Korea Engineering Consulting, Inc

Korea Engineering Consulting, Inc.FEA(유한요소해석) Procedures for Pressure Vessel

based on ASME/PD5500/FFS

January 1, 2008

Korea Engineering Consulting, Inc.FEA(유한요소해석) Procedures for Pressure Vessel

based on ASME/PD5500/FFS

January 1, 2008

2/41Korea Engineering Consulting, Inc.

Ⅰ FEM PROCEDURES

Ⅱ STRESS CRITERIA

Ⅲ STRESS LINERIZATION

Ⅳ IMPERFECTION VESSEL


▣ 가상공간 SIMULATION

1 단계 : 전처리(Pre/Processor) - 2D/3D 유한요소모델, 하중/경계조건, 재질,,,.

2 단계 : 연산(Numerical Solver)-열전달, 진동, 정력학, 크랙/파괴,,,.

3 단계 : 후처리(Post/Processor)-응력, 피로, 크랙, 변형결과분석,,,.


▣ 가상공간 COMPUTER CAE

도면의치수입력 : CAD기능(1) 도면,강도계산치수입력(2) 부식고려(3차원:두께, 2차원:I.D)

하중입력(1) 자중, 내압, 온도,Vacuum, Wind, Seismic, Nozzle하중

경계조건(1) Leg, Saddle, Lug : 기기설계특성(방향별Fixed/Free결정)

재질특성(1) 탄성계수, 포이승비, 열전달계수, 열팽창계수


▣ 3차원 H/E FE MODEL

Fixed(축방향고정) Sliding(축방향이동)

요소/압력/자중/두께/재질

경계조건


▣ FEM PROCEDURES(1)

1. 유한요소모델링(FEM, Finite Element M.)

-. 2차원축대칭. Main Shell, Top/Bottom Head, Skirt Support to HeadConical Shell, Internal Support Ring, Hot Box, Girth FlangeTop and Bottom Nozzle,,,.

-. 3차원(Shell/Solid) . 2차원축대칭해석불가경우적용(모델/하중조건,,,.). Thin Shell(R/T > 10), Thick Shell/Solid(R/T < 10). Nozzle, Lifting Lug, Trunnion Lug, Clip, Saddle Support,Support Lugs,,,.


THIN/THICK SHELL STRESS

Thin Shell = (R/t) > 10Stress : S1 > S2 > S3• Circumferential Stress(Hoop Stress, S1)S1 = (pd/2t)

• Vertical Stress(S2)S2 = (pd/4t)

• Radial Stress(S3) = -p/2• Stress Intensity = 2[(S1-S3)/2]Thick ShellStress Intensity=2[pro2/(ro2-ri2)]

S1

S2

S3

Thin Shell


ASME STRESS CRITERIA

• Div.1 : Normal Principal Stress(주응력이론)Design=Maximum Stress|S1, S2 , S3 |,Six StressesS1/S2/S3(First/Second/Third Principal Stress)

• Div.2 : Maximum Shear Stress(최대전단응력)Design=Maximum Stress| S1- S2, S2- S3, S3- S1|/2Stress Intensity : twice the Maximum ShearASME, Sec.VIII, Div.2, Appendix 4 for Stress AnalysisASME, Sec.VIII, Div.2, Appendix 5 for Fatigue AnalysisFEA적용시응력평가기준은 Div. 공사기준으로적용Div.1 = Allowable Stress, Div.2 = Stress Intensity

• Div.3 : High Pressure-Virtual Crack/FractureLBB/F(Leak-Before-Burst/Break/Fracture)


2D FE MODEL SAMPLE(1)

축대칭유한요소Mesh



TUBE BUNDLE

TUBESHEET

TUBESHEET HUB

TOP HEMI-HEAD

SKIRT SUPPORT



축대칭

내압

Radial Direction : FreeVertical Direction : Fixed(경계조건)

HOT BOX

INSULATION










▣ FEM Procedures(2)

→ →

2. 요소의특성및주의-. 요소의정도순서.정사각형→직사각형(응력1:3,가로:세로비율), 변형(1:6~8)→사다리형상→ 정삼각형(내각 60°) →직삼각형(120°<T<60°)

.응력의집중발생및구조형상에따라요소형상및비율결정

.삼각형요소사용금지(응력집중부위) -응력이크게발생



3. 요소의특성에따른응력분석-. FEA의응력에는향상 Peak Stress가포함된응력> Peak Stress. 기기수명에영향을주는응력. 기기주설계(Design)에적용되는응력이아님(이응력제외설계)

> FEA 응력분석(허용응력초과분석방법). 상기 Peak 응력이포함된응력산출되기때문에허용응력이초과해도문제가있는기기인지는 SLM을이용응력재분석

. 설계의기본은탄성기준이나하중/응력의발생조건에따라소성분석(Simplified Plastic Analysis)으로피로수명의계산가능

> Peak Stress를제거하기위한 FE Model. 2차원축대칭모델(Axisymmetric Model). 3차원입체(Solid Model) . 3차원쉘(Shell)은불가능(실형상두께가구현된 FE Model 만가능)

> Peak Stress 발생예상 : 구조가변단(Discontinuity)이되는부분


FEM STRESS LINEARIZATION(응력선형화)

SCL(Stress Classification Line)

Internal PressureInternal Support Ring

Cylindrical Shell

Membrane Bending Peak

Thickness

Stress

Linearized Membrane and Bending Stress Distribution

Linearized Membrane

Computed Stress Resultsfrom FEA(Finite Element Analysis)



-. 축에대한두께방향-. 요소의방향은두께방향에직각



SCL 1SCL 2



-----------------------------LINEARISED STRESS COMPONENTS-----------------------------

SXX SYY SZZ SXY SYZ SXZMEMBRANE

1.079E+01 4.039E+01 -1.635E+01 -2.096E+01 0.000E+00 0.000E+00

BENDING1.792E+01 7.219E+01 2.666E+01 -3.804E+01 0.000E+00 0.000E+00

Total At: 0.00E+002.871E+01 1.126E+02 1.030E+01 -5.900E+01 0.000E+00 0.000E+00

Total At: 5.06E+01-7.128E+00 -3.179E+01 -4.301E+01 1.708E+01 0.000E+00 0.000E+00

---------------------------------------------------------------PRINCIPAL STRESSES CALCULATED FROM LINEARISED STRESS COMPONENTS---------------------------------------------------------------

SIGMA1 SIGMA2 SIGMA3MEMBRANE 5.1252E+01 -6.4784E-02 -1.6351E+01TOTAL AT 0.000E+00 1.4303E+02 1.0305E+01 -1.7348E+00TOTAL AT 5.059E+01 1.6061E+00 -4.0527E+01 -4.3007E+01

---------------------------------------------------------------STRESS INTENSITIES CALCULATED FROM LINEARISED STRESS COMPONENTS---------------------------------------------------------------MEMBRANE 6.7603E+01TOTAL AT 0.000E+00 1.4476E+02TOTAL AT 5.059E+01 4.4613E+01===============================================================

FEM SCLPm=70.54 > 67.603PL+Pb=157.6 > 144.76PL+Pb=46.9 > 44.61 5~8%감소



-----------------------------LINEARISED STRESS COMPONENTS-----------------------------SXX SYY SZZ SXY SYZ SXZ

MEMBRANE-2.082E+00 4.902E+01 4.123E+01 -5.191E+00 0.000E+00 0.000E+00

BENDING6.266E+00 1.658E+01 5.011E+00 2.626E+00 0.000E+00 0.000E+00

Total At: 0.00E+004.184E+00 6.561E+01 4.624E+01 -2.565E+00 0.000E+00 0.000E+00

Total At: 4.60E+01-8.348E+00 3.244E+01 3.622E+01 -7.818E+00 0.000E+00 0.000E+00

---------------------------------------------------------------PRINCIPAL STRESSES CALCULATED FROM LINEARISED STRESS COMPONENTS---------------------------------------------------------------

SIGMA1 SIGMA2 SIGMA3MEMBRANE 4.9547E+01 4.1230E+01 -2.6039E+00TOTAL AT 0.000E+00 6.5714E+01 4.6241E+01 4.0775E+00TOTAL AT 4.600E+01 3.6218E+01 3.3890E+01 -9.7952E+00

---------------------------------------------------------------STRESS INTENSITIES CALCULATED FROM LINEARISED STRESS COMPONENTS---------------------------------------------------------------MEMBRANE 5.2151E+01TOTAL AT 0.000E+00 6.1637E+01TOTAL AT 4.600E+01 4.6013E+01

FEM SCLPm=54.66 > 52.15PL+Pb=83.94 > 61.63PL+Pb=47.06 > 46.01 0~25%감소



Peak Stress at corner radius area



4. 하중/경계조건-. 기기의 Operating 조건과구조특성기준결정

> Loading Conditions. 내압/외압, 자중, 노즐하중, 온도, Wind/Seismic, 볼트,,,.

> Support. Saddle/Skirt/leg/Lug Supports. 각각 Support 부분에각방향성자유이동을위해 Slot등의 Hole 확인.예) Sliding Side Saddle Support (축방향, Longitudinal Free)확인

Skirt Support : Radial Direction : Free. 각각해석 Part에따라구조특성에맞는경계조건을 Engineer가결정

5. 기기의기계적성질> 탄성계수, 포이승비, 열전달계수, 열팽창계수


▣ NUMERICAL SOLUATION

(1) 정역학해석(Static Analysis)(2) 열전달해석(Heat Analysis)(3) 열응력/충격해석(Thermal Stress/Shock Analysis)(4) Seismic Responses(5) Wind Induced Vibration-Fatigue(6) Natural Frequency (7) FPSO(Floating Production Storage & Offloading)

Wave Propagation Motion에따른 Fatigue Analysis


▣ ALLOWABLE STRESS CRITEIRA

1) Allowable Criteria(1) Design Code Div.1:

-. Div.1 Allowable Stress(S) / Maximum Principal(2) Design Code Div.2:

-. Div.2 Stress Intensity(Sm) / -. Stress Intensity : Maximum Shear Stress×2 times

2) Stress Analysis Direction(1) Stress : Tension/Compressive Stresses(좌굴)(2) Fatigue/Creep/Plastic Analysis/Crack-Fracture,,,.


▣ ALLOWABLE STRESS CRITERIA

3) Peak Stress제거(Stress Linearization Method)(1) 축대칭/3차원입체 Solid Model : 가능(2) 축대칭및 3차원 Shell Model : 불가

4) Stress Concentration Factor(SCF)5) Stress Reduction Factor(FRF)


▣ BUCKLING STRESS CRITERIA

1) Internal : Load-Stress Curve(linear)

2) External : ASME, Theoretical Buckling ASME : Stress-Strain Curve(log-log)

( )

ThicknesstCylindertheofradiusOutsideR

StrainAtRA

o

o

::

:

125.0=

ModuluesElasticEStresseCompressivAllowableB

AEB

::

2=

( )tREFuncTheretical

ocr

6.0.

=σ

( ) ( )tRE

tREB

Oo0625.016 ==

10 Times Safety


▣ FFS(API579), 적정성평가

• Weld Misalignment• Circumferential OOR(Out-Of-Roundness)• Ovalization• Bulge in A Cylindrical Shell/Spherical,,• Dent in A Cylinder• Peaking in A Shell• Stress Linearized Calculation(Uncrack/Crack/Notch,,,,)• Crack 전파에따른기기의수명및파괴예측• LBB(Leak Before Break) : Thick Wall에서발생 : DIV.3


FFS(API579), IMPERFECTION SHAPE








IMPERFECTION FE MODEL

350mm

6.5mm

1250mm

Support Skirt

[Geometric Model]


IMPERFECTION FE MODEL

[FE Model]

Skirt Support


FE STRESS ANALYSIS SAMPLE

[Tensile / Compressive Stresses on OOR]


FE BUCKLING ANALYSIS SAMPLE


IMPERFECTION MESUREMENT


FE IMPERFECTIONMODEL

5.8mm


FE IMPERFECTION ANALYSIS


FE IMPERFECTION ANALYSIS

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