Increments and iterations

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This article continues Convergence criterias, focusing on the differences between increments and iterations in Nonlinear analysis in AxisVM.

How should we use the increments and iterations? #

Recalling the picture for the SDOF case, it seems that increments and iterations play a similar role. One increment with 500 iterations seems more or less identical to ten increments with 50 iterations.

 

But taking a detailed view, we can see the difference. Its reason is that although both the red and green circles are located on the force response curve of the structure, it only means that the displacements at all of these points are compatible with the support conditions. But the equilibrium equations are fulfilled only at the exact solution points shown by the green circles. It means that the solver has to find the path between the solution points of subsequent increments going through a series of unequilibrated and unreal configurations.Looking at the maps for the MDOF case, it can be seen as well. A different map belongs to each load increment. Increasing the load level, the solution point moves far from the origin, and the surface becomes increasingly complex. Therefore, covering the long and bumpy way to the solution point needs a lot of iterations with weak convergence. Moreover, convergence can be impossible due to an infinite, alternating iteration process.

Inserting sub increments, the solver has to take shorter distances between the subsequent solution points. Starting the iteration process of the actual increment from the solution point of the previous one helps to avoid the complex territories of the map. It provides strong, monotonic, and fast convergence with a few iterations. We can say that it is usually worth using more increments because the total number of iterations during the whole calculation can be lower than in the case of just a few increments.

If the calculation converges well and lots of load cases are calculated, decreasing the number of increments below 10 is valid. But for troubleshooting any convergence problem, the number of increments has to be set to at least 10.