四边形元向三角形元退化的研究

L. Li, X.-P. Han, S.-q. Xu
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引用次数: 5

摘要

本文对四边形单元退化为三角形单元过程中所涉及的问题进行了深入的分析。其内容包括四边形单元单侧塌缩引起的几何映射的公式和形状函数的构造。首先研究了4节点双线性四边形(Q4)单元到3节点恒应变三角形(CST)单元,然后研究了8节点偶然性(Q8)单元到6节点三角形单元(T6)。在分析中,假定四边形单元和退化三角形单元被直边包围。理论结果表明,存在另一种更好的退化方法,即使采用传统的退化方法,也能更合理地解释退化CST单元的CST性质和退化T6单元中附加项的必要性等不明确的问题。版权所有©2004 John Wiley & Sons, Ltd
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Study on the degeneration of quadrilateral element to triangular element
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 © 2004 John Wiley & Sons, Ltd.
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