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As shown in Fig $1,$ a two$-$dimensional plate is discretised by only using one three$-$node triangular element, and the plate is loaded as follows.

Fig $1$: A two$-$dimensional plate structure

If we have already known the strain$-$displacement matrix $B$ and material property matrix $D$ and assume that the element thickness is $10mm,$

$[B]=\left[\begin{array}{cccccccccccccccc}0& 0& 2\mathrm{.}5& 0& -2\mathrm{.}5& 0& -5& 0& 0& 0& 5& 0& 0& 2\mathrm{.}5& 5& -2\mathrm{.}5\end{array}\right]$

$-5$

$-5$

$0(\frac{1}{m}),$ and

$[D]=2{10}^{11}\left[\begin{array}{ccccccc}1& 0\mathrm{.}3& 0& 1& 0& 0& \frac{1-0\mathrm{.}3}{2}\end{array}\right]$

$0$

$0\mathrm{.}3(\frac{N}{m^2})$

$(1)$ Calculate the displacement $\{u\}$ occurred at nodal No $2$ of the element.

$(2)$ Calculate the strain $\{\}$ and stress $\{\}$ at point A within the element.