Green's functions for the load sharing in multiple insulating glazing units

Insulating Glazing Units (IGUs) are glass panes held together by structural edge seals, entrapping a gas for thermal and acoustic insulation. The bending of one pane induces pressure variations in the cavities, which produce the load sharing through the gas with the other panes. Under mild hypotheses, the whole IGU behaves as a linear elastic system. Hence, for IGUs with panes and cavities of any number, shape, size and edge constraints, the Green's functions can be defined for the pressure variations and the pane displacements, so that these quantities can be expressed as convolution integrals with any applied load. The proposed Green's functions are calculated with a tailored used of Betti's reciprocal work theorem, referred to as Betti's Analytical Method (BAM), here generalized to multiple IGUs with N panes. Remarkably, the Green's functions for the pressure variations in the cavities are completely determined by the deformation field of a simply-supported plate, with the same shape of the IGU, under uniform pressure: this represents the universal expression, possibly tabulated, covering all possible cases. The proposed approach is validated through comparisons with prescriptions by standards and numerical simulations. Parametric analyses show the effect of the IGU geometry on the load sharing.