A new method of fictitious viscous damping determination for the dynamic relaxation method

Computers and Structures

Volumn 89, Issue 9-10, 2011, Pages 783-794

  Rezaiee Pajand, M ^a   Kadkhodayan, M ^a   Alamatian, J ^b   Zhang, L C ^c  

^a FERDOWSI UNIVERSITY OF MASHHAD   (Iran)

^b ISLAMIC AZAD UNIVERSITY   (Iran)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Dynamic relaxation; Fictitious viscous damping; Lowest eigenvalue; Nonlinear analysis

Indexed keywords

CONVERGENCE RATES; DYNAMIC RELAXATION; DYNAMIC RELAXATION METHOD; EIGEN-VALUE; ERROR MINIMIZATION; FICTITIOUS VISCOUS DAMPING; ITERATIVE PROCESS; KINETIC APPROACH; STRONG NONLINEARITY; SUCCESSIVE ITERATION; VISCOUS DAMPING;

CONVERGENCE OF NUMERICAL METHODS; DAMPING; EIGENVALUES AND EIGENFUNCTIONS; NONLINEAR ANALYSIS;

DYNAMIC ANALYSIS;

EID: 79953181348     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2011.02.002     Document Type: Article

References (47)

1. Felippa CA, Nonlinear finite element methods, ASEN 5017, course material, http://kaswww.colorado.edu/courses.d/NFEMD/ ; Spring 1999.
2. J.R.H. Otter Dynamic relaxation Proc Instn Civ Engrs 35 1966 633 656
3. A.S. Day An introduction to dynamic relaxation The Engineer 219 1965 218 221
4. S.P. Frankel Convergence rates of iterative treatments of partial differential equations Mathl Tabl Natn Res Coun 4 1950 65 75
5. A.K. Welsh Discussion on dynamic relaxation Proc Instn Civ Engrs 37 1967 723 750
6. A.C. Cassell, P.J. Kinsey, D.J. Sefton, and W.L. Wood Cylindrical shell analysis by dynamic relaxation Proc Instn Civ Engrs 39 1968 75 84
7. K.R. Rushton Large deflection of variable-thickness plates Int J Mech Sci 10 1968 723 735
8. J.S. Brew, and M. Brotton Non-linear structural analysis by dynamic relaxation method Int J Numer Methods Eng 3 1971 463 483
9. W.L. Wood Note on dynamic relaxation Int J Numer Methods Eng 3 1971 145 147
10. J.W. Bunce A note on estimation of critical damping in dynamic relaxation Int J Numer Methods Eng 4 1972 301 304
11. R.S. Alwar, N.R. Rao, and M.S. Rao Altenative procedure in dynamic relaxation Comput Struct 5 1975 271 274
12. A.C. Cassell, and R.E. Hobbs Numerical stability of dynamic relaxation analysis of non-linear structures Int J Numer Methods Eng 10 1976 1407 1410
13. nd International Conference on Numerical Methods in Geomechanics. Blacksburg, Virginia, June, 1976;1:132-50.
14. P.A. Frieze, R.E. Hobbs, and P.J. Dowling Application of dynamic relaxation to the large deflection elasto-plastic analysis of plates Comput Struct 8 1978 301 310 (Pubitemid 8582105)
15. M. Papadrakakis A method for automatic evaluation of the dynamic relaxation parameters Comput Methods Appl Mech Eng 25 1981 35 48 (Pubitemid 11459385)
16. P. Underwood Dynamic relaxation T. Belytschko, T.J.R. Hughes, Computational method for transient analysis. Computational methods in mechanics vol. 1 1983 Elsevier Science 245 256 Chapter 5
17. C.A. Felippa Dynamic relaxation under general increment control Math Prog 24 1982 103 133
18. O.C. Zienkiewicz, and R. Lohner Accelerated relaxation or direct solution future prospects for FEM Int J Numer Methods Eng 21 1985 1 11 (Pubitemid 15541672)
19. M.R. Barnes Form finding and analysis of prestressed nets and membranes Comput Struct 30 3 1988 685 695
20. F.A.N. Shawi, and A.H. Mardirosion An improved dynamic relaxation method for the analysis of plate bending problems Comput Struct 27 1987 237 240 (Pubitemid 18519374)
21. S. Qiang An Adaptive dynamic relaxation method for non-linear problems Comput Struct 30 1988 855 859
22. L.C. Zhang, and T.X. Yu Modified adaptive dynamic relaxation method and its application to elastic-plastic bending and wrinkling of circular plates Comput Struct 34 1989 609 614 (Pubitemid 20614024)
23. G.J. Turvey, and M. Salehi DR large deflection analysis of sector plates Comput Struct 34 1990 101 112
24. J.P. Bardet, and J. Proubet Adaptive dynamic relaxation for statics of granular materials Comput Struct 39 1991 221 229
25. G. Ramesh, and C.S. Krishnamoorthy Post-buckling analysis of structures by dynamic relaxation Int J Numer Methods Eng 36 1993 1339 1364
26. G. Ramesh, and C.S. Krishnamoorthy Inelastic post-buckling analysis of truss structures by Dynamic Relaxation method Int J Numer Methods Eng 37 1994 3633 3657
27. L.C. Zhang, M. Kadkhodayan, and Y.W. Mai Development of the maDR method Comput Struct 52 1994 1 8
28. M. Kadkhodayan, and L.C. Zhang A consistent DXDR method for elastic-plastic problems Int J Numer Methods Eng 38 1995 2413 2431
29. M. Kadkhodayan, L.C. Zhang, and R. Swerby Analysis of wrinkling and buckling of elastic plates by DXDR method Comput Struct 65 1997 561 574 (Pubitemid 127401037)
30. B.H.V. Topping, and A.I. Khan Parallel schemes for dynamic relaxation, engineering computations Int J Comput Aided Eng Software 11 1994 513 548
31. P. Ivanyi, and B.H.V. Topping Parallel dynamic relaxation form-finding M. Papadrakakis, B.H.V. Topping, Innovative Comput Meth Struct Mech 1999 Saxe-Coburg Publications Edinburgh 127 147 Chapter 7
32. I.P. Pasqualino, and S.F. Estefan A nonlinear analysis of the buckle propagation problem in deepwater piplines Int J Solids Struct 38 2001 8481 8502 (Pubitemid 33090038)
33. R.D. Wood A simple technique for controlling element distortion in dynamic relaxation form-finding of tension membranes Comput Struct 80 2002 2115 2120 (Pubitemid 35432592)
34. S.E. Han, and K.S. Lee A study on stabilizing process of unstable structures by Dynamic Relaxation method Comput. Struct. 80 2003 1677 1688
35. S.M.L. Adriaenssens, and M.R. Barnes Tensegrity spline beam and grid shell structures Eng Struct 23 2001 29 36
36. Hegyi Dezso, Sajtos Istvan, Geiszter Gyorgy, and Hincz Krisztian Eight-node quadrilateral double-curved surface element for membrane analysis Comput Struct 84 2006 2151 2158
37. B. Domer, E. Fest, V. Lalit, and I.F.C. Smith Combining dynamic relaxation method with artificial neural networks to enhance simulation of tensegrity structures ASCE J Struct Eng 129 5 2003 672 681 (Pubitemid 40001047)
38. G.J. Turvey, and M. Salehi Annular sector plates: comparison of full-section and layer yield prediction Comput Struct 83 2005 2431 2441 (Pubitemid 41383753)
39. B.H.V. Topping, and P. Ivanyi Computer aided design of cable-membrane structures 2007 Saxe-Coburg Publications on Computational Engineering Chapter 3, p. 39-82
40. M. Kadkhodayan, J. Alamatian, and G.J. Turvey A new fictitious time for the dynamic relaxation (DXDR) method Int J Numer Methods Eng 74 2008 996 1018 (Pubitemid 351659424)
41. M. Rezaiee-Pajand, and J. Alamatian Nonlinear dynamic analysis by dynamic relaxation method J Struct Eng Mech 28 5 2008 549 570 (Pubitemid 351690511)
42. R.A. Brualdi, and S. Mellendorf Regions in the complex plane containing the eigenvalues of a matrix Am Math Month 101 10 1994 975 985
43. R.W. Clough, and J. Penzien Dynamics of structures 2nd ed. 1993 McGraw Hill New York
44. A.K. Chopra Dynamics of structures; theory and applications to earthquake engineering 2nd ed. 2002 Prentice Hall India
45. R.D. Wood, and O.C. Zienkiewicz Geometrically nonlinear finite element analysis of beams, frames, arches and axisymmetric shells Comput Struct 7 1977 725 735 (Pubitemid 8569963)
46. Y.B. Yang, C.T. Yang, T.P. Chang, and P.K. Chang Effects of member buckling and yielding on ultimate strength of space trusses J Struct Eng ASCE 19 2 1997 179 191
47. J.G. Teng, and J.M. Rotter Elastic-plastic large deflection analysis of axisymmetric shells Comput Struct 31 2 1989 211 233