# Why does it take lesser iterations for a stiffer model in my FEA than a less stiffer model to converge?

I am currently using ANSYS FEA software and I conducted a simple geometric non-linear analysis of two same shaped bodies, but different cross sectional areas; one being quite bigger than the other. We know that the one with the bigger cross sectional area should be more stiff than the other. Anyhow, when I tried conducting a non-linear FEA analysis, it took more iterations to converge for the one which has lesser stiffness than the other.

Can anyone explain this phenomenon, like is this always the case and why does this happen?

• What did you find in the help files? Sep 20 at 15:12
• I assume because more stiff = less change per iteration and less changes in total. Sep 20 at 15:32
• @SolarMike, I couldn't find anything in the help files regarding this issue. I mean there might be some complex equations available in the Help manual, but I was just asking for a reason behind this in Layman terms, which could make me understand the concept behind it. Sep 20 at 16:22
• Probably because this software was not designed for use by a Layman... Sep 20 at 16:46
• As the old saying goes, "If you cannot describe what you are doing in layman's terms, then you probably are doing something wrong". Sep 20 at 17:33

depending on the type of non linear analysis you used, then conceptually the analysis takes the following steps (again depending on the type on analysis you use):

An iterative process starts:

1. A small increment of the load $$\Delta F$$ is applied (typically a percentage between 1% and 10%)
2. For those small load increments the displacements $$\delta_i$$ are calculated.
3. on the resulting structure the loads are applied again and the displacement is calculated $$\delta_{i+1}$$
4. The $$\delta_{i }$$ are compared to $$\delta_{i+1}$$. if $$|\delta_{i+1}- \delta_{i}|\le \epsilon$$ (where $$\epsilon$$ a small positive number), then you proceed to the next increment of the load. Otherwise you return to step 2 setting $$\delta_{i+1}$$ as your initial displacement and your repeat the process . If the cycles repeat more than a predetermined number of iteration $$n_{max}$$ then the algorithm returns to step 1 reduce further the $$\Delta F$$.

What happens in a less stiff structure, is that the displacement will be (invariably) larger for the same load. As a result, step 4 where the check occurs will take longer to converge because at each step $$|\delta_{i+1}- \delta_{i}|$$ is more likely to be larger.

Additionally you might have more occurrences where you need to go back to step 1 and reduce the increment.

In structural analysis, the second-order effects ($$P-\Delta$$ or $$P-\delta$$) are obtained through the non-linear analysis, so in general, a structure consisted of slender members would require more iterations to converge.