$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\Grad}{\operatorname{Grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$ $\newcommand{\Divg}{\operatorname{Div}}$ $\newcommand{\cay}{\operatorname{cay}}$ $\newcommand{\rot}{\operatorname{rot}}$

When a shell is sandwiched between two solid elements, we reassign the DOF ID's of the the solid $\mathbf{u}_{b}$ displacements facing the back of the shell to those of the shell $\mathbf{w}_{b}$ displacements stored in that same node. The DOF ID's of solid $\mathbf{u}_{b}$ displacements facing the front of the shell remain unchanged; they will coincide with those of the corresponding solid element nodes.