U-transformation finite element method in analysis of Reissner rectangular plates
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摘要: 将U变换法推广应用于Reissner矩形板的有限元分析中.对原结构进行等效变换,形成周期循环的板单元,使刚度矩阵成为循环矩阵,应用双重U变换解耦了有限元的矩阵方程,使有限元计算只须在一个板单元上进行,并且仍能方便分析整个板的一般分布载荷.所发展的U变换-有限元法不仅提高了计算效率,很快收敛于精确解,对于简支板还给出了精确分析的有限元解、准确的误差估计表达式和收敛速度,可以直接掌控计算精度,这是其它方法难以得到的.对简支和固支矩形板的数值算例及与其它方法的对比说明了U变换-有限元法的优点和重要的工程实用价值.
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关键词:
- Reissner矩形板 /
- U变换 /
- 有限元法 /
- 误差分析
Abstract: The U-transformation method was applied to the Reissner rectangular plates. The actual plate was extended to make up an equivalent cyclic periodicity system and the plate elements become cyclic periodic elements, whereby the stiffness matrix become a cyclic matrix and the finite element matrix equation was uncoupled by using double U-transformation. This method can easily analyze the plate with arbitrarily distributed loads and the calculation is only performed for one element. The method has high computational efficiency and can quickly converge to exact solutions. The exact analytical finite element solution, the exact error expression and exact convergence rate are derived. These results can be not obtained if other methods are used instead. Numerical examples of rectangular plates with simply supported or clamped edges and a comparison with other methods show the advantages and practical importance of the U-transformation finite element method in engineering analysis.-
Key words:
- Reissner rectangular plates /
- U-transformation /
- finite element method /
- error analysis
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[1] 党发宁,荣廷玉,孙训方.Reissner板问题的有限元广义混合法[J].计算力学学报,2000,17(2):218-221 Dang Faning,Rong Tingyu, Sun Xunfang. Generalized mixed finite elements method of Reissner plates[J]. Chinese Journal of Computational Mechanics,2000, 17(2):218-221(in Chinese) [2] Gagnon P,GosselIn C, Cloutier L.A finite strip element for the analysis of variable thickness rectangular thick plates[J]. Computers and Structures,1997,63(2):349-362 [3] Liu F L, Liew K M.Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method[J]. Journal of Sound and Vibration, 1999,225(5): 915-934 [4] Civalek O. Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method[J]. International Journal of Mechanical Sciences,2007,49(6):752-765 [5] Chan H C,Cai C W,Cheung Y K. Exact analysis of structures with periodicity using U-transformation[M]. Singapore: World Scientific, 1998 [6] 龙志飞,岑松.有限元法新论——原理·程序·进展[M].北京:中国水利水电出版社,2001 Long Zhifei, Cen Song. Finite element method: principle,program and advancement [M]. Beijing: China Water Conservancy and Hydropower Press, 2001(in Chinese) [7] 中国科学院北京力学研究所,固体力学研究室板壳组.夹层板壳的弯曲、稳定和振动[M].北京:科学出版社,1977 Chinese Academy of Science Beijing Mechanics Research Institute, Plate Group of Solid Mechanics Research Office. The bending, stabilization and vibration of sandwich plate and shell[M].Beijing:Science Press, 1977(in Chinese) -
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