Consider a simply supported beam of length \(L=1 \mathrm{~m}\) subjected to a uniformly distributed transverse load \(p_{0}=100 \mathrm{~N} / \mathrm{m}\). The cross section is rectangular with width \(w=0.01 \mathrm{~m}\) and height \(h=0.02 \mathrm{~m}\). Calculate the sensitivity of the vertical displacement at the center with respect to \(h\). Use one finite element with Young's modulus \(=80 \mathrm{GPa}\). Compare the sensitivity against the finite difference method with perturbation size \(1 \%\).

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Po E, I, L