chapter 8 nonlinearity

7/24/2019 Chapter 8 Nonlinearity

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Chapter 8: Nonlinear Structural Analysis

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8.1 What is Structural Nonlinearity?

%ou en&ounter stru&tural nonlinearities on a routine basis' (or instan&e) henever +ou stapleto pie&es of paper to,ether) the -etal staples are per-anentl+ bent into a different shape'./ee (i,ure "01.a' If +ou heavil+ load a ooden shelf) it ill sa, -ore and -ore as ti-e

passes' ./ee (i,ure "01.b' s ei,ht is added to a &ar or tru&) the &onta&t surfa&es beteenits pneu-ati& tires and the underl+in, pave-ent &han,e in response to the added load' ./ee(i,ure"01.&' If +ou ere to plot the load0defle&tion &urve for ea&h of these exa-ples) +ouould dis&over that the+ all exhibit the funda-ental &hara&teristi& of nonlinear stru&tural

behavior0a &han,in, stru&tural stiffness'

Figure 8-1 Common examples of nonlinear structural eha!ior

8.1.1 Causes of Nonlinear "eha!ior

Nonlinear stru&tural behavior arises fro- a nu-ber of &auses) hi&h &an be ,rouped intothree prin&ipal &ate,ories
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8.1.1.1 Changing Status #$nclu%ing Contact&

Man+ &o--on stru&tural features exhibit nonlinear behavior that isstatus-dependent' (orexa-ple) a tension0onl+ &able is either sla& or taut a roller support is either in &onta&t or notin &onta&t' /tatus &han,es -i,ht be dire&tl+ related to load .as in the &ase of the &able) or

the+ -i,ht be deter-ined b+ so-e external &ause'

/ituations in hi&h contacto&&urs are &o--on to -an+ different nonlinear appli&ations'Conta&t for-s a distin&tive and i-portant subset to the &ate,or+ of &han,in,0statusnonlinearities'

/ee Chapter #for detailed infor-ation on perfor-in, &onta&t anal+ses usin, N/%/'

8.1.1.' (eometric Nonlinearities

If a stru&ture experien&es lar,e defor-ations) its &han,in, ,eo-etri& &onfi,uration &an &ausethe stru&ture to respond nonlinearl+' n exa-ple ould be the fishin, rod shon in (i,ure "02' Geo-etri& nonlinearit+ is &hara&teri6ed b+ 7lar,e7 displa&e-ents and8or rotations'

Figure 8-' A fishing ro% %emonstrates geometric nonlinearity

8.1.1.) *aterial Nonlinearities

Nonlinear stress0strain relationships are a &o--on &ause of nonlinear stru&tural behavior'Man+ fa&tors &an influen&e a -aterial9s stress0strain properties) in&ludin, load histor+ .as inelasto0plasti& response) environ-ental &onditions .su&h as te-perature) and the a-ount ofti-e that a load is applied .as in &reep response'

8.1.' "asic $nformation Aout Nonlinear Analyses

N/%/ e-plo+s the 7Neton0:aphson7 approa&h to solve nonlinear proble-s' In thisapproa&h) the load is subdivided into a series of load in&re-ents' The load in&re-ents &an beapplied over several load steps' (i,ure"03illustrates the use of Neton0:aphson e;uilibriu-iterations in a sin,le


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>efore ea&h solution) the Neton0:aphson -ethod evaluates the out0of0balan&e load ve&tor)hi&h is the differen&e beteen the restorin, for&es .the loads &orrespondin, to the ele-ent

stresses and the applied loads' The pro,ra- then perfor-s a linear solution) usin, the out0of0balan&e loads) and &he&s for &onver,en&e' If &onver,en&e &riteria are not satisfied) the out0of0balan&e load ve&tor is re0evaluated) the stiffness -atrix is updated) and a ne solution isobtained' This iterative pro&edure &ontinues until the proble- &onver,es'

nu-ber of &onver,en&e0enhan&e-ent and re&over+ features) su&h as line sear&h) auto-ati&load steppin,) and bise&tion) &an be a&tivated to help the proble- to &onver,e' If &onver,en&e&annot be a&hieved) then the pro,ra- atte-pts to solve ith a s-aller load in&re-ent'

In so-e nonlinear stati& anal+ses) if +ou use the Neton0:aphson -ethod alone) the tan,entstiffness -atrix -a+ be&o-e sin,ular .or non0uni;ue) &ausin, severe &onver,en&e

diffi&ulties' /u&h o&&urren&es in&lude nonlinear bu&lin, anal+ses in hi&h the stru&tureeither &ollapses &o-pletel+ or 7snaps throu,h7 to another stable &onfi,uration' (or su&hsituations) +ou &an a&tivate an alternative iteration s&he-e) the arc-length method) to helpavoid bifur&ation points and tra& unloadin,'

The ar&0len,th -ethod &auses the Neton0:aphson e;uilibriu- iterations to &onver,e alon,an arc) thereb+ often preventin, diver,en&e) even hen the slope of the load vs' defle&tion&urve be&o-es 6ero or ne,ative' This iteration -ethod is represented s&he-ati&all+ in(i,ure"04'

Figure 8- ra%itional Ne+ton-,aphson *etho% !s. Arc-/ength *etho%

To su--ari6e) a nonlinear anal+sis is or,ani6ed into three levels of operation
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The 7top7 level &onsists of the load stepsthat +ou define expli&itl+ over a 7ti-e7 span

.see the dis&ussion of 7ti-e7 in Chapter2of theANSYS Basic Analysis ProceduresGuide' ?oads are assu-ed to var+ linearl+ ithin load steps .for stati& anal+ses'

@ithin ea&h load step) +ou &an dire&t the pro,ra- to perfor- several solutions

.substepsor time steps to appl+ the load ,raduall+'

t ea&h substep) the pro,ra- ill perfor- a nu-ber of equilibrium iterationsto

obtain a &onver,ed solution'

(i,ure"05illustrates a t+pi&al load histor+ for a nonlinear anal+sis' lso see the dis&ussion ofload steps) substeps) and e;uilibriu- iterations in Chapter2of theANSYS Basic Analysis

Procedures Guide'

Figure 8-0 /oa% steps susteps an% 2time2

The N/%/ pro,ra- ,ives +ou a nu-ber of &hoi&es hen +ou desi,nate &onver,en&e&riteria +ou &an base &onver,en&e &he&in, on for&es) -o-ents) displa&e-ents) or rotations)or on an+ &o-bination of these ite-s' dditionall+) ea&h ite- &an have a different&onver,en&e toleran&e value' (or -ultiple0de,ree0of0freedo- proble-s) +ou also have a&hoi&e of &onver,en&e nor-s'

%ou should al-ost ala+s e-plo+ a for&e0based .and) hen appli&able) -o-ent0based&onver,en&e toleran&e'


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throu,h anal+sis' Path dependent proble-s usuall+ re;uire that loads be applied slol+ .thatis) usin, -an+ substeps to the final load value'

Figure 8-6 Nonconser!ati!e #path-%epen%ent& eha!ior

8.1.'.' Susteps

@hen usin, -ultiple substeps) +ou need to a&hieve a balan&e beteen a&&ura&+ ande&ono-+ -ore substeps .that is) s-all ti-e step si6es usuall+ result in better a&&ura&+) butat a &ost of in&reased run ti-es' N/%/ provides auto-ati& ti-e steppin, that is desi,ned forthis purpose'

Automatic time steppingadAusts the ti-e step si6e as needed) ,ainin, a better balan&ebeteen a&&ura&+ and e&ono-+' uto-ati& ti-e steppin, a&tivates the N/%/

pro,ra-9s bisectionfeature'

>ise&tion provides a -eans of auto-ati&all+ re&overin, fro- a &onver,en&e failure' Thisfeature ill &ut a ti-e step si6e in half henever e;uilibriu- iterations fail to &onver,e andauto-ati&all+ restart fro- the last &onver,ed substep' If the halved ti-e step a,ain fails to&onver,e) bise&tion ill a,ain &ut the ti-e step si6e and restart) &ontinuin, the pro&ess until&onver,en&e is a&hieved or until the -ini-u- ti-e step si6e .spe&ified b+ +ou is rea&hed'

8.1.'.) /oa% an% 5isplacement 5irections

Consider hat happens to loads hen +our stru&ture experien&es lar,e defle&tions' In -an+instan&es) the loads applied to +our s+ste- -aintain &onstant dire&tion no -atter ho thestru&ture defle&ts' In other &ases) for&es ill &han,e dire&tion) 7folloin,7 the ele-ents asthe+ under,o lar,e rotations'

The N/%/ pro,ra- &an -odel both situations) dependin, on the t+pe of loadapplied'Accelerationsand concentrated forces-aintain their ori,inal orientation) re,ardlessof the ele-ent orientation' Surface loads ala+s a&t nor-al to the defle&ted ele-ent surfa&e)and &an be used to -odel 7folloin,7 for&es' (i,ure "0!illustrates &onstant0dire&tion andfolloin, for&es'

Note0Nodal &oordinate s+ste- orientations are not updated in a lar,e defle&tion anal+sis'Cal&ulated displa&e-ents are therefore output in the ori,inal dire&tions'
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Figure 8-7 /oa% %irections efore an% after %eflection

8.1.'. Nonlinear ransient Analyses

The pro&edure for anal+6in, nonlinear transient behavior is si-ilar to that used for nonlinearstati& behavior +ou appl+ the load in in&re-ental steps) and the pro,ra- perfor-se;uilibriu- iterations at ea&h step' The -ain differen&e beteen the stati& and transient

pro&edures is that ti-e0inte,ration effe&ts &an be a&tivated in the transient anal+sis' Thus)7ti-e7 ala+s represents a&tual &hronolo,+ in a transient anal+sis' The auto-ati& ti-esteppin, and bise&tion feature is also appli&able for transient anal+ses'

8.' sing (eometric Nonlinearities/-all defle&tion and s-all strain anal+ses assu-e that displa&e-ents are s-all enou,h thatthe resultin, stiffness &han,es are insi,nifi&ant'

In &ontrast) large strainanal+ses a&&ount for the stiffness &han,es that result fro- &han,es inan ele-ent9s shape and orientation' >+ issuin, N/(9*)=N .GBI path *ain*enu;Solution;Analysis ptions) +ou a&tivate lar,e strain effe&ts in those ele-ent t+pesthat support this feature' The lar,e strain feature is available in -ost of the solid ele-ents.in&ludin, all of the lar,e strain and h+perelasti& ele-ents) as ell as in -ost of the shell and

bea- ele-ents' ?ar,e strain effe&ts are not available in the N/%/8?inearPlus pro,ra-'

The lar,e strain pro&edure pla&es no theoreti&al li-it on the total rotation or strainexperien&ed b+ an ele-ent' .Certain N/%/ ele-ent t+pes ill be subAe&t to pra&ti&alli-itations on total strain0see belo' oever) the pro&edure re;uires thatstrain increments-ust be restri&ted to -aintain a&&ura&+' Thus) the total load should be

broen into s-aller steps'

Stress-Strain

In lar,e strain solutions) all stress0strain input and results ill be in ter-s of truestressand true .or logarithmic strain' .In one di-ension) true strain ould be expressed as D ln.E>.>8E>.>$' (or s-all0strain re,ions of response) true strain and en,ineerin, strain areessentiall+ identi&al' To &onvert strain fro- s-all .en,ineerin, strain to lo,arith-i& strain)
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use lnD ln .1 F en,' To &onvert fro- en,ineerin, stress to true stress) use trueD en,.1 F

en,' .This stress &onversion is valid onl+ for in&o-pressible plasti&it+ stress0strain data'

/arge 5eflections +ith Small Strain

This feature is available in all bea- and -ost shell ele-ents) as ell as in a nu-ber of thenonlinear ele-ents' IssueN/(9*=N .*ain *enu;Solution; Analysis ptions toa&tivate lar,e defle&tion effe&ts forin those ele-ents that are desi,ned for s-all strainanal+sis' t+pes that support this feature'

8.'.1 Stress Stiffening

The out0of0plane stiffness of a stru&ture &an be si,nifi&antl+ affe&ted b+ the state of in0planestress in that stru&ture' This &ouplin, beteen in0plane stress and transverse stiffness) nonasstress stiffening) is -ost pronoun&ed in thin) hi,hl+ stressed stru&tures) su&h as &ables or

-e-branes' dru-head) hi&h ,ains lateral stiffness as it is ti,htened) ould be a &o--onexa-ple of a stress0stiffened stru&ture'

ven thou,h stress stiffenin, theor+ assu-es that an ele-ent9s rotations and strains are s-all)in so-e stru&tural s+ste-s .su&h as in (i,ure"0".a) the stiffenin, stress is onl+ obtainable

b+ perfor-in, a lar,e defle&tion anal+sis' In other s+ste-s .su&h as in (i,ure "0".b) thestiffenin, stress is obtainable usin, s-all defle&tion) or linear) theor+'

Figure 8-8 Stress-stiffene% eams

To use stress stiffenin, in the se&ond &ate,or+ of s+ste-s) +ou -ust issue 4S,9S)=N .GBIpath *ain *enu;Solution;Analysis ptions in +our first load step'

?ar,e strain and lar,e defle&tion pro&edures in&lude initial stress effe&ts as a subset of theirtheor+' (or -ost ele-ents) initial stiffness effe&ts are auto-ati&all+ in&luded hen lar,edefor-ation effe&ts are a&tivated HN/(9*)=N .GBI path *ain*enu;Solution;Analysis ptions'

8.'.' Spin Softening

/pin softenin, adAusts .softens the stiffness -atrix of a rotatin, bod+ for d+na-i& -asseffe&ts' The adAust-ent approxi-ates the effe&ts of ,eo-etr+ &han,es due to lar,e defle&tion&ir&u-ferential -otion in a s-all defle&tion anal+sis' It is usuall+ used in &onAun&tion ith

prestressin, H4S,9S .GBI path *ain *enu;Solution; Analysis ptions) hi&h is&aused b+ &entrifu,al for&e in the rotatin, bod+' It should not be used ith the other
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defor-ation nonlinearities) lar,e defle&tion or lar,e strain' /pin softenin, is a&tivated b+theKSPNfield on the*9(A&o--and .GBI path *ain *enu;4reprocessor;/oa%s;-/oa%s- Apply;-Structural- ther;Angular


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The auto-ati& ti-e steppin, feature HAS .GBI path *ain *enu;Solution;ime>Fre@uenc;ime Susteps ill respond to plasti&it+ afterthe fa&t) b+ redu&in, theload step si6eaftera load step in hi&h a lar,e nu-ber of e;uilibriu- iterations as

perfor-ed or in hi&h a plasti& strain in&re-ent ,reater than 15J as en&ountered' If too

lar,e a step as taen) the pro,ra- ill bise&t and re0solve usin, a s-aller step si6e'

=ther inds of nonlinear behavior -i,ht also o&&ur alon, ith plasti&it+' In parti&ular) lar,edefle&tion and lar,e strain ,eo-etri& nonlinearities ill often be asso&iated ith plasti&-aterial response' If +ou expe&t lar,e defor-ations in +our stru&ture) +ou -ust a&tivate theseeffe&ts in +our anal+sis ith the N/(9*&o--and .GBI path *ain*enu;Solution;Analysis ptions' (or lar,e strain anal+ses) -aterial stress0strain

properties -ust be input in ter-s of truestress and logarithmicstrain'

4lastic *aterial ptions:

/everal options are available for des&ribin, plasti&it+ behavior' %ou -a+ in&orporate otheroptions into the pro,ra- b+ usin, Bser Pro,ra--able (eatures .see the Guide to ANSYS'ser Programmable (eaturesANSYS Advanced Analysis )echniques Guide'

The "ilinear Binematic ar%ening.>KIN option assu-es the total stress ran,e is e;ual toti&e the +ield stress) so that the >aus&hin,er effe&t is in&luded .see (i,ure "011' This optionis re&o--ended for ,eneral s-all0strain use for -aterials that obe+ von Mises +ield &riteria.hi&h in&ludes -ost -etals' It is not re&o--ended for lar,e0strain appli&ations' /tress0strain0te-perature data are de-onstrated in the folloin, exa-ple' (i,ure "01$.a illustratesa t+pi&al displa+ H"4/ of bilinear ine-ati& hardenin, properties'

MPTEMP,1,0,500 ! Define temperatures for Young's modulusMP,EX,1,12E6,E" ! #0 and #1 terms for Young's modulusT$,$%&,1,2 ! ()ti*ate a data ta+leT$TEMP,00 ! Temperature - 00T$D(T(,1,..E",12E6 ! Yield - ..,000/ Tangent modulus - 12E6T$TEMP,500 ! Temperature - 500T$D(T(,1,2""E",0E6 ! Yield - 2,""0/ Tangent modulus - 0E6T$&T,$%&,1 ! ist t3e data ta+le4X(E,0,001 ! Xa7is of T$P8T to e7tend from -0 to 001T$P8T,$%&,1 ! Displa9 t3e data ta+le

/ee the *49*4)*4) ") "9*4)"5AA) "/$S) >D,AN(9)

and"4/&o--and des&riptions for -ore infor-ation'
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Figure 8-1E#a& "ilinear inematic har%ening #& *ultilinear inematic har%ening

Figure 8-11 "auschinger effect

The *ultilinear Binematic ar%ening.MKIN option uses the >esselin, -odel) also

&alled the subla+er or overla+ -odel) so that the >aus&hin,er effe&t is in&luded' This option isnot re&o--ended for lar,e0strain anal+ses' T+pi&al stress0strain0te-perature data input isde-onstrated b+ this exa-ple' (i,ure "01$.b illustrates t+pi&al stress0strain &urves for thisoption'

MPTEMP,1,0,500 ! Define temperaturedependent EX,MP,EX,1,12E6,E" ! as in a+o*e e7ampleT$,M%&,1,2 ! ()ti*ate a data ta+leT$TEMP,,T(& ! e7t T$D(T( *alues are strainsT$D(T(,1,"6:E",5E",:E",10E",15E"! trains for all tempsT$TEMP,00 ! Temperature - 00T$D(T(,1,..E",50E",55E",60E",65E" ! tresses at temperature - 00T$TEMP,500 ! Temperature - 500T$D(T(,1,2""E",":E",.0"E",.":E",.:E" ! tresses at temperature -5004X(E,0,002T$P8T,M%&,1

Please see the *49*4) *4)")"9*4)"5AA)>D,AN(9)and"4/&o--and des&riptions for -ore infor-ation'

The *ultilinear $sotropic ar%ening.MI/= option uses the von Mises +ield &riteria&oupled ith an isotropi& or hardenin, assu-ption' This option is not re&o--ended for&+&li& or hi,hl+ nonproportional load histories in s-all0strain anal+ses' It is) hoever)re&o--ended for lar,e strain anal+ses' The MI/= option &an &ontain up to 2$ different

te-perature &urves) ith up to 1$$ different stress0strain points alloed per &urve' /train
http://mostreal.sk/html/guide_55/g-str/gstr8.htm#F8-10http://mostreal.sk/html/com_55/chapter3/CS3-M.htm#MPTEMPhttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#MPhttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBhttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBhttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBTEMPhttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBTEMPhttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBTEMPhttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBDATAhttp://mostreal.sk/html/com_55/chapter3/CS3-X.htm#/XRANGEhttp://mostreal.sk/html/com_55/chapter3/CS3-X.htm#/XRANGEhttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBPLOThttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBPLOThttp://mostreal.sk/html/guide_55/g-str/gstr8.htm#F8-10http://mostreal.sk/html/com_55/chapter3/CS3-M.htm#MPTEMPhttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#MPhttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBhttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBTEMPhttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBDATAhttp://mostreal.sk/html/com_55/chapter3/CS3-X.htm#/XRANGEhttp://mostreal.sk/html/com_55/chapter3/CS3-T.htm#TBPLOT


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points &an differ fro- &urve to &urve' The sa-e stress0strain0te-perature &urves fro- theprevious exa-ple ould be input for a -ultilinear isotropi& hardenin, -aterial as follos

MPTEMP,1,0,500 ! Define temperaturedependent EX,MP,EX,1,12E6,E" ! as in a+o*e e7ampleT$,M&8,1,2,5 ! ()ti*ate a data ta+leT$TEMP,00 ! Temperature - 00T$PT,DE;&,"6:E",2""E" ! train, stress at temperature - 0T$PT,DE;&,5E",50E"T$PT,DE;&,:E",55E"T$PT,DE;&,10E",60E"T$PT,DE;&,15E",65E"T$TEMP,500 ! Temperature - 500T$PT,DE;&,"6:E",2""E" ! train, stress at temperature - 500T$PT,DE;&,5E",":E"T$PT,DE;&,:E",.0"E"T$PT,DE;&,10E",.":E"T$PT,DE;&,15E",.:E"4X(E,0,002T$P8T,M&8,1

/ee the *49*4)*4) ") "9*4)"4) >D,AN(9)and "4/&o--anddes&riptions for -ore infor-ation'

The "ilinear $sotropic ar%ening.>I/= option is lie the -ultilinear isotropi& hardenin,option) ex&ept that a bilinear &urve is used instead of a -ultilinear &urve' Input is si-ilar tothat re;uired for the bilinear ine-ati& option) ex&ept that the "&o--and no uses thelabel >I/=' This option is often preferred for lar,e strain anal+ses'

The Anisotropic.NI/= option allos for different bilinear stress0strain behavior in the-aterial x) +) and 6 dire&tions as ell as different behavior in tension) &o-pression) and shear'This option is appli&able to -etals that have under,one so-e previous defor-ation .su&h asrollin,' It is not re&o--ended for &+&li& or hi,hl+ nonproportional load histories sin&e orhardenin, is assu-ed' The +ield stresses and slopes are not totall+ independent .seetheANSYS )heory %eferencefor details'

To define anisotropi& -aterial plasti&it+) use *4&o--ands .*ain *enu;Solution;ther;Change *at 4rops to define the elasti& -oduli .L) %) ) NBL%)

NB%) and NBL' Then) issue the "&o--and H")NI/= folloedb+ "5AA&o--ands to define the +ield points and tan,ent -oduli' ./ee/e&tion 2'5'1oftheANSYS $lements %eferencefor -ore infor-ation'

The 5rucer-4rager.


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The *ultilinear 9lastic.M?/ -aterial behavior option des&ribes a &onservative .path0independent response in hi&h unloadin, follos the sa-e stress0strain path as loadin,'Thus) relativel+ lar,e load steps -i,ht be appropriate for -odels that in&orporate this t+pe of-aterial nonlinearit+' Input for-at is si-ilar to that re;uired for the -ultilinear isotropi&hardenin, option) ex&ept that the"&o--and no uses the label M?/'

8.).1.) yperelasticity

-aterial is said to be h+perelasti& if there exists an elasti& potential fun&tion .or strainener,+ densit+ fun&tion) hi&h is a s&alar fun&tion of one of the strain or defor-ationtensors) hose derivative ith respe&t to a strain &o-ponent deter-ines the &orrespondin,stress &o-ponent'

+perelasti&it+ &an be used to anal+6e rubber0lie -aterials that under,o lar,e strains anddispla&e-ents ith s-all volu-e &han,es .nearl+ in&o-pressible -aterials' ?ar,e straintheor+ is re;uired HN/(9*)=N' representative h+perelasti& stru&ture .a balloon seal isshon in (i,ure "012'

Figure 8-1' yperelastic structure

The h+perelasti& ele-ents in the N/%/ pro,ra- use a penalt+ fun&tion extension of theelasti& potential fun&tion that expli&itl+ in&ludes to pressure variables the pressure obtainedfro- displa&e-ents and a separatel+ interpolated pressure' This redu&es the lielihood ofdispla&e-ent lo&in,) hi&h &an o&&ur hen a nearl+ in&o-pressible -aterial under,oeslar,e strains'

N/%/ ele-ent t+pes %P:5) %P:5")%P:!4) %P:15") and/??1"1useup to a nine0ter- Moone+0:ivlin elasti& potential fun&tion' If +ou alread+ no values forto0ter-) five0ter-) or nine0ter- Moone+0:ivlin &onstants) +ou &an enter the- dire&tl+ ith

the "fa-il+ of &o--ands' ./ee +ourANSYS )heory %eferencefor infor-ation on theMoone+0:ivlin fun&tion' (or these ele-ent t+pes) +ou &an also spe&if+ +our on -aterialfun&tion as a Bser Pro,ra--able (eature .see the Guide to ANSYS 'ser Programmable

(eatures'

n exa-ple of dire&t Moone+0:ivlin &onstant input follos

MP,


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T$D(T(,6,0000"2! =#onstants 5, :, , and default to 00 in t3is e7ample>

/ee the *4) ") and "5AA&o--and des&riptions for -ore infor-ation'

The Moone+0:ivlin &onstants for an+ ,iven h+perelasti& -aterial are not,enerall+ available

in the open literature' Conse;uentl+) +ou -i,ht have to use the G*N9=&o--and todeter-ine these &onstants fro- a set of non experi-ental test results' /o-eti-es the-anufa&turer of the -aterial ill be able to suppl+ so-e or all of the needed test data) but+ou -i,ht find that +ou need to obtain -ore data fro- a testin, laborator+'

+perelasti& -aterial behavior is -u&h -ore &o-pli&ated than t+pi&al -etalli& -aterialbehavior' +perelasti& stress0strain relationships usuall+ differ si,nifi&antl+ for tension)&o-pression) and shear -odes of defor-ation' Therefore) usin,G*N9=to ,enerate a,enerall+ appli&able h+perelasti& -aterial -odel ill re;uire test data that en&o-passes all

possible -odes of defor-ation tension) &o-pression and shear' /ee theANSYS )heory%eferencefor a dis&ussion of h+perelasti& test -ethods and e;uivalent defor-ation -odes'

If an in&o-plete set of data is provided .for instan&e) if onl+ uniaxial tension data areavailable) the pro,ra- &an still deter-ine usable h+perelasti& -aterial properties' oever)in su&h &ases the defor-ations experien&ed in the -odel should be li-ited to be of the sa-enature as those experien&ed in the tests' In other ords) the test data should represent all-odes of defor-ation and ran,es of response .strain that ill be experien&ed in the -odel'

This advi&e is si-pl+ &o--on sense0if +ou do not *no#ho the -aterial behaves in a&ertain -ode of defor-ation or ran,e of strain) +ou &annot a&&uratel+ predi&t the behavior ofa part that experien&es su&h defor-ations or strains' (or exa-ple) if all +ou have is uniaxialtension data) don9t -odel a part that experien&es si,nifi&ant shear defor-ations' If +our test

data extend onl+ fro- $J to 1$$J strain) don9t -odel a part that experien&es 15$J strain' If)after reviein, +our anal+sis) +ou dis&over that the available test data do not ade;uatel+&hara&teri6e the -odel9s response)get more test data+

%ou &an use the G*N9=&o--and to auto-ati&all+ deter-ine a set of Moone+0:ivlin&onstants fro- experi-ental test data' fter the pro,ra- deter-ines these &onstants) it storesthe- in the database and in an arra+ para-eter' dditionall+) it rites an /CII file.&obname'T> that re&ords the Moone+0:ivlin &onstants in the for- of a seriesof "and"5AA&o--ands' =n&e su&h a file exists) +ou &an use it in future anal+ses todefine that sa-e -aterial9s Moone+0:ivlin &onstants0+ou do notneed to usethe G*N9=&o--and ever+ ti-e to re,enerate these &onstants'

8.).1. 5etermining an% Applying *ooney-,i!lin Constants

The pro&edure for deter-inin, and appl+in, Moone+0:ivlin &onstants &onsists of five -ainsteps

1'


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4' valuate the ;ualit+ of the auto-ati&all+ deter-ined Moone+0:ivlin &onstants'

5' ppl+ the Moone+0:ivlin &onstants in +our anal+sis'

8.).1.0 5imension the Arrays

Co--and.sG5$*

GBI

tility *enu;4arameters;Array 4arameters;5efine>9%it

%ou -ust di-ension arra+s before usin, theG*N9=&o--and .GBI path *ain *enu;4reprocessor;*aterial 4rops;*ooney-,i!lin;Calc Constants' In -ost &ases) +ou illneed to di-ension at least six different arra+s' .%ou &an ,ive these arra+s an+ valid para-eterna-es) but for &onvenien&e) e ill use spe&ifi& arra+ na-es) su&h as /T:IN) /T://)et&') in our dis&ussion' %ou &an substitute an+ other valid para-eter na-es that +ou lie' Thesix arra+s are

/T:IN n arra+ of en,ineerin, strain data fro- -e&hani&al -aterial tests) arran,ed

in three &olu-ns n input strain0data arra+ of di-ension Nx3) hereNe;uals the-axi-u- nu-ber of data points in an+ of the three t+pes of tests) .that is) if +ouruniaxial tension test has 2$ data points and +our shear test has 1$ data points) use

ND2$) and ,represents the three t+pes of tests' This arra+ -ust al#aysbe Nx3) evenif feer than 3 t+pes of test data are available' lthou,h it -i,ht be preferable toinput +our data points in order of as&endin, strain values) it is not ne&essar+ to do so'

o Colu-n 1 uniaxial tension and8or &o-pression data

o Colu-n 2 e;uibiaxial tension and8or &o-pression data

o Colu-n 3 shear data .planar tension and8or &o-pression

This arra+ has the di-ensionsNx3) hereNe;uals the -axi-u- nu-ber of datapoints in an+ one of the three &olu-ns' (or exa-ple) if +ou have 2$ data points fro-uniaxial tension8&o-pression tests and 1$ data points fro- shear tests)ND2$' Thisarra+ -ust ala+s beNx3) even if feer than three t+pes of test data are available'

lthou,h it -i,ht be preferable to input the data points in order of as&endin, strainvalues) it is not ne&essar+ to do so'

/T:// n arra+ of en,ineerin, stress data fro- -e&hani&al -aterial tests inputstress0data arra+) also of di-ensionNx3' %ou -ust input stress data points in the sa-eorder as the &orrespondin, strain0data input'

C=N/T Moone+0:ivlin &onstant arra+ of di-ensionx1) heree;uals the

desired nu-ber of Moone+0:ivlin &onstants' .-ust be either 2) 5) or # an+ othervalue ill produ&e an error -essa,e henG*N9=is invoed' %ou a&tuall+ tellthe pro,ra- in this di-ensionin, operation ho -an+ Moone+0:ivlin &onstants +ouant' The G*N9=&o--and later reads the di-ensions of this arra+ to deter-ine
http://mostreal.sk/html/com_55/chapter3/CS3-D.htm#*DIMhttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#*MOONEYhttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#*MOONEYhttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#*MOONEYhttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#*MOONEYhttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#*MOONEYhttp://mostreal.sk/html/com_55/chapter3/CS3-D.htm#*DIMhttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#*MOONEYhttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#*MOONEYhttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#*MOONEY


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ho -an+ Moone+0:ivlin &onstants to ,enerate) and then rites the values of those&onstants to this arra+'

.o# many ooney-%ivlin constants should you use/

s a rule of thu-b) +ou should have at least ti&e as -an+ data points .N) as defined

above as the desired nu-ber of Moone+0:ivlin &onstants' Bsin, -ore ter-s illusuall+ i-prove the statisti&al ;ualit+ of +our &urve fit .that is) it ill probabl+ be-ore ti,htl+ fitted throu,h the data points) but the overall shape of the &urve -i,ht

be orse than that obtained ith feer ter-s' s a pra&ti&al -atter) +ou shouldprobabl+ tr+ to0ter-) five0ter-) and nine0ter- fun&tions in se;uen&e) and exa-inethe resultin, stress0strain &urves to de&ide hi&h fun&tion ,ives +ou the best&o-bination of ti,ht fit and satisfa&tor+ &urve shape'

ale 8-1 Suggeste% *ooney-,i!lin constants

Numer of 4oints in the Stress-strain Cur!e Suggeste% *ooney-,i!lin Function

Noinfle&tion points .that is) sin,le &urvature To0ter-

0neinfle&tion point .that is) double &urvature (ive0ter-

)#oinfle&tion points Nine0ter-

Figure 8-1) ypical hyperelastic stress-strain cur!es

C?C n output stress0data arra+ of di-ensionNx3 .hereNis as des&ribed above)in hi&h sorted &al&ulated stress values are stored' These stress values ill be sortedinto the sa-e order as their &orrespondin, sorted strain values .hi&h ill be sortedinto as&endin, order'

/=:T/N n arra+ of di-ensionNx3 in hi&h sorted input strain data are stored'

/=:T// n arra+ of di-ensionNx3 in hi&h sorted input stress data are stored'

(or exa-ple) if +our test data &ontained up to 2$ data points for an+ one test t+pe) andif +ou anted to ,enerate a five0ter- set of Moone+0:ivlin &onstants) +ou -i,ht issue

the folloin, &o--ands to di-ension the ne&essar+ arra+s .re-e-ber that +ou &ansubstitute an+ valid para-eter na-es for the ones shon here

@D&M,T(&,,20," ! Dim arra9 =T(&> for 20 input straindatapoints@D&M,TE,,20," ! Dim arra9 =TE> for input stress data =20pts>@D&M,#8T,,5,1! Dim arra9 =#8T> for 5term M )onstants@D&M,#(#,,20,"! Dim arra9 =#(#> for sorted )al)ulated stresses@D&M,8T,,20," ! Dim arra9 =8T> for sorted input strain data@D&M,8T,,20," ! Dim arra9 =8T> for sorted input stress data

/ee the G5$*&o--and des&ription for -ore infor-ation'

8.).1.6 Fill the $nput-5ata Arrays
http://mostreal.sk/html/com_55/chapter3/CS3-D.htm#*DIMhttp://mostreal.sk/html/com_55/chapter3/CS3-D.htm#*DIM


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=n&e +ou have di-ensioned +our arra+s) +ou &an then fill the /T:IN and /T:// arra+sith test data usin, the GS9&o--and .GBI path tility *enu; 4arameters;Scalar4arameters' .,ain) re-e-ber that +ou &an ,ive these arra+s an+ valid para-eter na-es

parti&ular arra+ na-es are used here onl+ for the &onvenien&e of this dis&ussion'

Note0The G*N9=&o--and interprets all input stress and strain data asen,ineerin,stress and en,ineerin,strain'

These arra+s are of di-ensionNx3) ith ea&h &olu-n of the arra+s &ontainin, datafro- onet+pe of test) in this order

(irst &olu-n Bniaxial tension and8or uniaxial &o-pression

/e&ond &olu-n ;uibiaxial tension and8or e;uibiaxial &o-pression

Third &olu-n /hear .planar tension or &o-pression

Note that these do not have a 11 relationship ith the -odes of defor-ation and theire;uivalen&ies' The first -ode of defor-ation) uniaxial tension) has equibia1ial&o-pressionas its e;uivalen&+) but the first &olu-n of the arra+ &ontains data fro- uniaxial tensionand8or unia1ial&o-pression' ?ieise) the se&ond -ode of defor-ation) e;uibiaxial tension)has unia1ial&o-pression as its e;uivalen&+) but the se&ond &olu-n of the arra+ &ontains datafro- e;uibiaxial tension and8or equibia1ial&o-pression'

ale 8-' 5ata locations in stress an% strain input arrays

*o%e of 5eformation 9@ui!alent est ypes Array /ocation for est 5ata

Bniaxial tensionBniaxial tension;uibiaxial &o-pression

Colu-n oneColu-n to

;uibiaxial tension;uibiaxial tensionBniaxial &o-pression

Colu-n toColu-n one

/hearPlanar tensionPlanar &o-pression

Colu-n threeColu-n three

If feer than three t+pes of tests are used) +ou -ust leave the -issin, &olu-ns blan'/&he-ati&all+) data input -i,ht be represented as shon in (i,ure"014'

Figure 8-1 5ata locations in stress an% strain input arrays
http://mostreal.sk/html/com_55/chapter3/CS3-S.htm#*SEThttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#*MOONEYhttp://mostreal.sk/html/guide_55/g-str/gstr8.htm#F8-14http://mostreal.sk/html/guide_55/g-str/gstr8.htm#F8-14http://mostreal.sk/html/com_55/chapter3/CS3-S.htm#*SEThttp://mostreal.sk/html/com_55/chapter3/CS3-M.htm#*MOONEYhttp://mostreal.sk/html/guide_55/g-str/gstr8.htm#F8-14


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Consider a &ase in hi&h data fro- uniaxial tension and shear tests are available' The&o--ands to store the strain and stress data in the input0data arra+s &ould loo so-ethin,lie this .of &ourse) the arra+s &an have an+ valid arra+ na-es) and the nu-ber of data pointsrepresented b+ N1 and N2 in this exa-ple &an be an+ inte,ral nu-bers

! , ! ;irst 10 strain data points@ET,T(&=11,1>, ! train data points 11 t3roug3 1 =if 1A21>@ET,TE=1,1>, ! ;irst 10 stress data points@ET,TE=11,1>, ! tress data points 11 t3roug3 1! 3ear Data@ET,T(&=1,">, ! train data points 1 t3roug3 2 =if 2A11>@ET,TE=1,">, ! tress data points 1 t3roug3 2

/ee the GS9&o--and des&ription for -ore infor-ation'

8.).1.7 5etermine the *ooney-,i!lin Constants

To ,enerate Moone+0:ivlin &onstants auto-ati&all+) first use the "&o--and)ith2abDM==N% and )B0P)D1' Next) issue the G*N9=&o--and) insertin, theappropriate na-es of arra+s that +ou have alread+ di-ensioned .parti&ular na-es have beenused in this exa-ple for &onvenien&e of dis&ussion onl+ +ou &an use an+ valid para-eterna-esT$,M88EY,MAT,NTEMP,,1@M88EY,T(&=1,1>,TE=1,1>,,#8T=1>,#(#=1>,8T=1>,

8T=1>,Fname,Ext

The pro,ra- auto-ati&all+ deter-ines the Moone+0:ivlin &onstants) stores the- in thedatabase and in the C=N/T arra+ .hi&h &an have an+ valid para-eter na-e) and rites aseries of "and "5AA&o--ands in the /CII file(name3$1t.default file na-e

D&obname'T>'

Bniaxial e;uations ill be used for the data in &olu-n 1) e;uibiaxial e;uations for the data in&olu-n 2) and planar .pure shear e;uations for the data in &olu-n 3'

Note0ll the laborator+ test data entered in the /T:IN and /T:// arra+s ill be used todeter-ine the Moone+0:ivlin h+perelasti& -aterial &onstants'

8.).1.8 9!aluate the Huality of the *ooney-,i!lin Constants

In +our printout .file&obname'=BT) exa-ine the 788TME(B7 and the 7#8E;;&ET 8; DETEM&(T&8'7 These to values ,ive +ou astatisti&al -easure of ho ell +our &al&ulated stress0strain &urve fits the experi-ental data

points' The root0-ean0s;uare error) hi&h is expressed as a per&enta,e .that is) a value of 2'5-eans 2'5 J) should be 7&lose7 to 6ero' The &oeffi&ient of deter-ination ill be less than1'$) but should be 7&lose7 to 1'$ .that is) t+pi&all+ $'## or better'

In addition) +ou should use the G9


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tension data onl+ .&olu-n 1 of the sorted /T:IN and /T:// arra+s' /i-ilarl+) +oushould &o-pare the &al&ulated uniaxial &o-pression &urve a,ainst the uniaxial &o-pressiondata onl+) and the &al&ulated shear &urve a,ainst the shear data onl+'

@hen +ou ,raph +our &al&ulated stress0strain &urves) +ou &an extend the displa+ed &urve into

re,ions that ere not defined b+ the experi-ental data' Graphin, +our &urves over su&h anextended ran,e &an help +ou ;ualitativel+ understand +our -odel9s behavior if its responseever happens to ex&eed the ran,e of experi-ental strain' oever) reali6e that if +ou extend adispla+ed &urve into a re,ion that represents a different -ode of defor-ation) then that

portion of the displa+ ill be -eanin,less' (or instan&e) +ou should ,raph a uniaxial tension&urve onl+ in re,ions of positive strain) and a uniaxial &o-pression &urve onl+ in re,ions of&o-pressive strain' :e-e-ber that ,ood pra&ti&e usuall+ re;uires that the test data shouldrepresent all -odes of defor-ation and ran,es of response .strain experien&ed b+ +our-odel'

The G*N9=&o--and auto-ati&all+ rites the Moone+0:ivlin &onstants to the C=N/T

arra+' >e&ause G9, define t3e strain range! =XM&,XM(X>, and use t3e M )onstants =#8T> to fill t3e strain =X(>! and stress =E#(#> arra9s it3 )al)ulated dataC@E(,1,2,#8T=1>,XMIN,XMAX,X(=1>,E#(#=1>! a+el t3e grap3 a7esC4(X($,X,Engineering train4(X($,Y,Engineering tress! Plot t3e )al)ulated unia7ial )ompression )ur*eC@P8T,X(=1>,E#(#=1>

./ee the G5$*) G9AD/A") and G


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8.).1. sing the *ooney-,i!lin Constants

If the &urve0fit statisti&s and the overall &urve shape are satisfa&tor+) then +ou &an pro&eed touse the ,enerated Moone+0:ivlin -aterial properties in +our anal+sis'.The G*N9=&o--and ill have stored these &onstants in the database' In futureanal+ses usin, the sa-e -aterial -odel) +ou &an si-pl+ read in H>$N4 thefile&obname'T> to load the &onstants into +our ne database' oever) don9t for,et todefine a value for Poisson9s ratio H*4)NBL%)'''' la+s re-e-ber to exa-ine +our anal+sisresults &arefull+) to deter-ine hether or not +our -odel9s -odes of defor-ation and valuesof -axi-u- strain ere properl+ represented b+ the ori,inal test data'

nal+ses involvin, h+perelasti& ele-ents are so-eti-es ver+ sensitive to -aterial propert+spe&ifi&ation and load appli&ation' /o-e values of Moone+0:ivlin &onstants result in ver+stable stiffness -atri&es hereas others do not' Therefore) &hoose &onstants ith &aution andexperi-ent ith sli,htl+ different values if at first the anal+sis is unsu&&essful' (or nearl+in&o-pressible -aterials ith Poisson9s ratio ,reater than $'4#) e re&o--end that +ou usethe h+perelasti& ele-ents ith -ixed B0P for-ulation .%P:5)%P:5") %P:!4)and%P:15"'

Note0The ele-ent t+pes%P:"4and %P:"are intended pri-aril+ for -odelin,&o-pressible) foa-0lie elasto-ers) usin, a >lat60Ko fun&tion to des&ribe the -aterial

properties' /ele&t the >lat60Ko option b+ settin, K%=PT.2D1 for these ele-ents) thenuse *4&o--ands to enter appropriate values for L and NBL% to define the initial-aterial shear -odulus' n in&o-pressible h+perelasti& -aterial option is also availablefor %P:"4and %P:") but it is li-ited to to0ter- Moone+0:ivlin onl+' In ,eneral) itis re&o--ended that +ou use%P:5)%P:5")%P:!4)or %P:15".not %P:"4or %P:" for all in&o-pressible h+perelasti& -aterials'

Proble-s usin, h+perelasti& ele-ents &an be sensitive to the rate of load appli&ation' In -ostinstan&es) load appli&ation should be slo so as not to over0distort ele-ents in the &onver,in,se;uen&e' a&h proble- -a+ be uni;ue and re;uire spe&ial &onsideration' >ifur&ation of thesolution) indi&atin, that to or -ore different ,eo-etri& &onfi,urations have the sa-e

-ini-u- potential ener,+) -a+ o&&ur at various ti-es durin, the loadin, histor+' uto-ati&
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ti-e steppin, ith bise&tion HAS)=N is often effe&tive in over&o-in, thesediffi&ulties'

8.).1.1E Creep

"reepis a rate dependent -aterial nonlinearit+ in hi&h the -aterial &ontinues to defor-under a &onstant load' Conversel+) if a displa&e-ent is i-posed) the rea&tion for&e .andstresses ill di-inish over ti-e .stress relaxation see (i,ure"01.a' The three sta,es of&reep are shon in (i,ure "01.b' The N/%/ pro,ra- has the &apabilit+ of -odelin, thefirst to sta,es .pri-ar+ and se&ondar+' The tertiar+ sta,e is usuall+ not anal+6ed sin&e iti-plies i-pendin, failure'

Figure 8-16 Stress relaxation an% creep

Creep is i-portant in hi,h te-perature stress anal+ses) su&h as for nu&lear rea&tors' (orexa-ple) suppose +ou appl+ a preload to so-e part in a nu&lear rea&tor to eep adAa&ent parts

fro- -ovin,' =ver a period of ti-e at hi,h te-perature) the preload ould de&rease .stressrelaxation and potentiall+ let the adAa&ent parts -ove' Creep &an also be si,nifi&ant for so-e-aterials su&h as prestressed &on&rete' T+pi&all+) the &reep defor-ation is per-anent'

The &reep strain rate -a+ be a fun&tion of stress) strain) te-perature) and neutron flux level'?ibraries of &reep strain rate e;uations are built into the N/%/ pro,ra- for pri-ar+)se&ondar+) and irradiation indu&ed &reep' ./ee/e&tion 2'5'!of theANSYS $lements

%eferencefor dis&ussions of) and input pro&edures for) these various &reep e;uations' Thesee;uations re;uire spe&ifi& units) as des&ribed in Tables 2'501 throu,h 2'5013 of theANSYS

$lements %eference' In parti&ular) te-peratures used in the &reep e;uations should be basedon an absolute s&ale' %ou &an in&orporate other &reep expressions into the pro,ra- b+ usin,

Bser Pro,ra--able (eatures 6see the Guide to ANSYS 'ser Programmable (eatures'

(or hi,hl+ nonlinear &reep strain vs' ti-e &urves) a s-all ti-e step -ust be used' &reepti-e step opti-i6ation pro&edure is available HAS) C,4/$* for auto-ati&all+adAustin, the ti-e step as appropriate'

8.).1.11


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strains are t+pi&all+ ver+ lar,e .for exa-ple) 5$J or ,reater) re;uirin, lar,e strain theor+HN/(9*)=N'

is&oplasti&it+ is -odeled ith ele-ent t+pes I/C=1$)I/C=1$!)andI/C=1$") usin,nand9s -odel for -aterial properties as des&ribed in/e&tion 2'5'1of theANSYS $lements

%eference'

Figure 8-17


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be related to other pheno-ena) su&h as -oisture &ontent' The N/%/ &o--ands for nu&learsellin, &an be used analo,ousl+ to define sellin, due to other &auses'

8. ,unning a Nonlinear Analysis in

ANS=S

N/%/ e-plo+s an auto-ati& solution &ontrol -ethod that) based on the ph+si&s of +ourproble-) sets various nonlinear anal+sis &ontrols to the appropriate values' If +ou are notsatisfied ith the results obtained ith these values) +ou &an -anuall+ override the settin,s'The folloin, &o--ands are set to opti-al defaults

AS 4,95 *N$,

59/$* N,4 N9H$

NS"S $N4 SS$F

CN


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iterations' The ,eneral pro&edure follos' /ee /e&tion "'5for a sa-ple proble- that als+ou throu,h a spe&ifi& nonlinear anal+sis'

1' /pe&if+ a ne or restart anal+sis and define the anal+sis t+pe in this &ase) stati&' Theanal+sis t+pe &annot be &han,ed after the first load step .that is) after +ou issue +our

firstS/? t+pe arra+ para-eter' /ee /e&tion 2'5'2'37ppl+in, ?oadsBsin, T>? T+pe rra+ Para-eters)7 for -ore infor-ation'

4' /pe&if+ ti-e8fre;uen&+ load step options Ti-e) nu-ber8si6e of ti-e steps) and

stepped8ra-ped loadin,'

Co--and.s

$*9

NS"S

59/$*

B"C

GBI

*ain *enu;Solution;-/oa% Step pts-ime>Fre@uenc;ime ime Step>ime

Sustep
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These options &an be &han,ed at an+ load step' /ee Chapter 2of theANSYS BasicAnalysis Procedures Guidefor -ore infor-ation on these options' dvan&edti-e8fre;uen&+ options) in addition to those listed here) are dis&ussed in/e&tion "'4'2'2) 7dvan&ed ?oad /tep =ptions'7 Note that +ou onl+ have to spe&if+stepped or ra-ped loads .B"C in a transient or d+na-i& anal+sis'

nonlinear anal+sis re;uires -ultiple substeps .or ti-e steps the to ter-s aree;uivalent ithin ea&h load step so that N/%/ &an appl+ the spe&ified loads,raduall+ and obtain an a&&urate solution' The NS"Sand 59/$*&o--ands

both a&hieve the sa-e effe&t .establishin, a load step9s startin,) -ini-u-) and-axi-u- step si6e) but b+ re&ipro&al -eans'NS"Sdefines the nu-ber ofsubsteps to be taen ithin a load step) hereas59/$*defines the ti-e step si6eexpli&itl+' If auto-ati& ti-e steppin, is off) then the startin, substep si6e is usedthrou,hout the load step'

5' /pe&if+ nonlinear load step options as ne&essar+ /olution ter-ination &riteria and ar&0len,th option'

Co--and.s

A,C,*

A,C/9N

GBI

*ain *enu;Solution;-/oa% Step pts-Nonlinear;Arc-/ength pts

These options &an be &han,ed at an+ load step' /ee Chapter 2of theANSYS BasicAnalysis Procedures Guidefor -ore infor-ation on these options' dvan&ednonlinear options) in addition to those listed here) are dis&ussed in /e&tion"'4'2'2)7dvan&ed ?oad /tep =ptions'7

' /pe&if+ birth and death options as ne&essar+'

Co--and.s

9B$//

9A/$


25/62

appropriate load step' @hen ele-ents are rea&tivated) the+ have a 6ero strain state)and .if N/(9*)=N their ,eo-etri& &onfi,uration .len,th) area) et&' is updated to-at&h the &urrent displa&ed positions of their nodes' /ee theANSYS Advanced

Analysis )echniques Guidefor -ore infor-ation'!' /pe&if+ output &ontrol options' /ee Chapter 2of theANSYS Basic Analysis Procedures

Guidefor -ore infor-ation on these options'

Co--and.s

4,

,9S

9,9SD

GBI

*ain *enu;Solution;-/oa% Step pts-utput Ctrls;Solu4rintout

*ain *enu;Solution;-/oa% Step pts-utput Ctrls;5">,esults File

*ain *enu;Solution;-/oa% Step pts-utput Ctrls;$ntegration 4t

Printed 0utputH4, in&ludes an+ results data on the output file.&obname'=BT'

7atabase and %esults (ile 0utputH,9S &ontrols the data on the results file.&obname3:/T' >+ default) onl+ the last substep is ritten to the results file in anonlinear anal+sis' To rite all substeps) set the (:O field on ,9Sto ??'=nl+ 1$$$ results sets .substeps &an be ritten to the results file) but +ou &an use the

&o--and >CNF$()N:/ to in&rease the li-it.see theANSYS Basic AnalysisProcedures Guide'$1trapolation of %esults H9,9SD &opies an ele-ent9s inte,ration point stress andelasti& strain results to the nodes instead of extrapolatin, the-) if nonlinear strains.plasti&it+) &reep) sellin, are present in the ele-ent' The inte,ration point nonlinearstrains are ala+s &opied to the nodes'/ee theANSYS Basic Analysis Procedures Guidefor -ore infor-ation on ho to usethese &o--ands properl+'

"' /ave a ba&0up &op+ of the database to a na-ed file'

Co--and.s

SA


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*ain *enu;Solution;-Sol!e-Current /S

1$' If +ou need to define -ultiple load steps) repeat steps 40" for ea&h additional load step'=ther -ethods for -ultiple load steps0the load step file -ethod and the arra+ para-eter-ethod0are des&ribed in theANSYS Basic Analysis Procedures Guide'

11' ?eave the /=?BTI=N pro&essor'

Co--and.s

F$N$S

GBI

Close the Solution menu.

8..'.1 A%!ance% Analysis ptions

Stress Stiffness

To a&&ount for bu&lin,) bifur&ation behavior) N/%/ in&ludes stress stiffness in all,eo-etri&all+ nonlinear anal+ses' If +ou are &onfident of i,norin, su&h effe&ts) +ou &an turnstress stiffenin, off .SS$F)=((' This &o--and has no effe&t ith several N/%/ele-ents see theANSYS $lements %eferencefor the des&ription of the spe&ifi& ele-ents+ou9re usin,'

Ne+ton-,aphson ption

N/%/9 auto-ati& solution &ontrol ill use the (B?? Neton0:aphson option ith adaptivedes&ent off if there is a nonlinearit+ present' oever) hen node0to0node) node0to0surfa&e&onta&t ele-ents are used for &onta&t anal+sis ith fri&tion) then adaptive des&ent isauto-ati&all+ turned on .for exa-ple)PIP2$)>M23) >M24) and PIP$' Theunderl+in, &onta&t ele-ents re;uire adaptive des&ent for &onver,en&e'

Bse this option onl+ in a nonlinear anal+sis' This option spe&ifies ho often the tan,ent-atrix is updated durin, solution' If +ou &hoose to override the default) +ou &an spe&if+ oneof these values

Pro,ra-0&hosen .N,4)BT= The pro,ra- &hooses hi&h of the options to use)based on the inds of nonlinearities present in +our -odel' daptive des&ent ill beauto-ati&all+ a&tivated) hen appropriate'

(ull.N,4)(B?? The pro,ra- uses the full Neton0:aphson pro&edure) in

hi&h the stiffness -atrix is updated at ever+ e;uilibriu- iteration'

If adaptive des&ent is on .optional) the pro,ra- ill use the tan,ent stiffness-atrix onl+ as lon, as the iterations re-ain stable .that is) as lon, as theresidual de&reases) and no ne,ative -ain dia,onal pivot o&&urs' If diver,enttrends are dete&ted on an iteration) the pro,ra- dis&ards the diver,ent iteration

and restarts the solution) usin, a ei,hted &o-bination of the se&ant andtan,ent stiffness -atri&es' @hen the iterations return to a &onver,ent pattern)
http://mostreal.sk/html/guide_55/g-bas/GBASToc.htmhttp://mostreal.sk/html/guide_55/g-bas/GBASToc.htmhttp://mostreal.sk/html/com_55/chapter3/CS3-F.htm#FINISHhttp://mostreal.sk/html/com_55/chapter3/CS3-S.htm#SSTIFhttp://mostreal.sk/html/elem_55/EBooktoc.htmhttp://mostreal.sk/html/elem_55/chapter4/ES4-20.htmhttp://mostreal.sk/html/elem_55/chapter4/ES4-20.htmhttp://mostreal.sk/html/elem_55/chapter4/ES4-20.htmhttp://mostreal.sk/html/elem_55/chapter4/ES4-23.htmhttp://mostreal.sk/html/elem_55/chapter4/ES4-24.htmhttp://mostreal.sk/html/elem_55/chapter4/ES4-60.htmhttp://mostreal.sk/html/com_55/chapter3/CS3-N.htm#NROPThttp://mostreal.sk/html/com_55/chapter3/CS3-N.htm#NROPThttp://mostreal.sk/html/guide_55/g-bas/GBASToc.htmhttp://mostreal.sk/html/com_55/chapter3/CS3-F.htm#FINISHhttp://mostreal.sk/html/com_55/chapter3/CS3-S.htm#SSTIFhttp://mostreal.sk/html/elem_55/EBooktoc.htmhttp://mostreal.sk/html/elem_55/chapter4/ES4-20.htmhttp://mostreal.sk/html/elem_55/chapter4/ES4-23.htmhttp://mostreal.sk/html/elem_55/chapter4/ES4-24.htmhttp://mostreal.sk/html/elem_55/chapter4/ES4-60.htmhttp://mostreal.sk/html/com_55/chapter3/CS3-N.htm#NROPThttp://mostreal.sk/html/com_55/chapter3/CS3-N.htm#NROPT


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the pro,ra- ill resu-e usin, the tan,ent stiffness -atrix' &tivatin,adaptive des&ent ill usuall+ enhan&e the pro,ra-9s abilit+ to obtain&onver,ed solutions for &o-pli&ated nonlinear proble-s but is supported onl+for ele-ents indi&ated under 7/pe&ial (eatures7 in Table 4'n'1 of theANSYS

$lements %eference'

Modified .N,4)M=


28/62

N/%/9 auto-ati& solution &ontrol turns auto-ati& ti-e steppin, on' n internal auto0ti-estep s&he-e ensures that the ti-e step variation is neither too a,,ressive .resultin, in -an+

bise&tion8&utba&s nor too &onservative .ti-e step si6e is too s-all' t the end of a ti-estep) the si6e of the next ti-e step is predi&ted based on four fa&tors

Nu-ber of e;uilibriu- iterations used in the last ti-e step .-ore iterations &ause theti-e step si6e to be redu&ed

Predi&tions for nonlinear ele-ent status &han,e .ti-e step si6es are de&reased hen a

status &han,e is i--inent

/i6e of the plasti& strain in&re-ent

/i6e of the &reep strain in&re-ent

Con!ergence Criteria

The pro,ra- ill &ontinue to do e;uilibriu- iterations until the convergencecriteriaHCN+ default) the pro,ra- ill &he& for for&e .and) hen rotational de,rees of freedo- area&tive) -o-ent &onver,en&e b+ &o-parin, the s;uare root su- of the s;uares ./:// of thefor&e i-balan&es a,ainst the produ&t of 5A2'$*)02$%' The default value of 5A2'$is the/:// of the applied loads .or) for applied displa&e-ents) of the Neton0:aphson restorin,for&es) orN%$(.hi&h defaults to $'$$1) hi&hever is ,reater' The default valueof )02$%is $'$$5' IfS/CN,/)=(() T=?: defaults to $'$$1 and MIN:(defaults to 1'$ for for&e &onver,en&e'

%ou should al-ost ala+s use for&e &onver,en&e &he&in,' %ou &an also add displa&e-ent.and) hen appli&able) rotation &onver,en&e &he&in,' (or displa&e-ents) the pro,ra- bases&onver,en&e &he&in, on the &han,e in defle&tions . u beteen the &urrent .i and the

previous .i01 iterations uDui0ui01'

Note0If +ou expli&itl+ define an+ &usto- &onver,en&e &riteria HCN


29/62

&ertain sets of units or has ver+ lo load levels) +ou -i,ht ant to spe&if+ a s-aller valueforN%$('

lso) e do not re&o--end puttin, to or -ore disAointed stru&tures into one -odel for thenonlinear anal+sis be&ause the &onver,en&e &he& tries to relate these disAointed stru&tures)

often produ&in, so-e unanted residual for&e'

"hec*ing "onvergence in a Single and ulti-70( System

To &he& &onver,en&e in a sin,le de,ree of freedo- .


30/62

N/%/9 auto-ati& solution &ontrol ill set4,95) =N if there are no bea- or shell ele-entspresent' If the ti-e step si6e is redu&ed ,reatl+ in the &urrent substep) 4,95is turned off'(or transient anal+sis) the predi&tor is also turned off'

%ou &an a&tivate a predi&tor on the e&ause the line sear&h al,orith- is intended to be an alternativeto theadaptive des&ent option HN,4) adaptive des&ent is notauto-ati&all+ a&tivated if the linesear&h option is on' @e do not re&o--end a&tivatin, both line sear&h and adaptive des&entsi-ultaneousl+'

@hen an i-posed displa&e-ent exists) a run &annot &onver,e until at least one of theiterations has a line sear&h value of 1' N/%/ s&ales the entire B ve&tor) in&ludin, thei-posed displa&e-ent value otherise) a 7s-all7 displa&e-ent ould o&&ur ever+hereex&ept at the i-posed


31/62

This &o--and provides finer &ontrol over bise&tions and &utba& in ti-e step si6e' >+default) the 7plsli-it7 .-axi-u- plasti& strain in&re-ent li-it is set to 15J' This field is setto su&h a lar,e value for avoidin, unne&essar+ bise&tions &aused b+ hi,h plasti& strain due toa lo&al sin,ularit+ hi&h is not nor-all+ of interest to the user' The 7&rpli-it7 .&reepin&re-ent li-it is set to 1$J) as before this is a reasonable li-it for &reep anal+sis' The

nu-ber of points per &+&le for se&ond order d+na-i& e;uations is set to NP=INTD13 b+default to ,ain effi&ien&+ at little &ost to a&&ura&+'

ime Step pen Control I4NCN,/J

This &o--and is available for ther-al anal+sis' It9s pri-ar+ use is in unstead+ state ther-alanal+sis here the final te-perature sta,e rea&hes a stead+ state' In su&h &ases) the ti-e step&an be opened ;ui&l+' The default is that if the TMP in&re-ent is s-aller than $'1 in three.NBM/TPD3 &onti,uous substeps) the ti-e step si6e &an be 7opened0up7 .value D$'1 b+default' The ti-e step si6e &an then be opened &ontinuousl+ for ,reater solution effi&ien&+'

Solution *onitoring I*N$,J

This &o--and provides a fa&ilit+ to -onitor a solution value at a spe&ified node in aspe&ified


32/62

If not) +ou probabl+ on9t ant to postpro&ess the results) other than to deter-ine

h+ &onver,en&e failed'

If +our solution &onver,ed) then &ontinue postpro&essin,'

2' nter P=/T1' If +our -odel is not &urrentl+ in the database) issue ,9S*9

Co--and.s

>4S1

GBI

*ain *enu;(eneral 4ostproc

3' :ead in results for the desired load step and substep) hi&h &an be identified b+ load stepand substep nu-bers or b+ ti-e' .Note) hoever) that ar&0len,th results should not beidentified b+ ti-e'

Co--and.s

S9

GBI

*ain *enu;(eneral 4ostproc;-,ea% ,esults-load step

%ou &an also use the S"S9or A449N5&o--ands to read in or -er,e results

data for sele&ted portions of the -odel onl+' The2S)ar,u-ent on an+ of these&o--ands lists the available solutions on the results file' %ou &an also li-it thea-ount of data ritten fro- the results file to the database throu,hthe $N,9S&o--and' dditionall+) +ou &an use the9A"/9&o--and to storeresult ite-s for sele&ted ele-ents' /ee the individual &o--and des&riptions intheANSYS "ommands %eferencefor -ore infor-ation'

Caution:If +ou spe&if+ a TIM value for hi&h no results are available) the N/%/pro,ra- ill perfor- a linear interpolation to &al&ulate the results at that value of TIM':eali6e that this interpolation ill usuall+ &ause so-e loss of a&&ura&+ in a nonlinear anal+sis.see (i,ure "01#' Thus) for a nonlinear anal+sis) +ou should usuall+ postpro&ess at a TIMthat &orresponds exa&tl+ to the desired substep'

Figure 8-1 /inear interpolation of nonlinear results can intro%uce some error
http://mostreal.sk/html/com_55/chapter3/CS3-R.htm#RESUMEhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#/POST1http://mostreal.sk/html/com_55/chapter3/CS3-S.htm#SEThttp://mostreal.sk/html/com_55/chapter3/CS3-S.htm#SUBSEThttp://mostreal.sk/html/com_55/chapter3/CS3-A.htm#APPENDhttp://mostreal.sk/html/com_55/chapter3/CS3-I.htm#INREShttp://mostreal.sk/html/com_55/chapter3/CS3-E.htm#ETABLEhttp://mostreal.sk/html/com_55/CBooktoc.htmhttp://mostreal.sk/html/com_55/CBooktoc.htmhttp://mostreal.sk/html/guide_55/g-str/gstr8.htm#F8-19http://mostreal.sk/html/com_55/chapter3/CS3-R.htm#RESUMEhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#/POST1http://mostreal.sk/html/com_55/chapter3/CS3-S.htm#SEThttp://mostreal.sk/html/com_55/chapter3/CS3-S.htm#SUBSEThttp://mostreal.sk/html/com_55/chapter3/CS3-A.htm#APPENDhttp://mostreal.sk/html/com_55/chapter3/CS3-I.htm#INREShttp://mostreal.sk/html/com_55/chapter3/CS3-E.htm#ETABLEhttp://mostreal.sk/html/com_55/CBooktoc.htmhttp://mostreal.sk/html/guide_55/g-str/gstr8.htm#F8-19


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4' 5SCA/9))1'

8..). ption: Contour 5isplays

Co--and.s4/NS/or 4/9S/

GBI

*ain *enu;(eneral 4ostproc;4lot ,esults;-Contour 4lot-No%al Solu or 9lement Solu

Bse these options to displa+ &ontours of stresses) strains) or an+ other appli&able ite-'If +ou have adAa&ent ele-ents ith different -aterial behavior .su&h as &an o&&ur ith

plasti& or -ultilinear elasti& -aterial properties) ith different -aterial t+pes) or ithadAa&ent dea&tivated and a&tivated ele-ents) +ou should tae &are to avoid nodalstress avera,in, errors in +our results' /ele&tin, lo,i& .des&ribed in theANSYS Basic

Analysis Procedures Guide provides a -eans of avoidin, su&h errors'TheK'N7field on 4/NS/and4/9S/,ives +ou the option of overla+in, theundefor-ed shape on the displa+'%ou &an also &ontour ele-ent table data and line ele-ent data

Co--and.s4/9A") 4//S

GBI

*ain *enu;(eneral 4ostproc;9lement ale;4lot 9lement ale*ain *enu;(eneral 4ostproc;4lot ,esults;-Contour 4lot-/ine 9lem ,es
http://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLDISPhttp://mostreal.sk/html/com_55/chapter3/CS3-D.htm#/DSCALEhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLNSOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLESOLhttp://mostreal.sk/html/guide_55/g-bas/GBASToc.htmhttp://mostreal.sk/html/guide_55/g-bas/GBASToc.htmhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLNSOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLESOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLESOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLETABhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLLShttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLDISPhttp://mostreal.sk/html/com_55/chapter3/CS3-D.htm#/DSCALEhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLNSOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLESOLhttp://mostreal.sk/html/guide_55/g-bas/GBASToc.htmhttp://mostreal.sk/html/guide_55/g-bas/GBASToc.htmhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLNSOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLESOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLETABhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLLS


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Bse the 4/9A"&o--and .*ain *enu;(eneral 4ostproc;9lement ale;4lot9lement ale to &ontour ele-ent table data and 4//S.*ain *enu;(eneral4ostproc;4lot ,esults;/ine elem ,es to &ontour line ele-ent data'

8..).0 ption: aular /istings

Co--and.s4,NS/.nodal results4,9S/.ele-ent0b+0ele-ent results4,,S/.rea&tion data4,9A"

4,$9,.substep su--ar+ data) et&'NS,

9S,

GBI

*ain *enu;(eneral 4ostproc;/ist ,esults;No%al Solution

*ain *enu;(eneral 4ostproc;/ist ,esults;9lement Solution

*ain *enu;(eneral 4ostproc;/ist ,esults;,eaction Solution

Bse the NS,and9S,&o--ands to sort the data before listin, the-'

8..).6 ther Capailities

Man+ other postpro&essin, fun&tions0-appin, results onto a path) report ;ualit+ listin,s) andso on0are available in P=/T1' /ee Chapter5of theANSYS Basic Analysis Procedures

Guidefor details' ?oad &ase &o-binations usuall+ are not valid for nonlinear anal+ses'

8..).7 ,e!ie+ing ,esults in 4S'6

31'%ou &an also revie the load0histor+ response of a nonlinear stru&ture usin, P=/T2) theti-e0histor+ postpro&essor' Bse P=/T2 to &o-pare one N/%/ variable a,ainst another'(or instan&e) +ou -i,ht ,raph the displa&e-ent at a node versus the &orrespondin, level ofapplied load) or +ou -i,ht list the plasti& strain at a node and the &orrespondin, )$value' t+pi&al P=/T2 postpro&essin, se;uen&e -i,ht follo these steps

1' erif+ fro- +our output file .&obname3=BT hether or not the anal+sis &onver,ed at all

desired load steps' %ou should not base desi,n de&isions on un&onver,ed results'

2' If +our solution &onver,ed) enter P=/T2' If +our -odel is not &urrentl+ in the database)issue ,9S*9'

Co--and.s

>4S'6

GBI

*ain *enu;imeist 4ostpro
http://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLETABhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLLShttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLLShttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PRNSOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PRESOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PRRSOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PRETABhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PRITERhttp://mostreal.sk/html/com_55/chapter3/CS3-N.htm#NSORThttp://mostreal.sk/html/com_55/chapter3/CS3-E.htm#ESORThttp://mostreal.sk/html/com_55/chapter3/CS3-N.htm#NSORThttp://mostreal.sk/html/com_55/chapter3/CS3-N.htm#NSORThttp://mostreal.sk/html/com_55/chapter3/CS3-E.htm#ESORThttp://mostreal.sk/html/com_55/chapter3/CS3-E.htm#ESORThttp://mostreal.sk/html/guide_55/g-bas/GBAS5.htm#C5http://mostreal.sk/html/guide_55/g-bas/GBAS5.htm#C5http://mostreal.sk/html/guide_55/g-bas/GBASToc.htmhttp://mostreal.sk/html/guide_55/g-bas/GBASToc.htmhttp://mostreal.sk/html/com_55/chapter3/CS3-R.htm#RESUMEhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#/POST26http://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLETABhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PLLShttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PRNSOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PRESOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PRRSOLhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PRETABhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#PRITERhttp://mostreal.sk/html/com_55/chapter3/CS3-N.htm#NSORThttp://mostreal.sk/html/com_55/chapter3/CS3-E.htm#ESORThttp://mostreal.sk/html/com_55/chapter3/CS3-N.htm#NSORThttp://mostreal.sk/html/com_55/chapter3/CS3-E.htm#ESORThttp://mostreal.sk/html/guide_55/g-bas/GBAS5.htm#C5http://mostreal.sk/html/guide_55/g-bas/GBASToc.htmhttp://mostreal.sk/html/guide_55/g-bas/GBASToc.htmhttp://mostreal.sk/html/com_55/chapter3/CS3-R.htm#RESUMEhttp://mostreal.sk/html/com_55/chapter3/CS3-P.htm#/POST26


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3'


36/62

In this sa-ple anal+sis) +ou ill run a nonlinear anal+sis of an elasti&0plasti& &ir&ular plateunder the a&tion of a dead load and a &+&li& point load' %ou ill define a ine-ati& hardenin,

plasti&it+ &urve) as ell as load step options) the -axi-u- and -ini-u- nu-ber of substepsfor a load step) and the various load steps that des&ribe externall+ applied loads' %ou ill alsolearn ho to interpret the -onitor file that N/%/ rites for a nonlinear anal+sis'

N/%/ uses an in&re-ental solution pro&edure to obtain a solution to a nonlinear anal+ses'In this exa-ple) the total external load ithin a load step is applied in in&re-ents over a&ertain nu-ber of substeps' s des&ribed earlier in this &hapter) N/%/ uses a Neton0:aphson iterative pro&edure to solve ea&h substep' %ou -ust spe&if+ the nu-ber of substepsfor ea&h load step) sin&e this nu-ber &ontrols the si6e of the initial load in&re-ent applied inthe first substep of the ea&h load step' N/%/ auto-ati&all+ deter-ines the si6e of the loadin&re-ent for ea&h subse;uent substep in a load step' %ou &an &ontrol the si6e of the loadin&re-ent for these subse;uent substeps b+ spe&if+in, the -axi-u- and -ini-u- nu-berof substeps' If +ou define the nu-ber of substeps) the -axi-u- and -ini-u- nu-ber ofsubsteps all to be the sa-e) then N/%/ uses a &onstant load in&re-ent for all substeps

ithin the load step'

8.0.1 4rolem 5escription

In this exa-ple) +ou ill use an axis+--etri& -odel for the plate) usin, four0node P?N42ele-ents ith the axis+--etri& option to -esh the -odel' %ou ill perfor- a ,eo-etri&all+nonlinear anal+sis' /pe&if+ the ine-ati& &onstraints as follos The nodes lo&ated at the&enter of the plate are &onstrained to have 6ero radial displa&e-ent' The nodes lo&ated at theouter ed,e are &onstrained to have 6ero radial and axial displa&e-ent' %ou ill appl+ the deadload in load step 1 and the &+&li& point load in six subse;uent load steps' /ee the Proble-

/et&h in /e&tion"'5'3'

%ou9ll spe&if+ 1$ substeps for the first load to ensure that the in&re-ent of the dead loadapplied over the first substep is 181$ of the total load of $'125N8-2' %ou9ll also spe&if+ a-axi-u- of 5$ and a -ini-u- of 5 substeps to ensure that if the plate exhibits a severenonlinear behavior durin, the solution) then the load in&re-ent &an be &ut ba& to 185$ thetotal load' If the plate exhibits -ild nonlinear behavior) then the load in&re-ent &an bein&reased up to 185 the si6e of the total load'

(or the subse;uent six load steps that appl+ the &+&li& point load) +ou9ll spe&if+ 4 substeps)ith a -axi-u- of 25 and a -ini-u- of 2 substeps'

(or this exa-ple) +ou9ll -onitor the histor+ over the entire solution of the verti&aldispla&e-ent of the node at the lo&ation here the point &+&li& load is applied and therea&tion for&e at the node lo&ated at the botto- of the &la-ped ed,e '

8.0.' 4rolem Specifications

The &ir&ular plate has a radius of 1'$ - and a thi&ness of $'1-' The folloin, -aterialproperties are used for this proble-

L D 1#11'23 Pa

NBL% D $'3The ine-ati& hardenin, plasti&it+ &urve for the -aterial is
http://mostreal.sk/html/guide_55/g-str/gstr8.htm#S8.5.3http://mostreal.sk/html/guide_55/g-str/gstr8.htm#S8.5.3


37/62

/og Strain rue Stress #4a&

$'$$1123514 1#'$

$'$$1"543 22'"

$'$$2524$2 25'$"

$'$$44!1!"" 2#'$!

$'$$4223"# 31'!3

The plate has a dead load a&tin, as a unifor- pressure of $'125N8-2' The histor+ of the &+&li&point load is shon here

Figure 8-'E Cyclic 4oint /oa% istory

8.0.) 4rolem Setch

8.0.).1 Set the Analysis itle an% Koname

1' Choose -enu path tility *enu;File;Change itle'

2' T+pe the text 7C+&li& loadin, of a fixed &ir&ular plate7

3' Cli& on =K'

4' Choose -enu path tility *enu;File;Change Koname' The Chan,e obna-e dialo,box appears'


38/62

5' T+pe axplate and &li& =K'

8.0.).' 5efine the 9lement ypes

1' Choose -enu path *ain *enu;4reprocessor;9lement ype; A%%>9%it>5elete'

2' Cli& on dd' The ?ibrar+ of le-ent T+pes dialo, box appears'

3' In the list on the left) &li& on&e on 7/tru&tural /olid'7

4' In the list on the ri,ht) &li& on&e on 7Ouad 4node 42'7

5' Cli& on =K' The ?ibrar+ of le-ent T+pes dialo, box &loses'

' Cli& on =ptions' TheP?N42ele-ent t+pe options dialo, box appears'

!' In the s&roll box for ele-ent behavior) s&roll to 7xis+--etri&7 and sele&t it'

"' Cli& on =K'

#' Cli& on Close in the le-ent T+pes dialo, box'

8.0.).) 5efine *aterial 4roperties

1' Choose -enu path *ain *enu;4reprocessor;*aterial 4rops; -Constant-$sotropic'The Isotropi& Material Properties dialo, box appears'

2' Cli& on =K to spe&if+ -aterial nu-ber 1' nother Isotropi& Material Properties dialo,box appears'

3' nter 1#11'23 for %oun,9s -odulus .L'

4' nter '3 for Poisson9s ration .NBL%'

5' Cli& on =K'

8.0.). 5efine an% Fill Binematic ar%ening tale #B$N&

1' Choose -enu path *ain *enu;4reprocessor;*aterial 4rops;5ataales;5efine>Acti!ate' The


39/62

' Choose -enu path *ain *enu;4reprocessor;*aterial 4rops;5ata ales;9%itActi!e' The Huit.

Note-If +ou are usin, @indos NT) +ou -ust press the Tab e+ before exitin, the

data table'

8.0.).0 /ael (raph Axes an% 4lot 5ata ales

1' Choose -enu path tility *enu;4lotCtrls;Style;(raphs;*o%ify Axes' The xesModifi&ations for Graph Plots dialo, appears'

2' nter 7Total /train7 for the L0axis label'

3' nter 7True /tress7 for the %0axis label and &li& =K'

4' Choose -enu path *ain *enu;4reprocessor;*aterial 4rops;5ata ales;(raph'The Graph


40/62

' nter 7$) thi&7 for %0&oordinates and &li& on =K' re&tan,le appears in the N/%/Graphi&s indo'

!' Choose -enu path tility *enu;4lot;/ines'

8.0.).7 Set 9lement SiLe

1' Choose -enu path *ain *enu;4reprocessor;*eshool' The MeshTool dialo, boxappears'

2' Cli& /i6e ControlsQ?inesQ/et' The le-ent /i6e on Pi&ed ?ines pi&in, -enu appears'Cli& on the to verti&al lines .2 and 4' Cli& =K on the pi&in, -enu' The le-ent /i6eson Pi&ed ?ines dialo, box appears'

3' nter " for nu-ber of ele-ent divisions and &li& on =K'

4' :epeat these steps .103) but &hoose hori6ontal lines 1 and 3) and spe&if+ 4$ ele-entdivisions'

8.0.).8 *esh the ,ectangle

1' =n the MeshTool) pi& Ouad and Map) then &li& Mesh' The Mesh reas pi&in, -enuappears'

2' Cli& on Pi& ll'

3' Cli& on /R on the N/%/ Toolbar'

4' Cli& on Close on the MeshTool'

8.0.). Assign Analysis an% /oa% Step ptions

1' Choose -enu path *ain *enu;Solution;Analysis ptions' The /tati& or /tead+0/tatenal+sis dialo, box appears'

2' Turn lar,e defor-ation effe&ts =N and &li& =K'

3' Choose -enu path *ain *enu;Solution;-/oa% Step pts-utput Ctrls;5">,esultsFile' The Controls for


41/62

1' Choose -enu path tility *enu;4arameters;Scalar 4arameters' The /&alarPara-eters dialo, box appears'

2' T+pe 7ntopDnode.$)thi&)$'$7 in the /ele&tion field and &li& &&ept'

3' T+pe 7nri,htDnode.radius)$'$)$'$7 in the /ele&tion field and &li& &&ept) then Close'

4' Choose -enu path *ain *enu;Solution;Nonlinear;*onitor' The Monitor pi&in,-enu appears'

5' T+pe 7ntop7 in the N/%/ input indo and press NT:' Cli& =K in the pi&in,-enu' The Monitor dialo, box appears'

' In the s&roll box for Ouantit+ to be -onitored) s&roll to 7B%7 and sele&t it' Cli& =K'

!' Choose -enu path *ain *enu;Solution;Nonlinear;*onitor' The Monitor pi&in,

-enu appears'

"' T+pe 7nri,ht7 in the N/%/ input indo and press NT:' Cli& =K in the pi&in,-enu' The Monitor dialo, box appears'

#' In the s&roll box for ariable to redefine) s&roll to 7ariable 27 and sele&t it' In the s&rollbox for Ouantit+ to be -onitored) s&roll to 7(%7 and sele&t it' Cli& =K'

8.0.).11 Apply Constraints

1' Choose -enu path tility *enu;Select;9ntities' The /ele&t ntities dialo, box appears'

2' /ele&t Nodes and >+ ?o&ation in the first to sele&tion boxes' erif+ that L &oordinatesare sele&ted) and enter 7radius7 in the Min)Max field' Cli& =K'

3' Choose -enu path *ain *enu;Solution;-/oa%s-Apply;-Structural-5isplacement;n No%es' The ppl+ B):=T on Nodes pi&in, -enu appears'

4' Cli& Pi& ll' The ppl+ B):=T on Nodes dialo, box appears'

5' Cli& on 7ll


42/62

11' Choose -enu path tility *enu;Select;9ntities' The /ele&t ntities dialo, boxappears' erif+ that Nodes and >+ ?o&ation are sele&ted'

12' Cli& on % &oordinates and enter 7thi&7 in the Min)Max field' Cli& =K'

13' Choose -enu path *ain *enu;Solution;-/oa%s-Apply;Structural- 4ressure;nNo%es' The ppl+ P:/ on Nodes pi&in, -enu appears'

14' Cli& on Pi& ll' The ppl+ P:/ on nodes dialo, box appears'

15' nter 71'257 in the ?oad P:/ value field and &li& =K'

1' Choose -enu path tility *enu;Select;9!erything'

8.0.).1' Sol!e the First /oa% Step

1' Choose -enu path *ain *enu;Solution;-/oa% Step pts-ime>Fre@uenc;ime an%Sustps' The Ti-e and /ubstep =ptions dialo, appears'

2' nter 1$ as the nu-ber of substeps) enter 5$ as the -axi-u- nu-ber of substeps) andenter 5 as the -ini-u- nu-ber of substeps' Cli& =K'

3' Choose -enu path *ain *enu;Solution;-Sol!e-Current /S' :evie the infor-ation inthe 8/TT indo) and &li& on Close'

4' Cli& on =K on the /olve Current ?oad /tep dialo, box'

5' Cli& on Close on the Infor-ation dialo, box hen the solution is done'

' Choose tility *enu;4lot;9lements'

8.0.).1) Sol!e the Next Six /oa% Steps

1' Choose tility *enu;4arameters;Scalar 4arameters' The /&alar Para-eters dialo,box appears'

2' nter 7fD$'$4257 in the /ele&tion field and &li& on &&ept' Cli& on Close'

3' Choose -enu path *ain *enu;Solution;-/oa% Step pts- ime>Fre@uenc;ime an%Sustp

chapter 8 nonlinearity

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