Thermal and elastic modeling of architectural glass unevenly heated by the environment. Formal symmetry from Biot's variational principle

The stress state resulting from an non-uniform temperature distribution in architectural glass panes, consequent to environmental actions and, in particular, to the shadows cast, is one of the main causes of failures experienced in building facades. We propose a dedicated thermo-elastic model, implemented in a finite element framework, to overcome the weakness of standardized prescriptions, the limits of simplified practical rules, and the difficulty in using general-purpose thermal softwares, not always interfaced with a structural analysis, in the common design practice. The formulation of the thermal problem is based on Biot's variational principle for heat transfer, which facilitates the numerical implementation, via a 2D mesh in case of sharply varying temperature fields, expected for the case at hand. The elastic problem considers a kinematics a la Kirchhoff-Love for the glass plate, enriched by a term accounting for a non-linear thermal strain distribution in the thickness. The same shape functions can be used for the two problems, establishing a convenient formal analogy that facilitates the implementation. The proposed approach is here used to evaluate the stress distribution on paradigmatic case studies. The obtained results allow to recognize the main aspects that influence the state of thermal stress, a result that could be used to conceive reliable simplified methods, which may be incorporated in standards.