薄板动力学分析. 力学学报, 2021, 53(8): 2323-2335 doi: 10.6052/0459-1879-21-199
引用本文: 王悦, 崔雅琦, 於祖庆, 兰朋, 陆念力. 基于T样条的变网格等几何薄板动力学分析. 力学学报, 2021, 53(8): 2323-2335 doi: 10.6052/0459-1879-21-199
Wang Yue, Cui Yaqi, Yu Zuqing, Lan Peng, Lu Nianli. Dynamic analysis of variable mesh isogeometric thin plate based on T-spline. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 2323-2335 doi: 10.6052/0459-1879-21-199
Citation: Wang Yue, Cui Yaqi, Yu Zuqing, Lan Peng, Lu Nianli. Dynamic analysis of variable mesh isogeometric thin plate based on T-spline. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 2323-2335 doi: 10.6052/0459-1879-21-199

基于T样条的变网格等几何薄板动力学分析

doi: 10.6052/0459-1879-21-199
基金项目: 国家自然科学基金(11802072)和湖南省科技重大专项(2018GK1040)资助项目
详细信息
    作者简介:

    兰朋, 副教授, 主要研究方向: 机械动力学, 多柔体系统动力学分析. E-mail: lan_p@sina.com

  • 中图分类号: O313.7

DYNAMIC ANALYSIS OF VARIABLE MESH ISOGEOMETRIC THIN PLATE BASED ON T-SPLINE

  • 摘要: 具有大位移、大变形的薄板在接触碰撞等工况下, 其局部应变会产生剧烈变化. 为了保证对其进行动力学分析的精度和计算效率, 本文整合计算机辅助设计(CAD)与计算机辅助工程(CAE)系统, 提出了一种基于T样条曲面的变网格柔性系统等几何分析方法. 首先, 建立基于T样条曲面单元的基尔霍夫薄板运动学模型, 并根据非线性格林−拉格朗日应变建立由T样条曲面单元离散的薄板弹性模型. 其次, 通过在T网格中的局部区域插入节点的方式, 达到T样条曲面网格局部更新的目的. 利用T样条混合函数细化算法得到计算新广义变量的转换矩阵, 并结合广义α法创建了变自由度系统动力学方程的求解算法, 形成了系统的T样条单元局部细化算法. 最后, 静力学算例与柔性单摆模型分别验证了T样条薄板弹性模型的正确性, 以及T样条薄板单元在动力学分析上的精度和收敛性. 通过对受冲击柔性薄板的动力学分析表明, 本文所提出T样条单元及局部细化算法可以只在接触碰撞等应变剧烈变化的区域实现局部网格细化, 从而控制系统自由度数, 提高计算效率.

     

  • 图  1  等几何基尔霍夫薄板积分过程

    Figure  1.  The process of isogeometric Kirchhoff thin plate integration

    图  2  局部细化策略的示意图

    Figure  2.  Schematic diagram of local refinement strategy

    图  3  变网格系统动力学分析流程图

    Figure  3.  Dynamic analysis flow chart of variable mesh system

    图  4  受端弯矩作用的悬臂薄板

    Figure  4.  Cantilever subjected to end bending moment

    图  5  端弯矩作用下, 变形后悬臂梁的构形图

    Figure  5.  Configuration of deformed cantilever under external moments

    图  6  四分之一圆环构件及其局部细化示意图

    Figure  6.  Diagram of a quarter of circular thin plate and its local refinement diagram

    图  7  局部细化后构件米塞斯应力云图

    Figure  7.  von-Mises stress nephogram after local refinement

    图  8  一端铰接的柔性薄板单摆

    Figure  8.  Flexible thin plate pendulum

    图  9  能量曲线

    Figure  9.  The energy balance curve

    图  10  等几何薄板中T样条单元的收敛性

    Figure  10.  Convergence of T-spline element in thin plate

    图  11  含有2 × 2个T样条单元的单摆的连续构型

    Figure  11.  Configuration of the pendulum with 2 × 2 T-spline elements

    图  12  自由坠落刚性球与柔性薄板的碰撞

    Figure  12.  The collision between a rigid ball and a flexible thin plate

    图  13  三组不同的网格构型

    Figure  13.  The mesh refinement for three groups

    图  14  球心z向位移

    Figure  14.  Vertical displacement of the center of the ball

    图  15  薄板质心的z向位移

    Figure  15.  Vertical displacement of the plate’s centroid

    图  16  薄板弹性能曲线

    Figure  16.  The elastic energy curve of thin plate

    图  17  计算消耗时间

    Figure  17.  Time consumption for three groups

    图  18  局部细化薄板的米塞斯应力云图

    Figure  18.  von-Mises stress distribution of the locally refined thin plate

    表  1  圆环构件最小和最大米塞斯应力

    Table  1.   Minimum and maximum von-Mises stress on circular thin plate

    ${\sigma _{\min }}$/MPa${\sigma _{\max }}$/MPa
    theoretical solution14.5326.67
    ANSYS solution (200 elements)14.4526.37
    IGA solution (28 elements)14.5226.68
    下载: 导出CSV

    表  2  材料参数

    Table  2.   Material parameters

    ParameterValue
    length $a$/m 2
    width $b$/m 2
    height $h$/m 0.01
    density $\rho $/(kg∙m−3) 7850
    young’s modulus $E$/MPa 2
    poisson ratio $\mu $ 0.3
    下载: 导出CSV

    表  3  接触算例的参数

    Table  3.   Parameters of the contact example

    ParameterNameValue
    the flexible
    thin plate
    length $a$/m 2
    width $b$/m 2
    height $h$/m 0.04
    density $\;{\rho _1}$/(kg∙m−3) 7850
    Young’s modulus $E$/MPa 20
    Poisson ratio $\mu $ 0.3
    the rigid ball radius $R$/m 0.1
    density $\;{\rho _2}$/(kg∙m−3) 1500
    initial position ${{\boldsymbol{P}}_{\rm{b}}}$ (1,1,0.2)
    下载: 导出CSV

    表  4  三组薄板的详细信息

    Table  4.   The detailed information of three groups

    GroupNumber of
    control point
    Number of
    element
    Element
    size/m2
    mesh 12891961/7 × 1/7 (all region)
    mesh 21691001/5 × 1/5 (all region)
    mesh 31851121/10 × 1/10 (contact region)
    下载: 导出CSV
  • [1] Zienkiewicz OC, Taylor RL. The Finite Element Method for Solid and Structural Mechanics, Seventh Edition. Stoneham/London: Butterworth-Heinemann, 2009: 1-20.
    [2] Hughes TJR, Cottrell JA, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005, 194(39-41): 4135-4195 doi: 10.1016/j.cma.2004.10.008
    [3] Shabana AA, Xu L. Rotation-based finite elements: reference-configuration geometry and motion description. Acta Mechanica Sinica, 2021, 37(1): 105-126 doi: 10.1007/s10409-020-01030-6
    [4] Lan P, Shabana AA. Integration of B-spline geometry and ANCF finite element analysis. Nonlinear Dynamics, 2010, 61(1): 193-206
    [5] Lan P, Shabana AA. Rational finite elements and flexible body dynamics. Journal of Vibration and Acoustics of the ASME, 2010, 132(4): 041007 doi: 10.1115/1.4000970
    [6] Lan P, Yu Z, Du L, et al. Integration of non-uniform Rational B-splines geometry and rational absolute nodal coordinates formulation finite element analysis. Acta Mechanica Solida Sinica, 2014, 27(5): 486-495 doi: 10.1016/S0894-9166(14)60057-4
    [7] Yu Z, Lan P, Lu N. A piecewise beam element based on absolute nodal coordinate formulation. Nonlinear Dynamics, 2014, 77(1-2): 1-15 doi: 10.1007/s11071-014-1248-x
    [8] Mikkola A, Shabana AA, Sanchez-Rebollo C, et al. Comparison between ANCF and B-spline surfaces. Multibody System Dynamics, 2013, 30(2): 119-138 doi: 10.1007/s11044-013-9353-z
    [9] Pappalardo CM, Yu Z, Zhang X, et al. Rational ANCF thin plate finite element. Journal of Computational and Nonlinear Dynamics, 2016, 11(5): 051009 doi: 10.1115/1.4032385
    [10] Yu Z, Cui Y. A new ANCF solid-beam element: relationship with bézier volume and application on leaf spring modeling. Acta Mechanica Sinica, 2021 (in press)
    [11] Ma L, Wei C, Ma C, et al. Modeling and verification of a RANCF fluid element based on cubic rational bezier volume. Journal of Computational and Nonlinear Dynamics, 2020, 15(4): 041005
    [12] Hamed AM, Jayakumar P, Letherwood MD, et al. Ideal compliant joints and integration of computer aided design and analysis. Journal of Computational and Nonlinear Dynamics, 2015, 10(2): 021015 doi: 10.1115/1.4027999
    [13] Mizuno Y, Sugiyama H. Sliding and nonsliding joint constraints of B-spline plate elements for integration with flexible multibody dynamics simulation. ASME Journal of Computational and Nonlinear Dynamics, 2014, 9(1): 011001 doi: 10.1115/1.4025277
    [14] 李新康, 张继发, 郑耀. Kirchhoff-Love壳的等几何分析. 固体力学学报, 2014, 35(S1): 129-133 (Li Xinkang, Zhang Jifa, Zheng Yao. Isogeometric analysis of Kirchhoff-Love shells. Chinese Journal of Solid Mechanics, 2014, 35(S1): 129-133 (in Chinese)
    [15] 李新康, 张继发, 郑耀. Mindlin板的等几何分析. 固体力学学报, 2013, 33(S1): 198-203 (Li Xinkang, Zhang Jifa, Zheng Yao. Isogeometric analysis of mindlin plates. Chinese Journal of Solid Mechanics, 2013, 33(S1): 198-203 (in Chinese)
    [16] Thai TQ, Rabczuk T, Zhuang X. Isogeometric cohesive zone model for thin shell delamination analysis based on Kirchhoff-Love shell model. Frontiers of Structural and Civil Engineering, 2020, 14(2): 267-279 doi: 10.1007/s11709-019-0567-x
    [17] 刘涛, 汪超, 刘庆运等. 基于等几何方法的压电功能梯度板动力学及主动振动控制分析. 工程力学, 2020, 37(12): 228-242 (Liu Tao, Wang Chao, Liu Qingyun, et al. Analysis for dynamic and active vibration control of piezoelectric functionally graded plates based on isogeometric method. Engineering Mechanics, 2020, 37(12): 228-242 (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.04.0266
    [18] Sederberg TW, Cardon DL, Finnigan GT, et al. T-spline simplification and local refinement. Acm Transactions on Graphics, 2004, 23(3): 276-283 doi: 10.1145/1015706.1015715
    [19] Kasik DJ, Buxton W, Ferguson DR. Ten CAD challenges. IEEE Computer Graphics Applications, 2005, 25(2): 81-92 doi: 10.1109/MCG.2005.48
    [20] Sederberg TW, Zheng J, Bakenov A, et al. T-splines and T-NURCCs. Acm Transactions on Graphics, 2003, 22(3): 477-484 doi: 10.1145/882262.882295
    [21] Sederberg TW, Finnigan GT, Li X, et al. Watertight trimmed NURBS. Acm Transactions on Graphics, 2008, 27(3): 1-8
    [22] Casquero H, Liu L, Zhang Y, et al. Arbitrary-degree T-splines for isogeometric analysis of fully nonlinear Kirchhoff–Love shells. Computer-Aided Design, 2017, 82: 140-153 doi: 10.1016/j.cad.2016.08.009
    [23] Casquero H, Wei X, Toshniwal D, et al. Seamless integration of design and Kirchhoff–Love shell analysis using analysis-suitable unstructured T-splines. Computer Methods in Applied Mechanics and Engineering, 2020, 360: 112765
    [24] Dimitri R, De Lorenzis L, Scott MA, et al. Isogeometric large deformation frictionless contact using T-splines. Computer Methods in Applied Mechanics and Engineering, 2014, 269: 394-414 doi: 10.1016/j.cma.2013.11.002
    [25] Uhm TK, Youn SK. T-spline finite element method for the analysis of shell structures. International Journal for Numerical Methods in Engineering, 2010, 80(4): 507-536
    [26] Bazilevs Y, Calo VM, Cottrell JA, et al. Isogeometric analysis using T-splines. Computer Methods in Applied Mechanics and Engineering, 2015, 199(5-8): 229-263
    [27] 刘登学, 张友良, 刘高敏. 基于适合分析T样条的高阶数值流形方法. 力学学报, 2017, 49(1): 212-222 (Liu Dengxue, Zhang Youliang, Liu Gaomin. Higher-order numerical manifold method based on analysis-suitable T-spline. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(1): 212-222 (in Chinese) doi: 10.6052/0459-1879-16-217
    [28] Li X, Zheng J, Sederberg TW, et al. On linear independence of T-spline blending functions. Computer Aided Geometric Design, 2012, 29(1): 63-76 doi: 10.1016/j.cagd.2011.08.005
    [29] Scott MA, Borden MJ, Verhoosel CV, et al. Isogeometric finite element data structures based on Bézier extraction of T-splines. International Journal for Numerical Methods in Engineering, 2011, 88(2): 126-156 doi: 10.1002/nme.3167
    [30] Gerstmayr J, Sugiyama H, Mikkola A. Review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems. Journal of Computational and Nonlinear Dynamics, 2013, 8(3): 031016 doi: 10.1115/1.4023487
    [31] Luo K, Liu C, Tian Q, et al. An efficient model reduction method for buckling analyses of thin shells based on IGA. Computer Methods in Applied Mechanics and Engineering, 2016, 309: 243-268
    [32] Sze KY, Liu XH, Lo SH. Popular benchmark problems for geometric nonlinear analysis of shells. Finite Elements in Analysis and Design, 2004, 40(11): 1551-1569 doi: 10.1016/j.finel.2003.11.001
    [33] 兰朋, 崔雅琦, 於祖庆. 完备化ANCF薄板单元及在钢板弹簧动力学建模中的应用. 力学学报, 2018, 50(5): 1156-1167 (Lan Peng, Cui Yaqi, Yu Zuqing. The completed form of elastic model for ANCF thin plate element and its application on dynamic modeling of the leaf spring. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1156-1167 (in Chinese) doi: 10.6052/0459-1879-18-133
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出版历程
  • 收稿日期:  2021-05-11
  • 录用日期:  2021-07-30
  • 网络出版日期:  2021-07-31
  • 刊出日期:  2021-08-18

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