Chinese Journal of Theoretical and Applied Mechani ›› 2010, Vol. 42 ›› Issue (1): 83-92.DOI: 10.6052/0459-1879-2010-1-2008-501
• Research paper •
Juan Chen Chongjun Li Wanji Chen
In general, there are two types of quadrilateral
isoparametric elements, Serendipity type and Lagrangian type. The S-type
elements only possess low order completeness, and are sensitive to mesh
distortions. The L-type elements possess high order completeness, but
include interior nodes. By using numerical integrations due to isoparametric
transformation, the overall stiffness matrix may remain singular. In this
paper, a kind of quadrilateral spline elements are constructed by using
triangular area coordinates interpolation and B-net method. These spline
elements have property of conformality, and are insensitive to mesh
distortions. The 8 and 12-node quadrilateral elements are represented by
bivariate splines of degree 2 and 3, respectively. The two elements possess
2 and 3 order completeness in Cartesian coordinates, higher than the
corresponding isoparametric elements with the same nodes. Some numerical
examples are employed to evaluate the performance of the proposed elements.
The results show that the new spline elements present higher precision and
efficiency in comparison with other quadrilateral elements.
Element bivariate spline,
8/12-node quadrilateral elements,
element completeness order
Juan Chen Chongjun Li Wanji Chen. Area coordinates and b-net method for quadrilateral spline elements[J]. Chinese Journal of Theoretical and Applied Mechani, 2010, 42(1): 83-92.
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