Q$3(20$ Points$)$ Design and Analysis of a Multi$-$Layered Window Panel

Multi$-$layered window panels, consisting of glass sheets and an air gap or polymer interlayer, are commonly used in buildings to provide thermal insulation and structural integrity, as shown in the figure below. The glass sheet has modulus $E_g$ and thickness $t_g,$ and the air gap or polymer interlayer has modulus $E_i$ and thickness $t_i.$

a$.$ What functions do the glass sheets, and the interlayer perform in the window panel?

$\backslash$table$[[$Glass sheet$],[$Polymer interlayer$]]$

b$.$ Derive the thermal conductivity across the window panel and the bending stiffness of the multi$-$layered structure.

c$.$ Is it possible to achieve the same functionality if the window panel is replaced by a composite structure made of glass fibers and a polymer matrix? The polymer matrix is transparent.

d$.$ Derive the thermal conductivity and bending stiffness for the composite structure.

e$.$ Use reference materials to find typical properties of glass and polymer interlayers $($or air gaps$)$ and compute the thermal conductivity and stiffness to support your argument for part $($c$).$