= Kelvin-Voigt cantilever creep
{c}
{title2=$\tau\dot\delta+\delta=F\ell^3/(3EI)$}
For a quasistatic cantilever of Kelvin-Voigt material, the bending moment is $M=EIy_{xx}+\eta_sIy_{xxt}$. A tip load gives $M=F(t)(\ell-x)$, so the free-tip displacement obeys the displayed equation with $\tau=\eta_s/E$. A step load gives a finite asymptotic deflection. If inertia is retained, the interior equation is $\rho Ay_{tt}+EIy_{xxxx}+\eta_sIy_{xxxxt}=0$, with the corresponding moment and shear conditions at the tip.
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