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Numerical model of elastic laminated glass beams under finite strain

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Laminated glass structures are formed by stiff layers of glass connected with a compliant plastic interlayer. Due to their slenderness and heterogeneity, they exhibit a complex mechanical response that is difficult to capture by single-layer models even in the elastic range. The purpose of this paper is to introduce an efficient and reliable finite element approach to the simulation of the immediate response of laminated glass beams. It proceeds from a refined plate theory due to Mau (1973), as we treat each layer independently and enforce the compatibility by the Lagrange multipliers. At the layer level, we adopt the finite-strain shear deformable formulation of Reissner (1972) and the numerical framework by Ibrahimbegović and Frey (1993). The resulting system is solved by the Newton method with consistent linearization. By comparing the model predictions against available experimental data, analytical methods and two-dimensional finite element simulations, we demonstrate that the proposed formulation is reliable and provides accuracy comparable to the detailed two-dimensional finite element analyzes. As such, it offers a convenient basis to incorporate more refined constitutive description of the interlayer.
Rocznik
Strony
734--744
Opis fizyczny
Bibliogr. 30 poz., tab., wykr.
Twórcy
autor
  • Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Prague 6, Czech Republic
autor
  • Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Prague 6, Czech Republic
autor
  • Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Prague 6, Czech Republic
Bibliografia
  • [1] M.Z. Aşık, Laminated glass plates: revealing of nonlinear behavior, Computers & Structures 81 (28-29) (2003) 2659–2671.
  • [2] M.Z. Aşık, S. Tezcan, A mathematical model for the behavior of laminated glass beams, Computers & Structures 83 (21–22) (2005) 1742–1753.
  • [3] R.A. Behr, J.E. Minor, M.P. Linden, C.V.G. Vallabhan, Laminated glass units under uniform lateral pressure, Journal of Structural Engineering 111 (5) (1985) 1037–1050.
  • [4] R.A. Behr, J.E. Minor, H.S. Norville, Structural behavior of architectural laminated glass, Journal of Structural Engineering 119 (1) (1993) 202–222.
  • [5] S.J. Bennison, A. Jagota, C.A. Smith, Fracture of Glass/Poly (vinyl butyral) (Butacite®) laminates in biaxial flexure, Journal of the American Ceramic Society 82 (7) (1999) 1761–1770.
  • [6] J.F. Bonnans, J.C. Gilbert, C. Lemaréchal, C.A. Sagastizábal, Numerical Optimization: Theoretical and Practical Aspects, Springer, 2003.
  • [7] P. Foraboschi, Behavior and failure strength of laminated glass beams, Journal of Engineering Mechanics 133 (12) (2007) 1290–1301.
  • [8] L. Galuppi, G.F. Royer-Carfagni, Effective thickness of laminated glass beams: new expression via a variational approach, Engineering Structures 38 (2012) 53–67.
  • [9] L. Galuppi, G.F. Royer-Carfagni, Laminated beams with viscoelastic interlayer, International Journal of Solids and Structures 49 (18) (2012) 2637–2645.
  • [10] M. Haldimann, A. Luible, M. Overend, Structural Use of Glass, Structural Engineering Documents, vol. 10, IABSE, Zürich, Switzerland, 2008.
  • [11] E. Hinton, J.S. Campbell, Local and global smoothing of discontinuous finite element functions using a least squares method, International Journal for Numerical Methods in Engineering 8 (3) (1974) 461–480.
  • [12] A. Hooper, On the bending of architectural laminated glass, International Journal of Mechanical Sciences 15 (4) (1973) 309–323.
  • [13] A. Ibrahimbegović, A. Delaplace, Microscale and mesoscale discrete models for dynamic fracture of structures built of brittle material, Computers & Structures 81 (12) (2003) 1255– 1265.
  • [14] A. Ibrahimbegović, F. Frey, Finite element analysis of linear and non-linear planar deformations of elastic initially curved beams, International Journal for Numerical Methods in Engineering 36 (19) (1993) 3239–3258.
  • [15] A. Ibrahimbegović, C. Knopf-Lenoir, A. Kučerová, P. Villon, Optimal design and optimal control of structures undergoing finite rotations and elastic deformations, International Journal for Numerical Methods in Engineering 61 (14) (2004) 2428–2460.
  • [16] H. Irschik, J. Gerstmayr, A continuum mechanics based derivation of Reissner's large-displacement finite-strain beam theory: the case of plane deformations of originally straight Bernoulli-Euler beams, Acta Mechanica 206 (1) (2009) 1–21.
  • [17] I.V. Ivanov, Analysis modelling and optimization of laminated glasses as plane beam, International Journal of Solids and Structures 43 (22-23) (2006) 6887–6907.
  • [18] M. Jirásek, Z.P. Bažant, Inelastic Analysis of Structures, John Wiley & Sons, Ltd., 2002.
  • [19] J. Kruis, Z. Bittnar, Reinforcement-matrix interaction modeled by FETI method, in: U. Langer, M. Discacciati, D.E. Keyes, O.B. Widlund, W. Zulehner (Eds.), Domain Decomposition Methods in Science and Engineering XVII, Lecture Notes in Computational Science and Engineering, vol. 60, Springer, Berlin, Heidelberg, 2008, pp. 567–573.
  • [20] J. Kruis, K. Matouš, Z. Dostál, Solving laminated plates by domain decomposition, Advances in Engineering Software 33 (7-10) (2002) 445–452.
  • [21] A. Kučerová, Optimisation de forme et contrôle de chargement des structures elastique soumis de rotation finis en utilisant les algorithmes génétiques, (Master's thesis), Ecole Normale Supérieure de Cachan, 2003 http://klobouk.fsv.cvut.cz/anicka/ publications/DEA_MaiSE_2003.pdf.
  • [22] S.T. Mau, A refined laminated plate theory, Journal of Applied Mechanics-Transactions of the ASME 40 (2) (1973) 606–607.
  • [23] H.S. Norville, K.W. King, J.L. Swofford, Behavior and strength of laminated glass, Journal of Engineering Mechanics 124 (1) (1998) 46–53.
  • [24] E. Reissner, On one-dimensional finite-strain beam theory: the plane problem, Journal of Applied Mathematics and Physics 23 (5) (1972) 795–804.
  • [25] T. Roubí ček, M. Kružík, J. Zeman, Delamination and adhesive contact models and their mathematical analysis and numerical treatment, in: V. Mantič (Ed.), Mathematical Methods and Models in Composites, Computational and Experimental Methods in Structures, vol. 5, World Scientific, 2013, pp. 349–400.
  • [26] S.-H. Schulze, M. Pander, K. Naumenko, H. Altenbach, Analysis of laminated glass beams for photovoltaic applications, International Journal of Solids and Structures 49 (15-16) (2012) 2027–2036.
  • [27] G. Sedlacek, K. Blank, J. Guesgen, Glass in structural engineering, Structural Engineer 73 (2) (1995) 17–22.
  • [28] C.V.G. Vallabhan, J.E. Minor, S.R. Nagalla, Stress in layered glass units and monolithic glass plates, Journal of Structural Engineering 113 (1987) 36–43.
  • [29] M. Šejnoha, Micromechanical Modeling of Unidirectional Fibrous Plies and Laminates, (Ph.D. Thesis), Rensselaer Polytechnic Institute, Troy, NY, 1996.
  • [30] A. Zemanová, J. Zeman, M. Šejnoha, Simple numerical model of laminated glass beams, Acta Polytechnica 48 (6) (2008) 22–26.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-43572a62-e107-4f4b-b7f5-d8801c375050
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