AN IMPLICIT SERIES PRECISE INTEGRATION ALGORITHM FOR STRUCTURAL NONLINEAR DYNAMIC EQUATIONS

• Published in: 固体力学学报（英文版） Vol. 18; no. 1; pp. 70 - 75
• Main Authors: Li Yuanyin, Jin Xianlong, Wang Yuanqing
• Format: Journal Article
• Language: English
• Published: High Performance Computing Center, Shanghai Jiaotong University, Shanghai 200030, China%School of Civil Engineering, Tsinghua University, Beijing 100084, China 01.03.2005
• Subjects: numerical integration; implicit series solution; exponential matrix; nonlinear dynamic system; precise integration method
• ISSN: 0894-9166
• DOI: 10.1007/s10338-005-0510-7

Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these algorithms. If the inversion of the matrix doesn't exist or isn't stable, the precision and stability of the algorithms will be affected. An explicit series solution of the state equation has been presented. The solution avoids calculating the inversion of a matrix and its precision can be easily controlled. In this paper, an implicit series solution of nonlinear dynamic equations is presented.The algorithm is more precise and stable than the explicit series solution and isn't sensitive to the time-step. Finally, a numerical example is presented to demonstrate the effectiveness of the algorithm.