$(20$ points$)$

Repeat Example $9\mathrm{.}2$ in the textbook with two triangular elements.

Example $9\mathrm{.}2$: Quadrilateral element

Consider a linear elasticity problem on the trapezoidal panel domain as shown in Figure $9\mathrm{.}11.$ The vertical left edge is fixed. The bottom and the right vertical edges are traction free, i$.$e$.\frac{?}{\text{b}\text{a}\text{r}}(t)=0.$ Traction $\frac{?}{\text{b}\text{a}\text{r}}(t{)}_y=-20N{m}^{-1}$ is applied on the top horizontal edge. Material properties are Young's modulus $E=3{10}^{7}Pa$ and Poisson's ratio

$u=0\mathrm{.}3.$ Plane stress conditions are considered. The problem is discretized using one quadrilateral element. The finite element mesh and nodal coordinates in meters are shown in Figure $9\mathrm{.}12.$

The constitutive matrix $D$ is

$D=\frac{E}{1-}$

$($