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 引用本文: 邢誉峰 杨阳. 形函数分段定义的弯矩梁特征单元[J]. 力学学报, 2008, 40(2): 222-228.
Yufeng Xing, Yang Yang. A bending moment beam eigenelement with piecewise shape functions[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(2): 222-228.
 Citation: Yufeng Xing, Yang Yang. A bending moment beam eigenelement with piecewise shape functions[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(2): 222-228.

## A bending moment beam eigenelement with piecewise shape functions

• 摘要: 基于势能原理，根据梁单胞在单位弯矩作用下的静力特性分析，提出了一种允许单元内部存在材料和几何性质不连续的新的梁特征单元，称之为弯矩梁特征单元. 与已有特征单元方法、均匀化方法和一般有限元方法进行了数值比较和分析，位移、内力和频率结果说明了弯矩梁特征单元在精度和效率方面的优越性. 弯矩梁特征单元具有双尺度特征，为构造编织等周期性复合材料结构的宏细观力学行为分析提供了一种思想和方法.

Abstract: The classic eigenelement method is proposed by XING Yufeng and TIAN Jinmei recently. This method can be used to deal with the macroscopic properties such as frequencies and elastic parameters of composites. Compared to conventional homogenization method, the classic eigenelement method calculates the global stiffness of unit cell directly, instead the homogeneous modules. The eigenelement method is more precise than the conventional homogenization method with the same number of elements, and the amount of computational work reduces greatly compared with the ordinary finite element method with a good agreement between them. In order to calculate microscopic properties more precisely, a bending moment beam eigenelement is proposed based on the variational principle, in which the eigen-shape functions are defined in segments, so the discontinuous of materials and geometries is allowed within the beam eigenelement.The bending moment beam eigenelement is derived in details according to the static analysis of the beam cell subjected to a unit bending moment at one end. In order to evaluate the new proposed bending moment beam eigenelement (BBEE), the displacements, stresses and inherent frequencies are computed by using the new beam eigenelement method, ordinary finite element method, the classic eigenelement method and conventional homogenization method respectively. The comparison among the results by different methods, show that the bending moment eigenelement method is more precise than the classic eigenelement method and conventional homogenization method with the same number of elements. The larger the difference of parameters for each subelement in eigenelement is, the larger the advantages of the eigenelement. And the amount of computational work reduces greatly compared to the ordinary finite element method with the same precision.

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