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What is Finite Element Analysis (FEA)?

 

Finite Element Analysis (FEA) is used to solve engineering problems that are too complex to be handled using the traditional mathematically closed form solutions.

 

According to my course notes from university: "the finite element method is a numerical method used to find an approximate solution for such complicated problems which involve irregular domains and difficult boundary and load conditions." In broad terms, a static analysis involves breaking the complex structure down into simpler elements, which are then solved as part of the whole. Stresses and displacements are some of the outputs based on applied loads and boundary conditions.

 

For CRN applications, the Finite Element method can be used when the component falls outside of the Code's standard configurations. UG-101(b), for determining MAWP using proof tests, gives guidelines that can be generally used to determine when an FEA would be permitted:

 

"The tests in these paragraphs may be used only for the purpose of establishing the maximum allowable working pressure of those elements or component parts for which the thickness cannot be determined by means of the design rules given in this Division."

ASME VIII-1, 2007 Ed, 2008 Add, UG-101(b)

 

FEA Examples
FEA Articles
Trip-Clamp Sanitary Fitting
This Tri-clamp connection is designed to comply with ASME B31.3-2008. It is an unlisted component because of its shape, hence the ASME VIII-1 Appendix-24 (24-1(b)) cannot be used to validate it. Two options remain for determining the MAWP:
1. A burst test per UG-101(m)
2. Finite Element Analysis (FEA) per ASME VIII-2, Part 5

The Tri-Clamp can be qualified using Option 2 under ASME B31.3 304.7.2(d).

Allowable stress should be taken from ASME B31.3 Table A-1 in place of the allowable stress from ASME VIII - II, Part 5.   

Here is a sample FEA report for the Tri-Clamp connection:
Sample Tri-Clamp Report (1.2 MB)
Finite Element Analysis (FEA) is used to investigate reasons why ASME VIII-1, FIG.UW-13.2, does not permit certain joint configurations for the attachment of welded unstayed flat heads:
1.
Joint Orientation: The eccentrically attached weld allows the joint to open under pressure.
2.
Fatigue Life: The peak stress created at the weld root limits the fatigue life.
3.
Weld size: The weld size is insufficient to satisfy the Code’s geometric requirements

To open sample discussion paper,
click here. (3.5 Mb)

Figure 1: Weld Examination

Figure 2: Weld Analysis by FEA
The weld shown in Figure 1 failed during a cyclic loading test. The subsequent investigation involved:

1. Weld Examination: The specimen was cut perpendicular to the weld, as shown in Figure 1, to view the weld at different locations. The vessel's shape made it impossible to use NDE methods such as X-Ray. The fracture has been darkened for emphasis.

2. Stress Analysis: The most plausible failure mechanism was determined to be fatigue failure. This conclusion was confirmed by a cycle-life prediction using stress values generated from the FEA (Figure 2).

3. Physical Testing: Similar vessels were pressure-tested to further confirm the theoretical results found in Step 2.

4. Design Revisions: The proposed design solutions mitigated the effect of cyclic loading.
Nozzle with ratio Rn/R > 0.7, requires additional verification per Appendix 1-7(b)(1)(c). Finite Element Analysis allowed per U-2(g).

Figure displays: Fatigue Calculation. Operating case run to compute the extreme operating stress state to be used in the shakedown and peak stress calculations
FEA and ASME
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