## Meshing for Nonlinear Structural Problems

Overcoming convergence difficulties in nonlinear structural problems can be a challenge. I’ve written a couple of times previously about tools that can help us overcome those difficulties:

- Overcoming Convergence Difficulties in ANSYS Workbench Mechanical, Part I: Using Newton-Raphson Residual Information
- Overcoming Convergence Difficulties in ANSYS Workbench Mechanical, Part II: Quick Usage of Mechanical APDL to Plot Distorted Elements

I’m pleased to announce a new tool in the ANSYS Mechanical tool belt in version 17.0.

With version 17.0 of ANSYS we get a new meshing option for structural simulations: *Nonlinear Mechanical Shape Checking*. This option has been added to the previously available Standard Mechanical Shape Checking and Aggressive Mechanical Shape Checking. For a nonlinear solution in which elements can become significantly distorted, if we start with better-shaped elements they can undergo larger deformations without encountering errors in element formulation we may encounter fewer difficulties as the nodes deflect and the elements become distorted. The nonlinear mechanical setting is more restrictive on the element shapes than the other two settings.

We’ve been recommending the aggressive mechanical setting for nonlinear solutions for quite a while. The new nonlinear mechanical setting is looking even better. Anecdotally, I have one highly nonlinear customer model that reached 95% of the applied load before a convergence failure in version 16.2. That was with the aggressive mechanical shape checking. With 17.0, it reached 99% simply by remeshing with the same aggressive setting and solving. That tells you that work has been going on under the hood with the ANSYS meshing and nonlinear technology. By switching to the new nonlinear mechanical shape checking and solving again, the solution now converges for the full 100% of the applied load.

Here are some statistics using just one measure of the ‘goodness’ of our mesh, element quality. You can read about the definition of element quality in the ANSYS Help, but in summary better shaped elements have a quality value close to 1.0, while poorly shaped elements have a value closer to zero. The following stats are for tetrahedral meshes of a simple turbomachinery blade/rotor sector model (this is not a real part, just something made up) comparing two of the options for element shape checking. The table shows that the new nonlinear mechanical setting produces significantly fewer elements with a quality value of 0.5 or less. Keep in mind this is just one way to look at element quality – other methods or a different cutoff might put things in a somewhat different perspective. However, we can conclude that the Nonlinear Mechanical setting is giving us fewer ‘lower quality’ elements in this case.

Shape Checking Setting |
Total Elements |
Elements w/Quality <0.5 |
% of elements w/Quality <0.5 |

Aggressive Mechanical | 31683 | 1831 | 5.8 |

Nonlinear Mechanical | 31865 | 1249 | 3.9 |

Here are images of a portion of the two meshes mentioned above. This is the mesh with the Aggressive Mechanical Shape Checking option set:

The eyeball test on these two meshes confirms fewer elements at the lower quality contour levels.

And this is the mesh with the Nonlinear Mechanical Shape Checking option set:

So, if you are running nonlinear structural models, we urge you to test out the new Nonlinear Mechanical mesh setting. Since it is more restrictive on element shapes, you may see longer meshing times or encounter some difficulties in meshing complex geometry. You may see a benefit in easier to converge nonlinear solutions, however. Give it a try!