Renewal precise time step integration method of structural dynamic analysis
结构动力方程的更新精细积分方法

The precise time step 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,it is more or less difficult when the algorithm is used to the non-homogeneous dynamic systems due to the inverse matrix calculation and the simulation accuracy of the applied loading.By combining the Gauss quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method,a new precise time step integration method (that is renewal precise time step integration method) is proposed.The new method avoids the inverse matrix calculation and the simulation of the applied loading and improves the computing efficiency.In particular,the method is independent to the quality of the matrix H.If the matrix H is singular or nearly singular,the advantage of the method is remarkable.The proposed method in this paper is a unconditionally stable algorithm having an arbitrary order of accuracy.Numerical examples are given to demonstrate the validity and efficiency of the algorithm.