Radial spline collocation method for static analysis of beams

Conventional spline collocation method (SCM) uses equally spaced knots in the computation of approximation. However, when load distribution, geometry, material property of structure are discontinuous, it will greatly reduce accuracy. The goal of this paper is mainly to develop unequally spaced knots to improve the disadvantage of using equally spaced knots. Applying the concept of radial basis functions (RBF), the spline function is transformed into radial spline function (RSF). Consequently, RSF can conveniently calculate the values for unequally spaced knots, so that the complicated beam problems with discontinuous characteristics can be solved accurately and efficiently by the proposed radial spline collocation method (RSCM) in this paper. The proposed RSCM also can be extended to solve other structural problems such as frame, plate, shell, etc.