A new function transform technique for the solution of FEM dynamic equations

A new function transform, based on the differential recurrence function series, is proposed, and its computational characteristics are investigated in this paper. The recurrence formulae, for the dynamic response analysis of structural systems, are established based on the proposed function transform algorithm. For a proposed kernel function M_k(t), the stability and computational accuracy of the algorithm are studied. In order to investigate the computational accuracy and efficiency of the proposed algorithm, two numerical examples are given. Example 1 shows that the algorithm holds the advantage of high precision. Especially at the tail of the response curves, the computational results obtained by the proposed algorithm are closer to the analytical solutions than those obtained by the Wilson θ method. The second example shows that even the transform kernel function is not orthogonal, the proposed algorithm holds the advantage of the short computational time since the solution of the equations is a continuous function of time.