Problem $1$: Plate Bending $(5$ pts $)$

See below an isotropic plate with a distributed, varying bending load $p$ over the right half of the plate,

but also a uniform tensile stress ${}_0.$ One end is simply supported while the other three ends of the plate

are simply supported and on a roller $($i$.$e$.$ they can move along the x $-$ or y $-$direction$).$

a$)$ Set a complete set of single$-$mode approximate deflections. You need to set an approximate deflection

in each $x-,y-,$ and z $-$direction, and use one mode for the deflection in each direction.

b$)$ Using the principle of minimum potential energy, solve for the approximate deflections. Both bending

and membrane energy cannot be ignored.

Problem $1$: Plate Bending $(5$ pts$)$

See below an isotropic plate with a distributed, varying bending load p over the right half of the plate,

but also a uniform tensile stress $.$ One end is simply supported while the other three ends of the plate

are simply supported and on a roller $($i$.$e$.$ they can move along the x$-$ or y$-$direction$).$

a$)$ Set a complete set of single$-$mode approximate deflections. You need to set an approximate deflection

in each x$-,$ y$-,$ and z$-$direction, and use one mode for the deflection in each direction.

b$)$ Using the principle of minimum potential energy, solve for the approximate deflections. Both bending

and membrane energy cannot be ignored.