Optimising Convergence

Mass and Inertia Factors

The user can modify the fictitious nodal masses and inertias used by the program by specifying Mass and Inertia Factors. It may be possible to speed up convergence by specifying factors of less than 1.0 to reduce the masses and inertias. However this method is less effective than adjusting the damping; the improvement in speed of convergence is limited to a factor of about 2. Factors of less than 0.5 should not be used and the user must be prepared for the solution process to “blow up” because the simulated damped vibration has become unstable.

The Inertia Factor only has an effect if the structure contains nodes to which moments are applied.

The mass button on the progress dialog box is used to adjust individual mass factors and it is normally not necessary. Setting individual mass factors is only necessary in the following circumstance. At a later stage of the analysis, the maximum residual stays at the same node in the same direction and the residual decreases very slowly. This may indicate that the dummy mass in that direction is too large, so the convergence rate may be boosted by setting a small mass factor for the node in the relevant direction. However, be aware that if the mass factor is too small, the analysis might diverge.

If the structural flexibility cannot be judged before the analysis, use the default dummy mass and inertia factor (1.0). After the analysis starts, the dummy mass factor can be adjusted according to the residual information shown. If the maximum residual reduces too slowly it may be necessary to reduce the dummy mass factor. Otherwise if the maximum residual does not tend to reduce but jumps around, this may suggest that a larger dummy mass factor or damping is needed.

Viscous Damping

There are two types of viscous damping, one is viscous damping and one is artificial viscous damping. Viscous damping will apply the specified (or automatically selected) percentage of the critical damping to the system and artificial viscous damping will artificially reduce the velocity at each cycle by the specified (or automatically selected) percentage. Once artificial viscous damping is used, kinetic damping will be disabled automatically. It is possible to modify the viscous damping applied each cycle to the linear and angular velocities of nodes. The damping is specified as a percentage (a percentage of 2 causes velocities to be factored by 0.98 each cycle if it is artificial viscous damping or applies 2% of the critical damping to the system if it is viscous damping ) and is applied separately to linear and angular velocities. The default percentages of damping is automatically selected by the program, if this does not help the analysis to converge, a fixed percentage of damping can be specified or altered during the analysis. Recommended percentage of damping are 0.1 to 20 percent for linear velocities and 1 to 40 percent for angular velocities.

The more closely a structure approximates to a tuning fork, piano string, drum membrane or anything else that has a single vibration mode, the greater the damping required for fast convergence. If such structures are insufficiently damped they will oscillate instead of coming to rest in their position of equilibrium. However most real structures, at least as simulated by the program, do not vibrate in a simple mode and require little damping.

It is possible to speed up the convergence of a typical complex structure by specifying a small damping percentage. In particular the damping should be small if a structure has to deflect significantly to achieve equilibrium, since the “terminal” velocity of the nodes as they shift towards their equilibrium position depends directly on the damping. The speed of convergence can be improved by factors of 10 or more, by reducing the damping in this case. However, the user must be prepared for the solution process to “blow up” if this is done.

With viscous damping, the theoretical ideal for a structure that vibrates in a simple mode is to have low damping initially and to increase the damping as the structure approaches its equilibrium position.

The damping for angular velocities will only have an effect if the structure contains beams. The damping for angular velocities should generally be greater than the damping for linear velocities. Since typically displacements are of a greater order than rotations, target values are met more quickly for moment residuals than for force residuals and convergence is not significantly delayed by increasing the damping for angular velocities.

Generally high damping (5 to 20%) should be used for soap film form-finding. If too low damping is used, the solution process is likely to “blow up”, and even with high damping convergence is usually quite rapid. Low damping (0.1 to 2%) should be used for force density form-finding.

Kinetic Damping

The program monitors the kinetic energy of the structure. When the maximum kinetic energy is passed, the analysis is automatically adjusted using the principles of kinetic damping outlined in the GSA Theory manual. The structure is brought to rest and the process restarted. If artificial viscous damping is used, kinetic damping will be disabled.

Modelling for Optimum Convergence

The speed of convergence depends primarily on the form of the structure and how it is modelled. GsRelax constructs the dummy mass and inertia of a node according to the stiffness of the elements to which it is connected. If the stiffness of some elements is much higher than that of others, the dummy mass at the relevant node will be very large. This can slow down the convergence, even causing divergence. Links and rigid constraints do not affect the dummy masses and inertias of nodes and should be used in preference to exceptionally stiff bars or beams.

If a GsRelax analysis “blows up” because the simulated damped vibration becomes unstable, the user should re-run the analysis with higher damping. If there are still problems the user should attempt to locate the spot where the forces first start to increase by watching the analysis progress dialog box. If the user is satisfied that the data file is correct and the analysis still blows up even with high damping (20%), the user should seek advice. The most likely causes of problems are extreme imposed displacements or imposed rotations, or a large difference between the specified “initial length” of a bar or a beam and the actual distance between its end nodes.

The smaller the residual target (Control Parameter) the more difficult it will be for GsRelax analysis to converge. If a larger residual is acceptable, do not try to set too small one in the analysis.

Even layouts of element meshes make the analysis converge more easily. In the example below, convergence will be quicker for the model with the most even mesh layout.