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Analiza liniara avansata in domeniul dinamic pe un cadru modelat cu elemente finite de
tip bara si cu elemente de volum
Se cunosc:
-E=2.1*104[MPa]
-=0.2
-=2500 [kg/m3
]-sec!unea "ans#e"sa$a a sa$%!$o": 0.4&0.4
-sec!unea "ans#e"sa$a a g"!n'!$o": 0.3&0.5
(na$!'a se #a "ea$!'a !n )oua ea%e:
(- (na$!'a s"ucu"!! "ea$!'aa )!n cu"+e s! )!sc"e!'aa cu e$emenu$ ,E(M 2
,- (na$!'a s"ucu"!! "ea$!'aa )!n #o$ume s! )!sc"e!'aa cu e$emenu$ S.
Cazul A
"!g!nea mo)e$u$u! ese !n o"!g!nea s!semu$u! )e coo")onae %"!n u"ma"e %uncu$ 1 #a !
!nce%e )!n 0 0. Punce$e "amase se #o" mo)e$a )e os !n sus %en"u !eca"e sa$%. !n Geo
Panel>Status1se#o" ac!#a %unce$ePT s!cu"+e$e CR, )u%a ca"e se #a sa$#a s! se #o" ac!#a
)e $a +uonu$Auto.
eoa"ece sun )oua sec!un! "ans#e"a$e )!e"!e !n aces ca' ( mo)e$u$ se #a e$a+o"a
!n )oua ea%e:
Ea%a (.1-se #a mo)e$a numa! sa$%!! %en"u ca"e se #a )e!n! en!aea 1 ce #a con!ne
!%u$ )e e$emen !n! %"o%"!ea!$e )e mae"!a$ consane$e "ea$e s! )!sc"e!'a"ea
Ea%a (.2-se #o" mo)e$a !n con!nua"e g"!n'!$e %en"u ca"e se #o" )e!n! en!aea 2 ce
#a con!ne !%u$ )e e$emen !n! %"o%"!ea!$e )e mae"!a$ consane$e "ea$e s! )!sc"e!'a"ea
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Cazul A - Etapa A.1
Se% (-1 : 6o$umns mo)e$!ng.
-e!n!ng !n!e e$emen 7%e "om:Propsets 8ElementGroup 8Element group: 1 8
Element name:BEAM 2D. n 9e secon) !n)o "ema!ns )eau$ a"!+ues.
-e!n!ng 9e c"oss sec!on )!mens!ons "om:Propsets8Beam Section8Associate
Element group: 1 9!s "ee" o 9e !"s 7%e o !n!e e$emen use) !n ou" mo)e$ 8 Real
Constant set:1 9!s !s 9e !"s g"ou% o consans a))e) o !"s !n!e e$emen. n 9e secon)
!n)o: 8Section num!er0: use" sec!on:1 +ecause one 1 means 9a e an o use a
san)a") s9a%e a#a!$a+$e !n 6osmosm.
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-"o. o# !eam section constants to !e entere: S%ec!7 9o man7 +oun)a"!es 9a#e ou" s9a%e
9a mus +e )e!ne). ;o" a "ecangu$a" s9a%e !s necessa"7 2 )!e"en +oun)a"7 9e!g9 uenc7O,uck$!ng8;"e>uenc7 %!ons
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-(na$7s!s8;"e>uenc7O,uck$!ng8Fun ;"e>uenc7
-Fesu$8!s8?au"a$ ;"e>uenc7
-7nam!c (na$7s!s: (na$7s!s8PSRB?(M68Se$. P (na$7s!s 7%e
2: Mo)a$ !me-9!so"7 ana$7s!s
10 50 0 0.2 0: ?ema"k.
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- (na$7s!s8PSRB?(M68PR@P@8Se P"!n %!ons
- (na$7s!s8PSRB?(M68P 6u"#es86u"#e 7%e
- (na$7s!s8PSRB?(M68P 6u"#es8e!ne
n 9e ne& !n)o PR6@FE;N !s !$$e) !9 !no"ma!on "om g"a%9!c.
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- (na$7s!s8PSRB?(M68PR@P@8Se P$o %!ons
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-!s%$a78AB P$o8(c!#ae P"e%"oc
--!s%$a78AB P$o8P$o 6u"#es
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-oa)s,68S"ucu"a$8;o"ce8e!ne +7 cu"#es. a$ue 1N means 9e cu"#e 1 )e!ne) !n
%"e#!ous.
-(na$7s!s8Pos 7nam!c8Fun Pos 7nam!c
-Fesu$ 8 P$o8 !s%$acemen/Fes%onse/Feac!on
Vector Plot
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-E)!8P$o86u"#es
(cce$e"og"am
-7nam!c (na$7s!s: (na$7s!s8PSRB?(M68Se$. P (na$7s!s 7%e
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-6on"o$8(c!#ae8Se En!786:!me 6u"#e
-(na$7s!s8PosR7nam!c8PR6u"#es86u"#e 7%e
HHHHH 2 o" 1HHHH
-(na$7s!s8PosR7nam!c8PR6u"#es8e!ne
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e"o +ecause e nee) o !m%o" a !$e.
ook !n: 6O6osmosmO%"o+sO()#7nam!cs 8($$*.*815.( 8 69eck e&ens!on !9
"!g9 c$!ck8P"o%e"!es. 9en o%en.
-!s%$a78ABRP$os8(c!#ae P"e%"oc8
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--!s%$a78AB P$o8P$o 6u"#es
-(na$7s!s8PosR7nam!c8PR,aseRE&c!a!on8,ase E&c!a!on ;aco"
,aseRcu" mu$!%$!e" com%. o" S.-(na$7s!s8PosR7nam!c8Fun Pos 7nam!c
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E"o"" a%%ea"e) us!ng 6u"#e $a+e$ 2. So$u!onH
-(na$7s!s8PosR7nam!c8PR6u"#es8e$ee. C9!c9 cu"#e !s )e$ee)H
-(na$7s!s8PosR7nam!c8PR6u"#es8e!ne
-ook !n 9e o$)e" 9e"e 9e mo)e$ !s c"eae) o" 9e !$e !9 9e mo)e$ name an) e&ens!on
*.6F1
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E""o" 9!c9 can a%%ea" ! as use) a "ong num+e" o" cu"#e $a+e$
oo) message ae" $oa)!ng
*.6F1
-!s%$a78ABRP$os8(c!#ae P"e%"oc8
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6$ea" 9e !n)o us!ng +uon
-!s%$a78ABRP$os8P$o 6u"#es
?one&!sen !no"ma!on: !s an e""o" a%%ea"e) us!ng a "ong num+e" o" cu"#e $a+e$ an) g"a%9
num+e".
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oo) message ae" %$o cu"#es
( sma$$ mo)!!ca!on: -(na$7s!s8PosR7nam!c8PR,aseRE&c!a!on8,ase E&c!a!on
;aco"
-!s%$a78ABRP$os8(c!#ae P"e%"oc8
-!s%$a78ABRP$os8P$o 6u"#es
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-oa)s,68oa)s %!ons8!me Pa"amee"s
-(na$7s!s8PosR7nam!c8P u%u8Se P"!n o%!ons
-(na$7s!s8PosR7nam!c8P u%u8Se P$o %!ons
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-(na$7s!s8PosR7nam!c8!s P (na$7s!s %!ons
9!s !s "om %"e#!ous ana$7s!s us!ng 9e #a"!a+$e o"ce acco")!ng 9e g"a%9.
-(na$7s!s8PosR7nam!c8Se$ec P (na$7s!s 7%e
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-(na$7s!s8 PosR7nam!c8Fun Pos 7nam!c
-Fesu$s8P$o8!s%$acemen/Fes%onse/Feac!on
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necessa"7 !s %oss!+$e o c"eae mo"e !n)os o s9o )!e"en "esu$s s!mu$aneous$7.
6$!ck !ce on ?e !nN 9en on !$eN
-Fesu$s8Seu%8Pos%"oces 7%e8!nea" S"ucu"a$
-Fesu$s8P$o8 !s%$acemen/Fes%onse/Feac!on8oa) case n". :1Ieco" %$o
-Fesu$s8Seu%8Pos%"oces 7%e8Pos 7nam!c
-Fesu$s8P$o8 !s%$acemen/Fes%onse/Feac!on8!me se% num+e": 12Ieco" %$o
o no o"kHHHH
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The Case B-The structure created with volumes and meshed usin !"#$% element.
-6"eae ke7 %o!ns o" 9e +ase o co$umns. 6oo")!naes !n AB %$ane: TP10 0 TP20 0.4
TP30.4 0.4 TP40.4 0 TP55 0 TPQ5 0.4 TPJ5.4 0.4 TPK5.4 0 TPL10 0
TP1010 0.4 TP1110.4 0.4 TP1210.4 0
-6"eae 3 su"aces us!ng ke7 %o!ns: eome"78Su"aces8e!ne +7 4 P.
!e o 9e !n)o o" 9!") su"ace.
-6"ea!on o 9e co$umns: ,eo"e sa" s!c9 o !some"!c #!e:
eome"78o$umes8ene"a!on8E&"us!on.
o" #o$ume n". 1
o" #o$ume n". 2: S!m!$a" o" #o$ume n".3.
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-,eams c"ea!on: !s sa"!ng !9 ke7 %o!ns on 9e ace o 9e co$umn n". 1.
6oo")!naes o ke7 %o!ns c"eae): TP250.4 0.05 2.5 TP2Q0.4 0.35 2.5 TP2J0.4 0.35
3 TP2K0.4 0.05 3 TP2L0.4 0.35 5.5 TP300.4 0.05 5.5 TP310.4 0.35 Q
TP320.4 0.05 Q
9e ne& se% !s o c"eae ke7 %o!ns on 9e ace o co$umns n".2 an) n". 3 o c"eae +eams.
9!s se% can +e so$#e) !n o a7s. ;!"s e can c"eae %o!n +7 %o!n ae" a coo")!naes
ca$cu$a!on o" 9e secon) a7 !s o co%7. n 9!s e&am%$e e !$$ co%7.
-6"eae a ne coo")!nae s7sem a 9e +ase o co$umn n".2:
eome"786oo")!naeRS7sems83 Po!ns.
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,eo"e %o!ns gene"a!on !s necessa"7 o go +ack !n !n!!a$ coo")!nae s7sem:
6on"o$8(c!#ae8Se En!786S: 6oo")!nae s7sem80.
-?o e an o co%7 %o!ns: eome"78Po!ns8ene"a!on86o%7
-(s e can see !n 9e ne& !mage 9as a%%ea"e) ne %o!ns "om 33 o 40. 9ese %o!ns !$$ +e
use) o c"eae su"aces on 9e ace o co$umn n".2 an) 9en c"eae #o$umes o" +eams +eeenco$umn n".2 an) n".3.
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-?o !s c"eae) a ne coo")!nae s7sem a 9e +ase o co$umn n".3 an) 9en !$$ co%7 %o!n
"om 9e ace o co$umn n". 2 eome"786oo")!naeRS7sems83 Po!ns.
(s a+o#e +eo"e gene"a!on o %o!ns !s necessa"7 o go +ack !n %"e#!ous coo")!nae s7sem:
6on"o$8(c!#ae8Se En!786S: 6oo")!nae s7sem83.
s no #e"7 s!m%$e an) akes !me as e$$ as coo")!naes ca$cu$a!on o" eac9 %o!n.
-,eams c"ea!on: ***Ce a"e !n 9e 6oo")!nae s7sem 4. ?o %"o+$emU
eome"78Su"aces8e!ne +7 4 P.
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eome"78o$umes8ene"a!on8E&"us!on.
-6"eae su"aces 31 an) 32 on 9e ace o co$umn n".2
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eome"78o$umes8ene"a!on8E&"us!on.
-6"eae su"aces 43 an) 44 on 9e ace o co$umn n".3
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eome"78o$umes8ene"a!on8E&"us!on.
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9e mo)e$ !s "ea)7U
-e!ne !n!e e$emen: P"o%eses8E$emen g"ou%
-e!ne Mae"!a$ %"o%e"!es: P"o%ses8Mae"!a$ P"o%e"7: ***#a$ues o +e !n [m].
9!s means 2500 [kg/m3]
9!s means 21V104MPa.
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-Mes9!ng8Pa"ame"!cMes98o$umes: ,ecause co$umns c"oss sec!on !s )ee"en "om
+eams 9e mes9 mus +e %e"o"me) se%a"ae$7. o +eg!n !9 co$umns.
6o$umn mes9
***C9en e a"e !9 9e a""o o 9e mouse !n 9e ce$$s o 9e !n)o %a"!cu$a"$7 !n ce$$s
?um+e" o e$emens on !"s secon) an) 9!") cu"#eN $e c$!ck "om secon) +7 secon) o
!n) 9e $!ne o 9e !"s #o$ume 9!c9 +ecome "om 9!e o magena co$o".
-,eams mes9!ng: Mes9!ng8Pa"ame"!cMes98o$umes8:
6$ea" 9e sc"een 9en: E)!8P$o8o$umes.
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oom !n on #o$umes 4 an) 5 o "e"es9 !n)o an) 9e e)ges o +ecome 9!e.
***Look closely because first and second curve changes its color almost imperceptible, is
observable just a change in texture !nsea) 9e co$o" o" 9!") cu"#e !s e$$ #!s!+$e.
***Mes9 se% +7 se% eac9 #o$ume "om 4 o L o !)en!7 %"o%e"$7 9ose 9"ee cu"#es. 9e
a!m !s o ge a co""e$a!on +eeen mes9 o 9e co$umn an) +eam !n o %$anes AB an) A.
6$ea" aga!n 9e sc"een an) 9en %$o #o$umes o con!nue !9 #o$ume n". 5.
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(+o#e e 9a#e co""e$a!on !n AB %$ane.
6"oss sec!on o co$umn on B a&!s as )!#!)e) !n K e$emens an) on A a&!s !n 4 e$emens. n
9e $eng9 o 9e co$umn on a&!s ! as )!#!)e) !n Q0 e$emens.
9e !)9 o +eam on B a&!s as )!#!)e) !n Q e$emens an) 9e!g9 on a&!s !n 5 e$emens o
ge co""e$a!on !9 co$umns. n 9e $eng9 o 9e +eam on A a&!s ! as )!#!)e) !n 23
e$emens.
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(+o#e e 9a#e co""e$a!on !n A %$ane.
@no"unae$7 some c9anges a"e necessa"7 +ecause #o$umes K an) L as )!#!)e) !n 23
e$emens on $eng9 +u 9e7 9a#e no a $eng9 o 4.Q as +eams +eeen co$umns 9e!" $eng9
!s us 2. ?o e !$$ )e$ee 9e mes9 o" 9ese o #o$umes an) mes9 aga!n. n !mage
un)e"nea9 !s #!s!+$e a )!e"ence !n )ens!7 a 9e "!g9 o co$umn 3 9e"e !s +eam K an) a
9e $e 9e"e !s a +eam +eeen co$umns.
Mes9!ng8Pa"ame"!cRMes98e$ee E$emens on o$ume
Mes9!ng8Pa"ame"!cRMes98o$umes
,ecause ae" mes9!ng !n a $o o e$emens 9e %"og"am "un s$o$7 9en ! %$o 9em on
sc"een !s "ecommen)e) o c$ea" 9e sc"een an) e)! on$7 #o$umes.
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?o %$o e$emens: E)!8P$oI8E$emens
?o 9e e$emens $eng9 o +eams ous!)e co$umn 3 !s ok
2/10=0.2 !s 9e same !9 9e e$emens $eng9 o 9e +eams +eeen co$umns 4/23=0.2.
9e mo)e$ !s u%s!)e )on !n AB %$ane an) e nee) ! !n u%"!g9 %os!!on. 6$ea" 9e
sc"een/P$o #o$umes/"oae a"oun) A a&!s un!$ e ge A %$ane/P$o e$emens.
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-n 9!s momen ou" mo)e$ !s !n s%ace an) ! !s no su%%o"e) so e mus o a%%$7 su%%o"s
an) o cance$ a$$ Q )eg"ee o "ee)om a 9e +ase o 9e co$umns !&e) su%%o"s. Mean!ng o!& su"ace 1 2 < 3.
oa),68S"ucu"a$8!s%$acemen8e!ne +7 Su"aces
-e o $oa) 9e s"ucu"e: oa),68S"ucu"a$8P"essu"e8 e!ne +7 Su"aces
We"e as a%%$!e) 9e %"essu"e us o" one
su"ace.
,u kno!ng #a$ue +eeen su"ace 3Q an) 4K 12 e 9a#e a%%$!e) 9e %"essu"e
s!mu$aneous$7. Su"aces [24 3Q < 4K] a"e u%%e" su"aces o" !ne"!o" +eam.
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Su"aces [30 42 < 54] a"e u%%e" su"aces o" su%e"!o" +eam an) 9e7 e"e $oa)e)
s!mu$aneous$7 acco")!ng !mage +e$$o.
(n) !na$$7 ou" s"ucu"e !s su%%o"e) an) $oa)e).
P"e%a"e 9e mo)e$ o" ana$7s!s: (na$7s!s8Sa!c8Sa!c (na$7s!s %!ons.
(c!#ae s"ess ca$cu$a!on: (na$7s!s8Sa!c8(c!#ae s"ess 6a$c
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Me"ge 9e no)es: Mes9!ng 8?o)es8Me"ge
6om%"ess 9e no)es: Mes9!ng 8?o)es86om%"ess
?o "un ana$7s!s: (na$7s!s8Sa!c8Fun Sa!c (na$7s!s
a$$ se%s as o$$oe) 9e ana$7s!s 9a) o "un %"o%e"$7 an) a$$o us o see "esu$s.
Fesu$s8P$o8!s%$acemen/Fes%onse/Feac!on. ***7%e 'e"oN !n 9e ce$$ co""es%on)!ng o
!"ec!on: A6om% an) B6om%.
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E)!8P$o8o$umes.
Fesu$s8E&"emes8!s%$acemens/Fes%onse/Feac!on8@: !s%$acemens.
Fesu$s8!s8!s%$acemens/Fes%onse/Feac!on8Se num+e"-2:Feac!on ;o"ces
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(na$7s!s8;"e>uenc7O,uck$!ng8;"e>uenc7 %!ons
-(na$7s!s8;"e>uenc7O,uck$!ng8Fun ;"e>uenc7: -Fesu$8!s8?au"a$ ;"e>uenc7
;o" com%a"!son !9 "e>uenc7 o 9e same s"ucu"e mo)e$e) !9 +eams.
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%&namic Anal&sis/Curve defined b& user'
;o$$o se%s s9on sa"!ng "om %age 22 un!$ %age 2J.
"a%9 !s ok.n 9e ne& !mages !s s9on "esu$ o 9e ana$7s!s 9!c9 can +e com%a"e) !9 "esu$s "om
9e case ( 9e same s"ucu"e mo)e$e) !9 beame$emen.
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%&namic Anal&sis/Curve created automaticall&(Acceleroram'
;o$$o se%s s9on sa"!ng "om %age 2K un!$ %age 3K.
9e ;FEX g"a%9 !s ok
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9e ME g"a%9 !s ok
(e" a co""ec "unn!ng o ana$7s!s acco")!ng %age 3J "esu$s a"e a#a!$a+$e o +e %$oe).
-Fesu$s8P$o8!s%$acemen/Fes%onse/Feac!on
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9en: E)!8P$o8o$umes
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