A family of spline finite elements

In this paper, a new family of plane quadrilateral spline elements is proposed. Four quadrilateral elements with 4, 8, 12 and 17 nodes are constructed, which possess completeness of orders 1, 2, 3 and 4 in the Cartesian coordinates, respectively. The displacement interpolation functions of the 8, 12 and 17-node elements possess higher order completeness than the corresponding quadrilateral isoparametric elements with the same nodes, and the resulting stresses are continuous within the element. Some numerical examples are given, in comparison with other known elements from the literatures, and the results show that the proposed elements are competitive.