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Computational Mechanics

, Volume 57, Issue 5, pp 843–858 | Cite as

A peridynamic model for the nonlinear static analysis of truss and tensegrity structures

  • Hui Li
  • Hongwu Zhang
  • Yonggang ZhengEmail author
  • Liang Zhang
Original Paper

Abstract

A peridynamic model is developed in this paper for the nonlinear static analysis of truss and tensegrity structures. In the present model, the motion equations of material points are established on the current configuration and the pairwise forces are functions of extension and direction of the bonds. The peridynamic parameters are obtained based on the equivalence between the strain energy densities of the peridynamic and classical continuum models. The present model is applied to the mechanical analysis of bimodular truss and tensegrity structures, in which the compressive modulus is set to be zero for the cables. Several representative examples are carried out and the results verify the validity and efficiency of the developed model by comparing with the conventional nonlinear finite element method.

Keywords

Peridynamic model Truss structures Tensegrity structures Nonlinearity Bimodularity Adaptive dynamic relaxation 

Notes

Acknowledgments

The supports from the National Natural Science Foundation of China (11232003, 11272003 and 91315302), the 111 Project (B08014), Program for New Century Excellent Talents in University (NCET-13-0088), Ph.D. Programs Foundation of Ministry of Education of China (20130041110050) and Fundamental Research Funds for the Central Universities are gratefully acknowledged.

References

  1. 1.
    Korkmaz SA (2011) A review of active structural control: challenge for engineering informatics. Comput Struct 89:2113–32CrossRefGoogle Scholar
  2. 2.
    Domer B, Smith I (2005) An active structure that learns. J Comput Civil Eng 19:16–24CrossRefGoogle Scholar
  3. 3.
    Ziegler F (2005) Computational aspects of structural shape control. Comput Struct 83:1191–204CrossRefGoogle Scholar
  4. 4.
    Sultan C (2009) Tensegrity: 60 years of art, science, and engineering. Adv Appl Mech 43:69–145CrossRefGoogle Scholar
  5. 5.
    Pugh A (1976) An introduction to tensegrity. Uniersity of California Press, OaklandGoogle Scholar
  6. 6.
    Motro R (2003) Tensegrity: structural systems for the future. Kogan Page, LondonCrossRefGoogle Scholar
  7. 7.
    Skelton RE, de Oliveira MC (2009) Tensegrity systems. Springer, New YorkzbMATHGoogle Scholar
  8. 8.
    Moored KW, Bart-Smith H (2003) Investigation of clustered actuation in tensegrity structures. Int J Solids Struct 18:209–23zbMATHGoogle Scholar
  9. 9.
    Pagitz M, Mirats Tur JM (2009) Finite element based form-finding algorithm for tensegrity structures. Int J Solids Struct 46:3235–40CrossRefzbMATHGoogle Scholar
  10. 10.
    Tran HC, Lee J (2010) Advanced forming-finding for cable-strut structures. Int J Solids Struct 47:1785–94CrossRefzbMATHGoogle Scholar
  11. 11.
    Xu X, Luo YZ (2010) Forming-finding of nonregular tensegrities using a genetic algorithm. Mech Res Commun 37:85–91CrossRefzbMATHGoogle Scholar
  12. 12.
    Li Y, Feng XQ, Cao YP, Gao HJ (2010) A Monte Carlo form-finding method for large scale regular and irregular tensegrity structures. Int J Solids Struct 47:1888–98CrossRefzbMATHGoogle Scholar
  13. 13.
    Zhang LY, Li Y, Cao YP, Feng XQ (2014) Stiffness matrix based form-finding method of tensegrity structures. Eng Struct 58:36–48CrossRefGoogle Scholar
  14. 14.
    Zhang HW, Zhang L, Gao Q (2011) An efficient computational method for mechanical analysis of bimodular structures based on parametric variational principle. Comput Struct 89:2352–60CrossRefGoogle Scholar
  15. 15.
    Zhang HW, Zhang L, Gao Q (2012) Numerical method for dynamic analysis of 2-D bimodular structures. AIAA J 50:1933–42CrossRefGoogle Scholar
  16. 16.
    Zhang L, Gao Q, Zhang HW (2013) An efficient algorithm for mechanical analysis of bimodular truss and tensegrity structures. Int J Mech Sci 70:57–68CrossRefGoogle Scholar
  17. 17.
    Nineb S, Alart P, Dureisseix D (2007) Domain decomposition approach for non-smooth discrete problems, example of a tensegrity structure. Comput Struct 85:499–511CrossRefGoogle Scholar
  18. 18.
    Oliveto ND, Sivaselvan MV (2011) Dynamic analysis of tensegrity structures using a complementarity framework. Comput Struct 89:2471–83CrossRefGoogle Scholar
  19. 19.
    Ali NBH, Rhode-Barbarigos L, Smith IFC (2011) Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm. Int J Solids Struct 48:637–47CrossRefzbMATHGoogle Scholar
  20. 20.
    Raja MG, Narayanan S (2007) Active control of tensegrity structures under random excitation. Smart Mater Struct 16:809–17CrossRefGoogle Scholar
  21. 21.
    Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Seleson P, Parks ML, Gunzburger M, Lehoucq RB (2009) Peridynamics as an upscaling of molecular dynamics. Multiscale Model Simul 8(1):204–27MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Silling SA, Epton M, Wechner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88:151–184MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Silling SA, Lehoucq RB (2010) Peridynamic theory of solid mechanics. Adv Appl Mech 44:173–68Google Scholar
  25. 25.
    Silling SA (2010) Linearized theory of peridynamic states. J Elast 99:85–111MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Lehoucq RB, Silling SA (2008) Force flux and the peridynamic stress tensor. J Mech Phys Solids 56:1566–77MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Weckner O, Abeyaratne R (2005) The effect of long-range forces on the dynamics of a bar. J Mech Phys Solids 53:705–28MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Bobaru F, Duangpanya M (2010) The peridynamic formulation for transient heat conduction. Int J Heat Mass Transf 53:4047–4059CrossRefzbMATHGoogle Scholar
  29. 29.
    Bobaru F, Duangpanya M (2012) A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities. J Comput Phys 231:2764–85MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Oterkus S, Madenci E, Agwai A (2014) Fully coupled peridynamic thermomechanics. J Mech Phys Solids 64:1–23MathSciNetCrossRefGoogle Scholar
  31. 31.
    Hu W, Ha YD, Bobaru F (2012) Peridynanic model for dynamic fracture in unidirectional fiber-reinforced composites. Comput Methods Appl Mech Eng 217–220:247–261MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Gerstle W, Sau N, Silling SA (2007) Peridynamic modeling of concrete structures. Nucl Eng Des 237:1250–1258CrossRefGoogle Scholar
  33. 33.
    O’Grady J, Foster JT (2014) Peridynamic beams: a non-ordinary, state-based model. Int J Solids Struct 51:3177–3183CrossRefGoogle Scholar
  34. 34.
    Katiyar A, Foster JT, Ouchi H, Sharma MM (2014) A peridynamic formulation of pressure driven convective fluid transport in porous media. J Comput Phys 261:209–229MathSciNetCrossRefGoogle Scholar
  35. 35.
    Le QV, Chan WK, Schwartz J (2014) A two-dimensional ordinary, state-based peridynamic model for linearly elastic solids. Int J Numer Methods Eng 98:547–561MathSciNetCrossRefGoogle Scholar
  36. 36.
    Kilic B (2008) Peridynamic theory for progressive failure prediction in homogeneous and heterogeneous materials. Ph. D. Dissertaion, The University of Arizona, TucsonGoogle Scholar
  37. 37.
    Kilic B, Madenci E (2009) Structural stability and failure analysis using peridynamic theory. Int J Nonlinear Mech 44:845–854CrossRefzbMATHGoogle Scholar
  38. 38.
    Newmark NM (1959) A method of computation for structural dynamics. ASCE J Eng Mech Div 85:67–94Google Scholar
  39. 39.
    Underwood P (1983) Dynamic relaxation. In: Achenbach JD, Belytschko T, Bathe KJ (eds) Computational methods for transient analysis, vol 1. Elsevier, Amsterdam, pp 245–265Google Scholar
  40. 40.
    Borst R, Crisfield MA, Remmers JJC, Verhoose CV (2012) Non-linear finite element analysis of solids and structures, 2nd edn. Wiley, ChichesterCrossRefGoogle Scholar
  41. 41.
    Sultan C, Corless M, Skelton RE (2001) The prestressability problem of tensegrity structures: some analytical solutions. Int J Solids Struct 38:5223–52CrossRefzbMATHGoogle Scholar
  42. 42.
    Sultan C, Corless M, Skelton RE (2002) Symmetrical reconfiguration of tensegrity structures. Int J Solids Struct 39:2215–2234CrossRefzbMATHGoogle Scholar
  43. 43.
    Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J, Du Croz J, Greenbaum A, Hammarling S, McKenney A, Sorensen D (1999) LAPACK users’ guide, 3rd edn. Society for Industrial and Applied Mathematics, PhiladelphiaCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Hui Li
    • 1
  • Hongwu Zhang
    • 1
  • Yonggang Zheng
    • 1
    Email author
  • Liang Zhang
    • 1
    • 2
  1. 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and MechanicsDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.Department of Engineering Mechanics, College of Aerospace EngineeringChongqing UniversityChongqingPeople’s Republic of China

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