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Element Behaviors of C3D8, C3D8R and C3D8I

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C3D8 ELEMENT

To !a#se the angle 5 to !hange #nder the #re moment, an in!orre!t arti !ial shear stresshas $een introd#!ed' This also means that the strain energ+ of the element is generatingshear deformation instead of $ending deformation'

The overall e4e!t is that the linear f#ll+ integrated element $e!omes lo!"ed or overl+ sti4#nder the $ending moment'

6rong dis la!ements, false stresses and s #rio#s nat#ral freen!ies ma+ $e re orted$e!a#se of the lo!"ing'

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C3D8R ELEMENT

The C3D8R element is a general #r ose linear $ri!" element, with red#!ed integration/ integration oint-' D#e to the red#!ed integration, the lo!"ing henomena o$served in

the C3D8 element do not show'

Figure 1: 8(node $ri!"element

Figure 3: /*/*/integration oint

s!heme in he*ahedralelements

Hourglass term !ome into i!t#re if +o# are #sing red#!ed7#nder integration elements'Be!a#se of #nder integration +o# will get s #rio#s modes, whi!h needs to $e avoided' Toavoid this s #rio#s modes, +o# a l+ ho#rglass !ontrol, and energ+ s ent for this ro!essis "nown as ho#rglass energ+'

The element tends to $e not sti4 eno#gh in $ending'9tresses, strains are most a!!#rate in the integration oints' The integration oint of theC3D8R element is lo!ated in the middle of the element' Th#s, small elements arereired to !a t#re a stress !on!entration at the $o#ndar+ of a str#!t#re'

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C3D8R ELEMENT

To vis#ali:e the deformation, noti!e that verti!al and hori:ontal dotted lines and angle 5remain #n!hanged' This means that normal stresses and shear stresses are :ero at theintegration oint and there are no strain energ+ generated $+ the deformation' This ;ero(energ+ mode is non h+si!al res onse, whi!h ma+ ro agate when !oarsemesh is #sed' The ro agation of s#!h a mode ma+ therefore rod#!e meaninglessres#lts'

The res#lts often indi!ate that the str#!t#re is e*!essivel+

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C3D8R ELEMENT

There are /) s #rio#s :ero energ+ modes leading to massive ho#r glassing0 this means that the

!orre!t sol#tion is s# er osed $+ ar$itraril+ large dis la!ements !orres onding to the :eroenerg+ modes' Th#s, the dis la!ements are !om letel+ wrong' 9in!e the :ero energ+ modes do not lead to an+stresses, the stress eld is still !orre!t'

In ra!ti!e, the C3D8R element is not ver+ #sef#l witho#t ho#rglass !ontrol' 9tarting withversion )'3 ho#rglass !ontrol is a#tomati!all+ a!tivated for this element'

The form#lation for red#!ed(integration elements !onsiders onl+ the linearl+ var+ing art of thein!remental dis la!ement eld in the element for the !al!#lation of the in!rement of h+si!alstrain'

The remaining art of the nodal in!remental dis la!ement eld is the ho#rglass eld and !an$e e* ressed in terms of ho#rglass modes' E*!itation of these modes ma+ lead to severe meshdistortion, with no stresses resisting the deformation'

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C3D8I ELEMENT The in!om ati$le mode eight(node $ri!" element is an im roved version of the C3D8(element'

C3D8I is rst(order element that are enhan!ed $+ in!om ati$le modes to im rove their$ending $ehavior'In addition to the standard dis la!ement degrees of freedom, in!om ati$le deformationmodes are added internall+ to the elements'

The rimar+ e4e!t of these modes is to eliminate the arasiti! shear stresses that!a#se the res onse of the reg#lar rst(order dis la!ement elements to $e too sti4 in$ending' in!om ati$le mode elements #se f#ll integration and, th#s, have no ho#rglassModes'

In arti!#lar, shear lo!"ing is removed and vol#metri! lo!"ing is m#!h red#!ed' Thedis la!ements in the mesh are orders of magnit#de smaller than in the realit+' This is!alled vol#metri! lo!"ing' In!om ressi$ilit+ is not as rare as one wo#ld thin", sin!e e'g'most lasti! matrial models or man+ h+ erelasti! material models ass#me iso!hori!

deformation'

This is o$tained $+ s# lementing the standard sha e f#n!tions with so(!alled $#$$lef#n!tions, whi!h have a :ero val#e at all nodes and non:ero val#es in $etween' InCal!#li>, the version detailed in ? @/A has $een im lemented' The C3D8I element sho#ld$e #sed in all instan!es, in whi!h linear elements are s#$=e!t to $ending' 5ltho#gh thealit+ of the C3D8I element is far $etter than the C3D8 element'

In!om ati$le mode elements !an give ver+ a!!#rate res#lts in ro$lemsdominated $+ $ending'
http://web.mit.edu/calculix_v2.4/CalculiX/ccx_2.4/doc/ccx/node590.htmlhttp://web.mit.edu/calculix_v2.4/CalculiX/ccx_2.4/doc/ccx/node590.html

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C NCL 9I N

In general terms, for all n#meri!al sim#lations the C3D8R nite element shows oor$ehavior !om ared to other nite element form#lations, es e!iall+ when in!reasing then#m$er of la+ers in thi!"ness dire!tion' This t+ e of nite element is !learl+ more sensitiveto shear lo!"ing henomenon'

6ith an o osite $ehavior, the C3D8I nite element resents good res#lts, im roving asthe n#m$er of la+er in thi!"ness dire!tion in!reases and with $etter a ro*imation toe* erimental res#lts'

5B5 9 element t+ es have #nie wa+s to handle the n#meri!al di !#lties of shearlo!"ing , vol#metri! lo!"ing and ho#rglassing' In the $ending a li!ation and the modalanal+sis, the f#ll+ integration rst order solid elements e*hi$it shear lo!"ing' ne m#st a+attention to this ossi$ilit+ and !onsider not #sing them in this !ase, the #ser !an em lo+in!om ati$le mode elements'

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511ENDI> 0 C5NTILE ER BE5M 5N5LF9I9

C5LC L5TED 5L E9

Length of Beam L G 3HmmLoad on end of $eam 1 G /HHN

Fo#ng s Mod#l#s E G )H@%1aDistan!e from ne#tral a*is to e*treme, ! G JmmMoment of Inertia, I G $h 3 7 /) G 833'333mm

Ma*' Dis G 1L 3 7 3EI G H'HHJ)KmmMa*' Bending 9tress G 1L7; G /8M a

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C5NTILE ER BE5M 5N5LF9I9

. R ELEMENT C3D8

M5>G/3'3@M1a

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. R ELEMENT C3D8

M5>GH'HH@J8J 3mm

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. R ELEMENT C3D8R

M5>G/' 3)M1a

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. R ELEMENT C3D8R

M5>GH'K8K)mm

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. R ELEMENT C3D8I

M5>G/K'/@M1a

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. R ELEMENT C3D8I

M5>GH'HHJ H@Kmm

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C5LC L5TED 5L E9

ELEMENT TF1E

9IM L5TI N9TRE99 M1a

-

9IM L5TI NDI91 mm-

C5LC L5TED

9TRE99 M1a-

C5LC L5TED

DI91 mm-

C3D8 /3'3@ H'HH@J8J /8 H'HHJ)K

C3D8R /' 3) H'K8K) /8 H'HHJ)K

C3D8I /K'/@ H'HHJ H /8 H'HHJ)K

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C3D8 9TRE99 DI91

/ ELEMENT T ICONE99 /3'3@ H'HH@J8@

) ELEMENT T ICONE99 /3'K@ H'HHJJK)

3 ELEMENT T ICONE99 /K' 3 H'HHJJ@@

K ELEMENT T ICONE99 /J')@ H'HHJ@KK

C3D8R 9TRE99 DI91

/ ELEMENT T ICONE99 /' 3) H'K8K)

) ELEMENT T ICONE99 /H')8 H'HH K/)

3 ELEMENT T ICONE99 /)'@8 H'HH@3J8

K ELEMENT T ICONE99 /)' / H'HH@HJ3

C3D8I 9TRE99 DI91

/ ELEMENT T ICONE99 /K'/@ H'HHJ H@

) ELEMENT T ICONE99 /K')K H'HHJJKJ

3 ELEMENT T ICONE99 /J'K H'HHJ@)

K ELEMENT T ICONE99 /J'JK H'HHJ@J

C5LC L5TED /8 H'HHJ)K

c3d8 Sandy

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