On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity

Kim Jie Koh; Airil Yasreen Mohd Yasreen

doi:10.1051/matecconf/201711101004

All issues

Volume 111 (2017)

MATEC Web Conf., 111 (2017) 01004

References

Open Access

Issue		MATEC Web Conf. Volume 111, 2017 Fluids and Chemical Engineering Conference (FluidsChE 2017)


Article Number		01004
Number of page(s)		8
Section		Advances in Fluids Flow and Mechanics
DOI		https://doi.org/10.1051/matecconf/201711101004
Published online		20 June 2017

K. J. Bathe, Finite element procedures, Klaus-Jurgen Bathe, 2006. [Google Scholar]
K. J. Bathe and A. P. Cimento, “Some practical procedures for the solution of nonlinear finite element equations,” Computer methods in applied mechanics and engineering, vol. 22, no. 1, pp. 59–85, 1980. [CrossRef] [Google Scholar]
K. J. Bathe and E. N. Dvorkin, “On the automatic solution of nonlinear finite element equations,” Computers & Structures, vol. 17, no. 5, pp. 871–879, 1983. [CrossRef] [Google Scholar]
J. R. Morison, J. W. Johnson and S. A. Schaaf, “The force exerted by surface waves on piles,” Journal of Petroleum Technology, vol. 2, no. 05, pp. 149–154, 1960. [Google Scholar]
S. Chakrabarti, Handbook of Offshore Engineering (2-volume set), Elsevier, 2005. [Google Scholar]
V. H. Safai, “Nonlinear dynamic analysis of deep water risers,” Applied Ocean Research, vol. 5, no. 4, pp. 215–225, 1983. [CrossRef] [Google Scholar]
N. Haritos and D. T. He, “Modelling the response of cable elements in an ocean environment,” Finite Elements in Analysis and Design, vol. 11, no. 1, pp. 19–32, 1992. [Google Scholar]
J. I. Gobat and M. A. Grosenbaugh, “Time-domain numerical simulation of ocean cable structures,” Ocean Engineering, vol. 33, no. 10, pp. 1373–1400, 2006. [CrossRef] [Google Scholar]
A. K. Jain, “Nonlinear coupled response of offshore tension leg platforms to regular wave forces,” Ocean Engineering, vol. 24, no. 7, pp. 577–592, 1997. [CrossRef] [Google Scholar]
M. H. Patel, S. Sarohia and K. F. Ng, “Finite-element analysis of the marine riser,” Engineering Structures, vol. 6, no. 3, pp. 175–184, 1984. [CrossRef] [Google Scholar]
J. N. Reddy, An Introduction to Nonlinear Finite element analysis: with applications to heat transfer, fluid mechanics, and solid mechanics., OUP Oxford, 2014. [Google Scholar]
H. M. Hilber, T. J. Hughes and R. L. Taylor, “Improved numerical dissipation for time integration algorithms in structural dynamics,” Earthquake Engineering & Structural Dynamics, vol. 5, no. 3, pp. 283–292, 1977. [Google Scholar]
K. J. Bathe and M. M. I. Baig, “On a composite implicit time integration procedure for nonlinear dynamics,” Computers & Structures, vol. 83, no. 31, pp. 2513–2524, 2005. [CrossRef] [Google Scholar]
K. J. Bathe, “Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme,” Computers & Structures, vol. 85, no. 7, pp. 437–445, 2007. [CrossRef] [Google Scholar]
J. Chung and G. M. Hulbert, “A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method,” Journal of Applied Mechanics, vol. 60, no. 2, pp. 371–375, 1993. [Google Scholar]
M. H. Patel and H. I. Park, “Combined axial and lateral responses of tensioned buoyant platform tethers,” Engineering Structures, vol. 17, no. 10, pp. 687–695, 1995. [CrossRef] [Google Scholar]
T. Belytschko, W. K. Liu, B. Moran and K. Elkhodary, Nonlinear finite elements for continua and structures, John Wiley & Sons, 2013. [Google Scholar]
B. P. Jacob and N. F. F. Ebecken, “An optimized implementation of the Newmark/Newton-Raphson algorithm for the time integration of non-linear problems,” Communications in Numerical Methods in Engineering, vol. 10, no. 12, pp. 983–992, 1994. [Google Scholar]

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[1] K. J. Bathe, Finite element procedures, Klaus-Jurgen Bathe, 2006. [Google Scholar]

[2] K. J. Bathe and A. P. Cimento, “Some practical procedures for the solution of nonlinear finite element equations,” Computer methods in applied mechanics and engineering, vol. 22, no. 1, pp. 59–85, 1980. [CrossRef] [Google Scholar]

[3] K. J. Bathe and E. N. Dvorkin, “On the automatic solution of nonlinear finite element equations,” Computers & Structures, vol. 17, no. 5, pp. 871–879, 1983. [CrossRef] [Google Scholar]

[4] J. R. Morison, J. W. Johnson and S. A. Schaaf, “The force exerted by surface waves on piles,” Journal of Petroleum Technology, vol. 2, no. 05, pp. 149–154, 1960. [Google Scholar]

[5] S. Chakrabarti, Handbook of Offshore Engineering (2-volume set), Elsevier, 2005. [Google Scholar]

[6] V. H. Safai, “Nonlinear dynamic analysis of deep water risers,” Applied Ocean Research, vol. 5, no. 4, pp. 215–225, 1983. [CrossRef] [Google Scholar]

[7] N. Haritos and D. T. He, “Modelling the response of cable elements in an ocean environment,” Finite Elements in Analysis and Design, vol. 11, no. 1, pp. 19–32, 1992. [Google Scholar]

[8] J. I. Gobat and M. A. Grosenbaugh, “Time-domain numerical simulation of ocean cable structures,” Ocean Engineering, vol. 33, no. 10, pp. 1373–1400, 2006. [CrossRef] [Google Scholar]

[9] A. K. Jain, “Nonlinear coupled response of offshore tension leg platforms to regular wave forces,” Ocean Engineering, vol. 24, no. 7, pp. 577–592, 1997. [CrossRef] [Google Scholar]

[10] M. H. Patel, S. Sarohia and K. F. Ng, “Finite-element analysis of the marine riser,” Engineering Structures, vol. 6, no. 3, pp. 175–184, 1984. [CrossRef] [Google Scholar]

[11] J. N. Reddy, An Introduction to Nonlinear Finite element analysis: with applications to heat transfer, fluid mechanics, and solid mechanics., OUP Oxford, 2014. [Google Scholar]

[12] H. M. Hilber, T. J. Hughes and R. L. Taylor, “Improved numerical dissipation for time integration algorithms in structural dynamics,” Earthquake Engineering & Structural Dynamics, vol. 5, no. 3, pp. 283–292, 1977. [Google Scholar]

[13] K. J. Bathe and M. M. I. Baig, “On a composite implicit time integration procedure for nonlinear dynamics,” Computers & Structures, vol. 83, no. 31, pp. 2513–2524, 2005. [CrossRef] [Google Scholar]

[14] K. J. Bathe, “Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme,” Computers & Structures, vol. 85, no. 7, pp. 437–445, 2007. [CrossRef] [Google Scholar]

[15] J. Chung and G. M. Hulbert, “A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method,” Journal of Applied Mechanics, vol. 60, no. 2, pp. 371–375, 1993. [Google Scholar]

[16] M. H. Patel and H. I. Park, “Combined axial and lateral responses of tensioned buoyant platform tethers,” Engineering Structures, vol. 17, no. 10, pp. 687–695, 1995. [CrossRef] [Google Scholar]

[17] T. Belytschko, W. K. Liu, B. Moran and K. Elkhodary, Nonlinear finite elements for continua and structures, John Wiley & Sons, 2013. [Google Scholar]

[18] B. P. Jacob and N. F. F. Ebecken, “An optimized implementation of the Newmark/Newton-Raphson algorithm for the time integration of non-linear problems,” Communications in Numerical Methods in Engineering, vol. 10, no. 12, pp. 983–992, 1994. [Google Scholar]