Adv. Appl. Math. Mech., 2 (2010), pp. 784-797.
Published online: 2010-02
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This paper analyzes a nonconforming 5-node quadrilateral transition finite element for Poisson equation. This element was originally proposed by Choi and Park [Computers and Structures, 32 (1989), pp. 295–304 and Thin-Walled Structures, 28 (1997), pp. 1–20] for the analysis of Mindlin plates. We show the consistency error of this element is only $\mathcal{O}(h^{1/2})$ over the transition edges of the quadrilateral subdivision. By modifying the shape functions with respect to mid-nodes, we get an improved version of the element for which the consistency error is $\mathcal{O}(h)$. Numerical examples are provided to verify the theoretical results.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m09110}, url = {http://global-sci.org/intro/article_detail/aamm/8360.html} }This paper analyzes a nonconforming 5-node quadrilateral transition finite element for Poisson equation. This element was originally proposed by Choi and Park [Computers and Structures, 32 (1989), pp. 295–304 and Thin-Walled Structures, 28 (1997), pp. 1–20] for the analysis of Mindlin plates. We show the consistency error of this element is only $\mathcal{O}(h^{1/2})$ over the transition edges of the quadrilateral subdivision. By modifying the shape functions with respect to mid-nodes, we get an improved version of the element for which the consistency error is $\mathcal{O}(h)$. Numerical examples are provided to verify the theoretical results.