A Step by Step Introduction to FEA

File: Sample 6, Last Updated: June 16, 2010, LB

Why FEA?

Pressure vessel code rules exist for the analysis of simple objects like pipes and heads and more complex objects like flanges and nozzles. Where the code rules exist, they have to be used. However, most code rules do not calculate real stresses. The best they can do is provide pass/fail acceptance criteria. Code rules do not exist for many pressurized objects.

Finite Element Analysis (FEA) provides a method of analyzing complex geometry, and when the results are interpreted correctly, pass/fail criteria can be determined. Because the FEA calculates stresses, the results can also be used to predict a cycle life.

This sample is a simple manifold block. A simplified description of the FEA process follows. The report linked at the bottom of the page has these and other pictures and more in depth analysis. This is a step by step description of the process used in the analysis.

Sample6_ManifoldBlock

Other samples on our web site show more complex analysis involving multiple bodies connected with bolting, studies with thermal stresses, and objects with higher stresses where the interpretation of stresses to code rules is more difficult.

Step 1 – Create a solid model of the object

Sample6_ExplodedView

A solid model of the manifold block has been created. The manifold has a series of pipe thread ports. The manifold will have pipes attached in service so here pipes have been added to the model to simulate the loads that they generate. Many of the model shots that follow have the pipes hidden. The stress in the pipes is not a concern in this report.

At PVEng we use SolidWorks to make the solid model.

Step 2 – Check the Drawing

Check_Drawing

The first quality control step is to create a drawing from the solid model. Once dimensioned, the drawing can be compared to the original part for accuracy.

Step 3 – Mesh the model

Sample6_Mesh

The FEA program divides the solid model into small regular shapes – here 3 sided pyramids are used. Although no stress formula exists for the complex manifold shape, formulas do exist for the small pyramids. The FEA program can calculate the deformation (and then stresses) in each small simple pyramid and combine the results for the overall complex object deformation (and stress).

At PVEng we use SolidWorks Simulation to do the meshing and the following stress analysis. Here SolidWorks has meshed the manifold and pipes into 290,000 solid pyramids each approximately 1/8″ on a side.

Two material properties for the SA-479 316 stainless material are required 1) the modulus of elasticity (28,000,000 psi) and 2) Poisons ratio (0.27). SolidWorks uses this information to calculate how much each element deforms under load, and from that, what the stresses of the elements will be. The code allowable stress for this material is 20,000 psi.

Step 4 – Apply Loads and Restraints

Sample6_ApplyLoad_1

The manifold and all pipes are pressurized on the inside. Here a pressure of 300 psi is applied to the inside of all the manifold and pipe surfaces.

Sample6_ApplyLoad_2

One pipe has no cap. It is fixed to anchor the whole model. This location will have zero displacement and reaction forces will be created here.

More complex models can have many more boundary conditions, and if they are symmetrical, can be split in half to reduce the run time. Here the manifold is not symmetric, so the model has not been split in half.

Step 5 – Run the Model with 2 Quality Checks

Sample6_Error_Plot

SolidWorks Simulation calculates the displacement and stress for each element (pyramid) in the model. But before looking at the results, some quick quality checks: firstly quality check #2 – check the error plot for elements with potentially high errors.

The zones of high error (>5% for pressure vessels) are limited to areas where the shape of the model is rapidly changing (sharp edges or tight radii or other changes in shape known as discontinuities). All large areas have less than 5% error therefore the 1/8″ mesh is acceptable (a courser mesh could have been used for this model).

The presence of elements with >5% error highlights a fact of life: FEA never produces perfect results “All FEA results are wrong” but with good techniques, the results can be very good and very useful.

Sample6_Balance_Model

We are anxious to get to the stress results, but first, quality check #3 – check the reaction forces. In theory, the anchored end of the pipe creates a force equal to the inside area of the pipe x the pressure – here 3.36in^2 x 300psi = 1008 lbs (imagine the pipe exploding with this force if it was cut). This matches the FEA reaction force for the model at 1009.6 lbs and indicates a very good run.

This simple quality control check is extremely powerful for catching models with improper anchoring or missed pressurized areas or other wrong loads.

Step 6 – Quality Check – Displacement Plots

Sample6_Check_Displacement

SolidWorks Simulation calculates the displacement of the model and then from that the stresses. It follows that if the displacement results are bad, so are the stress results.

Quality check #4 – check the displacement plot. This is the last quality check before getting to the stresses! Here the displacement of the model is magnified 500x. The model is stretching longer. It is bulging out around the large internal passage. The attached pipes are expanding. All of this makes sense – the stress results should make sense too.

Step 7 – Stress Results

Sample6_Stress_ResultsCOSMOS converts the deformation results into stress results. The stresses can be seen to be higher in areas that have more local deformation. The stress in every location of this model is below the code allowable membrane stress so it passes.

Higher stressed models will have stresses up to 3-4x nominal code allowables – but limited to small areas. The art of pressure vessel FEA is interpreting when these areas of high stress are acceptable. This is often the hardest part of FEA.

Step 8 – The Report

Pressure vessel calculations and FEA results are usually reviewed by Authorized Inspectors and/or third party engineers. At this time (May 2013) four provinces have differing requirements for writing a FEA report. See here for more details. Our web site has many more samples written to meet these guidelines.

Converting the results of a visual medium like FEA to a printed report is always challenging. It is important not to underestimate the challenge involved in writing a report to meet these varying requirements, and to meet various reviewers views on what these requirements really mean. It is not unusual for writing the report to take half of the total project time.

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