A new 8-node quadrilateral spline finite element

By using bivariate quadratic splines on triangulated quadrangulations (or FVS triangulations), we construct a new 8-node quadrilateral element, which reproduces polynomials of degree 2, and possesses second-order completeness in Cartesian coordinates. The computation of derivatives, integrals and products of the element shape functions can be simplified greatly by using their Bézier coefficients on each triangle cell. Some appropriate examples are employed to evaluate the performance of the proposed element. The numerical results show that the new spline element is superior to the standard 8-node isoparametric element, and is comparable to some other 8-node quadrilateral elements.