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Volume 42 Issue 6
Nov.  2012
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Article Navigation >  Advances in Mechanics  > 2012  >  42(6): 755-770
HU Ping, XIA Yang. SURVEY OF QUASI-CONFORMING FINITE ELEMENT METHOD[J]. Advances in Mechanics, 2012, 42(6): 755-770. doi: 10.6052/1000-0992-12-068
Citation: HU Ping, XIA Yang. SURVEY OF QUASI-CONFORMING FINITE ELEMENT METHOD[J]. Advances in Mechanics, 2012, 42(6): 755-770. doi: 10.6052/1000-0992-12-068
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SURVEY OF QUASI-CONFORMING FINITE ELEMENT METHOD

doi: 10.6052/1000-0992-12-068

  • School of Automotive Engineering, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

Funds:  The project was supported by the Key Project of the NSFC (10932003), NSFC (11272075), “863”Project of China (2009AA04Z101), “973”National Basic Research Project of China (2010CB832700) and“04”Great Project of Ministry of Industrialization and Information of China (2011ZX04001-21).
More Information
  • Corresponding author: HU Ping
  • Received Date: 2012-05-16
  • Rev Recd Date: 2012-07-04
  • Publish Date: 2012-11-25
    Abstract
  • Quasi-conforming analysis is an important and characteristic finite element method. The formulation of quasi-conforming element is simple and flexible, which unifies the conforming and non-conforming finite element method. In quasi-conforming formulation, the equilibrium equations as well as strain-displacement equations are weakened and the importance of basis functions of finite element space is emphasized. The convergence of quasi-conforming elements is guarded by the control of discrete precision of displacements and strains. The Taylor expansion test can also be used for direct analysis of convergence. Many excellent quasiconforming elements have been constructed and applied widely in engineering analysis, which is the reflection of the value of quasi-conforming finite element method. The formulation process, theory and the important elements of quasi-conforming are summarized in this paper. Finally prospective developments of quasi-conforming are suggested. The research on quasi-conforming is an original and fundamental work, which contributes to the development of computational mechanics.

     

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  • 1 Benioff M R, Lazowska E D. Computational science: ensuring america’s competitiveness. In: Reprot to the President. President’s Information Technology Advisory Committee,2005
    2 王勖成. 有限单元法. 北京: 清华大学出版社, 2003
    3 Zienkiewicz O C, Taylor R L. The Finite Element Method. Fifth edn. Oxford: Butterworth Heinemann, 2006
    4 Cook R D, Malkus D S, Plesha M E, et al. Concepts and applications of finite element analysis. 4th edn. NewYork: Wiley&Sons, 2007
    5 Bruce M I. Engineering applications of numerical integration in stiffness methods. AIAA Journal, 1966, 4(11):2035-2037  
    6 Wilson E L, Taylor R L, DohertyWP, et al. Incompatible displacement models. In: Fenves S J. ed. Numerical and Computer Methods in Structural Mechanics: Academic Press, 1973
    7 吴长春, 卞学鐄. 非协调数值分析与杂交元方法. 北京: 科学 出版社, 1997
    8 田宗漱, 卞学鐄. 多变量变分原理与多变量有限元方法. 北 京: 科学出版社, 2011
    9 岑松, 陈晓明, 李宏光, 等. 有限元新型自然坐标方法研究进 展. 工程力学, 2008, 25(S1): 18-32
    10 唐立民, 陈万吉, 刘迎曦. 有限元分析中的拟协调元. 大连工 学院学报, 1980, 19(2): 19-35
    11 Tang L, Chen W, Liu Y. String net function approximation and quasi-conforming element technique. In: Atluri S N, Gallagher R H, Zienkiewicz O C. eds. Hybrid and Mixed Finite Element Methods. New Jersey: John Wiley & Sons, Ltd, 1983. 96-111
    12 Kim K D, Lomboy G R, Voyiadjis G Z. A 4-node assumed strain quasi-conforming shell element with 6 degrees of freedom. International Journal for Numerical Methods in Engineering, 2003, 58(14): 2177-2200  
    13 Kim K D, Lomboy G R. A co-rotational quasi-conforming4-node resultant shell element for large deformation elastoplastic analysis. Computer Methods in Applied Mechanics and Engineering, 2006, 195(44-47): 6502-6522
    14 Park T Y, Kim K D, Han S C. Linear static and dynamic analysis of laminated composite plates and shells using a4-node quasi-conforming shell element. Composites Part B-Engineering, 2006, 37(2-3): 237-248
    15 Han S C, Lomboy G R, Kim K D. Mechanical vibration and buckling analysis of FGM plates and shells using a four-node quasi-conforming shell element. International Journal of Structural Stability and Dynamics, 2008, 8(2):203-229  
    16 Kim K D, Lomboy G R, Han S C. Geometrically nonlinear analysis of functionally graded material (FGM) plates and shells using a four-node quasi-conforming shell element. Journal of Composite Materials, 2008, 42(5):485-511
    17 Lomboy G R, Suthasupradit S, Kim K D, et al. Nonlinear formulations of a four-node quasi-conforming shell element. Archives of Computational Methods in Engi- neering, 2009, 16(2): 189-250  
    18 Hu P, Xia Y, Tang L. A Four-node reissner-mindlin shell with assumed displacement quasi-conforming method. Cmes-Computer Modeling in Engineering & Sciences,2011, 73(2): 103-135
    19 Voyiadjis G Z,Woelke P. General non-linear finite element analysis of thick plates and shells. International Journal of Solids and Structures, 2006, 43(7-8): 2209-2242
    20 龙驭球, 龙志飞, 岑松. 新型有限元论. 北京: 北京大学出版 社, 2004
    21 Long Y Q, Cen S, Long Z F. Advanced Finite Element Method in Structural Engineering. Beijing: Springer- Verlag GmbH Berlin Heidelberg & Tsinghua University Press, 2009
    22 王敏中, 王炜, 武际可. 弹性力学教程. 北京: 北京大学出版 社, 2002
    23 关玉璞. 多变量拟协调退化壳有限元研究. 大连: 大连理工 大学, 1991
    24 何东升, 唐立民. 拟协调元的位移函数及节点误差. 应用数 学和力学, 2002, 23(2): 119-127
    25 吕和祥, 徐苏宁, 唐立民. 一个有效的任意四边形薄板弯曲 单元. 计算结构力学及其应用, 1989, 6(1): 147-158
    26 吕和祥. 关于“拟协调元”的若干问题及在构造拱单元上的 应用. 固体力学学报, 1981, 3(4): 531-536
    27 陶政国. 拟协调九参数三角形板单元的性态分析. 上海力学,1982, (4): 65-74
    28 唐立民, 齐朝晖, 丁克伟, 等. 弹性力学弱形式广义基本方程 的建立和应用. 大连理工大学学报, 2001, 41(1)1-8
    29 丁克伟. 拟协调有限元与弱形式广义方程. 合肥工业大学学 报(自然科学版), 2009, 32(12): 1875-1879
    30 刘迎曦, 李宝元, 唐立民. 多变量拟协调E 函数单元. 计算 结构力学及其应用, 1987, 4(4): 35-43
    31 张鸿庆. 多套函数的广义分片检验与十二参拟协调元. 大连 工学院学报, 1982, 21(3): 11-19
    32 陈万吉, 刘迎曦, 唐立民. 拟协调元列式. 大连工学院学报,1980, 19(2): 37-50
    33 唐立民, 陈万吉, 刘迎曦. 薄板弯曲分析中的拟协调元. 建筑 结构学报, 1981, (2): 10-22
    34 张鸿庆, 王鸣. 多套函数有限元逼近与拟协调板元. 应用数 学和力学, 1985, 6(1): 41-52
    35 张鸿庆, 王鸣. 拟协调元空间的紧致性和拟协调元法的收敛 性. 应用数学和力学, 1986, 7(5): 409-423
    36 王鸣, 张鸿庆. 有限元空间的嵌入性质和紧致性. 应用数学 和力学, 1988, 9(2): 127-134
    37 Wang M. L ∞ convergence of quasi-conforming finite elements for the biharmonic equation. Journal of Computa- tional Mathematics, 1995, 13(2): 108-122
    38 石钟慈, 陈绍春. 九参拟协调元的直接分析. 计算数学, 1990,12(1): 76-84
    39 Shi Z C. On the accuracy of the quasiconforming and generalized conforming finite elements. Chinese Annals of Mathematics, 1995, (2): 108-122
    40 陈绍春. 拟协调元的双参数法分析. 高等学校计算数学学报,1990, 12(2): 188-194
    41 石东洋, 陈绍春. 拟协调元的精度分析. 高校应用数学学报A 辑, 2002, 17(1): 121-124
    42 刘迎曦, 石广玉, 唐立民. 关于有限元多余零能模式的讨论. 大连工学院学报, 1983, 22(3): 61-67
    43 吕和祥, 唐立民, 刘秀兰. 曲梁单元和它的收敛率. 应用数学 和力学, 1989, 10(6): 487-498
    44 刘迎曦, 石广玉, 唐立民. 拟协调厚薄通用梁、板单元. 大连 工学院学报, 1984, 23(3): 79-85
    45 吴敬东. 关于悬索问题的拟协调元分析. 沈阳化工学院学报,1996, (4): 307-313
    46 陈万吉, 唐立民. 等参拟协调元. 大连工学院学报, 1981,20(1): 63-74
    47 唐立民, 陈万吉, 周建清. 多变量拟协调平面四边元. 计算结 构力学及其应用, 1988, 5(1): 1-6
    48 Liu H, Limin T. Qusiconforming plane element with drilling degree of freedom. Computatinal Structural Me- chanics and Application, 1990, 7(4): 23-31
    49 刘铁林, 朱祎国, 吕和祥. 解析拟协调平面四边元. 计算力学 学报, 1998, 15(3): 324-328
    50 唐立民, 刘迎曦. 多变量拟协调元方法与罚函数近不可压缩 单元. 合肥工业大学学报, 1984, (2): 16-27
    51 吕和祥, 刘振华, 唐立民. 极坐标中的拟协调环形单元. 计算 结构力学及其应用, 1991, 8(1): 58-66
    52 陈万吉. 一个高精度八结点六面体单元. 力学学报, 1982,18(3): 262-271
    53 蒋和洋. 用拟协调元法推导高精度三角形板弯曲单元. 大连 工学院学报, 1981, 20(S2): 21-28
    54 欧阳华江, 邬瑞锋. 全预应力混凝土板长期挠度的计算. 计 算结构力学及其应用, 1986, 3(2): 25-33
    55 Zhao Z, Chen W. New finite element model for analysis of Kirchhoff plate. International Journal for Numerical Methods in Engineering, 1995, 38(7): 1201-1214  
    56 唐立民, 刘迎曦, 刘燕景. 九参数拟协调离散Kirchhoff 薄板 单元. 大连理工大学学报, 1990, 30(3): 263-269
    57 刘燕景, 刘迎曦. 新型拟协调模式的离散kirchhoff 薄板单 元(LDKT-9). 大庆石油学院学报, 1992, 16(1): 45-52
    58 Shi G Y, Voyiadjis G Z. A Simple C0 quadrilateral thick/thin shell element based on the refined shell theory and the assumed strain fields. International Journal of Solids and Structures, 1991, 27(3): 283-298  
    59 Shi G Y, Voyiadjis G Z. Efficient and accurate four-node quadrilateral plate bending element based on assumed strain fields. International Journal for Numerical Meth- ods in Engineering, 1991, 32(5): 1041-1055  
    60 孙建刚. 一个简单、有效的四节点板弯曲单元. 工程力学,1989, 6(4): 24-33
    61 孙建刚. 拟协调四节点板弯曲单元在薄板振动分析中的应 用. 地震工程与工程振动, 1995, (3): 69-72
    62 仝立勇, 唐立民. 四节点四边形拟协调Mindlin 板单元. 应 用力学学报, 1989, 6(2): 69-75
    63 朱菊芬, 陈万吉. 一种有效的厚薄板壳单元. 固体力学学报,1997, 18(4): 323-328
    64 金吾根. 拟协调曲边旋转壳元. 大连工学院学报, 1981,20(S2): 29-36
    65 朱菊芬, 郭兆璞. 复合材料旋转壳的大变形有限元分析. 大 连工学院学报, 1984, 23(3): 101-107
    66 刘迎曦, 吕和祥, 唐立民. 拟协调圆柱壳单元. 大连工学院学 报, 1981, 20(2): 23-30
    67 陈铁云, 吴水云. 圆柱薄壳结构的弹- 塑性有限元分析. 力学 学报, 1986, (S2): 264-275
    68 吴水云, 陈铁云. 近海平台管状接头弹- 塑性有限元分析. 上 海交通大学学报, 1987, 21(5): 1-12
    69 吴连元, 胡刚义. 板壳结构弹塑性稳定性的有限元分析. 应用 力学学报, 1993, 10(1): 106-110
    70 吕和祥, 刘迎曦. 有限元中的拟协调元及在构造双曲壳单元 上的应用. 大连工学院学报, 1981, 20(1): 75-87
    71 魏钢, 赵超燮. 拟协调大变形矩形扁壳元及其应用. 计算结 构力学及其应用, 1990, 7(1): 37-44
    72 刘红, 陈万吉. 拟协调SemiLoof 和Loof 扁壳元. 固体力学 学报, 1992, 13(3): 259-263
    73 吴连元, 纪多辙, 陈文良. 板壳非线性屈曲的拟协调元分析. 上海交通大学学报, 1992, 26(4): 51-58
    74 罗蜀榕, 吴连元. 板壳弹塑性屈曲的有限元分析. 固体力学 学报, 1993, 14(3): 237-240
    75 邓可顺,陈建云. 拟协调等腰梯形薄板弯曲元和薄壳元. 大 连理工大学学报, 1995, 35(1): 17-24
    76 邓可顺,陈健云. 拟协调等腰梯形壳元显式几何刚度阵及屈 曲分析. 计算结构力学及其应用, 1995, 12(2): 160-169
    77 Voyiadjis G, Shi G. Nonlinear postbuckling analysis of plates and shells by four-noded strain element. AIAA Journal, 1992, 30(4): 1110-1116  
    78 朱菊芬, 陈亮, 郑罡. 带旋转自由度拟协调三角形板壳单元. 大连理工大学学报, 2001, 41(1): 38-41
    79 Guan Y P, Tang L. A quasi-conforming nine-node degenerated shell finite element. Finite Elements in Analysis and Design, 1992, 11(2): 165-176  
    80 Guan Y P, Tang L. Nonlinear quasi-conforming finite element method. Acta Mechanica Sinica, 1993, 9(3): 269-276  
    81 Guan Y P, Tang L. A geometrically non-linear quasiconforming nine-node quadrilateral degenerated solid shell element. International Journal for Numerical Methods in Engineering, 1995, 38(6): 927-942  
    82 关玉璞, 唐立民. 拟协调九结点四边形层合板壳有限元. 南 京航空航天大学学报, 1994, 26(2): 278-282
    83 关玉璞, 张宗科. 拟协调轴对称三结点退化壳单元. 上海交 通大学学报, 1998, 32(11): 98-101
    84 Jiang Heyang. Quasi-conforming Mode Nonlinear Finite Element and Others. DaLian: Dalian Institute of Technology,1984
    85 蒋和洋. 拟协调模式非线性有限元. 计算结构力学及其应用,1984, 1(2): 49-60
    86 蒋和洋, 唐立民. 用拟协调元进行壳体非线性稳定分析. 工 程力学, 1985, 2(3): 12-19
    87 蒋和洋. 有初始缺陷的板壳的大挠度分析. 上海力学, 1987,8(1): 10-17
    88 蒋和洋. 拟协调模式大变形板壳单元的变分基础. 大连理工 大学学报, 1988, 28(3): 23-28
    89 邹贵平. 拟协调非线性任意四边形薄板单元. 沈阳建筑工程 学院学报, 1989, 5(4): 23-32
    90 关玉璞, 唐立民. 一个非线性拟协调退化壳有限元. 航空学 报, 1993, 14(9): 475-482
    91 关玉璞,唐立民,高德平. 非线性拟协调元与杂交／混合元: Ⅰ.关于Hellinger - Reissner 变分原理. 计算结构力学及其 应用, 1994, (4): 387-391
    92 关玉璞,唐立民,高德平. 非线性拟协调元与杂交／混合元: Ⅱ.关于Hu -Washizu 变分原理. 计算结构力学及其应用,1995, (1): 47-52
    93 Shi G Y, Voyiadjis G Z. Geometrically nonlinear analysis of plates by assumed strain element with explicit tangent stiffness matrix. Computers & Structures, 1991, 41(4):757-763  
    94 Wegmuller A W. Elastic-plastic finite element analysis of plates. Archive of Applied Mechanics, 1975, 44(2): 63-77
    95 Shi G Y, Voyiadjis G Z. A simple non-layered finite element for the elasto-plastic analysis of shear flexible plates. International Journal for Numerical Methods in Engi- neering, 1992, 33(1): 85-99  
    96 Shi G Y, Voyiadjis G. A computational model for FE ductile plastic damage analysis of plate bending. Journal of Applied Mechanics, 1993, 60: 749-758  
    97 Ueda Y, Yao T. The plastic node method: A new method of plastic analysis. Computer Methods in Applied Me- chanics and Engineering, 1982, 34(1-3): 1089-1104
    98 Shi G, Atluri S N. Elasto-plastic large deformation analysis of space-frames: A plastic-hinge and stress-based explicit derivation of tangent stiffnesses. International Jour- nal for Numerical Methods in Engineering, 1988, 26(3):589-615
    99 Wang X, Jiang H Y, Lee L H N. Finite deformation formulation of a shell element for problems of sheet metal forming. Computational Mechanics, 1991, 7(5): 397-411  
    100 Wang X, Lee L H N. Postbifurcation behavior of wrinkles in square metal sheets under Yoshida Test. International Journal of Plasticity, 1993, 9(1): 1-19  
    101 Woelke P, Voyiadjis G Z, Perzyna P. Elasto-plastic finite element analysis of shells with damage due to microvoids. International Journal for Numerical Methods in Engineering, 2006, 68(3): 338-380  
    102 陈浩然, 衣翃, 温玄玲. 复合材料层合板壳通用单元和等网 格加筋板壳的局部稳定性. 航空学报, 1988, 9(3): 177-183
    103 朱菊芬, 汪海. 大挠度层合板的拟协调罚单元. 复合材料学 报, 1989, 6(4): 39-47
    104 Huang B Z S, Vijay B, Atluri S N. A quasi-conforming triangular laminated composite shell element based on a refined first-order theory. Computational Mechanics, 1994,13(4): 295-314  
    105 Huang B Z, Atluri S N. A simple method to follow postbuckling paths in finite element analysis. Computers & Structures, 1995, 57(3): 477-489  
    106 杨刚, 张爱锋, 黄宝宗. 层合壁板的二次屈曲. 沈阳建筑工程 学院学报(自然科学版), 2001, 17(4): 249-251
    107 唐立民, 刘迎曦. 拟协调罚有限元法. 计算结构力学及其应 用, 1984, 1(3): 1-9
    108 Tang L, Liu Y. Quasi-conforming element techniques for penalty finite element methods. Finite Elements in Analysis and Design, 1985, 1(1): 25-33  
    109 陈浩然, 衣翃. 复合材料层板的拟协调罚单元. 复合材料学 报, 1987, 4(1): 67-72
    110 朱菊芬, 汪海. 层合板的压剪稳定性及其后屈曲性态研究. 大连理工大学学报, 1989, 29(5): 519-526
    111 朱菊芬, 周承芳. 加筋板壳稳定性分析中一种简单的有限元 模式. 应用力学学报, 1993, 10(4): 113-117
    112 郭兆璞, 弓俊青. 复合材料加筋板的动力分析. 复合材料学 报, 1990, 7(3): 75-81
    113 王家林. 薄壁杆系结构有限元的新算法. 机械强度, 1984,8(4): 68-73
    114 王家林. 车辆结构力学分析程序JJD 与4 ～ 9 节点过渡型 板壳单元. 吉林工业大学学报, 1983, (4): 13-19
    115 肖为民, 刘传义. 四结点等参拟协调薄板元. 浙江工学院学 报, 1988, (1): 45-52
    116 许焕然, 王家林. 拟协调4 节点等参板单元. 吉林工业大学 学报, 1982, (2): 1-5
    117 Qin Q H. Geometrically nonlinear analysis of shells by the variational approach and an efficient finite element formulation. Computers & Structures, 1995, 55(4): 727-733  
    118 唐立民, 刘迎曦. 多变量拟协调元法解流函数形式的两 维Navier-Stokes 方程. 大连工学院学报, 1987, 26(1): 1-7.
    119 刘迎曦, 尚选钰, 唐立民. 用惩罚拟协调元法分析二维N-S 问 题. 大连理工大学学报, 1989, 29(5): 511-518
    120 刘迎曦, 赵振峰, 王鸣, 等. Stokes 方程四节点有限单元的构 造及其收敛性研究. 水动力学研究与进展(A 辑), 1993, 8(2):176-183
    121 吴时强, 丁道扬, 刘金培. 三维对流问题的拟协调六面体单 元解法. 力学学报, 2000, 32(6): 676-685
    122 陈万吉, 陈伦元, 杨健. 拟协调奇异元. 固体力学学报, 1984, (3): 351-366
    123 汪小洪, 霍洪举, 金巨年. 表面裂纹拟协调有限元分析. 压力 容器, 1988, (4): 46-51
    124 汪小洪, 霍洪举, 金巨年. 拉弯复合应力下表面裂纹疲劳扩 展规律研究. 压力容器, 1990, 1(3): 25-29
    125 姚敬之. 奇应变拟协调元. 河海大学学报, 1988, 16(4): 72-83
    126 姚敬之. 关于奇应变拟协调元的一点注记. 河海大学学报,1991, 19(4): 127-129
    127 周建清, 高仁良. 三维奇性单元. 计算结构力学及其应用,1993, 10(1): 78-84
    128 Liu Y X, Tang L M. A triangular quasi-conforming finite element for transient dynamic analysis. Acta Mech Sinica,1990, 6 (1): 59-63  
    129 陈铁云, 周义先. 随机拟协调有限元. 计算结构力学及其应 用, 1990, 7(1): 17-24
    130 Hexiang L, Limin T, Xiaoling W. The upper bound on the collapse load of plate bending by using a quasi-conforming element and the Monte-Carlo method. Finite Elements in Analysis and Design, 1993, 13(1): 65-73  
    131 聂绍珉, 马克. 空间板系结构优化方法及应用. 东北重型机 械学院学报, 1989, 13(2): 7-13
    132 周承芳. 组合加肋旋转壳的强度和稳定性有限元分析. 计算 结构力学及其应用, 1990, 7(1): 45-53
    133 刘云忠. 纤维缠绕复合材料壳体的非线性大变形有限元分 析. 固体火箭技术, 1997, 20(2): 68-72
    134 常晓环, 李新钢, 刘应华. 正交各向异性旋转壳的极限分析. 清华大学学报(自然科学版), 2006, 46(11): 1908-1910
    135 刘均, 黄宝宗. 复合材料壁板中长桁的胶接应力分析. 辽宁 工程技术大学学报, 2007, 26(5): 679-681
    136 Pian T H H. State-of-the-art development of hybrid/ mixed finite element method. Finite Elements in Analysis and Design, 1995, 21(1-2): 5-20
    137 Zhang Z Q, Liu G R. An edge-based smoothed finite element method (ES-FEM) using 3-node triangular elements for 3D non-linear analysis of spatial membrane structures. International Journal for Numerical Methods in Engi- neering, 2010, 86(2): 135-154
    138 Zhang Z Q, Liu G R. Upper and lower bounds for natural frequencies: A property of the smoothed finite element methods. International Journal for Numerical Methods in Engineering, 2010, 84(2): 149-178
    139 Chen J S, Wu C T, Yoon S, et al. A stabilized conforming nodal integration for Galerkin mesh-free methods. Inter- national Journal for Numerical Methods in Engineering,2001, 50(2): 435-466  
    140 Liu G R, Nguyen T T. Smoothed Finite Element Methods. California: CRC Press, 2010
    141 Chen J S, Yoon S, Wu C T. Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering, 2002, 53(12): 2587-2615  
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