We split the model at Stress Classification Line (SCL) locations 1-9 as shown in the PTB-3 figures E5.2.1-10 and E5.2.1-11. The exact location was not provided for SCL 5 and SCL 9. We attempted to visually match the publication. We used exactly same location in both SWS and ABAQUS even if we could not exactly match PTB-3.
SCL Methods
Two issues stand in the way of getting good SCL data. 1) taking a SCL at a bad location, and 2) setting up the tool poorly. Getting good SCL locations is not always possible. Our article “ASME VIII-2 Permissible Cycle Life” discusses what to do when a good SCL is not possible. PTB-3 does not discuss the reason for the 9 SCL locations chosen. VIII-2 Annex 5-A.3 discusses the selection of SCLs Because we often encounter results from improperly configured SCL tools some detail is provided here.
The SCL starts with stress data taken from the model. The data set is taken on a straight line from the inside to the outside of the model. The data is rotated from global (or model) coordinates to local. When the SCL is on the X axis (like SCL #1 above) no rotation is required. The local direction 1-1 is the direction of the SCL. Stress in this direction is S11. Likewise S22 is perpendicular to the line on the plane of the SCL. S33 is perpendicular to the line out of plane. S12 is the shear stress in the plane of study. For 2D axisymmetric studies S13 and S23 are zero.
Two issues stand in the way of getting good SCL data. 1) taking a SCL at a bad location, and 2) setting up the tool poorly. Getting good SCL locations is not always possible. Our article “ASME VIII-2 Permissible Cycle Life” discusses what to do when a good SCL is not possible. PTB-3 does not discuss the reason for the 9 SCL locations chosen. VIII-2 Annex 5-A.3 discusses the selection of SCLs Because we often encounter results from improperly configured SCL tools some detail is provided here.
The SCL starts with stress data taken from the model. The data set is taken on a straight line from the inside to the outside of the model. The data is rotated from global (or model) coordinates to local. When the SCL is on the X axis (like SCL #1 above) no rotation is required. The local direction 1-1 is the direction of the SCL. Stress in this direction is S11. Likewise S22 is perpendicular to the line on the plane of the SCL. S33 is perpendicular to the line out of plane. S12 is the shear stress in the plane of study. For 2D axisymmetric studies S13 and S23 are zero.
The correct SCL components must be included to get the correct membrane and membrane + bending results in the SCL. The default settings in most SCL tools will not work for pressure vessel studies. The ABAQUS tool must be configured to include S11, S22, S33 and S12 (all the available data) in the membrane stress calculation. Here we have also included the same S11, S22, S33 and S12 components in the bending calculation – however the bending result has no defined meaning in pressure vessel studies and is ignored.
The “Bending Components for Computing Invariants” is the calculation of the averaged difference in stress from one end of the line to the other. Only bending components are included in the invariant calculation. For this 2D study stresses S11 in the direction of the SCL and shear stress S12 are not perpendicular to the SCL and can not create a stress bending the SCL. Stresses S11 and S12 are removed from the invariants.
The “Bending Components for Computing Invariants” is the calculation of the averaged difference in stress from one end of the line to the other. Only bending components are included in the invariant calculation. For this 2D study stresses S11 in the direction of the SCL and shear stress S12 are not perpendicular to the SCL and can not create a stress bending the SCL. Stresses S11 and S12 are removed from the invariants.
Going beyond this PTB-3 example, a 3D FEA study will have data points with 6 stress components: S11, S22, S33 and S12 as discussed above, with the addition of S13 and S23 (shear components not shown in the above diagram). Of these two new components, S23 produces a torsion of the SCL and is included. S13 is not perpendicular and is removed.
Results
PTB-3 does not discuss convergence of results or quality of the mesh. We used the Error plot built into SWS to determine if the model is adequately converged at the mesh size used. Acceptable mesh errors in non discontinuity zones is 5%. Discontinuity areas often have higher errors. For this model the error is less than 1% except at SCL 1 at the base of the flange to nozzle weld discontinuity where it is an acceptable 5%. ABAQUS does not have an error plot so it was only run in SWS.
PTB-3 does not discuss convergence of results or quality of the mesh. We used the Error plot built into SWS to determine if the model is adequately converged at the mesh size used. Acceptable mesh errors in non discontinuity zones is 5%. Discontinuity areas often have higher errors. For this model the error is less than 1% except at SCL 1 at the base of the flange to nozzle weld discontinuity where it is an acceptable 5%. ABAQUS does not have an error plot so it was only run in SWS.
We obtained displacement and stress plots from both SWS and ABAQUS that substantially matched the results published in PTB-3.
A comparison of our SCL results from SWS and ABAQUS vs PTB-3 is presented in Table 1. Our results matched PTB-3 within 4% of full scale stresses. Given the assumptions we had to make in modelling this comparison, we consider this to be a bulls eye. Our SWS results matched our ABAQUS results within 0.4%. We split the model at the SCL locations to remove sampling location errors between the two programs. Even so, we did not expect results this close, as this ABAQUS analysis is based on 4 sided elements with 8 nodes while SWS is based on 3 sided elements with 6 nodes. However, the model is highly converged as shown in the SWS error plot so the closeness of the results should not have been surprising.
SWS and ABAQUS in daily use
We use SolidWorks Simulation and ABAQUS for a variety of design tasks in our office. The programs have different characteristics that lead them to be suitable for different applications. SWS is a much easier to use program, usually resulting in finished results in half the time, however it does not have built in linearization results that are compatible with ASME methods. We wrote our own tool to get around this shortcoming.
ABAQUS allows a lot of control over the generated mesh vs SWS. This extra control also requires more effort. The ABAQUS quadralateral mesh is expected to be more accurate than the SWS triangular mesh, but for this overrefined example, the difference is turned out to be negligible. Without a doubt ABAQUS has the better results plots where screen updates happen much much faster than SWS’s leisurely pace. And for non-linear analysis, ABAQUS provides results more often and is more stable than SWS.
We use SolidWorks Simulation and ABAQUS for a variety of design tasks in our office. The programs have different characteristics that lead them to be suitable for different applications. SWS is a much easier to use program, usually resulting in finished results in half the time, however it does not have built in linearization results that are compatible with ASME methods. We wrote our own tool to get around this shortcoming.
ABAQUS allows a lot of control over the generated mesh vs SWS. This extra control also requires more effort. The ABAQUS quadralateral mesh is expected to be more accurate than the SWS triangular mesh, but for this overrefined example, the difference is turned out to be negligible. Without a doubt ABAQUS has the better results plots where screen updates happen much much faster than SWS’s leisurely pace. And for non-linear analysis, ABAQUS provides results more often and is more stable than SWS.
FEA is used for frequency and vibration analysis to determine the natural frequency of objects which cannot be obtained from classical calculations. The natural frequency can then be compared to the system resonance to ensure large amplitude oscillations will not occur. The natural frequency may also be used with building codes to determine a base shear force which can then be input to a stress analysis to validate designs subject to seismic or other oscillating conditions. A complete engineering report is available below representing a typical seismic analysis and report completed by Pressure Vessel Engineering.
Description:
Gimbal Expansion Joints are designed to allow angular movement in any plane by the use of two pairs of hinges affixed to a common floating gimbal ring. The gimbal ring, hinged and pins are designed to restrain the pressure thrust due to internal pressure and shear forces.
A gimbal ring is either round or square. For round gimbals the torsional moment shall be considered and for square gimbals the instability due to the bending shall be considered.
Gimbal Expansion Joints are designed to allow angular movement in any plane by the use of two pairs of hinges affixed to a common floating gimbal ring. The gimbal ring, hinged and pins are designed to restrain the pressure thrust due to internal pressure and shear forces.
A gimbal ring is either round or square. For round gimbals the torsional moment shall be considered and for square gimbals the instability due to the bending shall be considered.
Features:
1-Absorbs angular movements in all planes
2-Restrains pressure thrust forces
3-Transmits shear and wind loads
4-Supports dead weight
5-Avoid twisting the bellows
6-No main anchors required
1-Absorbs angular movements in all planes
2-Restrains pressure thrust forces
3-Transmits shear and wind loads
4-Supports dead weight
5-Avoid twisting the bellows
6-No main anchors required