4. P

relim

inar

y D

ecis

ions

Prel

imin

ary

Dec

isio

nsO

verv

iew

�B

efor

e st

artin

g an

ana

lysi

s in

AN

SYS,

you

nee

d to

mak

e a

few

dec

isio

ns, s

uch

as th

e an

alys

is ty

pe n

eede

d an

d th

e ty

pe

of m

odel

you

wan

t to

build

.

�In

this

cha

pter

, we

will

dis

cuss

som

e of

the

deci

sion

mak

ing

proc

ess.

The

pur

pose

is to

giv

e yo

u an

idea

of t

he a

mou

nt o

f pl

anni

ng g

ener

ally

nee

ded

befo

re �

jum

ping

in�

to d

o th

e an

alys

is.

�To

pics

cov

ered

:�

A.

Whi

ch a

naly

sis

type

?�

B.

Wha

t to

mod

el?

�C

. W

hich

ele

men

t typ

e?

Prel

imin

ary

Dec

isio

nsA

. Whi

ch a

naly

sis

type

?

�Th

e an

alys

is ty

pe u

sual

ly b

elon

gs to

one

of t

he fo

llow

ing

disc

iplin

es:

Stru

ctur

alM

otio

n of

sol

id b

odie

s, p

ress

ure

on s

olid

bod

ies,

or

con

tact

of s

olid

bod

ies

Ther

mal

App

lied

heat

, hig

h te

mpe

ratu

res,

or c

hang

es in

te

mpe

ratu

reEl

ectr

omag

netic

Dev

ices

sub

ject

ed to

ele

ctric

cur

rent

s (A

C o

r D

C),

elec

trom

agne

tic w

aves

, and

vol

tage

or

char

ge e

xcita

tion

Flui

dM

otio

n of

gas

es/fl

uids

, or c

onta

ined

gas

es/fl

uids

Cou

pled

-Fie

ldC

ombi

natio

ns o

f any

of t

he a

bove

�W

e w

ill fo

cus

on s

truc

tura

l ana

lyse

s in

this

dis

cuss

ion.

Prel

imin

ary

Dec

isio

ns...

Whi

ch a

naly

sis

type

?

�O

nce

you

choo

se a

str

uctu

ral a

naly

sis,

the

next

que

stio

ns

are: �

Stat

ic o

r dyn

amic

ana

lysi

s?�

Line

ar o

r non

linea

r ana

lysi

s?

�To

ans

wer

thes

e, re

mem

ber t

hat w

hene

ver a

bod

y is

su

bjec

ted

to s

ome

exci

tatio

n (lo

adin

g), i

t res

pond

s w

ith th

ree

type

s of

forc

es:

�st

atic

forc

es (d

ue to

stif

fnes

s)�

iner

tia fo

rces

(due

to m

ass)

�da

mpi

ng fo

rces

Prel

imin

ary

Dec

isio

ns...

Whi

ch a

naly

sis

type

?

Stat

ic v

s. D

ynam

ic A

naly

sis

�A

sta

tican

alys

is a

ssum

es th

at o

nly

the

stiff

ness

forc

es a

re

sign

ifica

nt.

�A

dyn

amic

anal

ysis

take

s in

to a

ccou

nt a

ll th

ree

type

s of

fo

rces

.

�Fo

r exa

mpl

e, c

onsi

der t

he a

naly

sis

of a

div

ing

boar

d.�

If th

e di

ver i

s st

andi

ng s

till,

it m

ight

be

suffi

cien

t to

do a

sta

tic a

naly

sis.

�B

ut if

the

dive

r is

jum

ping

up

and

dow

n, y

ou w

ill

need

to d

o a

dyna

mic

ana

lysi

s.

Prel

imin

ary

Dec

isio

ns...

Whi

ch a

naly

sis

type

?

�In

ertia

and

dam

ping

forc

es a

re u

sual

ly s

igni

fican

t if t

he

appl

ied

load

s va

ry ra

pidl

y w

ith ti

me.

�Th

eref

ore

you

can

use

time-

depe

nden

cy o

f loa

ds a

s a

way

to

choo

se b

etw

een

stat

ic a

nd d

ynam

ic a

naly

sis.

�If

the

load

ing

is c

onst

ant o

ver a

rela

tivel

y lo

ng p

erio

d of

tim

e,

choo

se a

sta

tic a

naly

sis.

�O

ther

wis

e, c

hoos

e a

dyna

mic

ana

lysi

s.

�In

gen

eral

, if t

he e

xcita

tion

freq

uenc

y is

less

than

1/3

of t

he

stru

ctur

e�s

low

est n

atur

al fr

eque

ncy,

a s

tatic

ana

lysi

s m

ay b

e ac

cept

able

.

Prel

imin

ary

Dec

isio

ns...

Whi

ch a

naly

sis

type

?

Line

ar v

s. N

onlin

ear A

naly

sis

�A

line

aran

alys

is a

ssum

es th

at th

e lo

adin

g ca

uses

neg

ligib

le

chan

ges

to th

e st

iffne

ss o

f the

str

uctu

re.

Typi

cal

char

acte

ristic

s ar

e:�

Smal

l def

lect

ions

�St

rain

s an

d st

ress

es w

ithin

the

elas

tic li

mit

�N

o ab

rupt

cha

nges

in s

tiffn

ess

such

as

two

bodi

es c

omin

g in

to

and

out o

f con

tact

Stra

in

Stre

ss

Elas

tic m

odul

us(E

X)

Prel

imin

ary

Dec

isio

ns...

Whi

ch a

naly

sis

type

?

�A

non

linea

rana

lysi

s is

nee

ded

if th

e lo

adin

g ca

uses

si

gnifi

cant

cha

nges

in th

e st

ruct

ure�

s st

iffne

ss.

Typi

cal

reas

ons

for s

tiffn

ess

to c

hang

e si

gnifi

cant

ly a

re:

�St

rain

s be

yond

the

elas

tic li

mit

(pla

stic

ity)

�La

rge

defle

ctio

ns, s

uch

as w

ith a

load

ed fi

shin

g ro

d�

Con

tact

bet

wee

n tw

o bo

dies

Stra

in

Stre

ss

Prel

imin

ary

Dec

isio

nsB

. Wha

t to

Mod

el?

�M

any

mod

elin

g de

cisi

ons

mus

t be

mad

e be

fore

bui

ldin

g an

an

alys

is m

odel

:�

How

muc

h de

tail

shou

ld b

e in

clud

ed?

�D

oes

sym

met

ry a

pply

?�

Will

the

mod

el c

onta

in s

tres

s si

ngul

ariti

es?

Prel

imin

ary

Dec

isio

ns...

Wha

t to

Mod

el?

Det

ails

�Sm

all d

etai

ls th

at a

re u

nim

port

ant t

o th

e an

alys

is s

houl

d no

t be

incl

uded

in th

e an

alys

is m

odel

. Yo

u ca

n su

ppre

ss s

uch

feat

ures

be

fore

sen

ding

a m

odel

to A

NSY

S fr

om a

CA

D s

yste

m.

�Fo

r som

e st

ruct

ures

, how

ever

, "sm

all"

det

ails

suc

h as

fille

ts o

rho

les

can

be lo

catio

ns o

f max

imum

str

ess

and

mig

ht b

e qu

ite

impo

rtan

t, de

pend

ing

on y

our a

naly

sis

obje

ctiv

es.

Prel

imin

ary

Dec

isio

ns...

Wha

t to

Mod

el?

Sym

met

ry

�M

any

stru

ctur

es a

re s

ymm

etric

in s

ome

form

and

allo

w o

nly

a re

pres

enta

tive

port

ion

or c

ross

-sec

tion

to b

e m

odel

ed.

�Th

e m

ain

adva

ntag

es o

f usi

ng a

sym

met

ric m

odel

are

:�

It is

gen

eral

ly e

asie

r to

crea

te th

e m

odel

.�

It al

low

s yo

u to

mak

e a

finer

, mor

e de

taile

d m

odel

and

ther

eby

obta

in b

ette

r res

ults

than

wou

ld h

ave

been

pos

sibl

e w

ith th

e fu

ll m

odel

.

Prel

imin

ary

Dec

isio

ns...

Wha

t to

Mod

el?

�To

take

adv

anta

ge o

f sym

met

ry, a

ll of

the

follo

win

g m

ust b

e sy

mm

etric

:�

Geo

met

ry�

Mat

eria

l pro

pert

ies

�Lo

adin

g co

nditi

ons

�Th

ere

are

diffe

rent

type

s of

sym

met

ry:

�A

xisy

mm

etry

�R

otat

iona

l�

Plan

ar o

r ref

lect

ive

�R

epet

itive

or t

rans

latio

nal

Prel

imin

ary

Dec

isio

ns...

Wha

t to

Mod

el?

Axi

sym

met

ry

�Sy

mm

etry

abo

ut a

cen

tral

axi

s, s

uch

as in

ligh

t bul

bs, s

trai

ght

pipe

s, c

ones

, circ

ular

pla

tes,

and

dom

es.

�Pl

ane

of s

ymm

etry

is th

e cr

oss-

sect

ion

anyw

here

aro

und

the

stru

ctur

e. T

hus

you

are

usin

g a

sing

le 2

-D �

slic

e� to

re

pres

ent 3

60° �

a re

al s

avin

gs in

mod

el s

ize!

�Lo

adin

g is

als

o as

sum

ed to

be

axis

ymm

etric

in m

ost c

ases

. H

owev

er, i

f it i

s no

t, an

d if

the

anal

ysis

is li

near

, the

load

s ca

n be

se

para

ted

into

har

mon

ic

com

pone

nts

for i

ndep

ende

nt

solu

tions

that

can

be

supe

rpos

ed.

Prel

imin

ary

Dec

isio

ns...

Wha

t to

Mod

el?

Rot

atio

nal s

ymm

etry

�R

epea

ted

segm

ents

arr

ange

d ab

out a

cen

tral

axi

s, s

uch

as in

tu

rbin

e ro

tors

.

�O

nly

one

segm

ent o

f the

str

uctu

re n

eeds

to b

e m

odel

ed.

�Lo

adin

g is

als

o as

sum

ed to

be

sym

met

ric a

bout

the

axis

.

This

mod

el il

lust

rate

s bo

th re

flect

ive

and

rota

tiona

l sym

met

ry

Prel

imin

ary

Dec

isio

ns...

Wha

t to

Mod

el?

Plan

ar o

r ref

lect

ive

sym

met

ry

�O

ne h

alf o

f the

str

uctu

re is

a m

irror

imag

e of

the

othe

r hal

f.

The

mirr

or is

the

plan

e of

sym

met

ry.

�Lo

adin

g m

ay b

e sy

mm

etric

or a

nti-s

ymm

etric

abo

ut th

e pl

ane

of s

ymm

etry

.

This

mod

el il

lust

rate

s bo

th re

petit

ive

and

refle

ctiv

e sy

mm

etry

.

Prel

imin

ary

Dec

isio

ns...

Wha

t to

Mod

el?

Rep

etiti

ve o

r tra

nsla

tiona

l sym

met

ry

�R

epea

ted

segm

ents

arr

ange

d al

ong

a st

raig

ht li

ne, s

uch

as a

lo

ng p

ipe

with

eve

nly

spac

ed c

oolin

g fin

s.

�Lo

adin

g is

als

o as

sum

ed to

be

�rep

eate

d� a

long

the

leng

th o

f th

e m

odel

.

Prel

imin

ary

Dec

isio

ns...

Wha

t to

Mod

el?

�In

som

e ca

ses,

onl

y a

few

min

or d

etai

ls w

ill d

isru

pt a

st

ruct

ure'

s sy

mm

etry

. Yo

u m

ay b

e ab

le to

igno

re s

uch

de

tails

(or t

reat

them

as

bein

g sy

mm

etric

) in

orde

r to

gain

the

bene

fits

of u

sing

a s

mal

ler m

odel

. H

ow m

uch

accu

racy

is

lost

as

the

resu

lt of

suc

h a

com

prom

ise

mig

ht b

e di

fficu

lt to

es

timat

e.

Prel

imin

ary

Dec

isio

ns...

Wha

t to

Mod

el?

Stre

ss s

ingu

larit

ies

�A

str

ess

sing

ular

ity i

s a

loca

tion

in a

fini

te e

lem

ent m

odel

w

here

the

stre

ss v

alue

is u

nbou

nded

(inf

inite

). E

xam

ples

:�

A p

oint

load

, suc

h as

an

appl

ied

forc

e or

mom

ent

�A

n is

olat

ed c

onst

rain

t poi

nt, w

here

the

reac

tion

forc

e be

have

s lik

e a

poin

t loa

d�

A s

harp

re-e

ntra

nt c

orne

r (w

ith z

ero

fille

t rad

ius)

�A

s th

e m

esh

dens

ity is

refin

ed a

ta

stre

ss s

ingu

larit

y, th

e st

ress

val

uein

crea

ses

and

neve

r con

verg

es.

Pσ

= P/

AAs

A ⇒

0, σ⇒

∞

Prel

imin

ary

Dec

isio

ns...

Wha

t to

Mod

el?

�R

eal s

truc

ture

s do

not

con

tain

str

ess

sing

ular

ities

. Th

ey a

re

a fic

tion

crea

ted

by th

e si

mpl

ifyin

g as

sum

ptio

ns o

f the

mod

el.

�So

how

do

you

deal

with

str

ess

sing

ular

ities

?�

If th

ey a

re lo

cate

d fa

r aw

ay fr

om th

e re

gion

of i

nter

est,

you

can

sim

ply

igno

re th

em b

y de

activ

atin

g th

e af

fect

ed z

one

whi

le

revi

ewin

g re

sults

.�

If th

ey a

re lo

cate

d in

the

regi

on o

f int

eres

t, yo

u w

ill n

eed

to ta

ke

corr

ectiv

e ac

tion,

suc

h as

:�

addi

ng a

fille

t at r

e-en

tran

t cor

ners

and

redo

ing

the

anal

ysis

.�

repl

acin

g a

poin

t for

ce w

ith a

n eq

uiva

lent

pre

ssur

e lo

ad.

��s

prea

ding

out

� di

spla

cem

ent c

onst

rain

ts o

ver a

set

of

node

s.

Prel

imin

ary

Dec

isio

nsC

. Whi

ch E

lem

ent T

ype?

�Th

is is

an

impo

rtan

t dec

isio

n yo

u us

ually

nee

d to

mak

e be

fore

beg

inni

ng th

e an

alys

is.

�Ty

pica

l iss

ues

are:

�W

hich

ele

men

t cat

egor

y? S

olid

, she

ll, b

eam

, etc

.�

Elem

ent o

rder

. Li

near

or q

uadr

atic

.�

Mes

h de

nsity

. U

sual

ly d

eter

min

ed b

y th

e ob

ject

ives

of t

he

anal

ysis

.

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

Elem

ent c

ateg

ory

�A

NSY

S of

fers

man

y di

ffere

nt c

ateg

orie

s of

ele

men

ts.

Som

e of

the

com

mon

ly u

sed

ones

are

:�

Line

ele

men

ts�

Shel

ls�

2-D

sol

ids

�3-

D s

olid

s

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

�Li

ne e

lem

ents

:�

Bea

mel

emen

ts a

re u

sed

to m

odel

bol

ts, t

ubul

ar m

embe

rs, C

-se

ctio

ns, a

ngle

iron

s, o

r any

long

, sle

nder

mem

bers

whe

re o

nly

mem

bran

e an

d be

ndin

g st

ress

es a

re n

eede

d.�

Spar

elem

ents

are

use

d to

mod

el s

prin

gs, b

olts

, pre

load

ed b

olts

, an

d tr

uss

mem

bers

.�

Sprin

gel

emen

ts a

re u

sed

to m

odel

spr

ings

, bol

ts, o

r lon

g sl

ende

r par

ts, o

r to

repl

ace

com

plex

par

ts b

y eq

uiva

lent

stiff

ness

es.

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

�Sh

ell e

lem

ents

:�

Use

d to

mod

el th

in p

anel

s or

cur

ved

surf

aces

.�

The

defin

ition

of �

thin

� de

pend

s on

the

appl

icat

ion,

but

as

a ge

nera

l gui

delin

e, th

e m

ajor

dim

ensi

ons

of th

e sh

ell s

truc

ture

(p

anel

) sho

uld

be a

t lea

st 1

0 tim

es it

s th

ickn

ess.

�2-

D S

olid

ele

men

ts:

�U

sed

to m

odel

a c

ross

-sec

tion

of s

olid

obj

ects

.�

Mus

t be

mod

eled

in th

e gl

obal

Car

tesi

an X

-Y p

lane

.�

All

load

s ar

e in

the

X-Y

plan

e, a

nd th

e re

spon

se (d

ispl

acem

ents

) ar

e al

so in

the

X-Y

plan

e.�

Elem

entb

ehav

iour

may

be

one

of th

e fo

llow

ing:

�pl

ane

stre

ss�

plan

e st

rain

�ax

isym

met

ric�

axis

ymm

etric

harm

onic

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

Y

X Z

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

�Pl

ane

stre

ssas

sum

es z

ero

stre

ssin

the

Z di

rect

ion.

�Va

lid fo

r com

pone

nts

in w

hich

the

Z di

men

sion

is s

mal

ler t

han

the

X an

d Y

dim

ensi

ons.

�Z-

stra

in is

non

-zer

o.�

Opt

iona

l thi

ckne

ss (Z

dire

ctio

n)

allo

wed

.�

Use

d fo

r str

uctu

res

such

as

flat

plat

es s

ubje

cted

to in

-pla

ne

load

ing,

or t

hin

disk

s un

der

pres

sure

or c

entr

ifuga

l loa

ding

.

Y

X Z

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

�Pl

ane

stra

inas

sum

es z

ero

stra

inin

the

Z di

rect

ion.

�Va

lid fo

r com

pone

nts

in w

hich

the

Z di

men

sion

is m

uch

larg

er th

an th

e X

and

Y di

men

sion

s.�

Z-st

ress

is n

on-z

ero.

�U

sed

for l

ong,

con

stan

t-cro

ss-s

ectio

n st

ruct

ures

suc

h as

str

uctu

ral b

eam

s.Y

X Z

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

�A

xisy

mm

etry

assu

mes

that

the

3-D

mod

el

and

its lo

adin

g ca

n be

gen

erat

ed b

y re

volv

ing

a 2-

D s

ectio

n 36

0° a

bout

the

Y ax

is.

�A

xis

of s

ymm

etry

mus

t coi

ncid

e w

ith th

e gl

obal

Y a

xis.

�N

egat

ive

X co

ordi

nate

s ar

e no

t per

mitt

ed.

�Y

dire

ctio

n is

axi

al, X

dire

ctio

n is

radi

al, a

nd Z

di

rect

ion

is c

ircum

fere

ntia

l (ho

op) d

irect

ion.

�H

oop

disp

lace

men

t is

zero

; hoo

p st

rain

s an

d st

ress

es a

re u

sual

ly v

ery

sign

ifica

nt.

�U

sed

for p

ress

ure

vess

els,

str

aigh

t pip

es,

shaf

ts, e

tc.

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

�A

xisy

mm

etric

harm

onic

is a

spe

cial

cas

e of

axis

ymm

etry

whe

re th

e lo

ads

can

be n

on-a

xisy

mm

etric

.�

The

non-

axis

ymm

etric

load

ing

deco

mpo

sed

into

Fou

rier s

erie

s co

mpo

nent

s, a

pplie

d an

d so

lved

sep

arat

ely,

and

then

com

bine

d la

ter.

No

appr

oxim

atio

n is

intr

oduc

ed b

y th

is s

impl

ifica

tion!

�U

sed

for n

on-a

xisy

mm

etric

load

s su

ch a

s to

rque

on

a sh

aft.

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

�3-

D S

olid

ele

men

ts:

�U

sed

for s

truc

ture

s w

hich

, bec

ause

of g

eom

etry

, mat

eria

ls,

load

ing,

or d

etai

l of r

equi

red

resu

lts, c

anno

t be

mod

eled

with

si

mpl

er e

lem

ents

. �

Als

o us

ed w

hen

the

mod

el g

eom

etry

is tr

ansf

erre

d fr

om a

3-D

C

AD

sys

tem

, and

a la

rge

amou

nt o

f tim

e an

d ef

fort

is re

quire

d to

conv

ert i

t to

a 2-

D o

r she

ll fo

rm.

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

Elem

ent O

rder

�El

emen

t ord

er re

fers

to th

e po

lyno

mia

l ord

er o

f the

ele

men

t�s

shap

e fu

nctio

ns.

�W

hat i

s a

shap

e fu

nctio

n?�

It is

a m

athe

mat

ical

func

tion

that

giv

es th

e �s

hape

� of

the

resu

lts

with

in th

e el

emen

t. S

ince

FEA

sol

ves

for D

OF

valu

es o

nly

at

node

s, w

e ne

ed th

e sh

ape

func

tion

to m

ap th

e no

dal D

OF

valu

es

to p

oint

s w

ithin

the

elem

ent.

�Th

e sh

ape

func

tion

repr

esen

ts a

ssum

edbe

havi

or fo

r a g

iven

el

emen

t.�

How

wel

l eac

h as

sum

ed e

lem

ent s

hape

func

tion

mat

ches

the

true

beh

avio

r dire

ctly

affe

cts

the

accu

racy

of t

he s

olut

ion,

as

show

n on

the

next

slid

e.

Qua

drat

ic d

istri

butio

n of

D

OF

valu

esAc

tual

qua

drat

ic

curv

e

Line

ar a

ppro

xim

atio

n (P

oor R

esul

ts)

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

Qua

drat

ic a

ppro

xim

atio

n(B

est R

esul

ts)

Line

ar a

ppro

xim

atio

n w

ith m

ultip

le e

lem

ents

(B

ette

r Res

ults

)

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

�W

hen

you

choo

se a

n el

emen

t typ

e, y

ou a

re im

plic

itly

choo

sing

and

acc

eptin

g th

e el

emen

t sha

pe fu

nctio

n as

sum

ed

for t

hat e

lem

ent t

ype.

The

refo

re, c

heck

the

shap

e fu

nctio

n in

form

atio

n be

fore

you

cho

ose

an e

lem

ent t

ype.

�Ty

pica

lly, a

line

ar e

lem

ent h

as o

nly

corn

er n

odes

, whe

reas

a

quad

ratic

ele

men

t als

o ha

sm

idsi

deno

des.

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

Line

ar e

lem

ents

�C

an s

uppo

rt o

nly

a lin

ear v

aria

tion

of d

ispl

acem

ent a

nd th

eref

ore

(mos

tly) o

nly

a co

nsta

nt s

tate

of

stre

ss w

ithin

a s

ingl

e el

emen

t.

�H

ighl

y se

nsiti

ve to

ele

men

t di

stor

tion.

�A

ccep

tabl

e if

you

are

only

in

tere

sted

in n

omin

al s

tres

s re

sults

.

�N

eed

to u

se a

larg

e nu

mbe

r of

elem

ents

to re

solv

e hi

gh s

tres

s gr

adie

nts.

Qua

drat

ic e

lem

ents

�C

an s

uppo

rt a

qua

drat

ic v

aria

tion

of d

ispl

acem

ent a

nd th

eref

ore

a lin

ear v

aria

tion

of s

tres

s w

ithin

a

sing

le e

lem

ent.

�C

an re

pres

ent c

urve

d ed

ges

and

surf

aces

mor

e ac

cura

tely

than

lin

ear e

lem

ents

. N

ot a

s se

nsiti

ve

to e

lem

ent d

isto

rtio

n.

�R

ecom

men

ded

if yo

u ar

e in

tere

sted

in h

ighl

y ac

cura

te

stre

sses

.

�G

ive

bette

r res

ults

than

line

ar

elem

ents

, in

man

y ca

ses

with

fe

wer

num

ber o

f ele

men

ts a

nd

tota

l DO

F.

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

�N

otes

:�

For s

hell

mod

els,

the

diffe

renc

e be

twee

n lin

ear a

nd q

uadr

atic

el

emen

ts is

not

as

dram

atic

as

for s

olid

mod

els.

Lin

ear s

hells

ar

e th

eref

ore

usua

lly p

refe

rred

.�

Bes

ides

line

ar a

nd q

uadr

atic

ele

men

ts, a

third

kin

d is

ava

ilabl

e,

know

n as

p-e

lem

ents

. P

-ele

men

ts c

an s

uppo

rt a

nyw

here

from

a

quad

ratic

to a

n 8t

h-or

der v

aria

tion

of d

ispl

acem

ent w

ithin

a

sing

le e

lem

ent a

nd in

clud

e au

tom

atic

sol

utio

n co

nver

genc

e co

ntro

ls.

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

Mes

h D

ensi

ty

�Th

e fu

ndam

enta

l pre

mis

e of

FEA

is th

at a

s th

e nu

mbe

r of

elem

ents

(mes

h de

nsity

) is

incr

ease

d, th

e so

lutio

n ge

ts

clos

er a

nd c

lose

r to

the

true

sol

utio

n.

�H

owev

er, s

olut

ion

time

and

com

pute

r res

ourc

es re

quire

d al

so in

crea

se d

ram

atic

ally

as

you

incr

ease

the

num

ber o

f el

emen

ts.

�Th

e ob

ject

ives

of t

he a

naly

sis

usua

lly d

ecid

e w

hich

way

the

slid

er b

ar b

elow

sho

uld

be m

oved

.

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

�If

you

are

inte

rest

ed in

hig

hly

accu

rate

str

esse

s:�

A fi

ne m

esh

will

be

need

ed, o

mitt

ing

no g

eom

etric

det

ails

at a

nylo

catio

n in

the

stru

ctur

e w

here

suc

h ac

cura

cy is

nee

ded.

�St

ress

con

verg

ence

sho

uld

be d

emon

stra

ted.

�A

ny s

impl

ifica

tion

anyw

here

in th

e m

odel

mig

ht in

trod

uce

sign

ifica

nt e

rror

.

�If

you

are

inte

rest

ed in

def

lect

ions

or n

omin

al s

tres

ses:

�A

rela

tivel

y co

arse

mes

h is

suf

ficie

nt.

�Sm

all g

eom

etry

det

ails

may

be

omitt

ed.

Prel

imin

ary

Dec

isio

ns...

Whi

ch E

lem

ent T

ype?

�If

you

are

inte

rest

ed in

mod

e sh

apes

(mod

al a

naly

sis)

:�

Smal

l det

ails

can

usu

ally

be

omitt

ed.

�Si

mpl

e m

ode

shap

es c

an b

e ca

ptur

ed u

sing

a re

lativ

ely

coar

se

mes

h.�

Com

plex

mod

e sh

apes

may

requ

ire a

uni

form

, mod

erat

ely

fine

mes

h.

�Th

erm

al A

naly

ses:

�Sm

all d

etai

ls c

an u

sual

ly b

e om

itted

, but

sin

ce m

any

ther

mal

an

alys

es a

re fo

llow

ed b

y a

stre

ss a

naly

sis,

str

ess

cons

ider

atio

ns g

ener

ally

det

erm

ine

this

.�

Mes

h de

nsity

is u

sual

ly d

eter

min

ed b

y ex

pect

ed th

erm

al

grad

ient

s. A

fine

mes

h is

requ

ired

for h

igh

ther

mal

gra

dien

ts,

whe

reas

a c

oars

e m

esh

may

be

suffi

cien

t for

low

gra

dien

ts.