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The aim of this paper is to develop a robust layer-wise theory for structural analysis of curved glass and photovoltaic panels. By the analogy to the existing theories of plates, governing equations for doubly curved layers including kinematic relations, equilibrium conditions and constitutive equations are introduced. Applying assumptions of shear rigidity of skin layers and moments-free core layer as well as approximations of thin shallow shell, a reduced form of governing differential equations is proposed. Compared to the classical theories of shells the derived system includes an additional second order differential equation. As a result, additional boundary conditions should be satisfied for any edge of the shell. The importance of these extensions is demonstrated for long cylindrical panel with for two examples of simple supports: one with free edges, where relative in-plane displacements of skins are allowed, and one with framed edges, where cross-section rotations of all layers are assumed the same. For both cases closed-form analytical solutions related to a shell strip approximation are presented. Displacement bounds in monolithic and layered cases are derived, and the dependence of deformation and stress characteristics on the radius of curvature and types of supports are illustrated. [ABSTRACT FROM AUTHOR]

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. [Copyright &y& Elsevier]