Ben Vanderloo, P.Eng.
[email protected]
5198809808 Ext. 242
How do you know you are getting the correct FEA results? ASME Book PTB3 Chapter 5 provides worked sample problems that we have compared with our FEA methods and got the same results. SolidWorks Simulation ships with a general engineering validation problem set, again we got the same results.
Getting good results is also dependent on checking the reaction forces, using the correct element types and choosing regular or large displacement settings. Contact locations like under bolt heads always report large errors – sometimes adjusting your expectations is also important.
Perfect results are useless unless others can understand what you have done. The Canadian B51 standard Annex J has some presentation requirements that must be met for Canadian use. We also have suggestions on how to take presentation screen shots.
PVE File File: PVE9128, June 9, 2015, By: CBM/BTV/LRB
ASME problem sample manuals PTB3 and PTB4 are well kept secrets. The samples that used to be in the back of ASME VIII1 in Appendix L have been changed, expanded and published as PTB4. The ASME VIII2 rewritten in 2007 got its own new PTB3 problem sample manual in 2010. PTB3 contains worked examples with numerical results. Although meant more as an educational guide than a verification set, here we compare our own results in both ABAQUS and SolidWorks against published PTB3 results.
PTB3 example E5.2.1 “Elastic Stress Analysis” covers the correct use of stress linearization and provides numerical results. The same model is used for sample E5.3.2 “Elastic Analysis”. Here both are run.
[From E5.2.1] Evaluate the vessel top head and shell region for compliance with respect to the elastic stress analysis criteria for plastic collapse provided in [VIII2] paragraph 5.2.2. Do not include the standard flanges or NPS 6 piping in the assessment for compliance to allowable stresses. Internal pressure is the only load that is to be considered. Relevant design data and geometry are provided below and in Figures E5.2.11 and E5.2.12.
In other words analyse the head and a nozzle in the top of a pressure vessel to determine its acceptability against ASME code rules for FEA. The instructions for E5.3.2 are:
Evaluate the vessel top head and shell region given in Example Problem E5.2.1 for compliance with respect to the elastic and elasticplastic local failure criteria provided in [VIII2] paragraphs 5.3.2 and 5.3.3. The same model and material conditions were used as in Example Problem E5.2.1.
This example provides enough dimensional and material information to attempt to duplicate the results. Exactly matching the published results is not possible because not all not all model geometry is given and some linearization locations are not exactly provided. The 2D 8 node ABAQUS element type CAX8R was provided, however mesh sizes were missing. Where information exists, we replicated the PTB3 exactly. Where information is missing, we tried to get a model that looked similar to the one in the publication. Given these limitations, we hoped for results that match PTB3 with less than 5% error.
The scope of study in Examples E5.2.1 and E5.3.2 is the shell, head and nozzle. These are symmetric about the centerline allowing a 2D axisymmetric analysis to be chosen by the authors. This reduced the complexity of the analysis and allows a refined mesh to be used. Most model dimensions were provided in drawings E5.2.11 and 2. We recreated the 2D model geometry in SolidWorks. Where model dimensions were not available, we made our model visually match the published drawing. A link to a drawing of our model is provided in the resources section below.
We used the same model in both ABAQUS – the software used by the authors and SolidWorks Simulation (SWS). We inferred the mesh size used by counting the number of elements in areas of known dimensions. We used this size of 0.015″ in both programs. The materials were modeled using the two different material moduli as outlined in PTB3. The exact location of the change in modulus was not given, so we chose SCL #4 as the transition.
We split the model at Stress Classification Line (SCL) locations 19 as shown in the PTB3 figures E5.2.110 and E5.2.111. 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 PTB3.
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 VIII2 Permissible Cycle Life” discusses what to do when a good SCL is not possible. PTB3 does not discuss the reason for the 9 SCL locations chosen. VIII2 Annex 5A.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 11 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.
Going beyond this PTB3 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.
PTB3 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 PTB3.
A comparison of our SCL results from SWS and ABAQUS vs PTB3 is presented in Table 1. Our results matched PTB3 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.
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 nonlinear analysis, ABAQUS provides results more often and is more stable than SWS.
Downloads the two reports for this validation exercise: ABAQUS and SolidWorks Simulation.
File: PVE9729 Last Updated: Oct 14 / 2016, Cameron Moore, Ben Vanderloo, Laurence Brundrett
SolidWorks Simulation ships with a series of validation sets. The “SOLIDWORKS Simulation Static Verification Problems” compare the results obtained by SolidWorks Simulation to theoretical textbook values or prior FEA studies. Here are our results using the 2016 release of SolidWorks Simulation:
A simply supported plate is first center point loaded and then uniformly loaded. The plate is 1″ thick and 40″ on a side. Modulus of elasticity = 3 X 10^7 psi, Poisson’s ratio = 0.3. Using symmetry restraints, only 1/4 of the plate is required. The outside edges are simply supported. A mesh size of 1/2″ with thin plate elements produces a close match between theory and our FEA results. The image shows displacement. 

Center Deflection Center point load = 400 lbs 
Center Deflection Uniform Pressure = 1 psi 

Theory  0.0027023  0.00378327 
PVEng  0.0027046  0.0037855 
%Error  0.0851%  0.0589% 
Timoshenko, S. P. and WoinowskyKrieger, “Theory of Plates and Shells,” McGrawHill Book Co., 2nd edition. pp. 120, 143, 1962. Center point load: UY = (0.0116 * F * b2) / D D = (E * h3) / (12* (1 – v2)) Uniform Pressure: UY = ( 0.00406 * q * b4) / D 
A cantilever beam is subjected to a concentrated load (F = 1 lb) at the free end. Determine the deflections at the free end and the average shear stress. Dimensions of the cantilever are: L = 10″, h = 1″, t = 0.1″.  
Deflection at free edge, inch  Average Shear Stress, psi  
Theory  0.001333  10 
PVEng  0.001341  9.9407 
%Error  0.6002%  0.5930% 
UY = (F*L3 ) / (3 * E * I ) Average shear stress: τxy ave = V / ( t * h) L = Beam length E = Modulus of Elasticity I = Area moment of inertia V = Shear force t = Beam thickness h = Beam height 
A circular beam fixed at one end and free at the other end is subjected to a 200 lb force. Determine the deflections in the X, Y direction. Radius of curvature of the beam = 10″. The beam width and thickness are 4″ and 1″ respectively. This problem is solved using thin shell elements.  
X Deflection at free edge, inch  Y Deflection at free edge, inch  
Theory  0.00712  0.01 
PVEng  0.007137  0.009992 
%Error  0.2388%  0.0800% 
Warren C. Young, “Roark’s Formulas for Stress and Strain,” Sixth Edition, McGraw Hill Book Company, New York, 1989. DX = ( 3/4 * π2)* H R3 / (E *I) , DY = (1/2*H*R3 ) / ( E* I ), Modulus of elasticity = 3 X 107 psi 
File: PVE3179, Last Updated: Jan. 22, 2009, By: BV
Reaction forces are the resulting loads seen at the restraints of a model being analyzed. They can be used to ensure an analysis is restrained from rigid body motion, and is static or in balance. The reaction forces are equal and opposite to the sum of the applied loads.
This report shows typical methods used for restraining models and compares the resulting displacement and stresses of identical models both in balance and out of balance for two different FEA models.
Theoretical Reaction Force Components:
X Reaction = 75,340.8 lb
Y Reaction = 78,079.2 lb
Z Reaction = 9,919.2 lb
Note: Component directions are generated by inspection of the pressure
Theoretical Resultant = SQRT ((75,340.8 lb)^2 + (78,079.2 lb)^2 + (9,919.2 lb)^2)
Theoretical Resultant = 108,954 lb
Actual Reaction Force Components: X Reaction = 75,344 lb Y Reaction = 78,075 lb Z Reaction = 9,922 lb Actual Resultant = SQRT ((75,344 lb)^2 + (78,075 lb)^2 + (9,922 lb)^2) Actual Resultant = 108,950 lb Error Calculation: Error = ((Resultant Theoretical  Resultant Actual) / Resultant Actual) * 100% Error = ((108,954 lb  108,950 lb) / 108,950 lb) * 100% Error = 0.00%
From the error calculation we can see that the actual results fall within 2% of the theoretical results. This criteria determines if a model is acceptable for analysis of stresses and displacements.
The hydraulic manifold block used in this example demonstrates how an out of balance model affects model displacement and stress results.
Three different methods of checking the model balance (unexpected displacement, unexpected stress and out of balance reactions) have all indicated the same thing: this model can not be used as is.
Reaction per Port = (0.864 in^2) * (300 lb/in^2) = 259.276 lb
Often the magnitude of the reaction force can be used to determine what is causing the imbalance.
Theoretical Reaction Summary:
Reaction X = 1008 lb
Reaction Y = Force Applied – Force Due to Exit Pressure
Reaction Y = 3 Ports * (259 lb 259 lb)
Reaction Y = 0
Reaction Z = 0
Theoretical Resultant = SQRT ((1008 lb)^2 + (0 lb)^2 + (0 lb)^2)
Theoretical Resultant = 1008 lb
Actual Reaction Force Components:
X Reaction = 1009.6 lb
Y Reaction = 4.03 lb
Z Reaction = 3.47 lb
Actual Resultant = SQRT ((1009.6 lb)^2 + (4.03 lb)^2 + (3.47 lb)^2)
Actual Resultant = 1009.6 lb
Error Calculation:
Error = ((Resultant Theoretical – Resultant Actual) / Resultant Actual) * 100%
Error = ((1008 lb – 1009.6 lb) / 1009.6 lb) * 100%
Error = 0.16 %
From the error calculation we can see that the actual results fall within 2% of the theoretical results. This model is in balance and can be used to calculate displacements and stresses.
Checking the model balance is an important step for verifying that all loads are acting upon restraints correctly. An out of balanced model provides invalid result that cannot be used.
This is part of a series of articles that examines the ABSA (Alberta Boilers Safety Association) requirements on writing FEA reports. These guidelines can be found at: ABSA Requirements. The use of 2nd or higher order elements is one of the requirements.
Pressure Vessel Engineering uses SolidWorks Simulation for Finite Element Analysis. It is expected that these results would also be applicable to other FEA programs.
1st Order integration is found in the Mesh Options box under quality. The Draft option produces first order elements. High option produces 2nd order or higher – the default option. Integration beyond 2nd degree has to be chosen through the analysis properties window. 2nd order is the highest order available for shell elements.
Which elements will produce better results for a simple tension load? The sample problem below is worked out in both 1st and 2nd order elements.
For this problem with a simple stress distribution, both the 1st and 2nd order elements produce excellent results as the mesh changed from 1/4 to 1/16″ size.
Using the same model from sample #1, the 1 lb tension load is changed to a 1 lb sideways or bending load. The moment of inertia is bh^3/12 = 1/12 in^4. The distance from neutral axis is 0.5″. The moment at the sample point is 3 in*lbs . The expected stress at the sample point is Mc/I = 3*0.5/(1/12) = 18 psi.
The stress pattern in this bar is a simple linear distribution – but the 1st order elements do a lousy job of representing it. The second order elements did a good job, even at the coarsest mesh size.
The reported error in all cases is much higher than the real error. For example the reported stress for the 1st degree elements at 1/4″ mesh is 16.5131 psi, theoretical stress is 18 psi. The real error is 8.3%, but it is reported at 21.8%. This over estimation is true for all the reported errors.
Simple uniform or linearly varying stresses do not often show up in real world FEA problems. How do the 1st and 2nd order elements handle more complex stress patterns?
The 1st and 2nd order elements are both converging to the same stress value. The 2nd order models are getting to the end value much faster. The 2nd order result was obtained at 1/8″ mesh size when the error was reported at 2%. The 1st order elements have not got there at 1/32″ – and the reported error is above 2%. From the COSMOSWorks help files:
It is highly recommended to use the High quality option for final results and for models with curved geometry. Draft quality meshing can be used for quick evaluation.
The degree of freedom of the model is related to the computer resources required to solve the problem. In this case, the 1st order model did not reach the result with a DOF of 18,000, but the 2nd order study got there by DOF = 4,800, a much better use of computer resources and users time.
The same mesh quality issues apply to 3D as to the previous 2D studies. Here is a part with a round hole. With a coarse mesh size, the 1st order model only slightly looks round. The second order results look much better.
File: PVE4048, Last Updated: March 2010, By: LB
This solar reflector uses a vacuum to pull the front and back surfaces together to focus the reflective surface. The deflected surface shape can be calculated using FEA, but the correct shape can only be computed with large deflection theory.
For this sample, a 0.064″ thick 16ft diameter stainless steel reflector is focused with a 0.1 psi vacuum. This reflector is studied first with linear theory:
What went wrong? The linear theory assumes that the stiffness of the reflector does not change as its shape changes. As a result the only stress computed is a flat panel bending stress. In reality, the application of the vacuum changes the shape from flat to spherical. After a very small deflection, the membrane stress in the deflected spherical shape is much higher than any bending stress.
SolidWorks Simulation suggests using large displacement theory to solve the problem:
From the SolidWorks Simulation help files:
The linear theory assumes small displacements… This approach may lead to inaccurate results or convergence difficulties in cases where these assumptions are not valid… The large displacement solution is needed when the acquired deformation alters the stiffness (ability of the structure to resist loads) significantly… The large displacement solution assumes that the stiffness changes during loading so it applies the load in steps and updates the stiffness for each solution step.
This perfectly describes this reflector. The application of a very small vacuum changes the shape from a flat plate to a curved shape. The correct analysis is membrane not bending.
SolidWorks Simulation applies the pressure in steps. The stiffness of the membrane is recalculated after each step. The large displacement solution takes a lot longer to run.
Membrane stresses – the stresses are approximately those of a sphere (where the stress would be uniform across the whole surface).
A plot of the actual deflection vs the deflection for a true sphere shows that the shape is not truly spherical, which matches the membrane stress plot which shows a non uniform stress distribution. The linear theory plot is different in shape and magnitude.
The SolidWorks Simulation help file has useful information on using large displacement solutions.
File: PVE6438, Last Updated: Aug. 20, 2012, By: BTV
Design and analysis of flanges in SolidWorks simulation often requires the use of a half bolt connector. This feature is available from the “Connections” group in the simulation tree.
1. Start by creating a standard bolt connector, selecting the inside edges where the bolt will terminate.
2. Specified the bolt head diameter, shank diameter and the material.
3. Select the axial preload and enter the total bolt preload for a full bolt ignoring the fact that this is a 1/2 bolt.
4. Open the advance option and check the 1/2 symmetry option. Select a plane that indicates where symmetry is taken about. Do not select a face or bolt connector loads will not report for this connector. Certain geometry may require a plane to be created.
5. Export the bolt loads to a .csv file by right clicking the “Results” folder and selecting “List Pin/ Bolt/ Bearing Force”.
6. Open the .csv file and locate the 1/2 connectors (connector 1 for this example). The total applied preload is 100 lb. Note that the .csv export will show 50 lb axial force. Multiply all of these forces (Axial, Bending and Shear) by 2 before calculating bolt stresses. The von Mises bolt stress for this example should be equal for all bolts.
7. The deflections around the outside of the flange show that the bolt preloads applied create a uniform load. The full bolt connectors create the same deflection as the half bolt connectors.
The verification for 1/2 connector application can be seen in the deflection plot. The image below shows an incorrect method of applying a half connector. Note that the deflection is not radial around the outside of the flange. This indicates that the 1/2 connectors are not setup correctly.
When possible half connector should be avoided due to the affect they have on the global reaction forces. Half connectors often apply forces against the symmetry plane that cannot be accounted for. This prevents a user from checking that the applied loads equal the simulation resulting forces. These force do not have any adverse affects on the displacement or stress.
File: PVE3179, Last Updated: Dec. 13, 2008, By: LRB
Error plots show how well the complexity of a mesh matches the complexity of the deflections in a model. Once the mesh complexity matches the model complexity the reported error is low. As a guideline, Pressure Vessel Engineering uses 5% error as an acceptance criterion.
It is possible to get stresses below 5% in general vessel areas by applying an appropriate mesh size. This report covers two areas where the error cannot be lowered to reach this acceptance criteria regardless of the mesh size used. These areas are: 1) stresses in and around the head of a bolt and 2) stresses at surface to surface contacts.
Other areas also exist in pressure vessels where mesh refinement can not be used to reduce errors to this 5% acceptance level. These areas: weld fillets, diameter transitions, nozzles, flanges and support legs and lug attachements are beyond the scope of this article.
ASME VIII2 (2287 Ed.) sets the stress limits for bolts at locations away from the stress concentrations.
VIII2 5.7.2(a): The maximum value of service stress, averaged across the bolt cross section and neglecting stress concentrations, shall not exceed two time the allowable stress values in paragraph 3.A.2.2. of annex 3.A
VIII2 5.7.2(b): The maximum value of service stress, except as restricted by paragraph 5.7.3.1(b) [fatigue assessment of bolts] at the periphery of the bolt cross section resulting from direct tension plus bending and neglecting stress concentrations shall not exceed three times the allowable stress values in paragraph 3.A.2 of Annex 3.A
The bolts are studied at some location other than under the head. Large stresses concentrations are also created at the location where the bolt threads into its parent material (not shown in this model). This area will also show a high indicated error.
Last Updated: Aug 19 2015, By: LRB
The requirements for FEA reports are outlined in CSA B5114 annex J “Annex J (normative) Requirements regarding the use of finite element analysis (FEA) to support a pressure equipment design submission”. These requirements are mandatory to B51, but not universally accepted across Canada. At this date (Aug 2015) Alberta reviews are still done to ABSA AB520, a similar but not identical document. Some extracts from the B51 standard are included in blue below.
This analysis method requires extensive knowledge of, and experience with, pressure equipment design, FEA fundamentals, and the FEA software involved. The FEA software selected by the designer shall be applicable for pressure equipment design.
FEA programs are physics engines. We have found that any of the main commercially available programs are suitable for pressure vessel analysis. In particular we use SolidWorks Simulation and ABACUS, but others also work.
FEA may be used to support pressure equipment design where the configuration is not covered by the available rules in the ASME Code. The designer should check with the regulatory authority to confirm that use of FEA is acceptable. When this method is used to justify code compliance of the design, the requirements in Clauses J.3 to J.10 shall be met.
In general we find it acceptable to use FEA for design of non code items or portions of items. It is important to include code calculations for those portions of the vessel that are code calculable. On rare occasions a product is forced to be redesigned so that regular code sections can be used. This is discussed further here.
The FEA analysis and reports shall be completed by individuals knowledgeable in and experienced with FEA methods. The FEA report shall be certified by a professional engineer.
We sometimes get asked to provide a report of our experience. See our Contacts page where we have posted qualification resumes for our review engineers. For example, the resumes of Ben, Cameron and Matt
have been written to present qualifications for performing FEA and reviewing FEA reports.
For the sections J.4 through J.10 we refer to sample reports found in our FEA samples section. These reports are written to meet this or various previous provincial guidelines. Beyond this CSA guideline, our sample reports are also modified to answer common questions from CRN review engineers and customers.
The FEA report shall contain an executive summary briefly describing how the FEA is being used to support the design, the FEA model used, the results of the FEA, the accuracy of the FEA results, the validation of the results, and the conclusions relating to the FEA results supporting the design submitted for registration.
The report introduction shall describe the scope of the FEA analysis relating to the design, the justification for using FEA to support the design calculations, the FEA software used for the analysis, the type of FEA analysis (static, dynamic, elastic, plastic, small deformations, large deformations, etc.), a complete description of the material properties used in the analysis, and the assumptions used for the FEA modelling.
The report shall include a section describing the FEA model used for the analysis. The description shall include dimensional information and/or drawings relating the model geometry to the actual pressure equipment geometry. Simplification of geometry shall be explained and justified as appropriate. The mesh and type (h, p, 2D, 3D), shape, degrees of freedom, and order (2nd order or above) of the elements used shall be described. If different types of elements (mixed meshes) are used, a description of how the different elements were connected together shall be included. When shell elements are being used, a description of the top or bottom orientation with plots of the elements shall be included and shall indicate if they are thick or thin elements.
The model description shall include a list of all assumptions.
The turn angle of each element used on inside fillet radii shall be indicated.
The turn angle is simply the number of elements it takes to go around a circle. This Inventor support page explains the use of a turn angle. It is normal that a mesher needs around 8 elements to get around a circular hole which would produce a turn angle of 45 degrees per element. Decreasing the turn angle increases the number of elements and the accuracy of the FEA results, however not all areas of a model need to be highly accurate. The turn angle does not provide any predictive value, and the B51 standard provides no acceptance criteria. The use of an error plot as discussed in J.6.8 below is a much more useful measure of mesh and results quality.
The method used to select the size of mesh elements with reference to global or local mesh refinement shall be indicated.
We use the error plot to determine if the mesh is adequately refined. Beyond the scope of this standard, it is important to realize that pressure vessels have areas of discontinuity where in theory the stress approaches infinity as the mesh size is decreased. In practice the vessel experiences stresses above the yield point. Refer to our sample jobs for linearization analysis that can deal with stresses approaching infinity.
When items in contact (e.g., flange joints, threaded joints) are modeled, the model shall describe how two separate areas in contact are linked. Adequate mesh size shall be used to ensure that the elements are small enough to model contact stress distribution properly.
Boundary conditions, such as supports, restraints, loads, contact elements, and forces, shall be clearly described and shown in the report (present the figures). The method of restraining the model to prevent rigid body motion shall also be indicated and justified. When partial models are used (typically based on symmetry), the rationale for the partial model shall be described with an explanation of the boundary conditions used to compensate for the missing model sections.
The FEA report shall include validation and verification of FEA results. Validation should demonstrate that FEA results correctly describe the reallife behavior of the pressure equipment, and verification should demonstrate that a mathematical model, as submitted for solution with FEA, has been solved correctly.
Verification is as simple as comparing the reaction forces from the FEA run with the theoretical loads that can be calculated at the boundary conditions. What is acceptable for validation varies by reviewer. Rarely FEA runs must be provided that predict burst test results. Occasionally strain gauge testing or displacement testing must be provided that can be run against a standard non destructive hydrotest. Other methods used are comparing Roark’s predicted radial displacement of a shell with the results of a model run. Most commonly, it is recognized that a FEA run that meets the other requirements of this standard is far more accurate than other available methods of study so no further physical testing proof is required.
The accuracy of the FEA results shall be included in the FEA report, either by the use of convergence studies or by comparison to the accuracy of previous successful inhouse models. An error of 5% or less from the convergence study shall be acceptable.
Note: FEA inaccuracy usually consists of discretization errors, which result from matching geometry and displacement distribution due to the inherent limitation of elements, and computational errors, which are roundoff errors from the computer floatingpoint calculation and the formulations of the numerical integration scheme.
A convergence study only proves that a single point of a model has converged, whereas an error plot proves a whole model, and does not required multiple FEA runs. As mentioned in J.6.4 we use error plots to prove convergence. Again as mentioned above, not all areas of a pressure vessel model converge, the areas that do not require special study that cannot be handled by convergence studies. These areas are usually handled by Linearization as outlined by ASME VIII2 part 5.
The criteria for acceptance of the FEA results shall be based on the code of construction and factor of safety established under that code. The FEA methodology may be based on another code. The acceptance criteria and code reference shall be presented in the report.
Note: For example, if the code of construction is Section VIII, Division 1, of the ASME Code, the allowable stress values are from Section VIII, Division 1, of the ASME Code. The FEA methodology could be based on Section VIII, Division 2, of the ASME Code (Figure 5.1).
The following information and figures in colored prints shall be presented:
(a) resultant displacements (plot);
(b) deformed shape with undeformed shape superimposed;
(c) stress plot with mesh that
(c)(i) shows fringes using discrete color separation for stress ranges or plots; and
(c)(ii) allows comparison between the size of stress concentrations and the size of the mesh;
(d) plot with element stress and a comparison of nodal (average) stress vs. element (nonaveraged) stress;
(e) reaction forces compared to applied loads (freebody diagrams);
(f) stress linearization methodology and the stress values in the area of interest; and
(g) accuracy of the FEA results.
The results shall be plotted to graphically verify convergence. The x axis of this plot shall show some indication of mesh density in the area of interest (number of elements on a curve, elements per unit length, etc.). This is necessary to show true convergence over apparent convergence that is due only to a relatively small change in the mesh.
When plots or figures are presented, an explanation relating to each figure shall be included to describe the purpose of the figure and its importance.
Overall model results, including areas of high stress and deformation, shall be presented with acceptance criteria. The analysis shall include a comparison of the results with acceptance criteria.
Results that are to be disregarded shall be identified, and the determination to disregard them shall be justified.
As a minimum, the conclusion shall include
(a) a summary of the FEA results in support of the design;
(b) a comparison of the results and the acceptance criteria; and
(c) overall recommendations.
In the balance, these provincial requirements leading up to and including the CSAB51 Annex J have been beneficial to the Canadian pressure vessel industry, even creating interest beyond the Canadian market. Many have experienced the frustration of being shown a couple of FEA screen shots and being told that a product is good. This standard is a significant improvement that outlines some valuable practices.
The other side must be considered as well. The people who wrote the standards leading up to this one are not FEA practitioners, and it shows. A real FEA report must follow the practices of ASME VIII2 Part 5 and PTB3. For example, the stress plots asked for in B51 are pretty, but that is not how pressure vessels are correctly analysed. Other problems also exist. Before other markets use this standard, or one derived from it, This annex J should be upgraded to match current ASME requirements.
This standard also gets used as a check list for reviewers without pressure vessel FEA experience to approved or reject FEA reports for CRN acceptance, a practice I do not support. FEA is too complex to review with a simple check list.
Last Updated: Oct. 20, 2008, LB
This article supplements ABSA’s (Alberta Boilers Safety Association) requirements on writing FEA reports: ABSA FEA Requirements. In particular refer to the section “Presentation of Results”. This report is based in part on these ABSA requirements and in part on our experience at Pressure Vessel Engineering Ltd.
Pressure Vessel Engineering uses SolidWorks Simulation for Finite Element Analysis. It is expected that these results would also be applicable to other FEA programs.
The ABSA FEA guideline has specific requirements for the Presentation of Results: The following figures must be presented (colored prints)
When plots or figures have been presented, there must be [a]discussion relating to each and every figure to explain what is the purpose of the figure and why it is of importance.
This image was captured using SnagIt at 952 x 540 pixels and shrunk by word to 60% of its original size to fit the page. The extra pixels provide good resolution for prints. Two images this size will fit on a page with space left over for captions. Have pity on the reader – do not try to fit more than 2 images on one page.
Here the background color has been set to R256, G256, B240. This is a light straw yellow that stands out slightly from a white page. The background color is set at Tools/Options/colors/Viewport background/Edit/custom colors .
A deformed model can make it easier to understand the stress results. However, it makes sense to choose a rational number. Here the scale has been set to 150x.
The Show max option allows the legend to be rescaled to whole numbers (here 30,000 psi instead of 35,700 psi). Rescale the graph from 0 (or negative numbers when justified). Change to floating format, only show decimal points for small numbers like displacement graphs – scientific format numbers are harder to understand. Choose a logical number of colors so that the legend shows whole numbers – here 10 colors are used.
The superimposed plot makes more sense on a deformation plot then on a stress plot.
Turn off unnecessary items like loads/restraints that have already been discussed.
Show at least one overall view and closeups as required. Have pity on the reader who can not enlarge or spin your model on the printed page!