Be aware that when stabilization is active, the results could vary if the number of substeps changes.
The behavior occurs because the pseudo velocity is different, which in turn causes different stabilization
forces. The more stable the system, the less significant the difference.
If restarting from a different substep, using a damping factor (STABILIZE,,DAMPING) can yield more
consistent results because the energy prediction may be different from substep to substep, which may
necessitate quite different damping factors.
Deactivating Stabilization
Each time that stabilization is deactivated (STABILIZE,OFF), the stabilization forces change suddenly,
which may cause convergence problems. Before completely deactivating stabilization in such cases,
use the reduced method of stabilization (STABILIZE,REDUCE) and specify the damping factor used for
the previous load step.
ExampleAssume that load step 1 is unstable but solvable with stabilization. Load step 2 is stable
and requires no stabilization, yet does not converge if you deactivate stabilization
(STABILIZE,OFF). In this scenario, you can add a pseudo load step (STABILIZE,RE-
DUCE,DAMPING,VALUE). The damping factor should be the value from load step 1. Do
not apply any new loads. This technique should help with convergence.8.11.2. Using the Arc-Length Method
The arc-length method (ARCLEN and ARCTRM) is another way to solve unstable problems. This method
is restricted to static analyses with proportional (ramped) loads only.
When choosing the number of substeps (NSUBST), consider that more substeps result in a longer
solution time but sometimes help the program to converge. Ideally, you want the minimum number
of substeps required to produce an optimally efficient solution.You might have to make an educated
guess of the desired number of substeps, and adjust and re-analyze as needed. The modification of the
MAXARC argument of the ARCLEN command can also help the program to converge by preventing
the reference arc-length radius from increasing too rapidly (MAXARC = 1).
When the arc-length method is active, do not use line search (LNSRCH), the predictor (PRED), adaptive
descent (NROPT,,,ON), automatic time stepping (AUTOTS,DELTIM), or time-integration effects (TIMINT).
Likewise, do not try to base convergence on displacement (CNVTOL,U); instead, use the force criteria
(CNVTOL,F).
If an arc-length solution fails to converge within the prescribed maximum number of iterations (NEQIT),
the program automatically bisects and continues the analysis. Bisection continues until a converged
solution is obtained or until the minimum arc-length radius is used. ( The minimum radius is defined by
NSBSTP (NSUBST) and MINARC (ARCLEN).
In general, you cannot use this method to obtain a solution at a specified load or displacement value
because the value changes (along the spherical arc) as equilibrium is achieved.Figure 8.4:Traditional
Newton-Raphson Method vs. Arc-Length Method (p. 196) illustrat es how the specified load
a(^1) is used
only as a starting point. The actual load at convergence is somewhat less. Similarly, it can be difficult
to determine a value of limiting load or deflection within some known tolerance when using the arc-
length method in a nonlinear buckling analysis. Generally, you must adjust the reference arc-length
radius (NSUBST) by trial-and-error to obtain a solution at the limit point.
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Unstable Structures