Eight‐node conforming straight‐side quadrilateral element with high‐order completeness (QH8‐C1)

Summary A new eight‐node conforming quadrilateral element with high‐order completeness, denoted as QH8‐C1, is proposed in this article. First, expressions for the interpolation displacement function satisfying the requirements for high‐order completeness in the global coordinate system are construct...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2020-08, Vol.121 (15), p.3339-3361
Main Authors: Zhang, Guoxiang, Xiang, Junyu
Format: Article
Language:English
Subjects:
antidistortion
Completeness
Computer simulation
conformity
Convergence
Coordinates
Derivation
Displacement
eight‐node quadrilateral element
Finite element method
high‐order completeness
high‐performance finite element
Interpolation
monotonic convergence
Polynomials
Quadrilaterals
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Summary:Summary A new eight‐node conforming quadrilateral element with high‐order completeness, denoted as QH8‐C1, is proposed in this article. First, expressions for the interpolation displacement function satisfying the requirements for high‐order completeness in the global coordinate system are constructed. Second, the displacement function expression in global coordinates is transformed into isoparametric coordinates, and the relationships between the two series of coefficients for the two kinds of displacement function expressions are found. Third, the displacement function expression is modified to satisfy the requirements of nodal freedom and interelement boundary continuity. The key to the new element construction is the derivation of the linear relationship expressions among 12 coefficients of element displacement interpolation polynomials in the global and isoparametric coordinate systems. As a result, the relationship between quadratic completeness and interelement continuity is explicitly given, and a proof of the completeness and the continuity was conducted to theoretically guarantee the validity of the derivation results. Furthermore, in order to verify the correctness of the theoretical work, nine numerical examples were performed. The computation results from these examples demonstrate that QH8‐C1 exhibited excellent performance, including high simulation accuracy, fast convergence, insensitivity to mesh distortion, and monotonic convergence.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6360