Quasi-Static Analysis |
 
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Quasi-Static Analysis |
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Very occasionally the response of a structure to static loading cannot be successfully found in a static analysis. This is normally due to the fact the structure is highly sensitive to changes in configuration from iteration to iteration, and a static analysis may tend to diverge rather than converge to a stable configuration. One of the most commonly occurring cases of this sensitivity is in systems which include significant water surface piercing, such as for example a buoyancy tank used during a riser tow-out. If an initial approximation to the equilibrium position of the structure actually has an excess of, say, buoyancy over gravity, in the next iteration the structure may be largely or wholly out of the water, and subsequent iterations may find alternately increasing portions of the structure exposed or submerged, and the solution rapidly diverges. In such circumstances, a quasi-static approach is more suitable, and the model will tend settle in a dynamic fashion, typically under the influence of damping, towards its static equilibrium configuration.
A quasi-static analysis is in reality a dynamic analysis in which the applied loads and displacements are constant after an initial ramping on period. Typically, a large mass damping coefficients is specified, and this damping increasingly dissipates inertia effects and the final solution achieved approaches a static one. The reason why a quasi-static analysis is successful where a static run is not is because the inertia of the system prevents the oscillations between unrealistic configurations described previously. In a quasi-static analysis a variable step is typically used, and the time-step tends to increase quickly as the transients dissipate. In choosing the optimum time-step, Flexcom bases the choice on the ambient current period value (as described in Variable Time Stepping earlier in this section) in the early part of the simulation when loads and displacements are being ramped on and the dynamic response may be significant. Beyond the ramp time however, the dynamics begin to dissipate and the use of the current period as a step size indicator is no longer suitable. As in the case of a static analysis, the choice of time-step during this phase is based only on the number of iterations required for convergence. In fact this dual strategy for computing the optimum time-step during the two phases of an analysis is the only way in which the conduct of a quasi-static analysis differs internally in Flexcom from a dynamic run.
In summary, the following general guidelines in relation to quasi-static analysis are useful:
(i)A variable time step should be used, with a relatively long run time to allow the structure to settle towards static equilibrium. In order to check if the run time you have chosen is sufficiently long, you should examine time histories of nodal displacements and/or velocities at critical locations. Note also that in some circumstances, it may be possible to successfully perform a subsequent static restart analysis.
(ii)A relatively small minimum time step should be specified in order to avoid any potential convergence issues.
(iii)A relatively large maximum step should be specified for efficiency. Caution is advised against the specification of an excessively large maximum time-step value in an effort to speed up the analysis. The variable time stepping algorithm will try to achieve the maximum value at every possible opportunity, and this can actually make the overall solution less efficient, or even affect solution robustness in certain circumstances.
(iv)The static loads should be ramped on relatively quickly, again for efficiency, by specifying a relatively short ramp time.
(v)Inclusion of a significant level mass-proportional damping is usually quite beneficial in dissipating transients. For example, a coefficient of 1.0 would not be unusual. Obviously this would be excessively high in the context of a normal dynamic analysis (e.g. regular wave or random sea), but a quasi-static analysis merely serves as a means to attaining a static equilibrium configuration.
•*ANALYSIS TYPE is used to specify the analysis type.
•*TIME is used to define time parameters for an analysis. Specifically, the STEP=VARIABLE inputs are used to specify fixed time step data.
•*DAMPING is used to incorporate damping into a dynamic analysis.
If you would like to see an example of how these keywords are used in practice, refer to E03 - Floating Hose.