# Weird (or not) issues in thin-walled cylindrical shell buckling modes

• Vigardo
In summary, the lower buckling factor increases as the mesh size decreases from 1 to 0.25 m, but the shape of the lowest buckling mode changes abruptly for mesh sizes finer than 0.35 m. The maximum displacements and utilisation are the same in all mesh sizes, but the BFs are slightly different (around 5%) between Alternate and UV meshes.
Vigardo
TL;DR Summary
Would you explain why I observe weird issues in the buckling modes of a thin-walled cylindrical shell? Are they physically sound?
Dear FEA experts,

I’m trying to analyse* some finite elements model of a thin walled cylinder with variable cross-section, but I’m observing four weird issues in the buckling modes. The structure is vertically (along z-axis) and horizontally (along y-axis) loaded on top. Would you help me to understand why? Thanks!

1. The lowest buckling factor (BF) increases as the mesh size decreases from 1 to 0.25 m (row number "3" in the yellow panels). Shouldn't it happen exactly the opposite? Shouldn't the structure be less stiff as element size is reduced?
2. In addition, it happens an abrupt change in the lowest buckling mode shape for mesh sizes finer that 0.35 m. This is accompanied by an steady increase in BF until about 0.25 or 0.1 m element size, where it converges to around 85-90 values. Note that the observed increase in BF (issue 1.) also occurs without mode shape change.
3. I tried two different triangular meshing patterns: Mesh-UV (left) and Alternate (right). It is apparent that the ripples of the first buckling mode are a bit twisted from the y-axis (green line, the direction of the horizontal load) for Mesh-UV meshing pattern. Only the Alternate meshing produces the expected horizontal ripples (because of loads symmetry). Would this be caused by the different triangular meshing?
4. As expected, the maximum displacements and utilisation (row "1" and "2" in yellow panels) are the same in all of them. However, the BFs are slightly different (around 5%) between Alternate and UV meshes, even at the finer mesh size. Shouldn't they converge?
*Using Karamba3D parametric engineering plugin (FEA) for Grasshopper/Rhino. Top ring elements are much thicker (50 cm) to prevent premature local buckling.

If the mesh is too coarse when compared with the radius of curvature you will be seeing the effect of the mesh size rather than the modeled object in the real world.

The fact that the numerical model changes behaviour is an indication that the model is failing at some mesh size. It is important to test the model sensitivity to mesh size. That is exactly what you have done and observed.

We know that too coarse a mesh will fail, and that too fine a mesh will work, but then computation will take too long. Trying to explain why a coarse mesh fails, in the particular way it does, is probably not a sensible use of your time.

Vigardo
You're right, perhaps I'm overthinking here. I will use the finer mesh for my calculations and not worry about the coarser mesh artefacts anymore. In fact, the finer mesh buckling factors are not so different (90 and 87) for both mesh types. Thank you very much for your kind explanation!

## 1. What is a thin-walled cylindrical shell?

A thin-walled cylindrical shell is a type of structure that is commonly used in engineering and construction. It is a hollow, cylindrical shape that is made of thin materials such as metal or plastic. These shells are often used to create pressure vessels, storage tanks, and pipes.

## 2. What is buckling in thin-walled cylindrical shells?

Buckling is a phenomenon that occurs when a thin-walled cylindrical shell is subjected to compressive forces. It is a failure mode in which the shell collapses or deforms due to the instability of its walls. This can happen when the compressive forces exceed the shell's ability to resist them, causing it to buckle or collapse.

## 3. What are the different buckling modes in thin-walled cylindrical shells?

There are several different buckling modes that can occur in thin-walled cylindrical shells, including axisymmetric buckling, circumferential buckling, and local buckling. Axisymmetric buckling is when the shell buckles in a circular shape, while circumferential buckling is when it buckles in a ring-shaped pattern. Local buckling is when a small portion of the shell buckles due to localized stress concentrations.

## 4. What factors can affect the buckling behavior of thin-walled cylindrical shells?

There are several factors that can affect the buckling behavior of thin-walled cylindrical shells, including the material properties of the shell, its geometry, and the magnitude and direction of the applied load. Other factors such as imperfections in the shell's shape or material defects can also play a role in its buckling behavior.

## 5. How can buckling in thin-walled cylindrical shells be prevented?

To prevent buckling in thin-walled cylindrical shells, engineers must carefully consider the design and material selection of the shell. This includes choosing materials with high strength and stiffness, as well as ensuring that the shell's geometry is optimized to resist buckling. Additionally, proper installation and maintenance can help to prevent buckling in these structures.