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66 Robert L. Taylor, Eugenio Oñate ˜ and Pere-Andreu Ubach
Fig. 10. Current configuration of the balloon after 120 time steps, displaying vertical
displacement (u3) contour
Fig. 11. Final configuration of the balloon, displaying absolute displacement u
The solution is computed using a backward Euler strategy neglecting the inertia
terms. The C matrix used is diagonal with c0 = ρ0. The transient solution is continued
for 120 time steps using a ∆t =0.01. A final static step is then computed in
which all the dynamic terms are dropped. Convergence for all the transient steps is
achieved in 4-6 iterations, while the final static step takes 33 iterations. The solution
state at the end of the transient steps is shown in Fig. 10 and the final state achieved
after the static step in Fig. 11.