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Tips & Tricks: Inplane and large displacements

A common analysis example is a flat-walled tank under a pressure load. With the basic free FEA add-in's available in most CAD packages (small displacement only), you can't actually get a correct answer. With the basic designer-level add-in's you can account for inplane and large displacement effects to get more accurate answers as shown below.

To compare the differences between small displacement, large displacement and inplane effects, each study was run under a series of pressure loads and the results recorded at the centre of the tank wall. In this case, quarter symmetry was used and is shown in the image below:

mesh2
Small displacement: The full load is applied in one step, and there is no change in the stiffness matrix
Inplane Effects: The analysis is run in two steps to account for changes in the stiffness matrix due to the applied loads, such as the development of diaphragm stress
Large displacement: The load is applied in steps determined by the software, and the stiffness matrix is updated at each step. Accounts for changes in load direction and the development of diaphragm stress
stress_plot disp_plot
Stress plot Displacement plot

Stress Results

stress

disp

Displacement Results

Even at the smallest pressure load, there is a 36% difference between the small and large displacement results, and this increases to 53% at the largest pressure load. Inplane Effects gives a better result, but it is still not correct. This can be explained by looking at the way the pressure load is carried by the side walls in the diagram below.

diagram

Step 1 in the diagram below shows the applied load carried in bending, with no deformation. This is how the Small Displacement solution is calculated.

Step 2 shows the load being carried by diaphragm stress developing as a result of initial deformation (and a recalculation of the stiffness matrix). The applied load is resisted by the vertical component of the tensile load, meaning that the resulting deflection is smaller than first calculated above. This is how the Inplane and Large Displacement solutions are calculated.

In deciding which solution type to use, and in order to verify your results, the only sure way to determine if Large Displacement effects come into play is to run the Large Displacement solution and compare results.

A general guideline on when a Large Displacement solution is needed is:

  • If deflection of the structure will change the way the load is carried

Note that Large Displacement solutions will take more time and computing power, and the results are only available for the last step. If intermediate results are required, or there is material nonlinearity or yielding occurring, you will need to run a full Non Linear study (available in analyst level FEA add-ins).

If the Large Displacement or Inplane solutions don't run, this can be an indication that your structure or part is not stiff enough and may need re-designing.

In the previous Tips & Tricks, the inplane result matched the large displacement result as two iterations were sufficient to capture the deformation and diaphragm effects.

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