Innovative FEM for the thermal analysis of architectural glazing exposed to solar radiation. Proposal for a simplified engineering approach
The non-uniform heating of architectural glazing due to cast shadows and frame shielding, produces an uneven temperature distribution, often called “thermal shock”, which may induce stresses leading to breakage. This is why the precise assessment of the temperature field is of paramount importance for safety and durability of building skins. In the design practice, reference is made to simplified approaches from Standards, which may be inaccurate when used to determine the thermal stresses. Dedicated Software can provide sophisticated analyses but, realistically, it can be used only for important projects.
Here, a dedicated 3D numerical formulation, specifically conceived for non-uniformly irradiated architectural glazing, is presented. It is based on the variational principle by M. Biot, allowing for steep temperature variations with no need of a very fine mesh. Convective and radiant heat exchange with the environment, different within the panel (regions directly hit by the sun, partially shaded or trapped in the window frame), as well as heat conduction and heat storage, are considered. Results are compared with those obtained from a simplified engineering approach, based on the assumptions that temperature is approximately uniform in the different pane regions, and that conductive heat exchange between adjacent regions occurs in thin interfaces strips. Paradigmatic examples are elaborated, considering the time variation of external temperature and sun radiation (transient state). A post-processor allows to directly determine the thermal stress, given the boundary conditions in the form proposed by standards.
Analytical solution and exact effective thickness for multilayered laminated glass beams of arbitrary composition. Application to cantilevered balustrades
Under the quasi-elastic approximation, assuming that the interlayer polymer is linear elastic with moduli parametrically depending on time and environmental temperature, we present a model for inflexed laminated glass beams in the pre-glass-breakage phase. This relies on a modified version of the refined zig-zag theory for composites, in which the glass plies are Euler–Bernoulli beams, whereas the interlayers provides for the shear- coupling of the glass plies. The field variables are the beam displacement and the mean sectional shear angle, defining the zig-zag warping of the cross section. A FEM implementation is proposed but, remarkably, the governing equations can be solved analytically, for multi-laminated packages of arbitrary composition, when the structure is statically determined.
The analytical solution is worked out for cantilevered laminated-glass balustrades, schematized as a short simply-supported laminated beam with a long cantilevered overhang. The cross-sectional warping allowed by the end constraint induces such strong asymmetrical deformation that traditional approaches based on the definition of the effective thickness of a monolith with equivalent bending properties, such as the Wölfel-Bennison or the EET methods, cannot be accurate. Geometric and natural boundary conditions, together with matching conditions at the intermediate roller constraint, necessary to solve the governing differential problem, are found variationally. The analytical solutions under concentrated and distributed loads exactly determine the effective thickness of the laminate, allowing for comparison with other recently proposed approximate approaches which, however, apply only to three-layered packages. The expressions proposed here can be directly used in the design practice.