Plates and Shells: Theory and Design, by Ugural, Problem $9\mathrm{.}9$ A simply supported square plate is under the action of a conentrated lateral load $P$ at its center $C$ and a uniform in$-$plane tension load $N($in the x direction only$).$ Derive the equation of the deflection surface, using the energy method $($not Castigliano's theorm$)$ and by retaining the first term of the series solution.