DOI QR코드

DOI QR Code

The dynamic relaxation method using new formulation for fictitious mass and damping

  • Rezaiee-Pajand, M. (Department of Civil Engineering, Ferdowsi University of Mashhad) ;
  • Alamatian, J. (Department of Civil Engineering, Ferdowsi University of Mashhad)
  • 투고 : 2008.07.05
  • 심사 : 2009.10.06
  • 발행 : 2010.01.10

초록

This paper addresses the modified Dynamic Relaxation algorithm, called mdDR by minimizing displacement error between two successive iterations. In the mdDR method, new relationships for fictitious mass and damping are presented. The results obtained from linear and nonlinear structural analysis, either by finite element or finite difference techniques; demonstrate the potential ability of the proposed scheme compared to the conventional DR algorithm. It is shown that the mdDR improves the convergence rate of Dynamic Relaxation method without any additional calculations, so that, the cost and computational time are decreased. Simplicity, high efficiency and automatic operations are the main merits of the proposed technique.

키워드

참고문헌

  1. Alwar, R.S., Rao, N.R. and Rao, M.S. (1975), "Altenative procedure in dynamic relaxation", Comput. Struct., 5, 271-274. https://doi.org/10.1016/0045-7949(75)90031-0
  2. Bardet, J.P. and Proubet, J. (1991), "Adaptive dynamic relaxation for statics of granular materials", Comput. Struct., 39, 221-229. https://doi.org/10.1016/0045-7949(91)90020-M
  3. Brew, J.S. and Brotton, M. (1971), "Non-linear structural analysis by dynamic relaxation method", Int. J. Numer. Meth. Eng., 3, 463-483. https://doi.org/10.1002/nme.1620030403
  4. Bunce, J.W. (1972), "A note on estimation of critical damping in dynamic relaxation", Int. J. Numer. Meth. Eng., 4, 301-304. https://doi.org/10.1002/nme.1620040214
  5. Cassell, A.C. and Hobbs, R.E. (1976), "Numerical stability of dynamic relaxation analysis of non-linear structures", Int. J. Numer. Meth. Eng., 10, 1407-1410. https://doi.org/10.1002/nme.1620100620
  6. Cassell, A.C., Kinsey, P.J. and Sefton, D.J. (1968), "Cylindrical shell analysis by dynamic relaxation", Proc. ICE, 39, 75-84. https://doi.org/10.1680/iicep.1968.8109
  7. Day, A.S. (1965), "An introduction to dynamic relaxation", The Engineer, 219, 218-221.
  8. Felippa, C.A. (1982), "Dynamic relaxation under general increment control", Math. Prog., 24, 103-133.
  9. Felippa, C.A. (1999), Nonlinear Finite Element Methods, ASEN 5017, Course Material, http://kaswww.colorado. edu/courses.d /NFEMD/;Spring.
  10. Frankel, S.P. (1950), "Convergence rates of iterative treatments of partial differential equations", Math. Tables Other Aids Comput., 4(30), 65-75. https://doi.org/10.2307/2002770
  11. Frieze, P.A., Hobbs, R.E. and Dowling, P.J. (1978), "Application of dynamic relaxation to the large deflection elasto-plastic analysis of plates", Comput. Struct., 8, 301-310. https://doi.org/10.1016/0045-7949(78)90037-8
  12. Han, S.E. and Lee, K.S. (2003), "A study on stabilizing process of unstable structures by dynamic relaxation method", Comput. Struct., 80, 1677-1688.
  13. Kadkhodayan, M. and Zhang, L.C. (1995), "A consistent DXDR method for elastic-plastic problems", Int. J. Numer. Meth. Eng., 38, 2413-2431. https://doi.org/10.1002/nme.1620381407
  14. Kadkhodayan, M., Alamatian, J. and Turvey, G.J. (2008), "A new fictitious time for the dynamic relaxation (DXDR) method", Int. J. Numer. Meth. Eng., 74, 996-1018. https://doi.org/10.1002/nme.2201
  15. Kadkhodayan, M., Zhang, L.C. and Swerby, R. (1997), "Analysis of wrinkling and buckling of elastic plates by DXDR method", Comput. Struct., 65, 561-574. https://doi.org/10.1016/S0045-7949(96)00368-9
  16. Murphy, J., Ridout, D. and McShane, B. (1988), Numerical Analysis Algorithms and Computation, Ellis Horwood Limited, New York.
  17. Otter, J.R.H. (1966), "Dynamic relaxation", Proc. ICE, 35, 633-656. https://doi.org/10.1680/iicep.1966.8604
  18. Papadrakakis, M. (1981), "A method for automatic evaluation of the dynamic relaxation parameters", Comput. Meth. Appl. Mech. Eng., 25, 35-48. https://doi.org/10.1016/0045-7825(81)90066-9
  19. Pasqualino, I.P. and Estefan, S.F. (2001), "A nonlinear analysis of the buckle propagation problem in deepwater piplines", Int. J. Solids Struct., 38, 8481-8502. https://doi.org/10.1016/S0020-7683(01)00113-5
  20. Qiang, S. (1988), "An adaptive dynamic relaxation method for non-linear problems", Comput. Struct., 30, 855- 859. https://doi.org/10.1016/0045-7949(88)90117-4
  21. Ramesh, G. and Krishnamoorthy, C.S. (1993), "Post-buckling analysis of structures by dynamic relaxation", Int. J. Numer. Meth. Eng., 36, 1339-1364. https://doi.org/10.1002/nme.1620360806
  22. Ramesh, G. and Krishnamoorthy, C.S. (1994), "Inelastic post-buckling analysis of truss structures by dynamic relaxation method", Int. J. Numer. Meth. Eng., 37, 3633-3657. https://doi.org/10.1002/nme.1620372105
  23. Rezaiee-Pajand, M. and Alamatian, J. (2008), "Nonlinear dynamic analysis by dynamic relaxation method", Struct. Eng. Mech., 28(5), 549-570. https://doi.org/10.12989/sem.2008.28.5.549
  24. Rushton, K.R. (1968), "Large deflection of variable-tickness plates", Int. J. Mech. Sci., 10, 723-735. https://doi.org/10.1016/0020-7403(68)90086-6
  25. Saka, M.P. (1990), "Optimum design of pin-jointed steel structures with practical applications", J. Struct. Eng., ASCE, 116, 2599-2619. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:10(2599)
  26. Shawi, F.A.N. and Mardirosion, A.H. (1987), "An improved dynamic relaxation method for the analysis of plate bending problems", Comput. Struct., 27, 237-240. https://doi.org/10.1016/0045-7949(87)90091-5
  27. Timoshenko, S. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, McGraw-Hill Book Company.
  28. Turvey, G.J. and Salehi, R.E. (2005), "Annular sector plates : Comparison of full-section and layer yield prediction", Comput. Struct., 83, 2431-2441. https://doi.org/10.1016/j.compstruc.2005.03.025
  29. Turvey, G.J. and Salehi, R.E. (1990), "DR large deflection analysis of sector plates", Comput. Struct., 34, 101- 112. https://doi.org/10.1016/0045-7949(90)90304-K
  30. Ugural, A.C. and Fenster, S.K. (1987), Advanced Strength and Applied Elasticity. Elsevier, New York.
  31. Undewood, P. (1983), "Dynamic relaxation. computational method for transient analysis", Chapter 5, 245-256.
  32. Welsh, A.K. (1967), "Discussion on dynamic relaxation", Proc. ICE, 37, 723-750. https://doi.org/10.1680/iicep.1967.8278
  33. Wood, R.D. (2002), "A simple technique for controlling element distortion in dynamic relaxation form-finding of tension membranes", Comput. Struct., 80, 2115-2120. https://doi.org/10.1016/S0045-7949(02)00274-2
  34. Wood, W.L. (1971), "Note on dynamic relaxation", Int. J. Numer. Meth. Eng., 3, 145-147. https://doi.org/10.1002/nme.1620030115
  35. Zhang, L.C. and Yu, T.X. (1989), "Modified adaptive dynamic relaxation method and its application to elasticplastic bending and wrinkling of circular plates", Comput. Struct., 34, 609-614.
  36. Zhang, L.C., Kadkhodayan, M. and Mai, Y.W. (1994), "Development of the maDR method", Comput. Struct., 52, 1-8. https://doi.org/10.1016/0045-7949(94)90249-6
  37. Zienkiewicz, O.C. and Lohner R. (1985), "Accelerated relaxation or direct solution future prospects for FEM", Int. J. Numer. Meth. Eng., 21, 1-11. https://doi.org/10.1002/nme.1620210103

피인용 문헌

  1. Fictitious Time Step for the Kinetic Dynamic Relaxation Method vol.21, pp.8, 2014, https://doi.org/10.1080/15376494.2012.699603
  2. Comparative analysis of three-dimensional frames by dynamic relaxation methods 2018, https://doi.org/10.1080/15376494.2017.1285462
  3. Mixing dynamic relaxation method with load factor and displacement increments vol.168, 2016, https://doi.org/10.1016/j.compstruc.2016.02.011
  4. Nonlinear bending analysis of annular FGM plates using higher-order shear deformation plate theories vol.93, pp.2, 2011, https://doi.org/10.1016/j.compstruct.2010.06.024
  5. Numerical study of dynamic relaxation with kinetic damping applied to inflatable fabric structures with extensions for 3D solid element and non-linear behavior vol.49, pp.11, 2011, https://doi.org/10.1016/j.tws.2011.07.011
  6. Displacement-based methods for calculating the buckling load and tracing the post-buckling regions with Dynamic Relaxation method vol.114-115, 2013, https://doi.org/10.1016/j.compstruc.2012.10.023
  7. Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm vol.48, pp.5, 2011, https://doi.org/10.1016/j.ijsolstr.2010.10.029
  8. Explicit dynamic analysis using Dynamic Relaxation method vol.175, 2016, https://doi.org/10.1016/j.compstruc.2016.07.008
  9. Efficiency of dynamic relaxation methods in nonlinear analysis of truss and frame structures vol.112-113, 2012, https://doi.org/10.1016/j.compstruc.2012.08.007
  10. Analysis of stabilizing process for stress-erection of Strarch frame vol.59, 2014, https://doi.org/10.1016/j.engstruct.2013.09.043
  11. A new formulation for fictitious mass of the Dynamic Relaxation method with kinetic damping vol.90-91, 2012, https://doi.org/10.1016/j.compstruc.2011.10.010
  12. Finding equilibrium paths by minimizing external work in dynamic relaxation method vol.40, pp.23-24, 2016, https://doi.org/10.1016/j.apm.2016.07.017
  13. An efficient explicit framework for determining the lowest structural buckling load using Dynamic Relaxation method vol.45, pp.4, 2017, https://doi.org/10.1080/15397734.2016.1238765
  14. Form finding and analysis of inflatable dams using dynamic relaxation vol.267, 2015, https://doi.org/10.1016/j.amc.2014.12.054
  15. Timestep Selection for Dynamic Relaxation Method vol.40, pp.1, 2012, https://doi.org/10.1080/15397734.2011.599311
  16. Large deflection analysis of shear deformable radially functionally graded sector plates on two-parameter elastic foundations vol.42, 2013, https://doi.org/10.1016/j.euromechsol.2013.06.006
  17. A vector-form hybrid particle-element method for modeling and nonlinear shell analysis of thin membranes exhibiting wrinkling vol.15, pp.5, 2014, https://doi.org/10.1631/jzus.A1300248
  18. Estimating the Region of Attraction via collocation for autonomous nonlinear systems vol.41, pp.2, 2012, https://doi.org/10.12989/sem.2012.41.2.263
  19. A dynamic-relaxation formulation for analysis of cable structures with sliding-induced friction vol.126-127, 2017, https://doi.org/10.1016/j.ijsolstr.2017.08.008
  20. On the application of the maximum entropy meshfree method for elastoplastic geotechnical analysis vol.84, 2017, https://doi.org/10.1016/j.compgeo.2016.11.015
  21. Creep and recovery of viscoelastic laminated composite plates vol.181, 2017, https://doi.org/10.1016/j.compstruct.2017.08.094
  22. A novel time integration formulation for nonlinear dynamic analysis vol.69, 2017, https://doi.org/10.1016/j.ast.2017.07.032
  23. Computing the structural buckling limit load by using dynamic relaxation method vol.81, 2016, https://doi.org/10.1016/j.ijnonlinmec.2016.01.022
  24. Dynamic Relaxation Method for Load Capacity Analysis of Reinforced Concrete Elements vol.8, pp.3, 2018, https://doi.org/10.3390/app8030396
  25. A fast and accurate dynamic relaxation scheme pp.2095-2449, 2018, https://doi.org/10.1007/s11709-018-0486-2
  26. An incremental iterative solution procedure without predictor step vol.27, pp.1, 2018, https://doi.org/10.1080/17797179.2018.1455028
  27. Geodesic shape finding of membrane structure with geodesic string by the dynamic relaxation method vol.39, pp.1, 2011, https://doi.org/10.12989/sem.2011.39.1.093
  28. Ultimate load capacity of unit Strarch frames using an explicit numerical method vol.13, pp.6, 2010, https://doi.org/10.12989/scs.2012.13.6.539
  29. A comparison of different methods for calculating tangent-stiffness matrices in a massively parallel computational peridynamics code vol.279, pp.None, 2010, https://doi.org/10.1016/j.cma.2014.06.034
  30. Comparison of viscous and kinetic dynamic relaxation methods in form-finding of membrane structures vol.2, pp.1, 2017, https://doi.org/10.12989/acd.2017.2.1.071
  31. Geometrically nonlinear analysis of shells by various dynamic relaxation methods vol.14, pp.5, 2017, https://doi.org/10.1108/wje-10-2016-0109
  32. Dynamic relaxation method based on Lanczos algorithm vol.112, pp.10, 2010, https://doi.org/10.1002/nme.5565
  33. A fast and accurate dynamic relaxation approach for form-finding and analysis of bending-active structures vol.34, pp.1, 2019, https://doi.org/10.1177/0956059919864279
  34. Finding buckling points for nonlinear structures by dynamic relaxation scheme vol.14, pp.1, 2010, https://doi.org/10.1007/s11709-019-0549-z
  35. A new formulation for fictitious mass of viscous dynamic relaxation method vol.48, pp.5, 2020, https://doi.org/10.1080/15397734.2019.1633342
  36. Lagrangian interpolation for kinetic dynamic relaxation method with the variable load factor vol.43, pp.2, 2021, https://doi.org/10.1007/s40430-021-02819-7