8. An elliptic plate of major and minor axes 2a and 2b and of small thickness t is clamped along its boundary and is subjected to a uniform pressure difference p between the two faces. Show that the usual differential equation for normal displacements of a thin flat plate subject to lateral loading is satisfied by the solution w ¼ w0 1 x2 a2 y2 b2 2 where w0 is the deflection at the center, which is taken as the origin. Determine w0 in terms of p and the relevant material properties of the plate and hence expressions for the greatest stresses due to bending at the center and at the ends of the minor axis.