$2\mathrm{.}11$ The stress function $=A{x}^2+Bxy+C{y}^2$ provides the direct and shear stresses in a thin rectangular

plate. One corner, which lies at the origin, is position$-$ and direction$-$fixed. Show that the displacements

for the diagonally opposite corner $(a,b)$ are: $u=2a\frac{C-vA}{E},v=2b\frac{A-vC}{E}.$

$2\mathrm{.}12$ If $$ in Exercise $2\mathrm{.}11$ applies to a thick plate in plane strain, where ${}_z=0,$ determine the

displacements at the comer $(a,b).$

Answer: $u=2x(1+v)\frac{C(1-v)-Av}{E},v=2y(1+v)\frac{A(1-v)-Cv}{E}$