In addition to general tips listed here, specific tips on the following topics are available:
Before performing an HBM analysis, it is advantageous to run a modal analysis and/or harmonic analysis analysis on your model that has been slightly modified to operate in a linear or near-linear regime, such as under small excitation and response or in a linear contact state (frictionless sliding or fully bonded). This will help you gain insights on the structural dynamic behavior of your model.
If your model does not exhibit rigid body motion when ignoring the non-linear elements, you may also start by running a preliminary HBM analysis where the non-linear elements are not taken into account by issuing HBMOPT,LINEAR. In this case, the solution is similar to a linear harmonic analysis as only the harmonic 1 solution is calculated.
If HBM convergence problems arise, running the nonlinear model in a full transient analysis can give useful information about the physics such as the contribution of subharmonics, the relative contributions of harmonics, etc.
In many practical cases, a solution using only a single harmonic is a good approximation of the response. However, checking the convergence of the response with respect to the number of harmonics by retaining more harmonics is recommended.
Consider these tips when your model includes node-to-node contacts (CONTA178).
When creating the node-to-node contacts (CONTA178), it is important to properly define the contact normal. In particular, when the two nodes of the contact are coincident:
use keyopt(5) to define the contact normal axis
define the nodes of the contact element in the desired order such that the gap opens/closes in the direction you expect. If you defined the contact elements using EINTF and the nodes are not in the right desired order, you can delete/re-create contact using EINTF,,,HIGH instead or add EINTF,,,REVE after EINTF (see Node-to-Node Contact in the Contact Technology Guide).
When contact is frictional, a constant normal force contribution is likely present in the model (preload). Because this force is essentially a stepped load, it may cause convergence failure at the first substep. To overcome this issue, first run a static analysis applying the constant force, and then use the static solution as an initial guess (HBMOPT,UINIT) in an HBM analysis. For an example problem that demonstrates this procedure, see Example 3: Two Jointed Beams with Frictional Contact Interface.
It is good practice to check the following items in the output (Jobname.out) file.
Check the size of the problem you are currently solving, for example:
Check that the nonlinear elements present in your model have been correctly identified by HBM, for example:
If you are solving an HBM cyclic analysis (HBMOPT,CYCLIC with
CYCkey=1), check the spatial and time harmonic of the single stage cyclic superelements by listing the detailed stage information (MSOPT,LIST,ALL,1).
Consider the following recommendations to improve convergence behavior or overcome convergence issues.
At the first substep, if the HBM solver does not converge (initial solution), it probably means that the nonlinear behavior is very significant at the starting frequency. To facilitate convergence, try starting from a frequency which is farther away from the resonance such that the initial solution is close to a mostly linear range of the response.
In general, if the HBM solver fails to converge, possible actions are:
Use more harmonics.
If continuation is on, decrease the continuation step size parameters (initial step size,
DS, and maximum step size,DSMAXon HBMOPT,CONTSET).If continuation is off, reduce the fixed frequency step (when using HARFRQ and NSUBST) or consider using a continuation method to help the convergence.
Relax the convergence criterion. It is especially true if the norm of the residual is small but not small enough to meet tolerance criterion during correction iterations. The reason may be that the criterion is too tight.
Use more time points for the AFT (increase
NTon HBMOPT,AFT). It is recommended to check that AFT transient periodic convergence is achieved by reviewing the output file (Jobname_1.out). See Results from the Alternating Frequency Time (AFT) Procedure.Define a smaller amplitude of excitation force for initial runs.
If the HBM solver takes too many iterations to converge at each substep, making the computational time impractical, try reducing the maximum number of iterations (
MAXITERon HBMOPT,NR). It will reduce the number of iterations before the arc-length is decreased and may accelerate convergence.The definition of the step size
DSand the maximum step sizeDSMAXof the continuation method (HBMOPT,CONTSET) plays a key role in the convergence and the performance of the analysis. A goodDS/DSMAXshould allow computing enough points on the response curve to accurately describe the resonance peaks without compromising solution performance. It is good practice to tune this parameter by first running a linear HBM analysis (HBMOPT,LINEAR,1) with solution vector scaling.Since solution vector scaling (HBMOPT,SCAL) affects the step size used by the solver, it should be included in the linear HBM solution for a proper assessment of
DS. The number of degrees of freedom should be considered when defining the scaling (HBMOPT,SCAL).
In a Newton-Raphson continuation procedure, when the orders of magnitude of the components of the solution vector are different, small numerical roundoff can lead to longer convergence patterns and even cause convergence failure. This is the case for HBM when the forcing frequency amplitude is very different from the response amplitude.
To circumvent this numerical issue, use the scaling feature (HBMOPT,SCAL) to linearly scale each component of the solution vector by a scalar value or by values provided in scaling vector (a 1D APDL array). Often, a unique scaling value for the displacements and a scaling value for the forcing frequency are enough to improve the convergence rate.
The equations that determine solution scaling are detailed in Equation Solution. For an example problem demonstrating the use of scaling, see Scaling the solution vector in the Harmonic Balance Method Analysis Guide.