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 • Previous Articles     Next Articles

Area coordinates and b-net method for quadrilateral spline elements

Juan Chen Chongjun Li Wanji Chen   

  1. Dalian University of Technology, Dalian 116023, China
  • Received:2008-08-25 Revised:2009-01-20 Online:2010-01-18 Published:2010-01-18

Abstract: 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.

Key words: Element bivariate spline, 8/12-node quadrilateral elements, Area coordinates, B-net method, element completeness order