Consider a clamped uniaxial bar subjected to a tip load as shown in figure 8.9. Use three elements of equal length to determine the tip displacement as a function of time. Use the central difference method for time integration and the consistent mass matrix. The properties of the bar are: \(E=100 \mathrm{GPa}, L=1 \mathrm{~m}, A=10^{-5} \mathrm{~m}^{2}, ho=4000 \mathrm{~kg} / \mathrm{m}^{3}\). The tip force is given by: \(F(t)=2 F_{\text {max }} t / t_{\max }\) for \(0t_{\max } / 2\), where \(F_{\text {max }}=0.001 E A\) and \(t_{\max }=3 \mathrm{~ms}\). Calculate the tip displacement \(u(t)\) for \(0

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u1 E 2 3 E2 E3 L= 1 m F. tmax 2 tmax Figure 8.9 A clampedfree uniaxial bar subjected to a tip force F(t) F(t) U 4