Browse > Article
http://dx.doi.org/10.12989/sem.2012.43.1.001

A fast precise integration method for structural dynamics problems  

Gao, Q. (State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology)
Wu, F. (State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology)
Zhang, H.W. (State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology)
Zhong, W.X. (State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology)
Howson, W.P. (Cardiff School of Engineering, Cardiff University)
Williams, F.W. (Cardiff School of Engineering, Cardiff University)
Publication Information
Structural Engineering and Mechanics / v.43, no.1, 2012 , pp. 1-13 More about this Journal
Abstract
A fast precise integration method (FPIM) is proposed for solving structural dynamics problems. It is based on the original precise integration method (PIM) that utilizes the sparse nature of the system matrices and especially the physical features found in structural dynamics problems. A physical interpretation of the matrix exponential is given, which leads to an efficient algorithm for both its evaluation and subsequently the solution of large-scale structural dynamics problems. The proposed algorithm is accurate, efficient and requires less computer storage than previous techniques.
Keywords
structural dynamics system; sparse matrix; precise integration method; matrix exponential; fast algorithm;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Bathe, K.J. and Wilson, E.L. (1976), Numerical Methods in Finite Element Analysis, Prentice-Hall, New Jersey.
2 Cai, Z.Q., Gu, Y.X. and Zhong, W.X. (2001), "A new approach of computing Floquet transition matrix", Comput. Struct., 79(6), 631-635.   DOI   ScienceOn
3 Chen, B.S., Gu, Y.X., Guan, Z.Q. and Zhang, H.W. (2001), "Nonlinear transient heat conduction analysis with precise time integration method", Numer. Heat Tr. B-Fund., 40(4), 325-341.   DOI   ScienceOn
4 Fu, M.H., Cheung, M.C. and Sheshenin, S.V. (2010), "Precise integration method for solving singular perturbation problems", Appl. Math. Mech., 31(11), 1463-1472.   DOI   ScienceOn
5 Fung, T.C. (1997), "A precise time-step integration method by step-response and impulsive-response matrices for dynamic problems", Int. J. Numer. Meth. Eng., 40(24), 4501-4527.   DOI   ScienceOn
6 Fung, T.C. and Chen, Z.L. (2006), "Krylov precise time-step integration method", Int. J. Numer. Meth. Eng., 68(11), 1115-1136.   DOI   ScienceOn
7 Gu, Y.X., Chen, B.S., Zhang, H.W. and Guan, Z.Q. (2001), "Precise time-integration method with dimensional expanding for structural dynamic equations", AIAA J., 39(12), 2394-2399.   DOI   ScienceOn
8 Hairer, E., Lubich, C. and Wanner, G. (2006), Geometric Numerical Integration: Structure-preserving Algorithm for Ordinary Differential Equations, 2nd Edition, Springer, New York.
9 Hairer, E., Norsett, S.P. and Wanner, G. (1993), Solving Ordinary Differential Equations I-nonstiff Problems, 2nd Edition, Springer, Berlin.
10 Hairer, E. and Wanner, G. (1996), Solving Ordinary Differential Equations II-stiff and Differential- Algebraic Problems, 2nd Edition, Springer, Berlin.
11 Jia, L., Shi, W. and Guo, J. (2008), "Arbitrary-difference precise-integration method for the computation of electromagnetic transients in single-phase nonuniform transmission line", IEEE Trans. Power Del., 23(3), 1488-1494.
12 Leung, A.Y.T. (2001), "Fast matrix exponent for deterministic or random excitations", Int. J. Numer. Meth. Eng., 50(2), 377-394.   DOI   ScienceOn
13 Lin, J.H., Shen, W.P. and Williams, F.W. (1995), "A high precision direct integration scheme for structures subjected to transient dynamic loading", Comput. Struct., 56(1), 113-120.   DOI   ScienceOn
14 Lin, J.H., Shen, W.P. and Williams, F.W. (1997), "Accurate high-speed computation of non-stationary random structural response", Eng. Struct., 19(7), 586-593.   DOI   ScienceOn
15 Lin, J.H., Shen, W.P. and Williams, F.W. (1997), "Accurate high-speed computation of non-stationary random structural response", Eng. Struct., 19(7), 586-593.   DOI   ScienceOn
16 Moler, C. and Loan, C.V. (1978), "Nineteen dubious ways to compute the exponential of a matrix", SIAM Rev., 20(4), 801-836.   DOI   ScienceOn
17 Moler, C. and Loan, C.V. (2003), "Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later", SIAM Rev., 45(1), 1-46.   DOI
18 Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech.-ASCE, 85(3), 67-94.
19 Shen, W.P., Lin, J.H. and Williams, F.W. (1995), "Parallel computing for the high precision direct integration method", Comput. Meth. Appl. M., 126(3-4), 315-331.   DOI
20 Wang, M.F. and Au, F.T.K. (2007), "Precise integration method without inverse matrix calculation for structural dynamic equations", Earthq. Eng. Vib., 6(1), 57-64.   DOI   ScienceOn
21 Wang, M.F. and Au, F.T.K. (2006), "Assessment and improvement of precise time step integration method", Comput. Struct., 84(12), 779-786.   DOI   ScienceOn
22 Wang, M.F. and Au F.T.K. (2009), "Precise integration methods based on Lagrange piecewise interpolation polynomials", Int. J. Numer. Meth. Eng., 77(7), 998-1014.   DOI   ScienceOn
23 Wang, M.F. (2011), "Reduced-order precise integration methods for structural dynamic equations", Int. J. Numer. Meth. Biomed. Eng., 27(10), 1569-1582.   DOI   ScienceOn
24 Zhang, H.W., Chen, B.S. and Gu, Y.X. (2001), "An adaptive algorithm of precise integration for transient analysis", ACTA Mech. Solida Sin., 14(3), 215-224.
25 Zhong, W.X., Zhu, J. and Zhong, X.X. (1996), "On a new time integration method for solving time dependent partial differential equations", Comput. Meth. Appl. M., 130(1-2), 163-178.   DOI
26 Zhang, H.W., Zhang, X.W. and Chen, J.S. (2003), "A new algorithm for numerical solution of dynamic elastic- plastic hardening and softening problems", Comput. Struct., 81(17), 1739-1749.   DOI   ScienceOn
27 Zhong, W.X. (2004), "On precise integration method", J. Comput. Appl. Math., 163(1), 59-78.   DOI   ScienceOn
28 Zhong, W.X. and Williams, F.W. (1994), "A precise time step integration method", P. I. Mech. Eng. C-J. Mec., 208(6), 427-430.   DOI