A layer-wise theory for laminated glass and photovoltaic panels

Abstract Laminated plates with glass skin layers and a core layer from soft polymers are widely used in the civil engineering. Photovoltaic panels currently available on the market are composed from stiff front and back layers and a solar cell layer embedded in a soft polymeric encapsulant. In this paper a layer-wise theory for the structural analysis of glass and photovoltaic laminates is developed. Starting from governing equations for individual layers, kinematical constraints and appropriate interaction forces, a twelfth order system of partial differential equations is derived. The primary variables in the theory include the Airy stress function, the deflection function and the vector of relative in-plane displacements of skin layers. For symmetric laminates a system of uncoupled differential equations with respect to scalar potentials is presented. Three of them correspond to the first order shear deformation plate. The new additional second order differential equation provides a correction function according to the layer-wise theory. Closed form analytical solutions for a plate strip are derived to illustrate the essential influence of this correction for laminates with soft core layer. The importance of additional boundary conditions is shown for examples of free and framed plate edges.

[1]  Ulrich Eitner,et al.  Use of digital image correlation technique to determine thermomechanical deformations in photovoltaic laminates: Measurements and accuracy , 2010 .

[2]  H. Altenbach,et al.  On the bending of viscoelastic plates made of polymer foams , 2009 .

[3]  Yao Koutsawa,et al.  Static and free vibration analysis of laminated glass beam on viscoelastic supports , 2007 .

[4]  Stefan Diebels,et al.  A numerical homogenisation method for sandwich plates based on a plate theory with thickness change , 2013 .

[5]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[6]  Holm Altenbach,et al.  Direct approach-based analysis of plates composed of functionally graded materials , 2008 .

[7]  Ivelin V. Ivanov,et al.  Analysis, modelling, and optimization of laminated glasses as plane beam , 2006 .

[8]  Erasmo Carrera,et al.  Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis , 2011 .

[9]  Holm Altenbach,et al.  Shear Correction Factors in Creep-Damage Analysis of Beams, Plates and Shells , 2002 .

[10]  H. Altenbach,et al.  Unsymmetric three-layer laminate with soft core for photovoltaic modules , 2013 .

[11]  J. G. Simmonds,et al.  The Nonlinear Theory of Elastic Shells , 1998 .

[12]  S. Kapuria,et al.  Three-dimensional extended Kantorovich solution for Levy-type rectangular laminated plates with edge effects , 2014 .

[13]  S. Kapuria,et al.  Extended Kantorovich method for coupled piezoelasticity solution of piezolaminated plates showing edge effects , 2013, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[14]  Erasmo Carrera,et al.  A unified formulation to assess theories of multilayered plates for various bending problems , 2005 .

[15]  H. Altenbach,et al.  Analysis of laminated glass beams for photovoltaic applications , 2012 .

[16]  Marco Paggi,et al.  A multi-physics and multi-scale numerical approach to microcracking and power-loss in photovoltaic modules , 2013, 1303.7452.

[17]  R. Szilard.  Theories and Applications of Plate Analysis , 2004 .

[18]  Holm Altenbach,et al.  Closed and approximate analytical solutions for rectangular Mindlin plates , 2001 .

[19]  M. Paggi,et al.  Thermomechanical deformations in photovoltaic laminates , 2011 .

[20]  B. Brank.  On boundary layer in the Mindlin plate model: Levy plates , 2008 .

[21]  C. Wang,et al.  An overview of the relationships between solutions of the classical and shear deformation plate theories , 2000 .

[22]  Paolo Foraboschi,et al.  Analytical model for laminated-glass plate , 2012 .

[23]  E. Carrera.  Historical review of Zig-Zag theories for multilayered plates and shells , 2003 .

[24]  Holm Altenbach,et al.  Creep bending of thin-walled shells and plates by consideration of finite deflections , 1997 .

[25]  Mehmet Zülfü Aşık,et al.  Laminated glass beams: Strength factor and temperature effect , 2006 .

[26]  H. Altenbach,et al.  A micro-polar theory for binary media with application to phase-transitional flow of fiber suspensions , 2003 .

[27]  H. Altenbach,et al.  Coupling of a structural analysis and flow simulation for short-fiber-reinforced polymers: property prediction and transfer of results , 2009 .