$3\mathrm{.}2[$Section $3\mathrm{.}4]$ The deformation of a plate in circular bending is given by

$x_1=(x_2+R)sin(\frac{x_1}{R}),x_2=x_2-(x_2+R)[1-cos(\frac{x_1}{R})],x_3=x_3,$

where $L$ is the length of the plate and $R$ is the radius of curvature.

Given a rectangular plate in the reference configuration with length $L$ in the $1-$direction and height $h$ in $2-$direction, draw the shape of the plate in the deformed configuration for some radius of curvature $R.$

Determine the deformation gradient $F(x)$ at any point in the plate.

Determine the Jacobian of the deformation $J(x)$ at any point in the plate.

Use the result for the Jacobian to show that the plate experiences expansion above the centerline and contraction below it$.$

Determine the element of oriented area at the end of the plate in the deformed configuration. In what direction is the end pointing and what is the change in its cross$-$sectional area?

Use the result for the oriented area to show that planes in the reference configuration remain plane in the deformed configuration.plz solve oit correctly