fea validation release rev1

8/8/2019 FEA Validation Release Rev1

http://slidepdf.com/reader/full/fea-validation-release-rev1 1/9

Pressure Vessel Engineering Ltd. provides: ASME Vessel Code Calculations - Finite ElementAnalysis (FEA) - Solid Modeling / Drafting - Canadian Registration Number (CRN) Assistance

Disclaimer: This document is provided for educational purposes only. Pressure Vessel EngineeringLtd. is not liable for its use.

Finite Element Analysis Validation – COSMOSWorks 2008 x64 SP5.0

Pressure Vessel Engineering Ltd. validates each release of Cosmos Designer with a simplevalidation set to confirm that the program produces results comparable to Roark’s Formulas

results. Roark’s formulas provide the exact derivation of the stresses of components of different

geometry under several loading conditions. These formulas can be compared with FEA results.

Figure 1A provides the formulas for stresses in a heavy wall cylindrical disk or shell with ends

caped and uniform internal pressure applied.

Figure 2A provides the formulas for stresses in a heavy wall spherical head with uniform internal

pressure.

A test case is run and these (2) examples are calculated and compared in the following pages.

Fig 1A – Roark’s formulas for stress in a heavy wall pipe

Fig 2A – Roark’s formulas for stress in a heavy wall sphere



FEA Validation Release Rev.1.doc - of 7

The geometry shown in Fig 1B is used for the heavy wall pipe & sphere comparison. The same

geometry will be calculated by Roark’s formulas and run in COSMOSWorks FEA.

A split line is added to the model as shown in Fig 1C, this provides nodes at the midplane to

probe so that stresses at the mid point may also be analyzed and compared to Roark’s formulasresults.

Fig 1B – Test Case Geometry

Fig 1C – Test Case Geometry

Pipe Test Points

Sphere Test Points

Split lineSplit line




Fig 1D shows symmetry boundary conditions applied to all faces, with the exception of (1) endof the pipe. An exit pressure force equal to the exit area of the pipe multiplied by the internal

pressure is applied to this face (7.068in^2)*(1000psi) = 7068lb. 1000 psi is applied to allinternal surfaces.

Fig 1E shows the resulting error plot for a ¼” mesh applied. Reported error is below 5% for the2nd order elements used. All nodes at test locations (in following pages) report error of less than

0.5%.

Fig 1D – Boundary Conditions & Loads Applied

Exit Pressure Force

Fig 1E – Mesh & Error Plot

Exit Pressure Area= 7.068 in^2

Pipe Test Points

Sphere Test Points




Fig 1H – Probe of Sz Stresses of pipe (Hoop)

Fig 2B – Probe of Sy Stresses (Equal to Sz) of sphere




The FEA results are compared to the results from Roark’s formulas on the following pages. Allresults are extremely close to the theoretical values.

Conclusion: The FEA program provided results very close to the exact theoretical derivationprovided by Roark’s formulas. The maximum difference between Roark’s and FEA is 0.8% for

this test section.

Fig 2C – Probe of Sx of sphere




Validation

For each version of Cosmos Designer released and used in Pressure Vessel Engineering Ltd’soffice, the 8” OD x 6” ID test specimen will be identically meshed and run. The difference

reported between COMOSWorks and Roark’s will be expected to be less than 1.0% for the

release to be accepted.

The release will be used once this validation is complete.

Job: PVE-3179

Test Shape: Verification Shape 3.sldprt

Excel File: COSMOSWorks Validation Calculations Rev.0.xls

Signoff:

_______________________ CosmosWorks Version

_______________________ Validated by

_______________________ Date



1 Heavy Wall Stress FEA Sample - ver 4.00 Page 1 of 1

2 FEA Inputs:

3 description

4 4.000 a [in] - Outside radius

5 3.000 b [in] - Inside radius

6 1,000.0 q [psi] - Inside pressure

7 r [in] = (a+b)/2 ~~ radius at mid thickness (4+3)/2 = 3.500

8 Maximum Stress Values:

9 s1max = q*b^2/(a^2-b^2) 1000*3^2/(4^2-3^2) = 1285.7

10 s2max = q*(a^2+b^2)/((a^2-b^2)) 1000*(4^2+3^2)/((4^2-3^2)) = 3571.4

11 s3max = -q -1000 = -1000.0

12 Stress at inner radius b (measured, calculated and compared):

13 1,285.0 mS1b [psi] - measured stress Sx on model

14 3,577.0 mS2b [psi] - measured stress Sz on model

15 -997.0 mS3b [psi] - measured stress Sy on model

16 s1b = q*b^2/(a^2-b^2) 1000*3^2/(4^2-3^2) = 1285.7

17 s2b = q*b^2*(a^2+b^2)/(b^2*(a^2-b^2)) 1000*3^2*(4^2+3^2)/(3^2*(4^2-3^2)) = 3571.4

18 s3b = -q*b^2*(a^2-b^2)/(b^2*(a 2̂-b^2)) -1000*3^2*(4^2-3^2)/(3^2*(4^2-3^2)) = -1000.0

19 Check_sb1 = abs((s1b-mS1b)/s1b) ABS((1285.7-1285)/1285.7) = 0.056%


21 Check_sb3 = abs((s3b-mS3b)/s3b) ABS((-1000--997)/-1000) = 0.300%

22 Stress at mid radius r (measured, calculated and compared):

23 1,286.0 mS1r [psi] - measured stress s1 at the mid radius

24 2,965.0 mS2r [psi]

25 -392.0 mS3r [psi]

26 s1r = q*b^2/(a^2-b^2) 1000*3^2/(4^2-3^2) = 1285.7

27 s2r = q*b^2*(a^2+r^2)/(r^2*(a^2-b^2)) 1000*3^2*(4^2+3.5^2)/(3.5^2*(4^2-3^2)) = 2965.0

28 s3r = -q*b^2*(a^2-r^2)/(r^2*(a^2-b^2)) -1000*3^2*(4^2-3.5^2)/(3.5^2*(4^2-3^2)) = -393.6

29 Check_sr1 = abs((s1r-mS1r)/s1r) ABS((1285.7-1286)/1285.7) = 0.022%

30 Check_sr2 = abs((s2r-mS2r)/s2r) ABS((2965-2965)/2965) = 0.000%

31 Check_sr3 = abs((s3r-mS3r)/s3r) ABS((-393.6--392)/-393.6) = 0.403%

32 Stress at outer radius a: 33 1,286.0 mS1a [psi] - measured stress s1 at the outer radius

34 2,572.0 mS2a [psi]

35 1.0 mS3a [psi]

36 s1a = q*b^2/(a^2-b^2) 1000*3^2/(4^2-3^2) = 1285.7

37 s2a = q*b^2*(a^2+a^2)/(a^2*(a^2-b^2)) 1000*3^2*(4^2+4^2)/(4^2*(4^2-3^2)) = 2571.4

38 s3a = -q*b^2*(a^2-a^2)/(a^2*(a 2̂-b^2)) -1000*3^2*(4^2-4^2)/(4^2*(4^2-3^2)) = 0.0

39 Check_sa1 = abs((s1a-mS1a)/s1a) ABS((1285.7-1286)/1285.7) = 0.022%


COSMOSWorks 2008 x64 SP5.0 Validation



1 Heavy Sphere Stress FEA Sample - ver 4.00 Page 1 of 1

2 FEA Inputs:

3 description

4 4.000 a [in] - Outside radius

5 3.000 b [in] - Inside radius

6 1,000.0 q [psi] - Inside pressure

7 r [in] = (a+b)/2 ~~ radius at mid thickness (4+3)/2 = 3.500

8 Maximum Stress Values:

9 s1max = ((q/2)*(a^3+2*b^3))/(a^3-b^3) ((1000/2)*(4^3+2*3^3))/(4^3-3^3) = 1594.6

10 s2max = ((q/2)*(a^3+2*b^3))/(a^3-b^3) ((1000/2)*(4^3+2*3^3))/(4^3-3^3) = 1594.6

11 s3max = -q -1000 = -1000.0

12 Stress at inner radius b (measured, calculated and compared):

13 1,597.0 mS1b [psi] - measured stress Sx on model

14 1,597.0 mS2b [psi] - measured stress Sz on model

15 -992.0 mS3b [psi] - measured stress Sx on model

16 s1b =

17 1594.6

18 s2b =

19 1594.6

20 s3b =

21 -1000.0



24 Check_sb3 = abs((s3b-mS3b)/s3b) ABS((-1000--992)/-1000) = 0.800%

25 Stress at mid radius r (measured, calculated and compared):

26 1,275.0 mS1r [psi] - measured stress s1 at the mid radius

27 1,275.0 mS2r [psi]

28 -360.0 mS3r [psi]

29 s1r =

30 1274.4

31 s2r =

32 1274.4

33 s3r =

34 -359.5



37 Check_sr3 = abs((s3r-mS3r)/s3r) ABS((-359.5--360)/-359.5) = 0.126%

38 Stress at outer radius a:

39 1,095.0 mS1a [psi] - measured stress s1 at the outer radius

40 1,095.0 mS2a [psi]

41 1.0 mS3a [psi]

42 s1a =

43 1094.6

44 s2a =

45 1094.6

46 s3a =

47 0.0



COSMOSWorks 2008 x64 SP5.0 Validation

(q*b^3/(2*b 3̂))*((a^3+2*b^3)/(a^3-b^3))

(1000*3^3/(2*3^3))*((4^3+2*3^3)/(4^3-3^3)) =

(q*b^3/(2*b 3̂))*((a^3+2*b^3)/(a^3-b^3))

(1000*3^3/(2*3^3))*((4^3+2*3^3)/(4^3-3^3)) =

(-q*b^3/(b^3))*((a^3-b^3)/(a^3-b^3))

(-1000*3^3/(3^3))*((4^3-3^3)/(4^3-3^3)) =

(q*b^3/(2*r 3̂))*((a^3+2*r^3)/(a^3-b^3))

(1000*3^3/(2*3.5^3))*((4^3+2*3.5^3)/(4^3-3^3)) =

(q*b^3/(2*r 3̂))*((a^3+2*r^3)/(a^3-b^3))

(1000*3^3/(2*3.5^3))*((4^3+2*3.5^3)/(4^3-3^3)) =

(-q*b^3/(r^3))*((a^3-r^3)/(a^3-b^3))

(1000*3^3/(2*4^3))*((4^3+2*4^3)/(4^3-3^3)) =

(-q*b^3/(a^3))*((a^3-a^3)/(a^3-b^3))

(-1000*3^3/(4^3))*((4^3-4^3)/(4^3-3^3)) =

(-1000*3^3/(3.5^3))*((4^3-3.5^3)/(4^3-3^3)) =

(q*b^3/(2*a 3̂))*((a^3+2*a^3)/(a^3-b^3))

(1000*3^3/(2*4^3))*((4^3+2*4^3)/(4^3-3^3)) =

(q*b^3/(2*a 3̂))*((a^3+2*a^3)/(a^3-b^3))

fea validation release rev1

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