# Shell Elements for Pressure Vessel Design

While solid elements are robust for local stress computations and require much less care in analysis setup, the problem size (number of elements and nodes) blows up pretty quickly if the extent of modelling is increased (Say modelling a local shell to nozzle region vs modelling entire shell with nozzle). This is where shell elements come into play and reduces the problem size considerably.

However though shell models are computationally efficient, their results are not as robust as solid elements and involves additional complexities in model setup. Some key points to consider while setting up a shell model are:

• For shells with R/t < 10 i.e. for thick shells, solid models shall be usually preferred as they give more realistic results.
• The shell normals shall be carefully oriented so that pressure loads get applied on the correct side.
• If a mid-surface model is used, the surfaces should be extended at junctions as required to achieve a shell to shell connection even if it results in an overlap of thicknesses.
• Fillet welds at a T-Junction or a similar junction can be modelled as shell elements with a thickness equal to the weld throat. The weld leg locations on the mid-surface model can be found by projecting normals from actual weld leg locations on to the mid-surfaces. The above two points are nicely illustrated in the following figure from ASME Sec VIII Div 2.

• While stress linearization requires identifying critical junctions and creating paths (Stress Classification Lines) in the solid model at these junctions, finding membrane and membrane + bending stresses in a shell model is a trivial process. The middle surface stress at any stress evaluation point (typically weld toes are critical points as shown in the above figure) gives the membrane stress, while the stress at the Top/Bottom surface gives the membrane + bending stress.
• To model a lap weld simply draw a shell from edge of the top plate to point of intersection of the normal through the weld toe to the mid-surface of the bottom plate as shown by orange lines in the figure below.

• Two parallel shell plates like that shown in the above lap joint arrangement if required to be modelled as integral can be joined using bonded contacts between the offset modelled mid-surfaces

These were some pointers to be considered while going for a shell model. Please let me know through comments any other important pointers which I might have missed.

## 1 thought on “Shell Elements for Pressure Vessel Design”

• Krishna says:

Hi Mr. Sandip,
I have a query in linearization of streses of shell and solid element. In Shell element, mid surface stresses are membrane and top/bottom surface stress are membrane + bending and peak stresses were not accounted.
But in solid element, stresses were linearized through the thickness and every point along the thickness, we will get M, M+B, peak stresses. Hence for solid element, providing M, M+B, M+B+Q at top and bottom surface is not required.
Confirm my understanding and provide me further clarity on this subject.
Thanks.