Vessel Pressure 2

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San Diego State University

DEPARTMENT OF MECHANICAL ENGINEERING

Stress analysis of Pressre !essel

Levi Lent"

#$%&$%'((


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Table of Contents

Table of Contents........................................................................................................2

List of Figures............................................................................................................. 2

List of Tables............................................................................................................... 3

Description................................................................................................................. 4

Problem Statement.....................................................................................................4

Steps.......................................................................................................................... 4

Assumptions............................................................................................................... 5

Moel !nformation...................................................................................................... 5

Stu" Properties.........................................................................................................5

#nits........................................................................................................................... $

Material Properties..................................................................................................... $Loas an %estraints.................................................................................................. &

Fi'ture..................................................................................................................... &

Loa........................................................................................................................ &

Mes( !nformation........................................................................................................&

%eaction Forces.......................................................................................................... )

Free*+o" Forces........................................................................................................)

Free*bo" Moments.................................................................................................... )

Stu" %esults..............................................................................................................,

Conclusion................................................................................................................ -&

Appeni' - /an Calculations.................................................................................-)

List of Figures

Figure -. Dimensions of t(e pressure 0essel. S(o1n (ere 1it( a (alf 0ie1 to s(o1

etail.......................................................................................................................... 3

Figure 2. 'ternal loas an constraints.....................................................................)

Figure 3. ormal ie1 of t(e Mes(ing of t(e part.......................................................,Figure 4. !sometric 0ie1 of t(e mes(ing of t(e part...................................................,

Figure 5. ormal 0ie1 of on*Mises Stress 1it( Ma'Min Stress...............................--

Figure $. !sometric 0ie1 of on*Mises Stress 1it( Ma'Min Stress............................-2

Figure &. ormal ie1 of isplacement of part.........................................................-2

Figure ). !sometric ie1 of %aial Stress Plot...........................................................-2

Figure ,. ormal %aial Stress Plot...........................................................................-3


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Figure -6. ormal Stress Probes............................................................................... -4

Figure --. %aial Stress Probe Plot...........................................................................-5

Figure -2. !sometric 0ie1 of Tangential Stress Plot...................................................-$

Figure -3. ormal ie1 of Tangential Stress Plot......................................................-$

Figure -4. Tangential Stress Probes..........................................................................-&

Figure -5. Plot of Tangential Stress Probes...............................................................-&

List of Tables

Table -. T(e grap(ical 7e" for Figure 2.......................................................................,

Table 2. Comparison of classical an FA results.....................................................-&


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Description

T)is is a FEM *ro+e,t ai-e. at analy"ing a *ressre vessel /it) an internal *ressre of (#01MPa an. an e2ternal

at-os*)eri, *ressre of ('(3Pa0 T)e goal is t)e )ave or reslts -at,) t)e )an. ,al,lations in t)e na-e of

e2*an.ing t)e engineering fiel.0

Problem Statement

Analy"e a *ressre vessel /it) t)e geo-etry s)o/n 4elo/ in Figre ( in Soli./or3s0 S)o/ t)e )an. ,al,lations to

s)o/ t)e si-ilarities 4et/een t)e t/o -et)o.s0 T)e vessel )as an internal *ressre of (#01M*a an. an e2ternal

*ressre of ('(3Pa0

Figure 1. Dimensions of the pressure vessel. Shown here with a half view to show detail.

Steps

(0 A**ly -aterial an. ,onstrain it *ro*erly0 5e se. an Alloy Steel /it) a sy--etri, ,onstraint on t)e ,t

srfa,e of t)e vessel /it) a fi2e. ,onstraint at t)e o*en en. of t)e ne,30 T)is flly ,onstraine. t)e -aterial

an. allo/e. s to *ro*erly a**ly t)e FEA loa.s0

%0 A**ly an internal *ressre of (6MPa to t)e interior srfa,e7 an. an e2ternal *ressre of 0('(3Pa to t)e

e2ternal srfa,e0 Rn t)e FEM analysis

80 Create a stress *lot for !on Mises7 ra.ial7 an. tangential stresses in a..ition to a .is*la,e-ent *lot of t)e

,ylin.er0 Use a *ro4e at t)e ,enter of t)e ,ylin.er to .eter-ine 4ot) t)e ra.ial an. tangential stresses at t)e

inner /all an. t)e e2ternal /all of t)e ,ylin.er0 Use Soli./or3s to *lot t)e stress vs0 no.e n-4er


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#0 Use t)e t)i,3 /alle. ,ylin.er e9ations to ,al,late t)e t)eoreti,al ra.ial an. tangential stresses at t)e

interior an. e2terior /alls0 Co-*are t)is reslt /it) t)e FEM sing t)e *er,ent .ifferen,e for-la s)o/n

4elo/:

%= −

resultsresultsresults

difference= [ (¿ FEA )−(¿ Elasticity ) ]∗100 /(¿ FEA)

Assumptions

5e ass-e t)e -aterial is an Alloy Steel /it) t)e internal an. e2ternal *ressres 4eing a**lie. nor-al to t)e fa,es

of t)e vessel0 5e ass-e t)at t)e vessel is rigi.ly ,onstraine. at t)e o*ening of t)e ne,3 to allo/ t)e vessel to

e2*an. in all ne,essary .ire,tions a/ay fro- t)e ne,30

Model Information

Document Name Configuration Document Path Date Modified

!essel Defalt ;:


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In,l.e fli. *ressre effe,ts fro- Soli.5or3s Flo/

Si-lation

Off

Fri,tion: Off

Ignore ,learan,e for srfa,e ,onta,t Off

Use A.a*tive Met)o.: Off

nits

Unit syste-: SI

Lengt)$Dis*la,e-ent --

Te-*eratre ?elvin

Anglar velo,ity ra.$s

Stress$Pressre N$-@%

Material Properties

No! "ody Name Material Mass #olume

( Soli.o.y (BFillet1 Alloy Steel BSS 6&0(8( 3g '0''&&% -@8

Material name$ Alloy Steel %SS&

Des,ri*tion:

Material Sor,e:

Material Mo.el Ty*e: Linear Elasti, Isotro*i,

Defalt Failre Criterion: Ma2 von Mises Stress

A**li,ation Data:

Property Name #alue nits #alue Type

Elasti, -o.ls %0(e'(( N$-@% Constant

Poissons ratio '0%& NA Constant


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S)ear -o.ls 0>e'(' N$-@% Constant

Mass .ensity '' 3g$-@8 Constant

Tensile strengt) 0%8&8e''& N$-@% Constant

iel. strengt) 60%'#%e''& N$-@% Constant

T)er-al e2*ansion

,oeffi,ient

(08e''1 $?elvin Constant

T)er-al ,on.,tivity 1' 5$B-0? Constant

S*e,ifi, )eat #6' $B3g0? Constant

Har.ening fa,tor B'0'(0'J

'0'Kisotro*i,J

(0'K3ine-ati,

'0&1 NA Constant

Loads and 'estraints

Fi(ture

'estraint name Selection set Description

Sy--etry( !essel on 8 Fa,eBs sy--etry

Fi2e.( !essel on ( Fa,eBs fi2e.0

Load

Load name Selection set Loading type Description

Pressre( !essel on (( Fa,eBs /it)

Pressre '0('( N$--@%

BMPa along .ire,tion

nor-al to sele,te. fa,e

Se9ential Loa.ing

Pressre% !essel on (( Fa,eBs /it)

Pressre (#01 N$--@%

BMPa along .ire,tion

nor-al to sele,te. fa,e

Se9ential Loa.ing

Mesh Information

Mes) Ty*e: Soli. Mes)


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Mes)er Use.: Stan.ar. -es)

Ato-ati, Transition: Off

S-oot) Srfa,e: On

a,o4ian C)e,3: # Points

Ele-ent Si"e: (%0>%> --

Toleran,e: '06#6#1 --

ality: Hig)

N-4er of ele-ents: %&%%#

N-4er of no.es: #%1

Ti-e to ,o-*lete -es)B))J--Jss: '':'':'1

Co-*ter na-e:

'eaction Forces

Selection set nits Sum ) Sum * Sum + 'esultant

Entire o.y N #(#8806 86'1#08 %0#886e''6 %0#8#%>e''6

Free,"ody Forces


Entire o.y N '06#(%>( %018%1% (0#&(& 80''8#

Free,body Moments


Entire o.y N- ' ' ' (e'88

Study 'esults


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Figure 2. External loads and constraints

Figure 2 abo0e can be e0aluate from t(e follo1ing 7e"

-range "lue 'ed Purple

./!0MPa InternalLoad !.1.MPaAtmospheric Load SymmetricConstraint Fi(ed 2eometryConstraintTable .! The graphical 3ey for Figure 4!


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Figure 3. Normal View of the eshing of the part.

Figure !. "sometric view of the meshing of the part.


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Default %esults

Name Type Min Location Ma( Location

Stress( !ON: von Mises

Stress

%0'#6&6e''6

N$-@%

No.e: (1'>

B8'#0(# --7

(&10666 --7

101> --

1066#%>e''&

N$-@%

No.e: (''

B%601#( --7

8(08%>> --7

(#08 --

Dis*la,e-ent( URES: Resltant

Dis*la,e-ent

' --

No.e: %6(

B60#%>#e'(1

--7

%#1 --7

1%01 --

%0(#>81 --

No.e: #1(%

B8'#0'6% --7

(&10>66 --7

(0'###e'(%

--

Strain( ESTRN:

E9ivalent

Strain

(0611#e''1

Ele-ent: (86'

B8#(0#>% --7

%&0>(8 --7

%0&&1# --

'0''(&8%((

Ele-ent: %%

B%#>0(#6 --7

(##06&6 --7

60%''(6 --

Stress8 S: Nor-al

Stress

#0%1(%1e''&

N$-@%

No.e: &%

B1%0166 --7

(&%01 --7

10(#11(e'(

--

60%616>e''&

N$-@%

No.e: #1#>%

B1%0>>> --7

(>018% --7

%0&8%e'(1

--

Stress# S;: ; Nor-al

Stress

%0&%(e''&

N$-@%

No.e: %(>('

B%1(0#&8 --7

101#6'6 --7

#01%8'6e'(#

--

#0%#%>e''&

N$-@%

No.e: 8>#&

B%1'0%&( --7

'0>%88>1 --7

(#10818 --


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Figure #. Normal view of Von$ises Stress with ax%in Stress

Figure &. "sometric view of Von$ises Stress with ax%in Stress


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Figure '. Normal View of displacement of part

Figure (. "sometric View of )adial Stress *lot


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Figure +. Normal )adial Stress *lot

Figure 1,. Normal Stress *ro-es


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Figure 11. )adial Stress *ro-e *lot


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Figure 12. "sometric view of angential Stress *lot

Figure 13. Normal View of angential Stress *lot


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Figure 1!. angential Stress *ro-es

Figure 1#. *lot of angential Stress *ro-es

/lassical FE0 Dierence

uter angential &,.$5 )-.$ 2.3),&6$

"nner angential ,4.65 ,3.3 *6.)63)$

uter )adial *6.-6- *6.-62 6.,)63,2

"nner )adial *-4.5 *-4.4 *6.$,444

Table 4! Comparison of classical and F5A results

Conclusion

After ,o-*leting or FEM analysis7 t)is *ressre vessel /as s)o/n to ,onverge al-ost e2a,tly to /)at or )an.,al,lations *re.i,te.0 T)e larges error /as a -eager %08&> on t)e oter tangential stress0 T)is large error ,ol.

)ave 4een .e to a variety of reason7 4t ,ol. 4e 4e,ase of t)e stress ,on,entrations ,ase. 4y t)e rat)er large

.is*la,e-ent of t)e oter /alls0 T)e goo. ,orrelation 4et/een or )an. ,al,lations an. or FEA analysis *roves

t)at t)e n-4ers t)at /e )ave fon. are )ig)ly a,,rate0 T)is -o.el ,an t)erefore 4e ass-e. to 4e an a,,rate

re*resentation of t)e *)ysi,al loa.ing of t)e syste-7 es*e,ially to analy"e t)e ,o-*le2 geo-etry aron. t)e inlet

an. e2its0


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Appendi( .$ 6and Calculations

Vessel Pressure 2

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