A generalized infinite element is presented by combining following aspects: (1) The geometry mapping in the Cartesian system is chosen so as to facilitate the generation of infinite element mesh; (2) The decay variable is defined as the in situ major axis of the confocal ellipse where the field point is located, so it is dependent not only on the infinite-directional coordinate but on the finite-directional one(s); (3) The shape function is constructed so that it exactly satisfies the multipole expansion along the edges of the infinite element; (4) The conjugated weighting function is adopted to eliminate the harmonic terms from the integrands; and (5) the more proper form of phase factor and weighting factor is recommended. Compared with the Bettess element and the Astley element, the present element greatly reduces the element number within the finite element zone for problems with a large aspect ratio. Compared with the Burnett element and the modified Burnett element, the present element permits the free orientation of the infinite element, and thereby is suitable for more general exterior problems, either of a closed surface (source) or of an opening surface (source). Several typical examples are given and their results show that the generalized infinite element is robust and flexible.

This paper presents a unified approach to predict the overall elastic properties of homogeneous and isotropic composite materials from the micromechanics point of view. Within the framework of the approach, the commonly used approaches such as dilute estimate, Voigt estimate (VE), Reuss estimate (RE), modified rule of mixture, self-consistent estimate (SCE), Mori-Tanaka estimate (MTE) and Wakashima-Tsukamoto estimate (WTE) are expressible in the same form solely with different parameters. Particularly, the Voigt bound (VB) and Reuss bound (RB), as well as the Hashin-Shtrikman bounds (HSBs), are easily obtained by properly choosing the homogeneous comparison material. Furthermore, in light of the present approach, tighter than Hashin-Shtrikman bounds are proposed that can also be regarded as two kinds of estimates.

In this paper, the problems involved in the process of degeneration of quadrilateral element into triangular element are thoroughly analysed. The contents include the formulation of the geometry mapping induced by collapsing one side of the quadrilateral element and the construction of the shape functions. The study focuses first on a 4-node bilinear quadrilateral (Q4) element to 3-node constant strain triangular (CST) element, and then on a 8-node serendipity (Q8) element to 6-node triangular element(T6). In the analysis, the quadrilateral element and degenerate triangular element are assumed to be enclosed by straight edges. The theoretical results show that there is another better approach to realize the degeneration, and that even for conventional approach of degeneration we can give more reasonable explanation to the unclear problems like the CST property in degenerate CST element and the necessity of the additional terms in degenerate T6 element. Copyright

A criterion is proposed first to quantitatively check the interpolation precision of quadrilateral elements. With this criterion, the necessary geometry constraints are derived for 8-node (Q8) element to exactly attain quadratic interpolation precision. The study is next to focus on improvement of the Q8 element with a bilinear configuration and the Q8 element is subsequently presented by slightly modifying the Q8 element. Theoretical analysis is conducted as well to confirm the interpolation precision predicted in the Q8 element. Through typical numerical examples, it is concluded that of all the tested elements the second-order integrated Q8 element is the most robust one for all cases.