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

For four-node quadrilateral shells, the shape functions are given by $$\begin{equation} \begin{aligned}M_{1} & =\frac{1}{4}\left(1-r\right)\left(1-s\right)\\ M_{2} & =\frac{1}{4}\left(1+r\right)\left(1-s\right)\\ M_{3} & =\frac{1}{4}\left(1+r\right)\left(1+s\right)\\ M_{4} & =\frac{1}{4}\left(1-r\right)\left(1+s\right) \end{aligned} \,.\label{eq398} \end{equation}$$ For eight-node quadrilateral shells the shape functions are $$\begin{equation} \begin{aligned}M_{1} & =\frac{1}{4}\left(1-r\right)\left(1-s\right)-\frac{1}{2}\left(M_{8}+M_{5}\right) & M_{5} & =\frac{1}{2}\left(1-r^{2}\right)\left(1-s\right)\\ M_{2} & =\frac{1}{4}\left(1+r\right)\left(1-s\right)-\frac{1}{2}\left(M_{5}+M_{6}\right) & M_{6} & =\frac{1}{2}\left(1-s^{2}\right)\left(1+r\right)\\ M_{3} & =\frac{1}{4}\left(1+r\right)\left(1+s\right)-\frac{1}{2}\left(M_{6}+M_{7}\right) & M_{7} & =\frac{1}{2}\left(1-r^{2}\right)\left(1+s\right)\\ M_{4} & =\frac{1}{4}\left(1-r\right)\left(1+s\right)-\frac{1}{2}\left(M_{7}+M_{8}\right) & M_{8} & =\frac{1}{2}\left(1-s^{2}\right)\left(1-r\right) \end{aligned} \,.\label{eq399} \end{equation}$$