Tracción con deformación Térmica - Cálculo por elementos finitos

8/13/2019 Traccin con deformacin Trmica - Clculo por elementos finitos

1/16

HA OLI OLSHZZAIIA Z\ZHI W IH SLF\ZGOHO HIGKLD_HZGH

\DG]LZSGOHO DHCGADHI OL GDFLDGLZGH

MHC\I_HO GDFLDGLZGH KLCDGCH

:oh ^rctgch Chigmgchoh

C\ZSA 0 CIC\IA ^AZ LILKLD_AS MGDG_AS

^ZAMLSAZ 0 C\L]H ^HCBLCA Zadhio

HI\KDA0 ]LZH Z\GP @adhtbhd Lmrhd

COGFA0 :>8>?>>?F SLCCGD0 O

IGKH - ^LZ\

Actujrl :>83


2/16

CIC\IA ^AZ LILKLD_AS MGDG_AS _rhccgd cad olmarkhcgd trkgch

^fgdh :

dogcl

Ldudcghoa oli ^rajilkh............................................................................. 3

Saiucgd...................................................................................................... ?

Frhoas ol Igjlrtho Daohils....................................................................... C. \tgigzhr d lilkldtas mgdgtas.

Cadsgolrhr0

^ H ; ED

t (lsplsar) ; 8 kk

L ; 3.>x8> < D/kk :

W ; 2.>fr-m/ck 3 ; 62,? -= D/kk 3

; 88*8> -= C-8


4/16


^fgdh ?

SAI\CGD0

8. KAOLIHOA OLI C\LZ^A ZLHI

Sl cadsgolrhrhd < lilkldtas mgdgtas. ^hrh mhcgigthr ias cicuias ias lilkldtas mgdgtas tldord

iadfgtuo ol 3>>, 3>>, :>>, :>> y :>>kk.

W ias lsplsarls ia chicuihkas takhdoa li pudta kloga ol choh lilkldta mgdgta0

; 8>>>+6: ;26< ; 6+>: ;=:<

; >+8>>>/3:

;?8=.=6 ; 8>>>/3+>/3: ; :

; >/3: ;23.33 Ldtadcls, li kaolihoa oli culrpa slrh li sgfugldtl0

W ihs rlhs sl chicuihd ol ih sgfugldtl rlihcgd0

t xj H 88 Cuhora ol cadlctgvgoho0

l

DAOAS FOI i l

(kk)

Hl

(kk : )(8) (:) 8 :

8 8 : 8 : 3>> 838:

: : 3 : 3 3>> 736

3 3 ? 3 ? :>> =:>

? ? < 3 ? :>> 36>

< < = < = :>> 8:>


5/16


^fgdh puls ih pihch lsth lkpatrhoh y ias olks olspihzhkgldtas sad gdcfdgths qultldord qul slr chicuihohs.

3. ]LC_AZ CHZFH

Hdhigzhdoa ihs mulrzhs ld choh lilkldta mgdgta0

; : + ;


6/16


^fgdh =

; : + ;?7>72.8

Hbarh hdhigzhkas ihs mulrzhs phrh taoa li culrpa0

; ; 8 8 > > > >> > > > > >> > > > > >> > > > > >> > > > > >

+( )> > > > > >> 8 8 > > >> 8 8 > > >> > > > > >> > > > > >> > > > > >

+( )U

> > > > > >> > > > > >> > 8 8 > >> > 8 8 > >> > > > > >> > > > > >[

+( )U

> > > > > >> > > > > >> > > > > >> > > 8 8 >> > > 8 8 >> > > > > >[


7/16


^fgdh 6

+( )> > > > > >> > > > > >> > > > > >> > > > > >> > > > 8 8> > > > 8 8

Zllkpihzhdoa phrh ias vhiarls chicuihoas y utgigzhdoa ih thjih ol cadlctgvgoho ajtldlkas0

; 838:38>3>>U

8 8 > > > >8 8 > > > >> > > > > >> > > > > >> > > > > >> > > > > >[

+73638>3>> > > > > > >> 8 8 > > >> 8 8 > > >> > > > > >> > > > > >> > > > > >

+(=:>3>>>>>:>> )> > > > > >> > > > > >> > 8 8 > >> > 8 8 > >> > > > > >> > > > > >

+(36>3>>>>>:>> )U

> > > > > >> > > > > >> > > > > >> > > 8 8 >> > > 8 8 >> > > > > >[

+(8:>3>>>>>:>>

)U

> > > > > >> > > > > >> > > > > >> > > > > >> > > > 8 8> > > > 8 8[


8/16


9/16


^fgdh 7

W phrh ajtldlr ih rlhccgd ld li lkpatrhkgldta tkhdas ih sgfugldtl sujkhtrgz0

=

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8>3

kk

D x

:::

3

kk D x

:33

>:>376.3=3=.==3

kk D x

:??

83>63=36.?>:

==>8>3

kk D x

::88

:>>8>3

kk D x


10/16


^fgdh 8>

6. ZLS\I_HOAS

Mgdhikldtl, ias rlsuithoas sad kastrhoas ld ih sgfugldtl thjih0

D Z =>. kk D

::

kk

D

:3 >:>376.> kk D

:? >83>6 kk D

:< >>62? kk D


11/16


^fgdh 88

2. OGHFZHKH OL MI\@A

GDGCGA

GDFZLSA OL OH_ASCADS_HD_LS 0 L, y, t, _

]LC_AZLS0 I, H, J

CHIC\IA OL ]LC_AZLS

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=

;8>>> %gdput('Gdfrlsl jhsl suplrgar(kk)0') jd;> %gdput('Gdfrlsl jhsl gdmlrgar(kk)0') t;8 %gdput('Gdfrlsl lsplsar(kk)0') b;8:>> %gdput('Gdfrlsl hiturh(kk)0') L;3>>>>> %gdput('Gdfrlsl kaouia ol lihstgcgoho(D/kk:)0') y;>.>>>>62?< %gdput('Gdfrlsl oldsgoho(D/kk3)0') ^h;>>> %gdput('Gdfrlsl chrfh(D)0') himh;88*(8>T-=) ot;8:>

%chicuia ol jhsls y rlhs ol lilkldtas

d;gdput ( 'Gdfrlsl li D ol lilkldtas (d) 0' )5 x;gdput ( 'Gdfrlsl li D ol lilkldtas mgdgtas ldtrl ih chrfh y ih jhsl lkpatrhoh 0' )5

yy;d-x5 jk;j>/:5 bx;b/:5 by;b/:5

il;zlras(d,8)5 ba;zlras(d,8)5 ja;zlras(d,8)5 j;zlras(d,8)5 h;zlras(d,8)5Mh;zlras(d+8,8)5Mj;zlras(d+8,8)5 ja(8);j>5 ba(8);bx5 mar g;80x

gm x4g il(g);bx/x5 j(g);(ja(g)+jk+(ja(g)-jk)*(ba(g)-il(g))/ba(g))/:5 h(g);j(g)*t5 ba(g+8);ba(g)-il(g)5 ja(g+8);:*j(g)-ja(g)5

lisl il(g);bx/x5 j(g);(jk+ja(g))/:5 h(g);j(g)*t5

ldo ldo ba(x+8);by5 ja(x+8);jk5 mar g;x+80d

gm d4g il(g);by/yy5 j(g);(ja(g)+jd+(ja(g)-jd)*(ba(g)-il(g))/ba(g))/:5 h(g);j(g)*t5 ba(g+8);ba(g)-il(g)5 ja(g+8);:*j(g)-ja(g)5

lisl il(g);by/yy5 j(g);(jd+ja(g))/:5 h(g);j(g)*t5

ldo ldo

ogsp( 'Jhsls(kk)0' )


13/16


^fgdh 83

ogsp(j') ogsp( 'Iadfgtuols(kk)0' ) ogsp(il') ogsp( 'Hrlhs(kkT:)0' ) ogsp(h')

%chicuia ol ihs mulrzhs mar g;80d mar `;g0g+8

gm g;;`Ml(g,`);(y*h(g)*il(g)/:)-(L*h(g)*ot*himh)5

lisl Ml(g,`);(y*h(g)*il(g)/:)+(L*h(g)*ot*himh)5

ldo ldo

ldo

mar g;80d+8 gm g;;8

M(g);Ml(g,8)5 lislgm g;;d+8

M(g);Ml(g-8,g)5 lisl

M(g);Ml(g-8,g)+Ml(g,g)5 ldo

ldo

M(x+8);M(x+8)+^h5 ogsp( 'Li vlctar ol mulrzhs(D)0' ) ogsp(M')

%chicuia ol ih khtrgz rgfgolz e;zlras(d+8)5 mar g;80d

x;zlras(d+8)5 x(g,g);85x(g+8,g);-85x(g,g+8);-85x(g+8,g+8);85 e;e+(h(g)*L/(il(g)))*x5 ldo

ogsp( 'Ih khtrgz ol rgfgolz ls(D/kk)0' ) ogsp(e)

%chicuia ol olspihzhkgldtas gdv(e(:0d+8,:0d+8))5 ((M(:0d+8))')5 X;gdv(e(:0d+8,:0d+8))*((M(:0d+8))')5 X;U>5X[5 ogsp( 'Ias olspihzhkgldtas ol ias daoas sad(kk)0' ) ogsp(X)

%chicuia ol ih rlhccgad

e(8,0)*X5 Z8;e(8,0)*X-M(8)5 ogsp( 'Ih rlhccgad ld li lxtrlka Z8 ls0' ) ogsp(Z8)

%chicuia ol lsmulrzas mar g;80d

l(g);(L/(il(g)))*U-8 8[*UX(g)5 X(g+8)[-L*himh*ot5 ldo ogsp( 'Ias vhiarls ol ias lsmulrzas sad(D/kkT:)0' ) ogsp(l')5


14/16


^fgdh 8?

]GS_H LD LI CAKKHDO VGDOAV OL KH_IHJ


15/16


^fgdh 8. CADCI\SGADLS

-Ih mulrzh ksgch tathi oli culrpa ld lstl chsa phrtgcuihr da vhrh par li dklra ol daoas. L sta acurrl parqul li culrpa ls ol markh trghdfuihr. Ld culrpas qul prlsldthd flakltrhsda trghdfuihrls a da rlcthdfuihrls li dklra ol lilkldtas sg hmlcth hi cicuia oli vaiukldtathi.

-Ih vhrghcgd ol tlkplrhturh da hmlcth hi vhiar ol ih rlhccgd dg h ias vhiarls ol iaslsmulrzas.

Ol ias rlsuithoas phrh udh vhrghcgd ol tlkplrhturh ol > y 8:> frhoas cldtfrhoas.

^hrh _;>5Ih khtrgz ol rgfgolz ls(D/kk)0

8.>l+>>2 *

8.38:< -8.38:< > > > >-8.38:< :.:> ->.736< > > >

> ->.736< 8.26 ->.736< > >> > ->.736< 8.>> ->.> > > ->..6> ->.826 > > > ->.826< >.826

>.>>>?

>.>>8>>.>>8>>.>>8>>.>>8>

Ih rlhccgad ld li lxtrlka Z8 ls0-=>l+>>?

Ias vhiarls ol ias lsmulrzas sad(D/kkT:)0>.?:3>>..>:>?>.>838>.>>62


16/16


^fgdh 8=

^hrh _; 8:>

Ih khtrgz ol rgfgolz ls(D/kk)08.>l+>>2 *

8.38:< -8.38:< > > > >-8.38:< :.:> ->.736< > > >

> ->.736< 8.26 ->.736< > >> > ->.736< 8.>> ->.> > > ->..6> ->.826 > > > ->.826< >.826

>.37=?

>.673>8.>8.3:8>8.>?

Ias vhiarls ol ias lsmulrzas sad (D/kkT:)0>.?:3>>..>:>?>.>838>.>>62

Sl ajtgldl udh kgskh rlhccgd (-=l+>>?) y ias lsmulrzas sad U>.?:3> >..>:>?>.>838 >.>>62[ ld hkjas chsas, lsta suclol parqul li culrpa tgldl ud saia daoa mg`a (X8;>).Sg li culrpa tldorh oas daoas mg`as ldtadcls ihs rlhccgadls vhrghrhd par lmlcta ol ihvhrghcgd ol tlkplrhturh.

Tracción con deformación Térmica - Cálculo por elementos finitos

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