Thickness

a) load on the top surface

$z=\frac{h}{2}$

${\sigma }_{13}={\sigma }_{23}=0$ , ${\sigma }_{33}={\sigma }_0\sin \left(\frac{m\pi x_1}{a}\right)\sin \left(\frac{n\pi x_2}{b}\right)$

$z=-\frac{h}{2}$

${\sigma }_{13}={\sigma }_{23}={\sigma }_{33}=0$

b) load on the bottom surface

$z=\frac{h}{2}$

${\sigma }_{13}={\sigma }_{23}={\sigma }_{33}=0$

$z=-\frac{h}{2}$

${\sigma }_{13}={\sigma }_{23}=0$ , ${\sigma }_{33}=-{\sigma }_0\sin \left(\frac{m\pi x_1}{a}\right)\sin \left(\frac{n\pi x_2}{b}\right)$