Skip to main content
SpringerLink
Log in

Nonlinear eccentric low-velocity impact analysis of a highly prestressed FGM rectangular plate, using a refined contact law

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In the present paper, a nonlinear analysis is presented for response prediction of a low-velocity eccentric impact between a functionally graded rectangular plate and a rigid sphere or a projectile with a spherical nose. Some of the novelties of the present paper are (i) considering the more general case of eccentric impact, (ii) investigating effects of the initial in-plane loads on the impact responses of the functionally graded plates, especially for compressive loads that are comparable but not equal to the buckling loads, (iii) using a contact law that incorporates influences of the transverse variations of the material properties of the substrate layers and the plate thickness, and (iv) using nonlinear strain-displacement relations instead of using the traditional infinitesimal deformations assumption for assessment of influences of the initial preloads. Due to using von Karman strain-displacement relations and a nonlinear contact law, the governing equations are highly nonlinear. For this reason, an iterative solution scheme is employed. A sensitivity analysis is performed to investigate influences of the specifications of the plate and the indenter, the eccentric value, and the in-plane preloads on the indentation and force time histories. Results reveal that due to the resulting increase in the contact force, slightly higher damages may be expected for impacted FGM plates subjected to initial compressive in-plane loads.

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. Shariyat M.: Vibration and dynamic buckling control of imperfect hybrid FGM plates with temperature-dependent material properties subjected to thermo-electro-mechanical loading conditions. Compos. Struct. 88, 240–252 (2009)

    Article  Google Scholar 

  2. Alipour M.M., Shariyat M.: An elasticity-equilibrium-based zigzag theory for axisymmetric bending and stress analysis of the functionally graded circular sandwich plates, using a Maclaurin-type series solution. Eur. J. Mech. A/Solids 34, 78–101 (2012)

    Article  MathSciNet  Google Scholar 

  3. Shariyat M., Alipour M.M.: Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations. Archive Appl. Mech. 81, 1289–1306 (2011)

    Article  Google Scholar 

  4. Shivakumar K.N., Elber W., Illg W.: Prediction of low-velocity impact damage in composite laminates. AIAA J. 23(5), 442–449 (1984)

    Google Scholar 

  5. Gong S.W., Lam K.Y.: Effects of structural damping and stiffness on impact response of layered structures. AIAA J. 38(9), 1730–1735 (2000)

    Article  Google Scholar 

  6. Jacquelin E., Laine’ J.-P., Bennani A., Massenzio M.: A modelling of an impacted structure based on constraint modes. J. Sound Vib. 301(3-5), 789–802 (2007)

    Article  Google Scholar 

  7. Pashah S., Massenzio M., Jacquelin E.: Prediction of structural response for low velocity impact. Int. J. Impact Eng. 35(2), 119–132 (2008)

    Article  Google Scholar 

  8. Anderson T.A.: An investigation of SDOF models for large mass impact on sandwich composites. J. Compos. B 36(2), 135–142 (2005)

    Article  Google Scholar 

  9. Abrate S.: Localized impact on sandwich structures with laminated facing. Appl. Mech. Rev. 50(2), 69–82 (1997)

    Article  Google Scholar 

  10. Abrate S.: Impact Engineering of Composite Structures, CISM. Springer, Udine (2011)

    Book  Google Scholar 

  11. Chai G.B., Zhu S.: A review of low-velocity impact on sandwich structures. Proc. Inst. Mech. Eng. L: J. Mater. Des. Appl. 225(4), 207–230 (2011)

    Google Scholar 

  12. Qiu X.M., Yu T.X.: Some topics in recent advances and applications of structural impact dynamics. Appl. Mec. Rev. 64(3), 034001 (2011)

    Article  Google Scholar 

  13. Nosier A., Kapania R.K., Reddy J.N.: Low-velocity impact of laminated composites using a layerwise theory. Comput. Mech. 13, 360–379 (1994)

    Article  MATH  Google Scholar 

  14. Sun D., Luo S.-N.: Wave propagation and transient response of a FGM plate under a point impact load based on higher-order shear deformation theory. Compos. Struct. 93, 1474–1484 (2011)

    Article  Google Scholar 

  15. Yigit A.S., Christoforou A.P.: On the impact between a rigid sphere and a thin composite laminate supported by a rigid substrate. Compos. Struct. 30(2), 169–177 (1995)

    Article  Google Scholar 

  16. Christoforou A.P., Yigit A.S.: Effect of flexibility on low velocity impact response. J. Sound Vib. 217, 563–578 (1998)

    Article  Google Scholar 

  17. Yigit A.S., Christoforou A.P.: Limits of asymptotic solutions in low-velocity impact of composite plates. Compos. Struct. 81, 568–574 (2007)

    Article  Google Scholar 

  18. Christoforou A.P., Yigit A.S.: Scaling of low-velocity impact response in composite structures. Compos. Struct. 91, 358–365 (2009)

    Article  Google Scholar 

  19. Shariyat M., Ghajar R., Alipour M.M.: An analytical solution for a low velocity impact between a rigid sphere and a transversely isotropic strain-hardening plate supported by a rigid substrate. J. Eng. Math. 75, 107–125 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  20. Guan Z., Yang C.: Low-velocity impact and damage process of composite laminates. J. Compos. Mater. 36, 851–871 (2002)

    Article  Google Scholar 

  21. Zheng D., Binienda W.K.: Semianalytical solution of wave-controlled impact on composite laminates. ASCE J. Aerospace Eng. 22, 318–323 (2009)

    Article  Google Scholar 

  22. Olsson R.: Analytical model for delamination growth during small mass impact on plates. Int. J. Solids Struct. 47, 2884–2892 (2010)

    Article  MATH  Google Scholar 

  23. Swanson S.R.: Hertzian contact of orthotropic materials. Int. J. Solids Struct. 41, 1945–1959 (2004)

    Article  MATH  Google Scholar 

  24. Swanson S.R.: Contact deformation and stress in orthotropic plates. Compos. A 36, 1421–1429 (2005)

    Article  Google Scholar 

  25. Chen P., Xiong J., Shen Z.: Thickness effect on the contact behavior of a composite laminate indented by a rigid sphere. Mech. Mater. 40, 183–194 (2008)

    Article  Google Scholar 

  26. Palazotto A.N., Herup E.J., Gummadi L.N.B.: Finite element analysis of low-velocity impact on composite sandwich plates. Compos. Struct. 49, 209–227 (2000)

    Article  Google Scholar 

  27. Larson, R.A., Palazotto, A.: Low velocity impact analysis of functionally graded circular plates. In: Proceedings of IMECE2006, 2006 ASME International Mechanical Engineering Congress and Exposition November 5–10, Chicago, Illinois, USA, paper No.: IMECE2006-14003 (2006)

  28. Yang J., Shen H.-S.: Dynamic response of initially stressed functionally graded thin plates. Compos. Struct. 21, 497–508 (2001)

    Article  Google Scholar 

  29. Choi I.-H.: Low-velocity impact analysis of composite laminates under initial in-plane load. Compos. Struct. 86, 251–257 (2008)

    Article  Google Scholar 

  30. Shariyat, M., Jafari, R.: Nonlinear low-velocity impact response analysis of a radially preloaded two-directional-functionally graded circular plate: A refined contact stiffness approach. Compos. Part B, doi:10.1016/j.compositesb.2012.05.014 (2012)

  31. Khalili S.M.R., Mittal R.K., Mohammad Panah N.: Analysis of fiber reinforced composite plates subjected to transverse impact in the presence of initial stresses. Compos. Struct. 77, 263–268 (2007)

    Article  Google Scholar 

  32. Heimbs S., Heller S., Middendorf P., Hähnel F., Weiße J.: Low velocity impact on CFRP plates with compressive preload: Test and modeling. Int. J. Impact Eng. 36, 1182–1193 (2009)

    Article  Google Scholar 

  33. Turner J.R.: Contact on a transversely isotropic half-space, or between two transversely isotropic bodies. Int. J. Solids Struct. 16, 409–419 (1980)

    Article  MATH  Google Scholar 

  34. Reddy J.N.: Theory and Analysis of Elastic Plates and Shells. 2nd edition. CRC Press, Boca Raton (2006)

    Google Scholar 

  35. Ugural A.C.: Stresses in Beams, Plates, and Shells. CRC Press, Boca Raton (2009)

    Google Scholar 

  36. Shariyat M.: Dynamic buckling of imperfect laminated plates with piezoelectric sensors and actuators subjected to thermo-electro-mechanical loadings, considering the temperature-dependency of the material properties. Compos. Struct. 88, 228–239 (2009)

    Article  Google Scholar 

  37. Shariyat M.: Non-linear dynamic thermo-mechanical buckling analysis of the imperfect sandwich plates based on a generalized three-dimensional high-order global-local plate theory. Compos. Struct. 92, 72–85 (2010)

    Article  Google Scholar 

  38. Shariyat M.: A generalized high-order global-local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads. Compos. Struct. 92, 130–143 (2010)

    Article  Google Scholar 

  39. Shariyat M.: Non-linear dynamic thermo-mechanical buckling analysis of the imperfect laminated and sandwich cylindrical shells based on a global-local theory inherently suitable for non-linear analyses. Int. J. Non-Linear Mech. 46(1), 253–271 (2011)

    Article  Google Scholar 

  40. Shariyat M.: A double-superposition global-local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: a complex modulus approach. Archive Appl. Mech. 81, 1253–1268 (2011)

    Article  Google Scholar 

  41. Shariyat M.: A nonlinear double-superposition global-local theory for dynamic buckling of imperfect viscoelastic composite/sandwich plates: A hierarchical constitutive model. Compos. Struct. 93, 1890–1899 (2011)

    Article  Google Scholar 

  42. Shariyat M.: Nonlinear thermomechanical dynamic buckling analysis of imperfect viscoelastic composite/sandwich shells by a double-superposition global-local theory and various constitutive models. Compos. Struct. 93, 2833–2843 (2011)

    Article  Google Scholar 

  43. Shariyat M.: A general nonlinear global-local theory for bending and buckling analyses of imperfect cylindrical laminated and sandwich shells under thermomechanical loads. Meccanica 47, 301–319 (2012)

    Article  MathSciNet  Google Scholar 

  44. Zienkiewicz O.C., Taylor R.L.: The Finite Element Method: Its Basis and Fundamentals. Butterworth-Heinemann, Oxford (2005)

    MATH  Google Scholar 

  45. Karas K.: Platten unter seitlichem Stoss. Ingenieur Arch. 10, 237–250 (1939)

    Article  MathSciNet  Google Scholar 

  46. Wu H.-Y.T., Springer G.S.: Impact induced stresses, strains and delaminations in composite plates. J. Compos.Mater. 22(6), 533–560 (1988)

    Article  Google Scholar 

  47. Yang, S.H., Sun, C.T.: Indentation law for composite laminates. NASA CR-165460 (1981)

  48. Ugural A.C., Fenster S.K.: Advanced Mechanics of Materials and Applied Elasticity. Prentice Hall, New Jersey (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Pardis Street, Molasadra Avenue, Vanak Square, Tehran, 19991-43344, Iran

    M. Shariyat & F. Farzan

Authors
  1. M. Shariyat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Farzan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Shariyat.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shariyat, M., Farzan, F. Nonlinear eccentric low-velocity impact analysis of a highly prestressed FGM rectangular plate, using a refined contact law. Arch Appl Mech 83, 623–641 (2013). https://doi.org/10.1007/s00419-012-0708-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-012-0708-3

Keywords

Search

Navigation