How to Apply Convergence Criteria to HyperFEA

Optionally, FEA Constraints can be applied to limit displacements, buckling eigenvalue, or frequency eigenvalue. See How to Define Constraints for FEA Iterations for more information.

Users can choose between running HyperFEA for a fixed number of iterations (default) or using the Convergence Criteria. To activate Convergence Criteria, click on the top half of the button to toggle the criteria on.

Click the bottom half of the button and select "Edit Convergence Criteria" from the dropdown to open the form where you define and edit criteria.

Convergence Criteria are defined in the table at the top of the form. Click “Add” to create a new criterion and open the "Criteria Definition" form.

The layout of the "Criteria Definition" changes depending on the selected type of Convergence Criteria. The three primary types of Convergence Criteria are described below.

Zone Type

Zone Convergence Criteria evaluate when the weight or stiffness has stopped changing within a user-specified threshold. First, you must choose "Weight" or "Stiffness" as the "Sub-Type" to specify whether the weight or stiffness data will define when the criterion is satisfied. Next, you must select the "Method" used to define the conditions that must be met to stop iterations. The two available methods are "Iteration Delta" and "Averaged Delta" and both have inputs to define the percentage of change over a number of iterations that would be considered convergent. Then, define the "Aggregation Method" to define which Zones to evaluate weight/stiffness data for convergence. Finally, you can optionally define a Set to limit the application of the Convergence Criterion to that Set.

Iteration Delta

If the metric (weight or stiffness) changes by less than the "% Delta" from one iteration to the next, for the user-specified number of iterations ("# Iterations"), then the criterion is satisfied. For example, with inputs of 5% and 2 iterations, the criteria would be met if two consecutive HyperFEA iterations occurred where the weight of the Structure changed by 5% or less from iteration to iteration.

Tip

This is the recommended method for "well-behaved" (smooth convergence) problems.

Averaged Delta

This method is meant to handle more noise in the metric than the previous. It evaluates the previous N iterations to determine when range of the metric (i.e. max minus min) is within the specified "Tolerance" of the average metric value over those N iterations. This allows convergence in the presence of variation that would violate the Iteration Delta method. However, more iterations are needed (3-4 minimum recommended) to get an accurate range and average for the metric.

Aggregation Methods

Related to the Convergence Methods described above, users can choose an aggregation approach to precisely define how the weight or stiffness from many different Zones is tracked for convergence.

• Sum - Only applicable to the Weight Sub-Type. Sums up the mass in the specified Set and uses that value as the metric.

• Min - When the metrics are evaluated for each Zone, check the one that gives the minimum % Delta to determine if it is within the user tolerance.

• Max - When the metrics are evaluated for each Zone, check the one that gives the maximum % Delta to determine if it is within the user tolerance.

• Average - When the metrics are evaluated for each Zone, check the one that gives the average % Delta to determine if it is within the user tolerance.

• % Met - Criteria is met when the defined percentage of all evaluated Zones meets the Convergence Criteria.

Constraint Type

Constraint Convergent Criteria track the FEA Constraints (manual or automated) that were applied to the HyperFEA process to define when the criterion is satisfied. This criterion can evaluate whether the FEA Constraints were either met or simply converged. The latter can be useful in situations where it may not be possible to meet an FEA Constraint due to material limitations, max gauge, etc.

This criterion type has the same Convergence Methods described for the Zone Type above (i.e. Iteration Delta and Averaged Delta), as well as an additional “Met” selection. The "Met" method is satisfied when all the FEA Constraints are satisfied. If Iteration Delta or Averaged Delta are chosen, see the Zone Type section above to understand the inputs and Aggregation Methods.

Iteration Type

The Iteration Convergence Criteria type is used to define a threshold for an iteration count. When the current iteration count is greater than or equal to the input value, the criterion is satisfied.

The primary use case for this criterion type is to prevent an infinite loop of the HyperFEA process if the other criteria are never met. However, it can be used in other ways when combined with the logical expressions described in the next step. For example, when placed inside of a “Not” group, it could be used to enforce a minimum number of iterations.

The bottom half of the Convergence Criteria form is used to combine the criteria from the top half using logical expressions.

The criteria are combined using a tree-like structure. Each node of the tree ("Expression Group") can be an "And", "Or", or "Not" statement. Each criterion is “true” if satisfied and “false” if not. The logical expression is evaluated at the end of each HyperFEA iteration. If the entire expression evaluates as “true,” then the HyperFEA process will stop. Otherwise, it will proceed to the next iteration.

Define each Expression Group as "And", "Or", or "Not" using the dropdown menu. Expression Groups can be added by clicking the green “+” button on a Group.

Criteria can be added to an Expression Group by either dragging and dropping them from the table onto the Group, or by right-clicking on the Group and clicking “Add Selected Criteria.”

Both Criteria and Groups can be removed by clicking the red “X” button next to the entity. Removing an Expression Group will also remove everything nested within that Group.

When you are satisfied with the Combined Criteria expression you've created, press “Apply” to save the changes then close the form.

The Convergence Criteria can be run in two stages to allow refined control over the iteration process. If either (or both) of the "Advanced Settings" options are active, the convergence process will be run twice before HyperFEA stops.

No FEA constraints in first stage

This setting will cause any active FEA Constraints to be ignored during the 1st stage of iteration, then considered in the 2nd stage. This is useful in scenarios where the load path needs to be converged prior to applying FEA Constraints (for example, if there were significant changes to the panel concept used).

Change activated analysis criteria based on iteration stage

This setting will disable user-specified failure criteria in each stage of the convergence process. An example application is to manage criteria that might conflict with FEA Constraints, such as panel buckling. When the setting is enabled, the "Analysis Criteria Settings" button will activate. Clicking that button opens the "Two-Stage Analysis Criteria Settings". Here, users to select any criteria currently active in the Project to disable for each stage using the arrows to "move" the criteria between enabled/disabled states separated by stage. For example, clicking the arrow button shown in the image below would disable the selected stiffness criteria during the first stage of iteration.

Templates are used to save the state of the Convergence Criteria form so that they can be reused in another Project. Both the Criteria and Expression Groups are saved in the template.

There are two template controls found at the top-right corner of the form: