Load increment methods

Autodesk Warp and Stress analyses provide two load increment methods for large deflection analysis: load control, and displacement control.

Load Control

Under load control, each step corresponds to a particular increment of load. The load increments can be automatically adjusted, or can be specified when preparing the input file for Warp or Stress analysis. During each step, the load is held constant while equilibrium iterations are performed. As the solution approaches a limit point (point of local maximum or minimum load), this algorithm will become unstable and convergence difficulties will occur. Even small unbalanced loads will lead to large changes in the displacements.

In order to successfully cross a limit point and to study the post-buckling behavior, we must abandon the iteration under constant load (load control) method in favor of the iteration under constant displacement (displacement control) method.

Displacement Control

The displacement control method involves the introduction of a displacement based constraint equation, enabling the load parameter to become an additional variable during iteration.

Under displacement control, each step corresponds to a particular increment of displacement for a specific node in the model which we call the control node. As with the load control, the increments (in this case displacement increments) can be automatically adjusted, or can be specified when preparing the input file for Warp or Stress analysis. There are two variations of the displacement control method available: manual or automatic.

With manual displacement control, you select the control node and the displacement direction to be used for the entire analysis. Although this option works well in many situations, it does however lack generality, and breaks down completely in cases where the equilibrium path for your chosen controlled displacement component is vertical or nearly vertical. This is analogous to the break down of the load control method when the equilibrium path is near horizontal.

With automatic displacement control, the analysis applies an initial small increment of load at the start of the first step, to find which node moves the most and in which direction. This node becomes the control node selection and the displacement incrementation method is started. The analysis may change the control node and also the control direction dynamically according to current conditions in the analysis. This has a beneficial effect on both efficiency (convergence rate) and robustness (ability to trace any load path).

Reference 1 contains a detailed description of the automatic displacement control method used in the program. The power of the method is that it is completely general and requires very little prior knowledge of structural response. In principle, by combining the method with the automatic strategy control system described in the section Automatic Control Techniques on Page 26, almost any load-deflection solution path can be traced automatically, including those exhibiting bifurcations, limit points, snap-through and snap-back.

Choice of Control Method

The suitable control method to choose depends on the type of analysis you are running (warpage with prescribed displacements) and the degree of non-linearity of the problem. Both methods have advantages and disadvantages, the most important of which are discussed in this section.

Advantages of Load Control/Disadvantages of Displacement Control

For mildly non-linear problems, load control is the more efficient method because it is less computationally intensive than the displacement control method. A buckling analysis can give an indication of whether a high degree of non-linearity can be expected in the load range that you are analyzing.

The load control method provides better control over the load level at the final step of the analysis. For example, if you set a maximum load factor of 1 in a displacement control analysis, the last displacement step will be the one which just passes the load factor of 1. The final load may be just over 1 (say 1.01) or well over 1 (say 1.2), depending on the displacement step size. If you are interested in the deflected shape at exactly 100% load, this lack of control in a displacement control analysis could be a disadvantage. On the other hand, if you accepted the option to keep temporary files, you could run a restart analysis with the following inputs:

  • Specify restart at the final step which exceeded 100% load
  • Select the Load Control method
  • Specify an initial load increment no greater than that required to reach 100% load
  • Specify a maximum load factor of 1

Choosing suitable initial increment and maximum increment values for displacement control analysis is generally far more difficult and less intuitive than for load control. As for load control, increments that are too small can lead to excessive analysis steps, and increments that are too large can lead to inaccurate prediction of non-linear behavior. An exception to this is prescribed displacement Stress analysis using manual displacement control. In this case, displacement increments are more meaningful than load increments and displacement control would be the preferred method.

Advantages of Displacement Control/Disadvantages of Load Control

For highly non-linear problems, displacement control is the more powerful method because it can trace any load-deflection path automatically. In contrast, load control is guaranteed to fail if a limit point exists in the path.

Displacement control is the preferred method for prescribed displacement analysis since displacement increments are more relevant to the problem than load increments.

References

  1. Trueb, U., "Stability problems of elasto-plastic plates and shells by finite elements", Ph.D. Thesis, University of London, 1983.