Question $3($use Matlab$)$:

The cartesian stress components $($in $2$Dimension$)$ for a semi$-$infinite elastic solid under

a concentrated point loading is defined found to be:

${}_x=-\frac{2P{x}^{2}y}{(x^2+y^2{)}^2}$

${}_y=-\frac{2P{y}^3}{(x^2+y^2{)}^2}$

${}_{xy}=-\frac{2Px{y}^2}{(x^2+y^2{)}^2}$

Using Matlab, plot the contours of the maximum shear stress, ${}_{\text{m}\text{a}\text{x}}.$ Assume $P=2.$ Take

$-3x3$ and $-3y3$