A New Rod Eigenelement and Its Application to Structural Static and Dynamic Analysis

The 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 the same precision. In order to calculate microscopic properties such stresses more precisely, a new eigenelement is proposed based on the variational principle and structural matrix eigenvector expansions, in which the eigen-shape functions are in zigzag form, then the discontinuous of materials and geometries is allowed in the eigenelement. Taking the composite rod, the new eigenelement is derived in details. In order to evaluate the new proposed eigenelement, the displacements, stresses and inherent frequencies are computed by using the 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 new 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.