SHELL ANALYSIS. THIN-WALLED PRESSURE VESSEL

Purpose of the analysis:

The purpose of the analysis is to compare the displacement and stress distributions in an axisymmetric pressure vessel loaded by internal pressure (p=0,1Mpa) for different thickness of the reinforcing ring.

Description of the model:

Type of model: It is a two-dimensional problem of deformable body mechanics. Applied finite elements:

Largest Number

Nodes . . . . . . . . . . . 7700 Elements. . . . . . . . . . 7437 Element types . . . . . 1

Real constant sets. . . . . 2 Material property sets. . . 1

Material properties: Pressure - p=0.1Mpa E = 2* 10^5 Mpa √=0.3

Shape of the model:

Number Defined

Number Selected

7673

7413 n.a.

1

2

n.a. n.a.

7700 7437

1

Discretization



What load cases were analyzed:

Type of analysis: axisymmetric

Boundary conditions:

Displacements = 0 at reinforcing ring. Internal pressure = 0.1 Mpa Simmetry at planes XZ and YZ



Results of analyzes for individual cases:

Stresses along lateral walls:

Stresses along the path at the lower part of the vessel:



Numerical values:

Von Mises equivalent stress from top, middle and bottom layer at the junction with the reinforcement ring. Values for different ring thicknesses:

SEQV 0.2 1

2 3 5 10

Top Middle Bottom

746.57 346.802

513.09 213.373 540.297 230.665

230.466 185.998 148.733 125.127 123.592 122.443 148.973 142.316 137.012

120.502 121.355 132.958

Graphs on the basis of the paths:

800" 700" 600" 500" 400" 300" 200" 100"

0"

0" 2" 4" 6" 8" 10" 12"

Top" Middle" Bottom"

On the above plot, we can see how the equivalent stresses change on the vessel depending on the reinforcing ring width. After 5mm width, the changes are minimal, so this could be an optimal width.

It must be noted that for the 10mm case, the maximal stresses are not anymore at the junction with the ring, but they are displaced slightly to the lower part of the vessel.

Contour maps:



0,2 mm ring

1 mm ring

2mm ring

3 mm ring

5mm ring

10 mm ring

Comparison of numerical results with the theoretical and conclusion:

We have seen from the stress plots along the lower part of the vessel, that stresses increased linearly according to what we expected from the theoretical calculations. Both hoop and meridional stresses start from 0 at the bottom of the vessel and rise to approximately their maximal theoretical values of 70.71 MPa meridional stress and 141.4 MPa of hoop stress. Those values can be clearly seen from the trend on the path plots.

It must be mentioned that although at the bottom of the vessel, the stresses are 0, the surface plot had some computational problems, and showed high levels of stress concentration on this point due to computational inaccuracies.

We can also observe on the lateral walls of the pressure vessel, the trend is again near to our theoretical distribution of 50MPa.

In the different cases studied, we observed that as the ring thickness got larger, stress concentrated at the edge of the pressure vessel decreased, and checking the graph we can estimate that a ring thickness of 5mm is enough to minimize those local stresses.

...