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工程力学  2014 

基于向量式有限元的三角形薄板单元

DOI: 10.6052/j.issn.1000-4750.2012.09.0663, PP. 37-45

Keywords: 平板结构,向量式有限元,DKT薄板单元,质量矩阵,阻尼参数

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Abstract:

向量式有限元是一种基于点值描述和向量力学理论的新型分析方法。该文基于向量式有限元基本原理,推导了三角形DKT薄板单元的基本公式,详细阐述了通过逆向运动处理薄板单元的平面内、外刚体位移从而获得单元节点纯变形位移的过程,以及进一步通过变形坐标系获得单元节点内力的求解方法;同时对质点的质量矩阵与惯性矩阵、应力计算的数值积分及插值方法、时间步长及阻尼参数的取值等问题提出了合理可行的处理方式。在此基础上编制了薄板单元的计算分析程序,并进行了算例验证。算例分析表明所编制的向量式有限元薄板单元程序可以很好地完成平板结构的静、动力分析,验证了理论推导的正确性和分析程序的可靠性。该文成果为进一步建立向量式有限元薄壳单元理论打下了必要的基础。

References

[1]  Wu T Y, Wang C Y, Chuang C C, Ting E C. Motion analysis of 3D membrane structures by a vector form intrinsic finite element [J]. Journal of the Chinese Institute of Engineers, 2007, 30(6): 961―976.
[2]  Timoshenko S, Woinowsk S. Theory of plates and shells [M]. 2nd ed. McGraw-Hill Book Company, Inc, 1959.
[3]  曹志远. 板壳振动理论[M]. 北京: 中国铁道出版社, 1989.
[4]  Cao Zhiyuan. Vibration theory of plates and shells [M]. Beijing: China Railway Publishing House, 1989. (in Chinese)
[5]  翁志远. 梁板壳静动力学译文集(I)[M]. 上海: 同济大学出版社, 1986.
[6]  Weng Zhiyuan. Static and dynamic translation set-beams, plates and shells [M]. Shanghai: Tongji University Press, 1986. (in Chinese)
[7]  Clough R W, Tocher J L. Finite element stiffness matrices for analysis of plate bending [C]. Proceedings of the Conference on Matrix Methods in Structural Mechanics, in AFFDL TR 66-80, 1966: 515―545.
[8]  Bazeley G P, Cheung Y K, Irons B M, Zienkiewicz O C. Triangular elements in plate bending, conforming and non-conforming solutions [C]. Proceedings of 1st Conference on Matrix Methods in Structural Mechanics, Wright-Patterson AFB, 1965: 547―576.
[9]  Batoz J, Bathe K, Ho L. A study of three-node triangular plate bending elements [J]. International Journal for Numerical Methods in Engineering, 1980, 15(12): 1771―1812.
[10]  Batos J. An explicit formulation for efficient triangular plate-bending element [J]. International Journal for Numerical Methods in Engineering, 1982, 18(7): 1077―1089.
[11]  Soh A K, Ling C. An improved discrete Kirchhoff triangular element for bending, vibration and buckling analyses [J]. European Journal of Mechanics A-Solids, 2000, 19(5): 891―910.
[12]  Ting E C, Shih C, Wang Y K. Fundamentals of a vector form intrinsic finite element: Part I. Basic procedure and a plane frame element [J]. Journal of Mechanics, 2004, 20(2): 113―122.
[13]  Ting E C, Shih C, Wang Y K. Fundamentals of a vector form intrinsic finite element: Part II. Plane solid elements [J]. Journal of Mechanics, 2004, 20(2): 123―132.
[14]  Ting E C, Shih C, Wang Y K. Fundamentals of a vector form intrinsic finite element: Part III. Convected material frame and examples [J]. Journal of Mechanics, 2004, 20(2): 133―143.
[15]  Wu T Y, Ting E C. Large deflection analysis of 3D membrane structures by a 4-node quadrilateral intrinsic element [J]. Thin-Walled Structures, 2008, 46(3): 261―275.
[16]  王勖成. 有限单元法[M]. 北京: 清华大学出版社, 2003: 150―152.
[17]  Wang Xucheng. Finite element method [M]. Beijing: Tsinghua University Press, 2003: 150―152. (in Chinese)
[18]  王勖成, 邵敏. 有限单元法基本原理和数值方法[M]. 第二版. 北京:清华大学出版社, 1997: 144―155.
[19]  Wang Xucheng, Shao Min. The basic principle and numerical method of finite element method [M]. 2nd ed. Beijing: Tsinghua University Press, 1997: 144―155. (in Chinese)
[20]  何东升, 唐立民. 弱连续条件下的九参三角形板元[J]. 力学学报, 2002, 34(6): 924―934.
[21]  He Dongsheng, Tang Limin. The 9-parameters triangular plate element in weak form [J]. Chinese Journal of Theoretical and Applied Mechanics, 2002, 34(6): 924―934. (in Chinese)

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