# 7 Ways You Must Know to Improve Convergence of Non-Linear Structural Analysis with ANSYS Mechanical

When solving geometric non-linear problems using ANSYS, convergence difficulties may occur due to unsuitable parameter settings with the default system configuration. This article summarizes several common adjustment methods for convergence difficulties in nonlinear solutions, for reference only.

1、Open Automatic Time Step (autots, on)

ANSYS uses time as a tracking parameter for all static and transient analyses, regardless of whether the analysis depends on time. When we encounter convergence difficulties, a very important method is to open the automatic time step. Opening the automatic time step often requires a relatively small minimum time step (or maximum number of steps, defined using DELTIM or NSUBST). During the nonlinear solution process, if the initial time step is too small, the automatic time step algorithm may cause your running time to be too long; on the other hand, if your minimum time step is too large, non-convergence may occur. Therefore, it is very important to set the initial time step appropriately, which can generally be determined through trial and error.

It is worth noting that when the automatic time step is adopted, the bisection method will be automatically activated. If convergence fails within a too large time step, this feature can halve the time step, allowing the calculation to continue.

When nonlinear convergence is difficult, the default Newton-Raphson options of the program can be adjusted. Although in general, using the automatic default options will yield the best convergence characteristics, it is not ruled out that other selections may be more effective. Proper use of adaptive descent factor can also improve the convergence of certain nonlinear elements.

3、Linear search

Linear search can be considered as an alternative to adaptive descent, and both should not be used at the same time. Linear search can generally achieve convergence in analysis, but the cost is a significant reduction in solving speed, especially for materials with nonlinearity. In general, when the structure is subjected to force loading or stiffness growth, or when analyzing thin films, the linear search can be turned on with the command LNSRCH.

4、Adjust the convergence criteria

There are four main ANSYS nonlinear convergence criteria: force, displacement, moment, and rotation. In commonly used analyses where force is used to control loading, the norm of residual force can be used to control convergence. When displacement is used to control loading, the norm of displacement is generally used to control convergence. The most common ANSYS nonlinear calculation screen is as follows:

FCRIT represents the force convergence criterion; FL2 is the convergence of the current iterative force; U is displacement, CRIT is the convergence criterion, and L2 is the current iterative displacement convergence. The convergence criterion can be relaxed through the CNVTOL command. The program’s default convergence value is 0.1%, which can generally be modified based on actual engineering needs. For example, in the nonlinear analysis of reinforced concrete, it can generally be relaxed to 5%.

5、Increase iteration count and load substeps

ANSYS defaults to a maximum of 25 equilibrium iterations per load step calculation. If the convergence criterion is not met within these equilibrium iterations, and the automatic time step is turned on, the program will continue the calculation using the bisection method. Otherwise, the analysis process will be terminated. Therefore, in actual calculations, if convergence is found to be difficult, it may be appropriate to increase the limit of equilibrium iteration counts and the number of load substeps. The relevant ANSYS commands are NEQIT, NSUBST, DELTIM

6、Using the arc length method

If it is anticipated that the structure will experience physical instability at some point during loading, such as when the slope of the load-displacement curve is zero or negative, the arc length method can be activated to obtain a stable numerical solution. This method is widely used in geometrically nonlinear solutions with large deformations.

7、Modifying element division and reducing element size

The size and division of structural elements directly affect the convergence performance of structural nonlinear solutions. If convergence still cannot be improved after adjusting all the methods mentioned above, consider adjusting the size of the structure’s elements and redividing them. Reduce the number of irregular elements and use hexahedral elements as much as possible for solid elements.

These are the commonly used methods for adjusting convergence in ANSYS nonlinear solutions. Sometimes, adjusting just one of these methods can result in a convergent solution for the structure, but more often, a combination of methods is required. The specific approach and direction of adjustment for each person may differ, and the above content only briefly mentions the adjustment ideas based on my own solving experience.

Good luck for you!