Abstract 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.

中文翻译：

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Green 在多个中空玻璃单元中的负载分配函数

摘要 隔热玻璃单元 (IGU) 是由结构边缘密封件固定在一起的玻璃板，其中夹带气体以实现隔热和隔音。一块玻璃板的弯曲会引起空腔中的压力变化，从而通过气体与其他玻璃板产生负载分担。在温和的假设下，整个 IGU 表现为线性弹性系统。因此，对于具有任意数量、形状、大小和边缘约束的窗格和空腔的 IGU，可以为压力变化和窗格位移定义格林函数，以便这些量可以表示为具有任何施加载荷的卷积积分。建议的格林函数是根据 Betti 的互易工作定理（称为 Betti 的分析方法 (BAM)）量身定制的，这里将其推广到具有 N 个窗格的多个 IGU。值得注意的是，空腔中压力变化的格林函数完全由简支板的变形场决定，具有相同形状的 IGU，在均匀压力下：这代表了通用表达式，可能是表格，涵盖所有可能的情况。所提出的方法通过与标准和数值模拟的处方进行比较来验证。参数分析显示了 IGU 几何形状对负载分配的影响。所提出的方法通过与标准和数值模拟的处方进行比较来验证。参数分析显示了 IGU 几何形状对负载分配的影响。所提出的方法通过与标准和数值模拟的处方进行比较来验证。参数分析显示了 IGU 几何形状对负载分配的影响。