Have you some experience with buckling analysis of composite cylinders?

Composite materials are used a lot in pressure vessels because of their great structural properties (see below), so I decided to write something about them in tha case of a buckling analysis (to continue on the previous post about buckling I wrote)

I found this awesome article on the topic yesterday and I decided to use it as a basis for this short article. I even made an interactive tutorial of the full simulation setting process (try it below).

Here’s a reminder for those not familiar with composite materials:

Composite materials are very good engineering materials with many advantages. They are strong, light and resist well to corrosion. They are made of a combination of other materials put together to achieve higher structural properties (They are generally more expensive though, cannot have everything, huh…). The individual materials do not dissolve or merge completely in the composite, but they act together as one. As the result, it is easy to figure out, that properties of the composite material are superior to the properties of the individual materials from which it is constructed.

In the industry, composite pressure vessels are used for: air suspension reservoirs, pneumatic brake reservoirs for passenger rail cars, nitrogen gas storage vessels, compressed natural gas fluid tanks and much more.

Now let’s back to the study of buckling of this composite cylinder and let’s do a parametric study using finite element method to determine the effect of the **length to mean radius** (L/r), the **mean radius to thickness ratio** (R/t) and the** lay up sequence** on the results !

The software I am using is midas NFX, which is rather convenient for such analysis combining composite and linear/nonlinear buckling.

## 1. Create the cylinder geometry

Geometry is so simple that there is not too much to say about it… I created also an Excel file with the different values I’ll take to perform the parametric study.

## 2. Composite Material Data

I am using CRPF (Carbon Fiber Reinforced Polymer) Material defined with the coefficients below

## 3. Lay-up Sequence, Mesh and material orientation

I created several composite 2D shell plate properties with different thickness and for each of them I defined different stack-up fore the layers.

For the element formulation, i prefer using the reduced formulation to avoid difficulties such as shear locking or hourglassing. Material Orientation is related to material coordinate system alignment for composite shell element. It’s mandatory to check or setup this to assure the right orientation for each layer.

## 4. Boundary conditions

I applied the constraints at the bottom and the top edge of the circumference. The bottom side is fixed and all of the degrees of freedom except of TZ are fixed at the top of the cylinder.

## 5. Interactive tutorial: experience the workflow directly

To grasp this simple workflow and perform the same on your vessel model, I decided to create an interactive tutorial to show you all the process as if you were using the software yourself (and without installing anything).

Just click here or on the photo to start

Start the interactive tutorial

Just one remark… you will need to try it on a computer, not a portable device because you’ll need the keyboard.

## 6. Results of The buckling analysis of the composite cylinders

I like this workflow because the model is easy to set up and midas NFX allows easily to perform multiple case scenarios, which include all data and then generate all the curves I need on one unique graph.

Here you have the curves of the parametric study for symmetric balanced and unbalanced lay-ups:

And here is the final buckling shape I got:

Everything was perfectly matching the article I read and it just made me happy (nothing more frustrating than results which are not matching…)

I have much more to write about this case study (eigenvalue analysis, nonlinear study, etc..) but it will be for the next post !

Hope you enjoyed the reading

Piotr Stepien