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8/18/2019 FEA Assignment OTHER

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Application of Finite Element

Modelling in Stress Analysis

BRUNEL UNIVERSITY

Fabrizio Andrea Valentini

Student ID: 11155!


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SUMMARY

"#e problem t#at #as been in$estigated treats t#e analysis of stress on asemi%&nite plate t#at presents ' ro(s of staggered #oles and is sub)ectedto a tension force* "#e stress (ill be identi&ed ta+ing under consideration

t#e $ariation of t#e plate t#ic+ness, t#e stress concentration factor -, t#e#orizontal pitc#%#oles diameter ratio and t#e angle of staggered #oles .*

"#e e/perimental $alues of t#e stress obtained t#roug# computationalFinite Element Analysis (ill be compared (it# t#e t#eoretical ones and t#eAnsys modelling strategies (ill be discussed*

INTRODUCTION

0o(adays Finite Element Analysis #as become $ery important in $arious&elds of researc# and application biomedical, ci$il, a$iation andautomoti$e engineering2: setting standards in many companies, it is usedin e$ery stage of t#e de$elopment of ne( products or components,allo(ing cutting costs, sa$ing time during early state of concept designand guaranteeing safety and 3uality criterions*

In engineering, t#e in$estigation of stresses in plates of di4erent materialsit #as al(ays been of important consideration, especially (#en t#ese arepart of structures or mo$ing system* It is critical t#en to analyze t#emagnitude of t#e stress along t#e ob)ect in use* If t#e used plate isconsistent and uniform, t#e stress distribution (ill be uniform accordinglybut (#en #oles are present along it, t#e distribution of t#e stress c#anges*

"#ese geometry irregularities increase t#e magnitude of t#e stress $eryclose to t#em and t#at is (#ere usually failures occur* "#e stressconcentration at t#e edge of a #ole is calculated as:

σ max

= K ∙ σ 0

It can be seen t#at in order to calculate it, a factor -2 is used: t#e socalled stress%concentration factor*

"#is factor is de&ned by t#e follo(ing formula:

K tn=

σ max

σ nom12

#ereσ

max is t#e E3ui$alent ma/imum stress Von Mises2 andσ

nom is

t#e nominal stress*

#en t#e practical $alues are calculated t#roug# t#e data obtained fromAnsys, t#ey (ill be compared to t#e t#eoretical ones t#at are ta+en from

t#e grap# in 6eterson7s Stress 8oncentration Factors*


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PROBLEM UNDER INVESTIGATION

"#e problem under analysis, as said before, concerns a plate (it#staggered #oles t#at is sub)ected to a uniform tension stress 9*

"#e plate #as &/ed lengt# and (idt# and its t#ic+ness is going to $aryt#roug#out t#e e/periment* "#e #oles #a$e a &/ed diameter and t#ey areseparated from eac# ot#er (it# a distance b: in addition, t#e staggered#oles present a distance c bet(een t#e t(o ro(s of t#e #oles (#en t#eangle bet(een t#em is increased*

"#e $ariables are $aried in order to create multiple arrangements andt#erefore to in$estigate #o( t#e stress is a4ected by eac# of t#em*Ansys (ill be used to sol$e comple/ structural stress calculations &ndingt#e magnitude of t#e ma/imum stress around t#e #oles: a mes# (ill becreated on t#e geometry of t#e plate and t#erefore obtain a global resultfor t#e entire ob)ect*

"#e symmetry of t#e plate t#at is presented across t#e central $erticala/is could be used as an ad$antage to analyze #alf of t#e plate andt#erefore reduce computational time*

% oundary 8onditions

"#e initial conditions present: l ; '5< mm= ( ; 1


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"#e distancec (ill be $aried

t#roug#out t#e e/periment (it# $alues range of * Additionally, t#estress concentration factor increases as t#e angle . increases until !


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"#e initial step to face t#e e/periment (as to create a (or+ space inAnsys or+benc# under t#e static structural domain* During t#e creationof t#e geometry t#e parameters t#at (ere supposed to $ary furt#er on int#e e/periment (ere parameterized to a$oid t#e creation of many

di4erent &les= in addition, it (as possible to 3uic+ly set t#e (antedcon&guration of t#ic+ness and t#e distance bet(een ro(s of #ole*nce t#e plate (as created respecting t#e geometric boundaries, t#emodelling (as ta+en to t#e ne/t step= t#e material (as assigned (it# t#erig#t properties t#roug# t#e engineering library and t#e relati$e tensionstress of 1*' +0 (as applied in t#e upper plate edge* In t#e lo(er part oft#e plate and as (ell as in t#e rig#t one, ' displacement support (ereapplied respecti$ely= t#e &rst (it# t#e / motion set as free and t#e latter(it# t#e y motion set as free*ne of t#e purposes of t#e e/periment carried out is to in$estigate t#ee4ect of $arying mes#es on t#e results of stress magnitude and stressconcentration factor= > types of mes#es #a$e been applied to t#e pre$iouscreated model: Automatic, Mapped Face, and e&nement*

"#e best mes# out of t#e c#osen > #as been t#en used to t#e 'geometries in order to in$estigate t#e practical - $alues against t#et#eoretical one for e$ery angle .*For t#is particular e/periment and for a license limitation2, t#e ma/imummes#ing nodes allo(ed #ad a limit of >'


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% Mapped Face Mes#ing

"#e Mapped Face mes# can be $ery useful (#en you need an ideal mes#around an interested area or surface= its algorit#m forces t#e nodes gridto adapt to t#e round s#ape in t#is case2 and can produce 3uite accurateresults in t#e stress regions* #en t#is mes# #as been used on t#e model,a long computational time (as needed to ac#ie$e results especially (it#a #ig# number of di$isions and a &ne edge mes#ing2: circular faces #a$ebeen printed around t#e staggered #oles to guarantee a #ig#er density ofnodes in t#e studied area* Gsually applying t#is +ind of mes# (it# defaultparameters generates a fair mapped grid on t#e analyzed geometry butan engineering )udgment in necessary to &nd t#e rig#t balance bet(eensol$ing time, less nodes and uniform grid*

% e&nement Mes#ing

"#e re&nement mes# control allo(s to concentrate t#e grid on a particulararea of t#e surface and t#erefore obtain better results= for t#is model, t#egrid #as been re&ned selecting t#e #oles edges* For t#e rest of t#e platet#e grid #as been controlled (it# face sizing in order to maintain a uniform

Figure . - Ma//e! Fa'e Me$

Figure 0 - Re(ee(t Me$


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pattern* #en applied to t#e model, > di4erent con$ergence processes#a$e been obtained: t#e e&nement ele$ance #as been $aried in eac#one of t#em from 1 to >2 and t#e element sizing (as $aried from 5 to


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t#e con&guration of t#e geometry (as +ept constant (it# t#e #olesforming one ro( . ; HH' nodes (it# a - tg e3uals to '*!'2 but is t#e e&nement (it#rele$ance set at > t#at #as been found tobe t#e best mes#, con$erging at a lo(ernumber of nodes H


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< 1< '< >< ?< 5< !< <

<

>*5

?

?*5

5

2tg a(! 2t +$ 9 3#r Di33ere(t Ti':(e$$e$

"#ic+ness ; >

"#ic+ness ; 5

"#ic+ness ;

"#eoretical -

9

2tg

For e$ery distance bet(een t#e #oles ro(s c, t#e number of elements andt#e e3ui$alent ma/imum stress (ere noted do(n* "#e &rst set of dataconcerned t#e plate (it# a t#ic+ness of > mm "able 1 in t#e appendi/2: asit can be noticed t#e ma/imum stress magnitude (as calculated to be

ranging from ?*H at


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decreases to '*


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cost and t#e use of materials, t#e function of t can be minimized alt#oug#maintaining enoug# safe factor range*

CONCLUSIONS

"#e use of Ansys soft(are pac+age as a tool for Finite Element Analysis ispro$en to be $ery useful and gi$es $ery good appro/imations of results* Ina no(adays mar+et, al(ays mo$ing to(ards fast, t#e use of t#ese +ind ofanalysis on concept or impro$ement stages set standards of time sa$ing,cost cutting, and better 3uality of t#e &nal product*

it# t#e e/periment t#at #as been carried out t#e follo(ing conclusions#as been reac#ed:

% Semi%&nite plates t#at present geometry irregularities li+e #oles#a$e a greater tendency to structural failure*

% If t#e #oles are small and t#ey are separated from a long distance,t#e E3ui$alent ma/imum stress doesn7t c#ange (it# t#e decrease of t#e ro(s angle of staggered #oles* In contrary, closer #oles t#atinuence eac# ot#er ma+e t#e magnitude of t#e stress increase*

% In addition t#e closer t#e #oles get to t#e edge of t#e plate and t#emore t#e c#ances of failure*

% "#e edges of t#e #oles are t#e parts t#at (it#stand t#e #ig#eststress*

% From t#e results obtained, it can be noticed t#at t#e stressconcentration factor doesn7t $ary (it# t#e increase of t#ic+ness*

% "#e di4erent bet(een t#e t#eoretical $alues and t#e practical onecan be considered acceptable * J o42*

APPENDI=


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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

"#ic+ness

Angle 8

0umber fElements

E3ui$alentStress

0ominalStress -

> < < ''1 ?*H>>1*H1H1H1H

1H'*!>'1*

H 1< ''H

1*H1H1H1H1H

'*'>!5

> ?5 '5 ''H!H ?*H5'

Ta%le 1 - Be$t Me$ #( , Ti': Plate at Di5ere(t 9

"#ic+ness

Angle 8

0umber fElements

E3ui$alentStress

0ominalStress -

5 < < '>'5 '*H!?1*'> '*>1!

1*<5

5 ?5 '5 ''H!H '*1H?1*'5

55?*?! >5 ''H> '*H'!

1*


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5!

Ta%le ) - Be$t Me$ #( 0 Ti': Ta%le at Di5ere(t 9

"#ic+ness

Angle 8

0umber fElements

E3ui$alentStress

0ominalStress -

< < ''H> '*

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