HOMOGENIZED PRECISE INTEGRATION METHOD BASED ON FOURIER TRANSFORMATION

The precise integration method proposed for linear time-invariant homogeneous dynamic system can give precise numerical results approaching to the exact solution at the integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equations is converted into homogeneous dynamic equations, nonlinearly varying loadings are decomposed into Fourier components, a kind of precise integration method without the inverse matrix calculation is set up, the cut-off criteria of determining the truncated integer q are presented, and the numerical stability and accuracy of the proposed algorithm are discussed in detail. The proposed algorithm has enhanced the present precise integration method by benefiting the computational accuracy and computational efficiency. Two numerical examples are given to demonstrate the validity and efficiency of these algorithms.