Key Points: Geometrically exact compatibility vs approximate compatibility relationship, Equilibrium equations

written for undeformed vs deformed structure, Solution of a system of nonlinear algebraic quations

using an appropriate software

For the pin jointed symmetric structure subjected to a vertical force F$,$ bars are made of a

linear elastic material with $E=2\mathrm{.}5$GPa,$v=0\mathrm{.}29.$ They all have the same cross$-$sectional area,

$A=100m{m}^2.$ Assuming bars do not fracture and remain elastic,

Plot F vs $y_D($where $y_D$ is the vertical displacement of point D$)$ up to $y_D=100mm,$

a$)$ by using small displacement assumption,

b$)$ by using geometrically exact $($nonlinear$)$ formulation, which was derived in class.

Use an appropriate software for solution and plotting.

Show both plots on the same graph to facilitate comparison.