Area coordinates and b-net method for quadrilateral spline elements

In general, there are two types of quadrilateralisoparametric elements, Serendipity type and Lagrangian type. The S-typeelements only possess low order completeness, and are sensitive to meshdistortions. The L-type elements possess high order completeness, butinclude interior nodes. By using numerical integrations due to isoparametrictransformation, the overall stiffness matrix may remain singular. In thispaper, a kind of quadrilateral spline elements are constructed by usingtriangular area coordinates interpolation and B-net method. These splineelements have property of conformality, and are insensitive to meshdistortions. The 8 and 12-node quadrilateral elements are represented bybivariate splines of degree 2 and 3, respectively. The two elements possess2 and 3 order completeness in Cartesian coordinates, higher than thecorresponding isoparametric elements with the same nodes. Some numericalexamples are employed to evaluate the performance of the proposed elements.The results show that the new spline elements present higher precision andefficiency in comparison with other quadrilateral elements.