Thermal analysis of architectural glazing in uneven conditions based on Biot's variational principle: part I-description of the finite element modelling

Breakages in architectural glazing are very often due to the thermal stress consequent to uneven heating of the glass pane, typically resulting from irregular shading. In thermal analyses to determine the insulating capacity of the fenestration, the temperature is conveniently assumed in-plane homogeneous, but a 3D approach is necessary to calculate the stress. Here, we present a semi-analytical formulation specifically conceived for architectural glazing, which is based on Biot's variational principle for heat transfer. Compared to the differential form of the thermal problem, the principle does not involve temperature gradients and, therefore, can well represent sharp variations in temperature and heat-flux. The Euler-Lagrange equations present an analogy with the mechanics of damped elastic systems with negligible inertia. Here, this approach is implemented in a dedicated FE model, allowing to assess the temperature field in non-uniformly irradiated glazing.