B-spline finite element method based on node moving adaptive refinement strategy

•A spline element method constructed in practical domain can be dealt with as a meshless method.•A simple node moving strategy is proposed to refine the nodal distribution.•The Euler–Bernoulli beam and planar elasticity problems have been solved efficiently.

In this paper, an adaptive refinement procedure in conjunction with the B-spline finite element method is presented for the effective and efficient analysis of Euler–Bernoulli beam and planar elasticity problems. The B-spline plays a key role in the construction of stable wavelet on the interval, and there is actually no limitation for the interval. The spline elements are constructed in practical domain in this paper, and the spline bases concerns nodes distributed on the interval. As a result, the B-spline finite element method can be reconsidered as a meshless method. By repositioning the nodes of the spline bases, the accuracy of the method can be improved, and a simple node moving strategy is proposed to displace the nodal points to the areas indicated by the higher values of the error indicator. The efficiency and effectiveness of proposed B-spline finite element method and adaptive refinement technique are tested on some benchmark examples with the available analytical solutions and the results are presented.