finite element analysis- prabhakar

8/2/2019 Finite element analysis- Prabhakar

1/37

MU\UGU - ^iupo|g`{gpk Kdohdkk|hdo gd` Mgdgokmkdp ^|io|gmmk - ^KM^

3Ahdhpk Kckmkdp Gdgcxuhu4

GUUHODMKDP

Mi`{ck Ei`k GMK ;>5

Mi`{ck Dgmk Ahdhpk Kckmkdp Gdgcxuhu

Ei{|uk M$Ue$ VKdoo] hd Mgebhdk|x @kuhod$

@k~g|pmkdp Mkebgdhegc ! Mgd{agep{|hdo Kdohdkk|hdo$

Dgmk ia pbk Up{`kdp ^|glbgfk|$

\ko$ Di LGL>877>>8

Lgpeb A{cc-Phmk 77$

Mi`{ck Ckg`k| @|$ Qhdi` f{mg| Lgdpbhg

IUPO\G@[GPKKD

OHDKK\HDO

GD@MG

DGOKMKDP^\IO\GMMK"^KM^(

M$U$\gmghgb Uebiic ia G`qgdek` Up{`hku^iupo|g`{gpk Kdohdkk|hdo gd` Mgdgokmkdp ^|io|gmmku"^KM^(

%0?>-^ ^kkdxg Hd`{up|hgc G|kg# 0pb ^bguk# ^kkdxg# Lkdogc{|{-;1> >;2

Pkc6 >2> 08>1 ;;;;# wkluhpk: www$mu|ugu$i|o


2/37

3 AHDHPK KCKMKDP GDGCXUHU 4

hh

@kecg|gphid Ubkkp

Up{`kdp Dgmk ^\GLBGFG\$^

\ko$ Di LGL>877>>7

Ei{|uk MGEBHDK\X @KUHOD Lgpeb A{cc-Phmk 77

Lgpeb AP77

Mi`{ck Ei`k GMK ;>5

Mi`{ck Phpck AHDHPK KCKMKDP GDGCXUHU

Mi`{ck @gpk >8 >7 7< pi 7 7 mg|fu Mi|k pbgd Pi kkfu cgpk: Aghc - >+ |kei|`k` "A(

Gcc cgpk guuhodmkdpu: m{up lk u{lmhppk` pi Geg`kmhe \kei|`u Iaahek "G\I($ Hp hu xi{| |ku~iduhlhchpx pi

kdu{|k pbgp pbk |kekh~p ia g cgpk guuhodmkdp hu |kei|`k` hd pbk G\I$ Ha gd krpkduhid gu go|kk # pbk

g{pbi|hzgphid ubi{c` lk u{lmhppk` pi G\I `{|hdo pbk u{lmhuuhid ia guuhodmkdp$

Pi kdu{|k guuhodmkdp |k~i|pu g|k |hppkd eidehukcx# pbk ckdopb ubi{c` lk |kup|hepk` pi g chmhp

hd`hegpk` hd pbk guuhodmkdp ~|ilckm upgpkmkdp$ Guuhodmkdp |k~i|pu o|kgpk| pbgd pbhu ckdopb mgx

hde{| g ~kdgcpx ia idk o|g`k "; mg|fu($ Kgeb `kckogpk hu |kw{h|k` pi |kpghd g ei~x ia pbkguuhodmkdp |k~i|p$

@kecg|gphidPbk guuhodmkdp u{lmhppk` bk|khpb hu g |ku{cp ia mx id hdqkuphogphidu gd` pbgp H bgqk eidai|mk` pi pbk

o{h`kchdku goghdup ~cgohg|hum gu cgh` i{p hd pbk ^KM^ Up{`kdp Bgd`liif$ Gcc ukephidu ia pbk pkrp gd`|ku{cpu# bheb bgqk lkkd ilpghdk` a|im ipbk| ui{|eku# g|k a{ccx |kak|kdek`$ H {d`k|upgd` pbgp ebkgphdo gd`

~cgohg|hum eiduphp{pk g l|kgeb ia [dhqk|uhpx |ko{cgphidu gd` hcc lk `kgcp hpb geei|`hdocx$

Uhodgp{|k ia pbk up{`kdp @gpk

U{lmhuuhid `gpk upgm~"lx G\I(

Uhodgp{|k ia pbk Mi`{ck Ckg`k| gd` `gpk Uhodgp{|k ia Bkg` ia pbk @k~g|pmkdp gd` `gpk


3/37



hhh

Glup|gep

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Pbk Ahdhpk kckmkdp gdgcxuhu mi`{ck ogqk pbk h`kg ia pbk g~~|igeb upk~ hdqicqk` hd ahdhpk

kckmkdp mkpbi` ai| uicqhdo pbk ~|ilckm gd` gcui qgch`gphdo pbk |ku{cp bkd ilpghdk` gu pbk

uic{phid lguk` id bheb pbk guuhodmkdp hu uicqk`$ Pbk ^g|p-G guuhodmkdp hu pbk `klgpk id

eidqk|okdek gd` qg|hi{u px~ku ia eidqk|okdek {uk` hd AKG chfk b-mkpbi`# ~-mkpbi` gd` b~-

mkpbi`$ Pbkuk g|k {uk` pi ilpghd pbk lkppk| |ku{cpu hd AKG gcc pbkuk pb|kk px~ku g|k h`kcx {uk`

l{p kgeb bgu hpu id chmhpgphidu gd` eidup|ghdu hp hu |kw{h|k` pbk gdgcxuhup ubi{c` bgqk pbk eckg|

h`kg lguk` id pbk ~|ilckm `kahdhphid ubi{c` ebiiuk pbk ~|i~k| eidqk|okdek ilpghd pbk ~|i~k|

|ku{cp$ Pbk `klgpk hu gli{p ai| up|{ep{|gc gdgcxuhu bheb eidqk|okdek ~|iqh`ku pbk lkup |ku{cp hu

`hue{uuk`$

Pbk ^g|p-L hu pbk Bk|pz eidpgep up|kuu ~|ilckm ai| pbk ohqkd `hgmkpk| gd` pbk cig` pbk

~|i~k| h`kgchzgphid hu ìdk gd` lx g~~cxhdo pbk li{d`g|x eid`hphidu gd` cigù uic{phid hu

ilpghdk` |ku{cpu ia qg|hi{u ~cipu gd` o|g~bu g|k ubid k|k ai| uicqhdo gdgcxuhu piic Gduxu hu

{uk` ai| uicqhdo hd bheb gcc pbk i~k|gphidu ia mi`kchdo# kckmkdp ukckephid# li{d`g|x

eid`hphidu kpe# g|k eg||hk` i{p gd` |ku{cpu g|k ilpghdk` gd` pi qgch`gpk pbk |ku{cp bgd`

egce{cgphidu g|k ìdk gd` pbk |ku{cpu ilpghdk` a|im pbk Gduxu g|k qk|hahk` pbk bgd` egce{cgphidu

g|k gppgebk` hd g~~kd`hr-7$ A|im pbk ^g|p-L hp hu |kw{h|k` pi {d`k|upgd` pbk |ku{cp ilpghdk` gu

pbhu hu {uk` gu pbk lkdeb mg|f mi`kc ai| uicqhdo pbk ^g|p-E guuhodmkdp$

Pbk ^g|p-E hu pbk ~|ilckm hu lguk id okg|u hd eidpgep k|k pbk ohqkd HOKU ahck hu

mkubk` {uhdo pbk `k`hegpk` mkubhdo uiapg|k Bx~k|mkub$ Gd` hp hu pgfkd gu pbk hd~{p pi pbk

Gduxu pbkd pbk kckmkdp ukckephid# li{d`g|x eid`hphidu# eidpgep ~|i~k|phku kpe# k|k guuhodk`

gd` pbk uic{phid hu ilpghdk` pi qgch`gpk pbk ilpghdk` lx eiduh`k| hd pbk ^g|p-L Bk|pz eidpgep

uic{phid gu lkdeb mg|f mi`kc gu pbk okg| bgu pbk hdqic{pk ~|iahck pbk eidpgep lkpkkd pbk

|icck|u hu uhmhcg| pi pbk eidpgep lkpkkd pbk okg|u gd` gcui pbk kckmkdp ukckephid gd` eidpgep

~|i~k|phku g|k ugmk ai| ^g|p-L gd` ^g|p-e$ Hd ^g|p E hu uicqk` hd pi upk~u ah|up pbk li{d`g|x

eid`hphidu gd` cigù g~~chk` pi pbk uhdock piipb gd` pbk |ku{cp hu ilpghdk` gd` pbkd pbk |ku{cp

ilpghdk` ai| pbk okg|u hd eidpgep lipb pbk |ku{cpu k|k eim~g|k` gd` qk|hahk`$


4/37


hq

Eidpkdpu


Eidpkdpu

@kecg|gphid Ubkkp $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ hhGlup|gep $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ hhhEidpkdpu $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$hqChup ia Pglcku $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$qhChup ia Aho{|ku $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ qhh7$7Hdp|i`{ephid: $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 87$7$; ~-mkpbi` hu lkppk| pbgd b-mkpbi` gd` b~-mkpbi`: $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 7>7$1 Eidec{uhid: $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 77^g|p-L$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 7


5/37



q

5$7 Pbk uebkmk {uk` ai| e|kgphdo pbk mi`kc: $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$


6/37


qh

Chup ia Pglcku


Pglck Di$ ^o$Di$Pglck 7$ 7 Eim~g|huid ia ~# b ! b~ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

Pglck

5>


7/37



qhh

Chup ia Aho{|ku


Aho{|k Di$ Phpck ia pbk aho{|k ^o$Di$

Aho 7$ 7 ^icxdimhgc i|`k|u ia ~ ! b mkpbi` $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 7>Aho 7$ < Eim~g|huid ia b ! ~ kckmkdpu $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 7>Aho 7$ 5 \ku{cp eim~g|huhid ia ~# b ! b~ mkpbi` $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 77

Aho


8/37



qhhh

Aho 5$ 72 bipi kcguphe pbki|x h`kgchzgphid ai| uhdock okg| $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 55


9/37


8

^G\P-G

EBG^PK\ 7

7$7 Hdp|i`{ephid:Hd ahdhpk kckmkdp mkpbi` |ku{cpu g|k ilpghdk` lx uhm~chaxhdo pbk ~|ilckm# k|k pbk iljkep hu

`kue|kphuk` hdpi umgcc kckmkdpu gd` pbk |ku{cpu g|k ilpghdk`$ Pbkuk |ku{cpu `k~kd` id qg|hi{u

~g|gmkpk|u chfk kckmkdp ukckephid# Mkub w{gchpx gd` Li{d`g|x eid`hphidu kpe$ Pbk `klgpk hu gli{p

qg|hi{u px~ku ia eidqk|okdek {uk` hd AKG pi ilpghd pbk lkppk| |ku{cp$ Gu pbk uic{phid hd AKG

`k~kd`u id qg|hi{u agepi|u gd` pbk uiapg|k ohqku pbk uic{phid bheb hu mi|k pbgd pbk ugphuagepi|x

ckqkc l{p dip pbk krgep uic{phid# Pbk uic{phid `k~kd`u id mi`kchdo ia kckmkdpu bheb egd gcui

|kak||k` gu ^# B gd` B^ px~k eidqk|okdek$

7$


10/37



7>

7$0 Gee{|gex gd` `ko|kku ia a|kkìm hd eidqk|okdek:Hd b eidqk|okdek hd i|`k| pi ilpghd pbk lkppk| |ku{cp hp hu |kw{h|k` pi ì ahdk mkubhdo gu kgeb

di`k bgu D-@IA "`ko|kku ia a|kkìm( lx hde|kguhdo pbk d{mlk| ia di`ku lx ahdk mkub pbk `ko|kku

ia a|kkìm hu hde|kguk`$ Hd ~ eidqk|okdek d{mlk| ia di`ku hd pbk kckmkdp hu hde|kguk` hd p{|d

hde|kguku pbk `ko|kku ia a|kkìm$ Hd mgdx eguku pbk ukckephid ia eidqk|okdek `k~kdù id gee{|gex

gd` eim~{pgphidgc phmk lguk` id pbgp eidqk|okdek hu ukckepk` $Pbk b~ hu ~k|akep mkpbi` pi uicqk

did chdkg| ~|ilckmu k|k hp g{pimgphegccx |kahdku pbk o|hù g|i{d` pbk uhdo{cg|hphku gd`

g{pimgphegccx hde|kguku pbk ~icxdimhgc i|`k| k|k pbk |ku{cp |kw{h|k` pi lk umiipb pb{u pbk `ko|kku

ia a|kkìm okpu hde|kguk`$

Aho 7$ 7 îcxdimhgc i|`k|u ia ~ ! b mkpbi`

Pbk Aho 7$7 ubiu pbgp hde|kguk hd ~icxdimhgc |ku{cp hd hde|kguk hd di`k hd p{|d hde|kguk pbk

ackrhlhchpx gd` @IA hd pbk kckmkdp bheb ~|iqh`ku lkppk| |ku{cp$

7$; ~-mkpbi` hu lkppk| pbgd b-mkpbi` gd` b~-mkpbi`:

_bhck eim~g|hdo gcc pbkuk mkpbiù b-mkpbi` hu h`kcx {uk` gu hp hu hdhphgccx `kqkci~k` gd`

gqghcglck hd gcc hdhphgc uiapg|k `kqkci~k` ai| mkubhdo pbk b-|kahdkmkdp mkpbi` bgu lkkd mi|k

h`ku~|kg` hd pbk eimmk|ehgc ~|io|gmu pbgd pbk ~-|kahdkmkdp mkpbi`$ L{p pbk mgpbkmgphegc

g~~|igeb gd` chpk|gp{|k ~|iqku pbgp ~-mkpbi` hu pbk lkup mkpbi` pbgd b-mkpbi`$ Lx uhm~ck mkub

gd` hpb ckuu hpk|gphid uic{phid hu ilpghdk` hd ~-mkpbi`$ Gd` ai| eim~chegpk` ~|iahcku ia e{|qk`

~i|phid b-mkpbi` hu dip u{hpglck gu ubid hd pbk aho 7$< lkci

Aho 7$ < Eim~g|huid ia b ! ~ kckmkdpu


11/37



77

_bhck eim~g|hdo pbk |ku{cpu ia pbk ugmk ubg~k lx b-mkpbi`# ~-mkpbi` !b~-mkpbi` gu

ubid lkci hd pbk Aho-7$5 k egd iluk|qk pbgp pbk b~-mkpbi` ubiu pbk lkppk| |ku{cp pbgd pbk

ipbk| pi mkpbi`u gd` ~-mkpbi` ubi` ubiu pbk lkppk| |ku{cp idcx gapk| pbk ahdk |kahdkmkdp ia pbk

mkub gd` pbk b-mkpbi` ~|iqh`ku pbk lkppk| |ku{cp kqkd hd pbk eig|uk mkub$ A|im pbhu k egd

kchmhdgpk pbk b~-mkpbi` kqkd pbi{ob hp ~|iqh`ku pbk lkppk| |ku{cp `{k pi pbk aiccihdo

h(Hp bgu ahdk mkub gu b-mkpbi` hde|kguku eim~{pgphid phmk$

hh(Hp ~|iqh`ku gee{|gpk |ku{cp pbgd ipbk| pi mkpbi`u ai| up|{ep{|gc gdgcxuhu u{eb gee{|gex mgx dip

lk |kw{h|k` hd okdk|gc eguku$

b-mkpbi` hu pbk hdhphgccx `kqkci~k` mkpbi` bheb hu h`kcx {uk` gee{|gex hcc lk hde|kguk` lx

hde|kguhdo pbk mkub uhzk kqkd hd pbk ahdk mkub hp hu dip ~|iqh`hdo ui gee{|gpk |ku{cp gu ubid hd pbk

Aho lkci$

Hd ~-mkpbi` mkub uhzk hu cg|ok| pbgd pbk b-mkpbi` gd` b~-mkpbi` gd` idcx pbk ~icxdimhgc i|`k| hu

hde|kguk` bheb ~|iqh`ku lkppk| |ku{cpu pbgd b-mkpbi` gd` eciuk| |ku{cp pi b~-mkpbi` k|k pbk

eim~{pgphid phmk hu ckuu pbgd pbk ipbk| pi bkdek ~-mkpbi` hu mi|k u{hpglck mkpbi` pbgd ipbk| pi

mkpbi`$

g(Hdhphgc mkub l(b-mkpbi` e(~-mkpbi` `(b~-mkpbi`

V;]Aho 7$ 5 \ku{cp eim~g|huhid ia ~# b ! b~ mkpbi`

7$1 Eidec{uhid:

Gu pbk `klgpk hu gli{p pbk eidqk|okdek ai| pbk up|{ep{|gc gdgcxuhu pbk |ku{cp ilpghdk` a|im

pbk ~-mkpbi` hu u{aahehkdp gu hp bgu pbk chdkg| qg|hgphid iqk| pbk `kai|mgphid# up|kuu gd` up|ghd gd`

w{g`|gphe qg|hgphid iqk| pbk kckmkdp ia grhgc `hu~cgekmkdp gd` hpb eig|uk mkub pbk lkppk| |ku{cp hu

ilpghdk` pbk ~-mkpbi` hu lkppk| pbgd ipbk| pi mkpbi`$


12/37



7$>00mm pgfku ~cgek hd pbk exchd`k|$

Gu pbk |ku{cp ilpghdk` hu eim~g|k` hpb pbk gdgcxphegc uic{phid pbk |ku{cp ilpghdk` a|im pbk

Gduxu hu >$>00mm gd` pbk |ku{cp ilpghdk` lx pbk gdgcxphegc uic{phid hu >$>02 pbk qg|hgphid hd pbk

|ku{cp hu ia pbk geek~pk` chmhp$

Aho


20/37



Gu pbk cig` g~~chk` hu hd X grhu pbk up|kuu hu bhobk| pbgd ipbk| pi grku gr 7$$>58

< Mgrhm{m |kuu{|k 228$8?5 Up|kuuku hd R-grhu 228$85M^g 2?2$755 77$?8?

0 Up|kuuku hd X-grhu 228$85M^g 2?2$755 77$?8?

; Up|kuuku hd Z-grhu ;55$;5M^g ;00 >$>>0

Pglck


21/37



Hdp|i`{ephid:

Pbk ^g|p-E hu gli{p pbk okg| mkubhdo ~|ilckm bheb hu pi lk uicqk` hpb pbk fdickòk

ilpghdk` a|im pbk ^g|p-L k|k Bk|pz eidpgep up|kuu gu ai{d` lkpkkd pbk |icck|u pbk ~|ilckm egd

lk eiduh`k|k` gu uhmhcg| gu pbk okg| bgu hdqic{pk ~|iahck gd` bhck okg| mkubhdo pbk eidpgep pgfku

~cgek lkpkkd pbk okg| hcc lk uhmhcg| pi pbk eidpgep pgfku ~cgek lkpkkd pbk exchd`k|$ Hd ^g|p-E lx

ahdhpk kckmkdp gdgcxuhu pbk okg| ~|iahck hu pi lk mkubk` gd` cigù g|k pi lk g~~chk` gd` pbk |ku{cpu

g|k pi lk qk|hahk`$

5$7 Pbk uebkmk {uk` ai| e|kgphdo pbk mi`kc:

Pbk HOKU okg| ahck gu ~|iqh`k` ai| uicqhdo pbk ^g|p-E guuhodmkdp$ Pbk ahck hu ah|up

hm~i|pk` pi pbk Bx~k| mkub gd` mkubhdo hu eg||hk` lx pgfhdo idcx pi okg| hu hd eidpgep idk ~|iahck

ia `|hqk| gd` idk ~|iahck ia `|hqkd gu pbk |ku{cp ilpghdk` ai| pbk idk pkkpb hcc lk ugmk ai| gcc bhck

pbk mkubhdo# li{d`g|x eid`hphid gd` cigù g|k ugmk$ Pi |k`{ek pbk eim~{phdo phmk pbhu ~|iekuu hu

eg||hk` i{p gapk| eim~ckphdo pbk mkubhdo hd bx~k| mkub pbk ahck hu kr~i|pk` gu $e`l bheb hu pbk

hd~{p ai| Gduxu ahck$

Aho 5$ 7 Mkub e|kgpk` hd bx~k| mkub


22/37



$>8 0 di`k w{g` kckmkdpu k|k {uk` g|i{d` pbk

li{d`g|x e|kgpk` u{||i{d`hdo ia pbk eidpgep gd` pbk eig|uk mkub hu e|kgpk` hd pbk |kup ia pbk

~i|phidu hd pbk okg|$

5$


23/37




24/37




25/37



$0;0M^g hu ilpghdk` bheb hu mgrhm{m gp pbk ~ihdp ia cig` g~~chk`$

5$5$0 Pbk eidpgep up|kuu ai| okg| piipb hd eidpgep gp R-grhu:

Aho 5$ ; Up|kuu hd R-grhu ai| eidpgep okg|

Ai| pbk li{d`g|x eid`hphidu ai| eidpgep okg| piipb bkd cig` hu g~~chk` pbk up|kuu hd R-grhu ia

770$8


26/37




27/37



$2?8M^g hu ilpghdk` bheb hu mgrhm{m gp pbk ~ihdp ia cig` g~~chk`$

Pbk |ku{cp ilpghdk` ai| uhdock okg| hu


28/37




30/37



5>

Ai| pbk li{d`g|x eid`hphidu g~~chk` pi eidpgep okg| piipb bkd cig` hu g~~chk` pbk |iip

up|kuu g|k ilpghdk` a|im qid-mheku eid`hphid hd pbk aho{|k pbk cig` g~~chk` uh`k kr~k|hkdeku pbk

pkduhid gd` pbk i~~iuhpk uh`k kr~k|hkdeku pbk eim~|kuuhid pbk qgc{k ia mgrhm{m up|kuu hu

2$2;?M^g hu ilpghdk` bheb hu mgrhm{m gp pbk ~ihdp ia cig` g~~chk`$

5$0 Eim~g|huid ia |ku{cp ia uhdock gd` eidpgep ~gh| okg|u:

Aho 5$7< Up|kuu `kqkci~k` hd uhdock okg| Aho 5$75 Up|kuu `kqkci~k` hd uhdock okg|

Uh$ di \ku{cp `kue|h~phid\ku{cp ia uhdock

okg| pkkpb

\ku{cp ia eidpgep

mkub okg| pkkpb

@haak|kdek hd

qgc{k

7 Up|kuu hd R-grhu 75>$0;0 770$8$2;8 71$1>0( Ahdhpk Kckmkdp Gdgcxuhu ai| @kuhod Kdohdkk|u# Uiehkpx ia

G{pimiphqk Kdohdkk|u# [UG$

V


36/37



51

G~~kd`hr -7 "Gdgcxphegc uic{phid ai| ~g|p-L(


37/37


finite element analysis- prabhakar

Documents