es04 3d elements

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FE analysis with 3D elements

E. Tarallo, G. Mastinu

POLITECNICO DI MILANO, Dipartimento di Meccanica


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Summary 2

Subjects covered in this tutorial

An introduction to 3D elements

Formulations and problems of solidcontinuum elements

A guided example to evaluate a simple

structure through the use of FEM

Comparison between standard and explicitsolver

Other few exercises (to include in exercises

boo!"


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3D element – topic 3

The solid element librar incl!des isoparametric elements" #!adrilaterals

in t$o dimensions and “bricks” (hexahera! in three dimensions% These

isoparametric elements are &enerall pre'erred 'or most cases beca!se

the are !s!all the more cost-e''ecti(e o' the elements that are pro(ided

in Aba#!s% The are o''ered $ith 'irst- and second-order interpolation

)tandard 'irst-order elements are essentiall constant strain elements"

the isoparametric 'orms can pro(ide more than constant strain response,b!t the hi&her-order content o' the sol!tions the &i(e is &enerall not

acc!rate and, th!s, o' little (al!e%

The second-order elements are capable o' representin& all possible linear

strain 'ields% Th!s, in the case o' man problems *elasticit, heatcond!ction, aco!stics+ m!ch hi&her sol!tion acc!rac per de&ree o'

'reedom is !s!all a(ailable $ith the hi&her-order elements% There'ore, it

is &enerall recommended that the hi&hest-order elements a(ailable be

!sed 'or s!ch cases" in Aba#!s this means second-order elements%


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3D element – settin"s an problems (#! $

F%&& or 'ED%ED )*+E,'-+).*" red!ced inte&ration !ses a lo$er-orderinte&ration to 'orm the element sti''ness% The mass matri and distrib!ted loadin&s

!se '!ll inte&ration% ed!ced inte&ration red!ces r!nnin& time, especiall in threedimensions% .or eample, element tpe C/D0 has 1 inte&ration points, $hile

C/D0 has onl 23 there'ore, element assembl is ro!&hl /% times more costl

'or C/D0 than 'or C/D0 *!se onl $ith heahedra elements+%

/.%',&-SS ho!r&lassin& can be a problem $ith 'irst-order, red!ced-inte&rationelements *CP)4, CA54, C/D2, etc%+ in stress6displacement analses% )ince

the elements ha(e onl one inte&ration point, it is possible 'or them to distort in

s!ch a $a that the strains calc!lated at the inte&ration point are all 7ero, $hich, in

t!rn, leads to !ncontrolled distortion o' the mesh% Co!ntermeas!re" !se 'iner mesh

S/E-' 1 .&%E+') &.4)*," )hear loc8in& occ!rs in 'irst-order, '!llinte&rated elements *CP)4, CPE4, C/D2, etc%+ that are s!b9ected to bendin&% The

n!merical 'orm!lation o' the elements &i(es rise to shear strains that do not reall

eist:the so-called parasitic shear *elements too sti'' in bendin&+

Co!ntermeas!re" !se 'iner mesh thro!&h the thic8ness o' the section


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3D element – settin"s an problems (2! 5

/67')D F.'%&-+).*" ;brid elements are intended primaril 'or !se $ithincompressible and almost incompressible material beha(ior3 these elements are

a(ailable onl in Aba#!s6)tandard% eca!se o' the added internal de&rees o' 'reedom d!e to the incompatible modes *4

'or CP)4I3 'or CPE4I, CA54I, and CPE=4I3 and ?/ 'or C/D2I+, these elements are

some$hat more epensi(e than the re&!lar 'irst-order displacement elements3

ho$e(er, the are si&ni'icantl more economical than second-order elements% The

incompatible mode elements !se '!ll inte&ration and, th!s, ha(e no ho!r&lassmodes%


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3D Element recommenations (#! 9

For both -ba:us;Stanar an -ba:us;Explicit

?% Ma8e all elements as @$ell shaped as possible to impro(e con(er&ence andacc!rac%

% I' an a!tomatic tetrahedral mesh &enerator is !sed, !se the second-order

elements C/D?0 *in Aba#!s6)tandard+ or C/D?0M *in Aba#!s6Eplicit+%

/% I' contact is present in Aba#!s6)tandard, !se the modi'ied tetrahedral element

C/D?0M i' the de'a!lt @hard contact relationship is !sed or in analses $ith

lar&e amo!nts o' plastic de'ormation%4% I' possible, !se heahedral elements in three-dimensional analses since the

&i(e the best res!lts 'or the minim!m cost%


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3D Element recommenations (#! <

For only -ba:us;Stanar

?% .or linear and @smooth nonlinear problems !se red!ced-inte&ration, second-order elements i' possible%

% Bse second-order, '!ll inte&rated elements close to stress concentrations to

capt!re the se(ere &radients in these re&ions% ;o$e(er, a(oid these elements

in re&ions o' 'inite strain i' the material response is nearl incompressible%

/% Bse 'irst-order #!adrilateral or heahedral elements or the modi'ied trian&!lar

and tetrahedral elements 'or problems in(ol(in& contact or lar&e distortions% I'the mesh distortion is se(ere, !se red!ced-inte&ration, 'irst-order elements%

4% I' the problem in(ol(es bendin& and lar&e distortions, !se a 'ine mesh o' 'irst-

order, red!ced-inte&ration elements%

% ;brid elements m!st be !sed i' the material is '!ll incompressible *ecept

$hen !sin& plane stress elements+% ;brid elements sho!ld also be !sed in

some cases $ith nearl incompressible materials%

% Incompatible mode elements can &i(e (er acc!rate res!lts in problems

dominated b bendin&%


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Exercise # =

8art /D solid homo&ene!s

aterial" E?0 =Pa, 0%/

8roblem?% Per'orm static analysis

% .ind ma de'lection

/% E(al!ate (on mises stress chan&in& the mesh

*n!mber and order o' elements+4% Per'orm ynamic analysis *0%00 s time step,

? e#!all spaced inter(al sa(e o!tp!t+

N>" densit F8&6mm/G3 E F8&6mm6sG

% Plot Internal ener&, 8inetic ener& and

displacement (s time


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Exercise # > results ?


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Exercise 2 #0


&oa" .78N3 ./8N3 T?008Nmm

-nalysis )tatic

Element compare di''erent elements

8roblem 'ind ma (on mises stresses on the notches

.7

.


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Exercise 2 > results ##

E i 3


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Exercise 3 #2


&oa" ./08N

-nalysis )tatic

Element!se partition to mesh $ith

;E5 linear or #!adratic

8roblem 'ind ma (on misesstresses on the notches

E i 3 lt


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Exercise 3 > results #3

es04 3d elements

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