Skip to main content
SpringerLink
Log in

Nonlinear analysis of cable structures using the dynamic relaxation method

  • Research Article
  • Published:
Frontiers of Structural and Civil Engineering Aims and scope Submit manuscript

Abstract

The analysis of cable structures is one of the most challenging problems for civil and mechanical engineers. Because they have highly nonlinear behavior, it is difficult to find solutions to these problems. Thus far, different assumptions and methods have been proposed to solve such structures. The dynamic relaxation method (DRM) is an explicit procedure for analyzing these types of structures. To utilize this scheme, investigators have suggested various stiffness matrices for a cable element. In this study, the efficiency and suitability of six well-known proposed matrices are assessed using the DRM. To achieve this goal, 16 numerical examples and two criteria, namely, the number of iterations and the analysis time, are employed. Based on a comprehensive comparison, the methods are ranked according to the two criteria. The numerical findings clearly reveal the best techniques. Moreover, a variety of benchmark problems are suggested by the authors for future studies of cable structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Underwood P. Computational Method for Transient Analysis. North Holland, 1983

  2. Day A S. An Introduction to Dynamic Relaxation. The Engineer, 1965

  3. Bunce J W. A note on the estimation of critical damping in dynamic relaxation. International Journal for Numerical Methods in Engineering, 1972, 4(2): 301–303

    Article  Google Scholar 

  4. Cassell A C, Hobbs R E. Numerical stability of dynamic relaxation analysis of non-linear structures. International Journal for Numerical Methods in Engineering, 1976, 10(6): 1407–1410

    Article  Google Scholar 

  5. Qiang S. An adaptive dynamic relaxation method for nonlinear problems. Computers & Structures, 1988, 30(4): 855–859

    Article  MATH  Google Scholar 

  6. Zhang L G, Yu T X. Modified adaptive dynamic relaxation method and its application to elastic-plastic bending and wrinkling of circular plates. Computers & Structures, 1989, 33(2): 609–614

    Article  MATH  Google Scholar 

  7. Zhang L C, Kadkhodayan M, Mai Y W. Development of the MADR method. Computers & Structures, 1994, 52(1): 1–8

    Article  MATH  Google Scholar 

  8. Rezaiee-Pajand M. Nonlinear analysis of truss structures using dynamic relaxation. International Journal of Engineering, 2006, 19: 11–22

    Google Scholar 

  9. Kadkhodayan M, Alamatian J, Turvey G J. A new fictitious time for the dynamic relaxation (DXDR) method. International Journal for Numerical Methods in Engineering, 2008, 74(6): 996–1018

    Article  MATH  Google Scholar 

  10. Rezaiee-Pajand M, Alamatian J. The dynamic relaxation method using new formulation for fictitious mass and damping. Structural Engineering and Mechanics, 2010, 34(1): 109–133

    Article  Google Scholar 

  11. Rezaiee-Pajand M, Sarafrazi S R. Nonlinear structural analysis using dynamic relaxation method with improved convergence rate. International Journal of Computational Methods, 2010, 7(4): 627–654

    Article  MathSciNet  MATH  Google Scholar 

  12. Rezaiee-Pajand M, Sarafrazi S R. Nonlinear dynamic structural analysis using dynamic relaxation with zero damping. Computers & Structures, 2011, 89(13–14): 1274–1285

    Article  Google Scholar 

  13. Rezaiee-Pajand M, Sarafrazi S R, Rezaiee H. Efficiency of dynamic relaxation methods in nonlinear analysis of truss and frame structures. Computers & Structures, 2012, 112–113: 295–310

    Article  MATH  Google Scholar 

  14. Alamatian J. Displacement-based methods for calculating the buckling load and tracing the post-buckling regions with Dynamic Relaxation method. Computers & Structures, 2013, 114–115: 84–97

    Article  Google Scholar 

  15. Rezaiee-Pajand M, Rezaee H. Fictitious time step for the kinetic dynamic relaxation method. Mechanics of Advanced Materials and Structures, 2014, 21(8): 631–644

    Article  Google Scholar 

  16. Rezaiee-Pajand M, Estiri H. Computing the structural buckling limit load by using dynamic relaxation method. International Journal of Non-linear Mechanics, 2016, 81: 245–260

    Article  MATH  Google Scholar 

  17. Rezaiee-Pajand M, Estiri H. Finding equilibrium paths by minimizing external work in dynamic relaxation method. Applied Mathematical Modelling, 2016, 40(23–24): 10300–10322

    Article  MathSciNet  MATH  Google Scholar 

  18. Rezaiee-Pajand M, Estiri H. Mixing dynamic relaxation method with load factor and displacement increments. Computers & Structures, 2016, 168: 78–91

    Article  MATH  Google Scholar 

  19. Rezaiee-Pajand M, Estiri H. A comparison of large deflection analysis of bending plates by dynamic relaxation. Periodica Polytechnica. Civil Engineering, 2016, 60(4): 619–645

    Article  MATH  Google Scholar 

  20. Rezaiee-Pajand M, Estiri H. Comparative analysis of three-dimensional frames by dynamic relaxation methods. Mechanics of Advanced Materials and Structures, 2018, 25(6): 451–466

    Article  Google Scholar 

  21. Rezaiee-Pajand M, Alamatian J, Rezaee H. The state of the art in Dynamic Relaxation methods for structural mechanics Part 1: Formulations. Iranian Journal of Numerical Analysis and Optimization, 2017, 7(2): 65–86

    MATH  Google Scholar 

  22. Rezaiee-Pajand M, Alamatian J, Rezaee H. The state of the art in Dynamic Relaxation methods for structural mechanics Part 2: Applications. Iranian Journal of Numerical Analysis and Optimization, 2017, 7(2): 87–114

    MATH  Google Scholar 

  23. Labbafi S F, Sarafrazi S R, Kang T H K. Comparison of viscous and kinetic dynamic relaxation methods in form-finding of membrane structures. Advances in Computational Design, 2017, 2(1): 71–87

    Article  Google Scholar 

  24. Rezaiee-Pajand M, Mohammadi-Khatami M. A fast and accurate dynamic relaxation scheme. Frontiers of Structural and Civil Engineering, 2019, 13(1): 176–189

    Article  Google Scholar 

  25. Rezaiee-Pajand M, Estiri H, Mohammadi-Khatami M. Creating better dynamic relaxation methods. Engineering Computations, 2019, 36(5): 1483–1521

    Article  Google Scholar 

  26. Ozdemir H. A finite element approach for cable problems. International Journal of Solids and Structures, 1979, 15(5): 427–437

    Article  MATH  Google Scholar 

  27. Pevrot A H, Goulois A M. Analysis of cable structures. Computers & Structures, 1979, 10(5): 805–813

    Article  Google Scholar 

  28. Monforton G R, El-Hakim N M. Analysis of truss-cable structures. Computers & Structures, 1980, 11(4): 327–335

    Article  MATH  Google Scholar 

  29. Jayaraman H B, Knudson W C. A curved element for the analysis of cable structures. Computers & Structures, 1981, 14(3–4): 325–333

    Article  Google Scholar 

  30. Lewis W J, Jones M S, Rushton K R. Dynamic relaxation analysis of the non-linear static response of pretensioned cable roofs. Computers & Structures, 1984, 18(6): 989–997

    Article  MATH  Google Scholar 

  31. Kmet S, Kokorudova Z. Nonlinear analytical solution for cable truss. Journal of Engineering Mechanics, 2006, 132(1): 119–123

    Article  Google Scholar 

  32. Deng H, Jiang Q F, Kwan A S K. Shape finding of incomplete cable-strut assemblies containing slack and prestressed elements. Computers & Structures, 2005, 83(21–22): 1767–1779

    Article  Google Scholar 

  33. Andreu A, Gil L, Roca P. A new deformable catenary element for the analysis of cable net structures. Computers & Structures, 2006, 84(29–30): 1882–1890

    Article  Google Scholar 

  34. Yang Y B, Tsay J Y. Geometric nonlinear analysis of cable structures with a two-node cable element by generalized displacement control method. International Journal of Structural Stability and Dynamics, 2007, 07(04): 571–588

    Article  MathSciNet  MATH  Google Scholar 

  35. Chen Z H, Wu Y J, Yin Y, Shan C. Formulation and application of multi-node sliding cable element for the analysis of Suspen-Dome structures. Finite Elements in Analysis and Design, 2010, 46(9): 743–750

    Article  MathSciNet  Google Scholar 

  36. Thai H T, Kim S E. Nonlinear static and dynamic analysis of cable structures. Finite Elements in Analysis and Design, 2011, 47(3): 237–246

    Article  Google Scholar 

  37. Vu T V, Lee H E, Bui Q T. Nonlinear analysis of cable-supported structures with a spatial catenary cable element. Structural Engineering and Mechanics, 2012, 43(5): 583–605

    Article  Google Scholar 

  38. Huttner M, Maca J, Fajman P. Numerical analysis of cable structures. In: Proceedings of the Eleventh International Conference: Computational Structures Technology. Stirlingshire: Civil-Comp Press, 2012

    Google Scholar 

  39. Ahmadizadeh M. Three-dimensional geometrically nonlinear analysis of slack cable structures. Computers & Structures, 2013, 128: 160–169

    Article  Google Scholar 

  40. Temur R, Bekdaş G, Toklu Y C. Analysis of cable structures through total potential optimization using meta-heuristic algorithms. In: ACE2014, the 11th International Congress on Advances in Civil Engineering. 2014, 21–25

  41. Hashemi S K, Bradford M A, Valipour H R. Dynamic response of cable-stayed bridge under blast load. Engineering Structures, 2016, 127: 719–736

    Article  Google Scholar 

  42. Gale S, Lewis W J. Patterning of tensile fabric structures with a discrete element model using dynamic relaxation. Computers & Structures, 2016, 169: 112–121

    Article  Google Scholar 

  43. Anitescu C, Atroshchenko E, Alajlan N, Rabczuk T. Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials and Continua, 2019, 59(1): 345–359

    Article  Google Scholar 

  44. Guo H, Zhuang X, Rabczuk T. A deep collocation method for the bending analysis of Kirchhoff plate. Computers, Materials & Continua, 2019, 59(2): 433–456

    Article  Google Scholar 

  45. Rabczuk T, Ren H, Zhuang X. A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem. Computers, Materials & Continua, 2019, 59(1): 31–55

    Article  Google Scholar 

  46. Torkamani M A M, Shieh J H. Higher-order stiffness matrices in nonlinear finite element analysis of plane truss structures. Engineering Structures, 2011, 33(12): 3516–3526

    Article  Google Scholar 

  47. Hüttner M, Máca J, Fajman P. The efficiency of dynamic relaxation methods in static analysis of cable structures. Advances in Engineering Software, 2015, 89: 28–35

    Article  Google Scholar 

  48. Rezaiee-Pajand M, Naserian R. Using more accurate strain for three-dimensional truss analysis. Asian Journal of Civil Engineering, 2016, 17(1): 107–126

    Google Scholar 

  49. Lewis W J. The efficiency of numerical methods for the analysis of prestressed nets and pin-jointed frame structures. Computers & Structures, 1989, 33(3): 791–800

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, 9177948974, Iran

    Mohammad Rezaiee-Pajand & Mohammad Mohammadi-Khatami

Authors
  1. Mohammad Rezaiee-Pajand
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Mohammadi-Khatami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Rezaiee-Pajand.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rezaiee-Pajand, M., Mohammadi-Khatami, M. Nonlinear analysis of cable structures using the dynamic relaxation method. Front. Struct. Civ. Eng. 15, 253–274 (2021). https://doi.org/10.1007/s11709-020-0639-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11709-020-0639-y

Keywords

Search

Navigation