$**$Plz do and show all work for each bulletin point!$**$

Exercise $1$: $3$D Elasticity cantilever beam with uniform load

We consider the following stress distribution for a cantilever beam under uniform distributed

load w

I is the Inertia moment of area, c and b are constant $($dimensions of section$)$

${}_{}=\frac{w}{2\text{I}}y{x}^2,{}_{yy}=-\frac{w}{6\text{I}}(2c^3+3y{c}^2-y^3)$

${}_{xy}=\frac{w}{2\text{I}}x(c^2-y^2)$

Verify if the field stresses defined above is compatible with equilibrium equations $($the

weight of the beam is neglected$)$

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

$\{\}=\{[{}_{}],[{}_{yy}],[{}_{xy}]\},$ and $,\{[{}_{}],[{}_{yy}],[{}_{xy}]\}=[C]\{[{}_{}],[{}_{yy}],[{}_{xy}]\}$

Using the strains compatibility equations, are the strains distribution compatible?

Define the field displacement $u(x,y)$ and $v(x,y)$; are the strains distribution compatible $?$