Precise integration method without inverse matrix calculation for structural dynamic equations

• Published in: Earthquake Engineering and Engineering Vibration Vol. 6; no. 1; pp. 57 - 64
• Main Author: 汪梦甫 F．T．K．Au
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.03.2007; Department of Civil Engineering, Hunan University, China%Department of Civil Engineering, The University of Hong Kong, China
• Subjects: Algorithms; Crout分解法; Decomposition; Dynamical systems; Mathematics; Structural engineering; 可逆矩阵计算; 数值积分; 结构动力学方程; 计算精度; numerical integration; matrix exponential function; inverse matrix calculation; Crout decomposed method; structural dynamics
• ISSN: 1671-3664; 1993-503X
• DOI: 10.1007/s11803-007-0661-2

The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at 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 equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.