Buckling of a Cylinder

1. Introduction
For those of you who are choosing a cylinder for the body of the ROV, this note gives some tips about carrying out FEA for the analysis of a cylinder.

2. FEA Model Details
It was assumed that the cylinder was:

3a. Using Solid Works and COSMOSWorks

The following is probably the easiest way to do the analysis assuming there are no ends in the cylinder, but that it is constrained from buckling by reinforcements (restraints) at 1 m intervals. A 90 degree arc of the cylinder will be modelled, as by using appropriate constraints (roller / sliding on the straight edges) this allows first mode buckling to be simulated. Only half the length is modelled (0.5m) and with one end un-constrained and the other end fixed, this provides the equivalent to 1 m length, but simplifies model set up.

3b. Results of the Static Analysis
These results are away from the constrained end.
The three principal stresses on the outer curved surface away from the ends were:

The theoretical hoop stress, sigma = pressure x radius/thickness = -25 MPa.

3c. Results of the Buckling Analysis
The buckling factor was 4.519, indicating that the theoretical external pressure to cause buckling was 4.5MPa. Under an external pressure of 4.5 MPa the maximum von Mises stress would be just under 115 MPa, which is below the yield strength of most aluminium alloys.

4a. Using Pro/E and Mechanica Structure

Here it is assummed that a cylinder with flat ends is being modelled:

Autogem produced 1316 elements

4b. Results of the Static Analysis
The three principal stresses on the outer curved surface away from the ends were:

The theoretical hoop stress, sigma = pressure x radius/thickness = -25 MPa.

4c. Results of the Buckling Analysis
The constraints applied allow the expected first buckling mode for a cylinder, but it should be noted that achieving in practice the theoretical results depends upon high geometric accuracy of the manufactured item, even very minor variation from the stated dimensions can cause large reductions in the buckling loads.
The buckling load factor, mode 1, was 3.4 from the Mechanica analysis. This means that buckling would occur at an external pressure of 3.4 MPa. This would give a von Mises stress of 69MPa, which is well below the yield strength of any aluminium alloy.

5. Differences in Results
It should be noted that what seem like minor differences between these two approaches has given quite different results. The reason for this is:

The Cosmos model had no closed ends and no axial load and zero axial stress, whereas the Mechanica model had closed ends, with pressure applied to them and consequently an axial stress equal to half the radial stress.

You should note that although these differences are significant, even very minor changes or errors in loads and especially in restraints can make very big differences to results.

The mode 1 deformed shape from COSMOSWorks is shown below:

The mode 1 deformed shape from Mechanica is shown below:

The calculation below uses the approximate formula from Roark for a short cylinder length L with the ends held circular but not otherwise constrained:

This gives the failure pressure as 2.46 MPa, somewhat lower than the 3.4 MPa and 4.5 MPa computed by the FEA, above.

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David J Grieve, 12th September 2006, (previously 26th February 2003).