Analysis of rigid frame by spline collocation method

In this paper, the application of the spline collocation method (SCM) to the analysis of rigid frame structures under various loading conditions is demonstrated originally and successfully. The derivation of the spline functions in the SCM is extended and simplified compactly through a finite difference approach that can be easily accepted by engineers. Without complicated calculation, the coefficient matrix for the weighting coefficients can be assembled simply by finding from the table the values of the quintic splines at knots. Since the coefficient matrix is invertible when the buckling problems of rigid frame are not considerered, the solution for the weighting coefficients always exists physically and uniquely. The feasibility of the proposed SCM formulation is first studied by the problem of the generalized beam analysis and excellent accuracy is achieved. The frame structure is considered to be the composition of beam elements approximately, then, the accuracy and efficiency of the SCM for frame structure analysis are illustrated numerically by practical examples. It is shown that the analysis of the two-dimensional frame problem by the SCM is stable and convergent, and its results agree well with FEM and DQM. Besides, the ease of using this method has been clearly shown.