An assumption that Linear Static analysis makes is that the stiffness of the structure remains constant no matter what type of load is being applied. This is usually a good assumption when the displacements are relatively small. But what about in cases when the load is applied in such a way that it causes the stiffness of the structure to change? Fortunately, in most scenarios such as these, the software warns you with the message shown in Figure 1 below.
If you click Yes to this message, the software turns on a Large Displacement Flag (LDF) and therefore no longer assumes the stiffness is constant. In order to do this, the software changes the stiffness again and again during the solution process. This usually makes the run-time take at least 5 times longer. In some cases it may take 50 times longer, or it may even fail!
If you click No to this message, then you’ll usually get some results almost instantly after making the selection, but you may have to question their accuracy.
Some questions that come to mind may be:
Is it worth waiting the extra time for a LD solution when I could run small displacement instead? And if the small displacement result looks questionable, won’t I get better results than either of these studies if I run a Nonlinear Static analysis?
To try to develop some insight into these questions, I decided to run a test on the simple model shown in Figure 2.
I designed the thin (0.05in), 10-inch long steel model in such a way that when I applied 1 lb of bending force, I got 1 in of displacement. Therefore the stiffness seemed to be 1lb/in under this type of load. This seems to imply that if I apply 2 lbs I should get about 2 inches of displacement. However, it doesn’t make much sense to say that if I apply 20 lbs I would get 20 inches of displacement. This would seem to mean that the model stretches to be about twice its original length! So it seems apparent that this overall stiffness value should change with the load. Also, the material may yield at some point which is another effect I may need to take account of for certain loads.
I noticed that in this model, the stiffness seemed to change with only a small amount of loading. I ran the study with small displacement and also with the LDF activated and I compared these results. I could see how the stiffness was increasing. A summary of the comparison is shown in the Figure 3.
I noticed that in this model it took only about 0.3 lbs of force for the LD dialog to pop up, yet about 4-5 lbs were required to get the material to yield. In order to test the influence this yielding had on my model, I decided to run two Nonlinear studies: one with the LDF activated and one with small displacement. These results are compared to the linear Static studies from before in the graphic below.
If I accept the Nonlinear LD solution as the most accurate solution under all loading up to and beyond the yield point, I may conclude from these studies that as long as my material doesn’t yield, enabling the LDF in Static analysis provides me with good results. On the other hand, if the material does yield, I may want to consider running a Nonlinear analysis.
Also, for many cases, the results between small displacement and large displacement may differ if I continue to increase the load well above the point at which I receive the LDF dialog.
Finally, it is important to note that the results above only directly apply to the thin beam model that I constructed and the curves may look totally different for other models.