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On the durable critic load in creep buckling of viscoelastic laminated plates and circular cylindrical shells

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Abstract

Based on the first order shear deformation theory and classic buckling theory, the paper investigates the creep buckling behavior of viscoelastic laminated plates and laminated circular cylindrical shells. The analysis and elaboration of both instantaneous elastic critic load and durable critic load are emphasized. The buckling load in phase domain is obtained from governing equations by applying Laplace transform, and the instantaneous elastic critic load and durable critic load are determined according to the extreme value theorem for inverse Laplace transform. It is shown that viscoelastic approach and quasi-elastic approach yield identical solutions for these two types of critic load respectively. A transverse disturbance model is developed to give the same mechanics significance of durable critic load as that of elastic critic load. Two types of critic loads of boron/epoxy composite laminated plates and circular cylindrical shells are discussed in detail individually, and the influencing factors to induce creep buckling are revealed by examining the viscoelasticity incorporated in transverse shear deformation and in-plane flexibility.

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References

  1. Yang T Q, Zhang X C, Gang Q G. Temporal characteristics of loading for creep buckling of plates. Acta Mech Sin (in Chinese), 2000, 32(3): 319–325

    Google Scholar 

  2. Peng F, Fu Y M. Characteristics of creep buckling for viscoelastic laminated plates. Acta Mech Sin (in Chinese), 2003, 35(2): 353–356

    Google Scholar 

  3. Wilson D W, Vinson J R. Viscoelasticitic analysis of laminated plate buckling. AIAA J, 1984, 22(7–12): 982–988

    Article  MATH  ADS  Google Scholar 

  4. Vinogradov A M, Glockner P G. Buckling of spherical viscoelastic shells. Proc ASCE, 1980, 106(ST1): 59–67

    Google Scholar 

  5. Kim C G, Hong C S. Viscoelastic sandwich plates with cross-ply faces. J Struct Eng, 1988, 114(2): 150–164

    Article  Google Scholar 

  6. Huang N N. Viscoelastic buckling and postbuckling of circular cylindrical laminated shells in hygrothermal environment. J Marine Sci Tech, 1994, 2(1): 9–16

    Google Scholar 

  7. Sun Y X, Ma H Z, Gao Z T, et al. Creep buckling of cross-ply laminated plates. Acta Mech Solida Sin (in Chinese), 1998, 19(4): 347–354

    Google Scholar 

  8. Minahen T M, Knauss W G. Creep buckling of viscoelastic structures. Int J Solids Struct, 1993, 30(8): 1075–1092

    Article  Google Scholar 

  9. Wang Y J, Wang Z M. Creep buckling of cross-ply symmetric laminated cylindrical panels. Appl Math Mech (in Chinese), 1993, 14(4): 295–300

    Google Scholar 

  10. Ishakov V I. Stability analysis of viscoelastic thin shallow hyperbolic paraboloid shells. Int J Solids Struct, 1999, 36(28): 4209–4223

    Article  MATH  Google Scholar 

  11. Akbarov S D, Yahnioglu N, Kutug Z. On the three-dimensional stability loss problem of the viscoelastic composite plate. Int J Eng Sci, 2001, 39(13): 1443–1457

    Article  Google Scholar 

  12. Szyszkowski W, Glockner P G. The stability of viscoelastic perfect columns: A dynamic approach. Int J Solids Struct, 1985, 21(6): 545–559

    Article  MATH  Google Scholar 

  13. Chandiramani N K, Librescu L, Aboudi J. The theory of orthotropic viscoelastic shear deformable composite flat panels and their dynamic stability. Int J Solids Struct, 1989, 25(5): 465–482

    Article  MATH  Google Scholar 

  14. Peng F, Fu Y M. Dynamic stability of circular cylindrical shells under constant axial compression. Eng Mech (in Chinese), 2002, 19(6): 49–53

    Google Scholar 

  15. Ding R, Zhu Z Y, Chen C J. Some dynamical properties of a viscoelastic cylindrical shell. Appl Math Mech (in Chinese), 1999, 20(3): 221–228

    Google Scholar 

  16. Chen C J, Fan X J. Critical loads and the dynamical stability of viscoelastic annular plates. Acta Mech Sin (in Chinese), 2001, 33(3): 365–375

    Google Scholar 

  17. Bellman R, Kalaba R E, Lockett J. Numerical Inversion of The Laplace Transform. New York: Elsevier Publishing Co., 1966

    MATH  Google Scholar 

  18. Swanson S R. Approximate Laplace transform inversion in dynamic viscoelasticity. J Appl Mech ASME, 1980, 47(6): 769–774

    Article  MATH  Google Scholar 

  19. Taylor R L, Pister K S, Goudreau G L. Thermomechanical analysis of viscoelastic solids. Int J Numer Method Engin, 1970, 2(1): 45–51

    Article  MATH  Google Scholar 

  20. Bradshaw R D, Brinson L C. Mechanical response of linear viscoelastic composite laminates incorporating nonisothermal physical aging effects. Comp Sci Technol, 1999, 59(9): 1411–1427

    Article  Google Scholar 

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Correspondence to Fan Peng.

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Supported jointly by the Natural Science Foundation of Hunan Province (Grant No. 05JJ3008) and the National Natural Science Foundation of China (Grant No 10572049)

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Peng, F., Fu, Y. & Liu, Y. On the durable critic load in creep buckling of viscoelastic laminated plates and circular cylindrical shells. Sci. China Ser. G-Phys. Mech. Astron. 51, 873–882 (2008). https://doi.org/10.1007/s11433-008-0091-9

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  • DOI: https://doi.org/10.1007/s11433-008-0091-9

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