A multi-step transversal linearization (MTL) method in non-linear structural dynamics

Journal of Sound and Vibration

Volumn 287, Issue 1-2, 2005, Pages 203-226

  Roy, D ^a   Kumar, Rajesh ^b  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

DAMPING; INTEGER PROGRAMMING; INTEGRATION; INTERPOLATION; LAGRANGE MULTIPLIERS; NONLINEAR SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; OSCILLATORS (MECHANICAL); RUNGE KUTTA METHODS; STIFFNESS MATRIX; STRUCTURAL ANALYSIS; VECTORS;

LOCALLY TRANSVERSAL LINEARIZATION (LTL); MULTI-STEP TRANSVERSAL LINEARIZATION (MTL) METHOD; NONLINEAR OSCILLATORS; VELOCITY VECTORS;

LINEARIZATION;

EID: 22344444345     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2004.11.032     Document Type: Article

References (26)

1. N.M. Newmark A method of computation for structural dynamics Journal of Engineering Mechanics Division ASCE 85 1955 67 94
2. T. Belytschko T.J.R. Hughes Computational Methods for Transient Analysis 1983 North-Holland Amsterdam
3. R.I. McLachlan, G.R.W. Quispel, and N. Robidoux Geometric integration using discrete gradients Proceedings of the Academy of the Royal Society (London) 357 1999 1021 1045
4. R.D. Richtmyer, and K.W. Morton Difference Methods for Initial Value Problems 1967 Interscience New York
5. R.I. McLachlan, G.R.W. Quispel, and G.S. Turner Numerical integrators that preserve symmetries and reversing symmetries SIAM Journal of Numerical Analysis 35 1998 586 599
6. O.C. Zienkiewicz, and R.L. Taylor The Finite Element Method - Vol. 2 1991 McGraw Hill United Kingdom
7. A. Iserles, and S.P. Norsett On the solution of linear differential equations in Lie groups Proceedings of the Academy of the Royal Society (London) 357 1999 983 1019
8. S. Blanes, and F. Casas Optimization of Lie group methods for differential equations Future Generation Computer Systems 19 2003 331 339
9. A. Zanna Collocation and relaxed collocation for the Fer and the Magnus expansions SIAM Journal of Numerical Analysis 36 1999 1145 1182
10. A. Marthinsen Interpolation in Lie groups SIAM Journal Numerical Analysis 37 1999 269 285
11. D. Roy, and L.S. Ramachandra A generalized local linearization principle for non-linear dynamical systems Journal of Sound and Vibration 41 2001 653 679
12. D. Roy, and L.S. Ramachandra A semi-analytical locally transversal linearization method for non-linear dynamical systems International Journal for Numerical Methods in Engineering 51 2001 203 224
13. L.S. Ramachandra, and D. Roy A new method for non-linear two-point boundary value problems in solid mechanics ASME, Journal of Applied Mechanics 68 2001 776 786
14. L.S. Ramachandra, and D. Roy A novel technique in the solution of axisymmetric large deflection analysis of circular plates ASME, Journal of Applied Mechanics 68 2001 814 816
15. D. Roy A family of lower- and higher-order transversal linearization techniques in non-linear stochastic engineering dynamics International Journal of Numerical Methods in Engineering 61 2004 764 790
16. G.W. Wei, D.S. Zhang, D.J. Kouri, and D.K. Hoffman A robust and reliable approach to nonlinear dynamical problems Computer Physics Communicators 111 1998 87 92
17. N. Saito, and G. Beylkin Multi-scale representations using autocorrelation functions of compactly supported wavelets IEEE Transactions on Signal Processing 41 1993 3584 3590
18. C. Moler, and C. Van Loan Nineteen dubious ways to compute the exponential of a matrix; twenty five years later SIAM Review 45 2003 3 49
19. J.H. Verner Some Runge-Kutta formula pairs SIAM Journal of Numerical Analysis 28 1991 496 511
20. T.E. Simos, and G. Papakaliatakis Modified Runge-Kutta Verner methods for numerical solution of initial and boundary-value problems with engineering applications Applied Mathematical Modelling 22 1999 657 670
21. W. Magnus On the exponential solution of differential equations for a linear operator Communications in Pure and Applied Mathematics 7 1954 649 673
22. J.C. Simo, and L. Vu-Quoc A three-dimensional finite strain rod model - part II: computational aspects Computer Methods in Applied Mechanics and Engineering 58 1986 79 116
23. A. Cardona, and M. Geradin A beam finite element nonlinear theory with finite rotations International Journal of Numerical Methods in Engineering 26 1988 2403 2438
24. K. Hoffman, and R. Kunze Linear Algebra Second Edition 1991 Prentice-Hall Englewood Cliffs, NJ
25. J.D. Lawson Generalized Runge-Kutta processes for stable systems with large Lipschitz constants SIAM Journal on Numerical Analysis 4 1967 372 380
26. D. Roy A new numerical-analytical principle for nonlinear deterministic and stochastic dynamical systems Proceedings of the Academy of the Royal Society (London) 457 2001 539 566