SpringerLink
Log in

Theoretical Analysis of Laminated Glass

  • Chapter
  • First Online:
Impact Behavior and Pedestrian Protection of Automotive Laminated Windshield

  • 396 Accesses

Abstract

Experimental investigations and theoretical analysis of laminated glass in different physical models were presented in the previous section. In this section, we introduce the different mathematical models of laminated glass beam or plate in detail based on numerous investigation results to ensure further understanding.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
GBP 19.95
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
GBP 119.50
Price includes VAT (United Kingdom)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
GBP 149.99
Price includes VAT (United Kingdom)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. S. Hallström, J.L. Grenestedt, Failure analysis of laminated timber beams reinforced with glass fibre composites. Wood Sci. Technol. 31, 17–34 (1997)

    Article  Google Scholar 

  2. J.A. Hooper, On the bending of architectural laminated glass. Int. J. Mech. Sci. 15, 309–323 (1973)

    Article  Google Scholar 

  3. R.A. Behr, J.E. Minor, M.P. Linden, C.V.G. Vallabhan, Laminated glass units under uniform lateral pressure. J. Struct. Eng.-ASCE 111, 1037–1050 (1985)

    Article  Google Scholar 

  4. R.A. Behr, J.E. Minor, H.S. Norville, Structural behavior of architectural laminated glass. J. Struct. Eng. 119, 202–222 (1993)

    Article  Google Scholar 

  5. C.V.G. Vallabhan, Iterative analysis of nonlinear glass plates. J. Struct. Eng. 109, 489–502 (1983)

    Article  Google Scholar 

  6. H.S. Norville, K.W. King, J.L. Swofford, Behavior and strength of laminated glass. J. Eng. Mech. 124, 46–53 (1998)

    Article  Google Scholar 

  7. I.V. Ivanov, Analysis, modelling, and optimization of laminated glasses as plane beam. Int. J. Solids Struct. 43, 6887–6907 (2006)

    Article  Google Scholar 

  8. M.Z. Aşık, S. Tezcan, A mathematical model for the behavior of laminated glass beams. Comput. Struct. 83, 1742–1753 (2005)

    Article  Google Scholar 

  9. M.Z. Aşık, E. Dural, M. Yetmez, T. Uzhan, A mathematical model for the behavior of laminated uniformly curved glass beams. Compos. B Eng. 58, 593–604 (2014)

    Article  Google Scholar 

  10. A. Zemanová, J. Zeman, M. Šejnoha, Numerical model of elastic laminated glass beams under finite strain. Arch. Civ. Mech. Eng. 14, 734–744 (2014)

    Article  Google Scholar 

  11. C.V.G. Vallabhan, J.E. Minor, S.R. Nagalla, Stresses in layered glass units and monolithic glass plates. J. Struct. Eng. 113, 36–43 (1987)

    Article  Google Scholar 

  12. M.Z. Aşik, C.V.G. Vallabhan, On the convergence of nonlinear plate solutions. Comput. Struct. 65, 225–229 (1997)

    Article  Google Scholar 

  13. M.E. Mohareb, A mathematical model for the nonlinear analysis of laminated glass plates subjected to lateral press. Texas Tech University (1990)

    Google Scholar 

  14. C.V.G. Vallabhan, Y.C. Das, M. Magdi, M. Asik, J.R. Bailey, Analysis of laminated glass units. J. Struct. Eng. 119, 1572–1585 (1993)

    Article  Google Scholar 

  15. M.Z. Aşık, Laminated glass plates: revealing of nonlinear behavior. Comput. Struct. 81, 2659–2671 (2003)

    Article  Google Scholar 

  16. M.Z. Asik, E. Dural, Effect of support conditions on the vibration of laminated composite beams. J. Vib. Control 13, 1361–1368 (2007)

    Article  Google Scholar 

  17. X. Sun, M.A. Khaleel, Effects of different design parameters on stone-impact resistance of automotive windshields. Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. 219, 1059–1067 (2005)

    Article  Google Scholar 

  18. X. Sun, M.A. Khaleel, R.W. Davies, Modeling of stone-impact resistance of monolithic glass ply using continuum damage mechanics. Int. J. Damage Mech. 14, 165–178 (2005)

    Article  Google Scholar 

  19. S. Zhao, L.R. Dharani, L. Chai, S.D. Barbat, Analysis of damage in laminated automotive glazing subjected to simulated head impact. Eng. Fail. Anal. 13, 582–597 (2006)

    Article  Google Scholar 

  20. S. Zhao, L.R. Dharani, X. Liang, Analysis of damage in laminated architectural glazing subjected to blast loading. Adv. Struct. Eng. 11, 129–134 (2008)

    Article  Google Scholar 

  21. M. Timmel, S. Kolling, P. Osterrieder, P.A.D. Bois, A finite element model for impact simulation with laminated glass. Int. J. Impact Eng 34, 1465–1478 (2007)

    Article  Google Scholar 

  22. P.A.D. Bois, S. Kolling, W. Fassnacht, Modelling of safety glass for crash simulation. Comput. Mater. Sci. 28, 675–683 (2003)

    Article  Google Scholar 

  23. S. Zhao, L.R. Dharani, X. Liang, L. Chai, S.D. Barbat, Crack initiation in laminated automotive glazing subjected to simulated head impact. Int. J. Crashworthiness 10, 229–236 (2005)

    Article  Google Scholar 

  24. S. Zhao, L.R. Dharani, L. Chai, S.D. Barbat, Dynamic response of laminated automotive glazing impacted by spherical featureless headform. Int. J. Crashworthiness 11, 105–114 (2006)

    Article  Google Scholar 

  25. B. Lawn, R. Wilshaw, Review: indentation fracture: principles and applications. J. Mater. Sci. 10, 1049–1081 (1975)

    Article  Google Scholar 

  26. C.G. Knight, M.V. Swain, M.M. Chaudhri, Impact of small steel spheres on glass surfaces. J. Mater. Sci. 12, 1573–1586 (1977)

    Article  Google Scholar 

  27. M.Y. Zang, L.I. Jun, Z. Lei, Study on impact fracture behavior of Bi-layer laminated glass based on DEM. Sci. Technol. Eng. (2009)

    Google Scholar 

  28. M. Zang, Static characteristic and impact fracture behavior of automobile glass. Chin. J. Mech. Eng. 45, 268–272 (2009)

    Article  Google Scholar 

  29. M.Y. Zang, Z. Lei, S.F. Wang, Investigation of impact fracture behavior of automobile laminated glass by 3D discrete element method. Comput. Mech. 41, 73–83 (2007)

    Article  Google Scholar 

  30. S. Chen, M. Zang, D. Wang, S. Yoshimura, T. Yamada, Numerical analysis of impact failure of automotive laminated glass: a review. Compos. B Eng. 122, 47–60 (2017)

    Article  Google Scholar 

  31. L.M. Kachanov, Introduction to Continuum Damage Mechanics (M. Nijhoff, 1986)

    Google Scholar 

  32. X. Sun, M.A. Khaleel, Modeling of glass fracture damage using continuum damage mechanics-static spherical indentation. Int. J. Damage Mech. 13, 263–285 (2004)

    Article  Google Scholar 

  33. Z. Lei, M. Zang, An approach to combining 3D discrete and finite element methods based on penalty function method. Comput. Mech. 46, 609–619 (2010)

    Article  MathSciNet  Google Scholar 

  34. A new method for growing multiple cracks without remeshing and its application to fatigue crack growth. Model. Simul. Mater. Sci. Eng. 12, 901–915 (2004)

    Google Scholar 

  35. X.P. Xu, A. Needleman, Numerical simulations of fast crack growth in brittle solids. J. Mech. Phys. Solids 42, 1397–1434 (1994)

    Article  Google Scholar 

  36. G.T. Camacho, M. Ortiz, Computational modelling of impact damage in brittle materials. Int. J. Solids Struct. 33, 2899–2938 (1996)

    Article  Google Scholar 

  37. Y. Peng, J. Yang, C. Deck, R. Willinger, Finite element modeling of crash test behavior for windshield laminated glass. Int. J. Impact Eng 57, 27–35 (2013)

    Article  Google Scholar 

  38. M.Y. Zang, Research on finite element model of PVB laminated glass

    Google Scholar 

  39. L. Qi, J. Liu, M. Qiang, D. Wang, X. Tang, Simulation and test validation of windscreen subject to pedestrian head impact. J. Automot. Saf. Energy (2011)

    Google Scholar 

  40. X. Xu, J. Xu, J. Chen, P. Li, B. Liu, Y. Li, Investigation of dynamic multi-cracking behavior in PVB laminated glass plates. Int. J. Impact Eng. 100, 62–74 (2017)

    Article  Google Scholar 

  41. M.Y. Zang, Z.L. Song, Z.G. Yang, Finite element model of windscreen for pedestrian protection. J. South China Univ. Technol. 42, 143–148 (2014)

    Google Scholar 

  42. D. Wang, Y. Wang, Y. Shi, W.U. Shenrong, Z. Zhao, W.U. Te, C.A. Co, Numerical simulation and test validation of automotive laminated windshield glass. J. Automot. Saf. Energy 5, 263–269 (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Automotive Engineering, Beihang University, Bei**g, China

    Jun Xu

  2. Department of Automotive Engineering, Tsinghua University, Bei**g, China

    Yibing Li

Authors
  1. Jun Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yibing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Xu .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Science Press, Bei**g and Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Xu, J., Li, Y. (2019). Theoretical Analysis of Laminated Glass. In: Impact Behavior and Pedestrian Protection of Automotive Laminated Windshield. Springer, Singapore. https://doi.org/10.1007/978-981-13-2441-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-2441-3_5

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-2440-6

  • Online ISBN: 978-981-13-2441-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation