Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Calculation model for layered glass

  • Received : 2023.06.15
  • Accepted : 2023.09.04
  • Published : 2023.12.25
⟨ Previous Next ⟩

Abstract

This paper presents a mathematical model suitable for the calculation of laminated glass, i.e. glass plates combined with an interlayer material. The model is based on a beam differential equation for each glass plate and a separate differential equation for the slip in the interlayer. In addition to slip, the model takes into account prestressing force in the interlayer. It is possible to combine the two contributions arbitrarily, which is important because the glass sheet fabrication process changes the stiffness of the interlayer in ways that are not easily predictable and could introduce prestressing of varying magnitude. The model is suitable for reformulation into an inverse procedure for calculation of the relevant parameters. Model consisting of a system of differential-algebraic equations, proved too stiff for cases with the thin interlayer. This novel approach covers the full range of possible stiffnesses of layered glass sheets, i.e., from zero to infinite stiffness of the interlayer. The comparison of numerical and experimental results contributes to the validation of the model.

Keywords

Acknowledgement

This work was supported by project HRZZ 7926 "Separation of parameter influence in engineering modeling and parameter identification", project KK.01.1.1.04.0056 "Structure integrity in energy and transportation" and University of Rijeka grant 'uniri-tehnic-18-108', for which we gratefully acknowledge.

References

  1. Araujo, T.J.P. (2019), "Experimental and numerical analysis of two-layer composite beams", Thesis, Instituto Superior De Engenharia De Lisboa
  2. Bedon, C., Markovic, D., Karlos, V. and Larcher, M. (2023), "Numerical investigation of glass windows under near-field blast", Couple. Syst. Mech., 12, 167-181. https://doi.org/10.12989/csm.2023.12.2.167.
  3. Bohmann, D. (2015), SJ MEPLA Theory Manual, SJ Software GmbH, Aachen.
  4. Campi, F. and Monetto, I. (2013), "Analytical solutions of two-layer beams with interlayer slip and bi-linear interface law", Int. J. Solid. Struct., 50, 687-698. http://doi.org/10.1016/j.ijsolstr.2012.10.032.
  5. Challamel, N. and Girhammar, U.A. (2011), "Boundary layer effect in composite beams with interlayer slip", J. Aerosp. Eng., ASCE, 24(2), 199-209. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000027.
  6. Foraboschi, P. (2009), "Analytical solution of two-layer beam taking into account nonlinear interlayer slip", J. Eng. Mech., 135(10), 1129-1146. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000043.
  7. Gahleitner, J. and Schoeftner, J. (2021), "A two-layer beam model with interlayer slip based on two-dimensional elasticity", Compos. Struct., 274, 114283. https://doi.org/10.1016/j.compstruct.2021.114283.
  8. Hartmann, S. and Dileep, P.K. (2019), "Classical beam theory with arbitrary number of layers", Technical Report Series, Technische Universitat Clausthal.
  9. Hirsh, M.W., Smale, S. and Devaney, R.L. (2004), Differential Equations, Dynamical Systems and An Introduction to Chaos, Elsevier, Amsterdam.
  10. Ibrahimbegovic, A. (2009), Nonlinear Solid Mechanics: Theoretical Formulations and Finite Element Solution Methods, Vol. 160, Springer, Science & Business Media.
  11. Ibrahimbegovic, A. and Markovic, D. (2003), "Strong coupling methods in multi-phase and multi-scale modeling of inelastic behaveior of heterogeneous structures", Comput. Meth. Appl. Mech. Eng., 192, 3089-3107. https://doi.org/10.1016/S0045-7825(03)00342-6.
  12. Kozar, I. and Ozbolt, J. (2010), "Some aspects of load-rate sensitivity in visco-elastic microplane model", Comput. Concrete, 7, 317-329. https://doi.org/10.12989/cac.2010.7.4.317.
  13. Kozar, I., Bede, N., Mrakovčic, S. and Bozic, Z. (2021), "Layered model of crack growth in concrete beams in bending", Procedia Struct. Integrit., 31, 134-139. https://doi.org/10.1016/j.prostr.2021.03.022.
  14. Kozar, I., Bede, N., Mrakovčic, S. and Bozic, Z. (2022), "Verification of a fracture model for fiber reinforced concrete beams in bending", Eng. Fail. Anal., 138, 106378. https://doi.org/10.1016/j.engfailanal.2022.106378.
  15. Kozar, I., Rukavina, T. and Ibrahimbegovic, A. (2018), "Method of incompatible models-Overview and applications", Gradevinar, 70, 19-29. https://doi.org/10.14256/JCE.2078.2017.
  16. Kozar, I., Toric Malic, N. and Rukavina, T. (2018), "Inverse model for pullout determination of steel fibers", Couple. Syst. Mech., 7, 197-209. https://doi.org/10.12989/csm.2018.7.2.197.
  17. Lemaitre, J. and Chaboche, L.J. (1994), Mechanics of Solid Materials, Cambridge University Press, Cambridge.
  18. Nikolic, M., Karavelic, E., Ibrahimbegovic, A. and Misčevic, P. (2018), "Lattice element models and their peculiarities", Arch. Comput. Meth. Eng., 25(3), 753-784. https://doi.org/10.1007/s11831-017-9210-y.
  19. O'Regan, C. (2015), Structural Use of Glass in Buildings, The Institution of Structural Engineers, London.
  20. Rukavina, T., Ibrahimbegovic, A. and Kozar, I. (2019), "Fiber-reinforced brittle material fracture models capable of capturing a complete set of failure modes including fiber pull-out", Comput. Meth. Appl. Mech. Eng., 192, 3089-3107. https://doi.org/10.1016/j.cma.2019.05.054.
  21. Wolfram Research Inc., Mathematica (2023), https://www.wolfram.com/mathematica/