displacement field

u $=1+3$x $+4$x$3+6$xy$2$

v $=$ xy $-7$x$2$

is imposed on the square element shown in Fig. P$1\mathrm{.}6.$

x

y

$(1,1)$

$(1,1)$

FIGURE P$1\mathrm{.}6$

$($a$)$ Write down the expressions for Px$,$ Py $,$ and gxy $.$

$($b$)$ Plot contours of Px$,$ Py $,$ and gxy using, say, MATLAB software.

$($c$)$ Find where Px is maximum within the square.