Advanced Steel Construction

Vol. 16, No. 2, pp. 124-136 (2020)




Zhi-xia Ding 1, Zuo-lei Du 1, Wei Su 2, * and Yao-peng Liu 1,3

1 Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

2 School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou, 510275, China

3 Nida Technology Co. Ltd., Hong Kong Science Park, Shatin, N.T., Hong Kong, China

* (Corresponding author: E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.)

Received: 13 April 2019; Revised: 17 November 2019; Accepted: 3 December 2019




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In this paper, a refined precise integration method (RPIM) is proposed for nonlinear dynamic analysis of structures. It extends the conventional precise integration method (PIM) from linear analysis to nonlinear analysis through a novel algorithm to improve the conventional Duhamel integration method for nonhomogeneous parts in nonlinear equations. In the RPIM, the stiffness matrix of the motion equation can be updated during the analysis, leading to the proposed method applicable to nonlinear structural problems. With the introduction of a new velocity vector, the original exponential matrix in PIM is reduced to a 2×2 matrix and the efficiency of RPIM is highly improved for both computation time and storage space. The analysis of stability and accuracy shows that the RPIM is unconditionally stable with highly precision. Four examples, including linear analysis of free and forced vibration and nonlinear analysis of two structures, i.e. truss and membrane, are analyzed to verify the efficiency and accuracy of the proposed RPIM.



Refined precise integration method, Nonlinear dynamic analysis, Stiffness matrix, Efficiency and accuracy


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