$**$Plz show and do all work with explanations, thank you!!$**$

Exercise $2$: $3$D Elasticity bending beam.

We consider the following stress field defined as:

${}_{}=-\frac{P}{\text{I}}(L-x)z$ and ${}_{yy}={}_{xy}=0$

I: Inertia moment of area; $P$ force applied at extremity

${}_{xz}=\frac{P}{2\text{I}}(\frac{h^2}{4}-z^2)$ and ${}_{yz}={}_{zz}=0$

Define the vector strain associated assuming the material linear isotropic elastic $(E,)$

$\{\}=\{[{}_{}],[{}_{zz}],[{}_{xz}]\},$ and $,\{[{}_{}],[{}_{zz}],[{}_{xz}]\}=[C]\{[{}_{}],[{}_{zz}],[{}_{xz}]\}$

Define the displacements field $u(x,z)$ and $w(x,z)$ associated $($from strain$)$

Applying the following boundary conditions, define the full expression of $u(x,z)$ and

$w(x,z)$:

$u=w=u_{,z}=0atx=z=0$