prac1+2-clamped beam and plate

7/27/2019 Prac1+2-clamped beam and plate

1/13

Example 1: Cantilever Beam

Practical exercises with the FEM program ANSYS (to !"#$

Example 1: Cantilever Beam

For a steel Cantilever Beam, built in at one end only, calculate the first three natural bendingfrequencies f1 to f3, and determine the corresponding natural oscillation modes. For comparison,

calculate solutions for different numbers of elements and element types (beam, shell and solid

elements).

Fig% 1%1: Cantilever beam

l & h E

!! mm 1! mm "! mm "1! !!! #$mm" %&'! g$m3

1%1 'heoretical Calclation (see )ectre *+,namics o- Machiner,. /#$:

he natural angular frequency is calculated from*

44 )( LA

IEA

L

IEA KKK

=

=

+ith*

1- 3,'" "- "",/ 3- 1,%

0et as inputs, this results in*

2,/%!/-f&!,"1 11

1 S=

2"',/!-f!,1&'&"

1" S=

2&1/,''-f,'11%3

13 S=


2/13

A1%/ Example 1: Cantilever Beam

1%/ Mo0al anal,sis script: cantilever &eam with -inite &eam elements

ntro

-inish finish actual processing mode

2clear3nostart clear the database

Pre4Processing

2-ilname3p1mo0al&eam35 change the job name for the analysis

2prep6 enter pre-processing

2title3onesi0e0 clampe0 &eam (BEAM$ title for actual problem

et313&eam! define finite element type 1

7as83par9eight3&eam height m# ;35%5/ user input: beam height

7as83par


3/13

Example 1: Cantilever Beam A1%!

Post4Processing

/post1 enter post1-processor

flag=1 set flag parameter to 1

*dowhile,flag testing flag parameter: if 0*lea#e do-loop

*ask,varMode,'show eigenform [0=exit]',1 user input: eigenform to display

*if,varMode,eq,0,then testing #ar+ode parameter on e'uals 0

flag=0 set flag parameter to 0

*elseif,varMode,le,nmModes,thentesting #ar+ode parameter on lower e'ual

num+odes

set,,,,,,,varMode select calculated eigenform number to display

pldisp,1 display eigenform number

*endif close if 'uery

*enddo close do-loop

finish lea#e post1-processor


4/13

A1% Example 1: Cantilever Beam

1%! Mo0al anal,sis Deslts: cantilever &eam with -inite &eam elements

Fig% 1%/: 1steigenmo0e @%5? 9

Fig% 1%!: /n0eigenmo0e /5%@? 9

Fig% 1%: !r0eigenmo0e ?11%?1? 9


5/13

Example 1: Cantilever Beam A1%"

1% Mo0al anal,sis script: cantilever &eam with -inite shell elements

ntroSee intro chap! 1!

Pre4Processing2-ilname3p1mo0alshell35 change the jobname for the analysis

2prep6 enter pre-processing

2title3onesi0e0 clampe0 &eam (S9E))$ title for actual problem

et313shell@! define finite element type 1

7as83par'hic83shell thic8ness m# ;35%51 user input: enter shell thickness

r313par'hic8 define property set 1

7as83parEMo0ls3mo0ls elasticit, N2m>/# ;3/%1e11 user input: enter modulus of elasticity

mp3ex313parEMo0ls define material elasticity for set 1

7as83par+ensit,30ensit, 8g2m>!# ;36?"5%5 user input: enter material density

mp30ens313par+ensit,define material density for set 1

7as83par)at3lateral contraction 4# ;35%! user input: enter lateral contraction

mp3nx,313par)at define material lateral contraction for set 1


7as83par)ength3&eam length m# ;35%@ user input: beam length

&lc35353par)ength3par9eightdefines rectangular area with parenght and

par.eight

aatt313131353 connect finite element attributes with area 1

7as83parElem)ength3mean element length m# ;35%55" user input: mean element si/e

esie3parElem)ength353 define pre#ious entered mean element si/e

msh8e,31 switching to mapped meshing

amesh31 create elements on areamsh8e,35 switching to free meshing

0l333all3 define boundary conditions on line

0a3133 define boundary conditions on area 1

0a313rotx3 define boundary conditions on area 1

0a313rot,3 define boundary conditions on area 1

2view31313131 define the #iewing direction for the display

2p&c3all331 display option for all boundary symbols

eplot produce an element display

-inish lea#e pre processor

save3p1mo0alshell30&33all sa#e database in p1modalshell!db

Soltion4Processingsee Solution-rocessing chap! 1!

Post4Processingsee ost-rocessing chap! 1!


6/13

A1%@ Example 1: Cantilever Beam

1%" Mo0al anal,sis reslts: cantilever &eam with -inite shell elements

Fig% 1%": 1steigenmo0e @%5" 9

Fig% 1%@: /n0eigenmo0e /?%/ 9

Fig% 1%6: !r0eigenmo0e ?5%/!? 9


7/13

Example 1: Cantilever Beam A1%6

1%@ Mo0al anal,sis script: cantilever &eam with -inite soli0 elements

ntrosee intro chap! 1!

Pre4Processing

2-ilname3p1mo0alsoli035 change the jobname for the analysis

2prep6 enter preprocessing

2title3onesi0e0 clampe0 &eam (S)+$ title for actual problem

et313soli0" define finite element type 1

7as83parEMo0ls3mo0ls elasticit, N2m>/# ;3/%1e11 user input: enter modulus of elasticity

mp3ex313parEMo0ls define material elasticity for set 1

7as83par+ensit,30ensit, 8g2m>!# ;36?"5%5 user input: enter material density

mp30ens313par+ensit, define material density for set 1




7as83par)ength3&eam lenght m# ;35%@ user input: beam length

7as83par


8/13

A1%? Example 1: Cantilever Beam

1%6 Mo0al anal,sis reslts: cantilever &eam with -inite soli0 elements

Fig% 1%?: 1steigenmo0e ?%@@6 9

Fig% 1%: /n0eigenmo0e !5!%/ 9

Fig% 1%15: !r0eigenmo0e ?/%6! 9


9/13

Example 1: Cantilever Beam A1%


10/13

A/%5 Example /: 'rianglar )ea- Spring

Example /: 'rianglar )ea- Spring

4n this e5ample the first three natural oscillation modes of a riangular 6eaf 0pring are to be investigated. he

natural frequency of the first eigenmode (natural mode) can be compared +ith the appro5imation calculation using

7ayleigh.

Fig% /%1* 8eometric layout of the triangular leaf spring

)

mm#

B

mm#

t

mm#

E

N2mm/#

8g2m!#

/!! 1/! mm / mm "1! !!! #$mm

"

%&'! g$m

3

/%1 'heoretical Calclation:

he angular natural frequency is calculated according to 7ayleigh from*

3

-

-

4 ( 5 ( y ( d (

( 6 ( y ( d (

9

( ) ( ) 9 ( )

( ) ( ) 9 ( )

=

!

!

!

!

:here*4() * 4 * constant, () * * constant

6 ( b t (

-6

(

-

5 ( b t (

-5

(

-

( )

( ) ;

=

=

=

=

1 1

1 "1 1

!

!

ppro5imate description of the 1stbending mode is*

=

= "cos9/9

)("cos1)( !! -

(

-(y-

(

(y


11/13

Example /: 'rianglar )ea- Spring A/%1

Fitting these into the above equation*

3

-

-

4 5 (

- -

(

-d (

6 (

-

(

-d (

"

!

!

"

!

!

"

1/ "

1 1"

=

9

9c o s

c o s

4nserting the limits ! and 6 in the above integrals*

3

4 5

-

4 5

-

6 - 6 -

"

!

/

3

!

"

3

! !

"

/ 1

3

/

%=

+

fter simplification the equation has the form*

3

4 5

6 -

" !

/ "

!

/ "

/

1 3 " &=

+

( )

( )

fter inserting the values, the fundamental natural angular frequency, according to 7ayleigh, results in*

! = /653/12s - D1= !35 9 G - exact

Deslts -rom ANSYS: -1= /3"? 9H


12/13

A/%/ Example /: 'rianglar )ea- Spring

/%/ Mo0al anal,sis script: 'rianglar lea- spring with -inite shell elements

ntrosee intro chap! 1!

Pre4Processing

2-ilname3p/mo0alshell35 change the jobname for the analysis

2prep6 enter preprocessing

2title3trianglar lea- spring (S9E))$ title for actual problem

et313shell@! define finite element type 1

7as83par)ength3trianglar 0epth m# ;35% user input: height of triangle, see!fig!!1:

)=par)ength define height of triangle

7as83par!# ;36?"5%5 user input: enter material density

mp30ens313par+ensit, define material density for set 1



7as83par'hic83thic8ness o- shell m# ;35%55 user input: thickness of triangular leaf

r313par'hic8 define thickness of triangular leaf

831353534&2/3 define keypoint 1 at specified coordinate

83/35353&2/3 define keypoint at specified coordinate

83!3l35353 define keypoint 8 at specified coordinate

lstr313/ define line between keypoint 1 and

lstr3/3! define line between keypoint and 8

lstr3!31 define line between keypoint 8 and 1

al313/3! define area for triangular leaf spring

2view31313131 define the #iewing direction for the display

aatt313131353 connect finite element attributes with area 1

7as83parElem)ength3mean element length m# ;35%51 user input: mean element si/e

esie3parElem)ength353 define pre#ious entered mean element si/e

msh8e,35 acti#ate free meshing

amesh31 mesh area 1

0l3133all boundary condition for line 1

-inish lea#e pre processor

save3p/mo0alshell30&33all sa#e database in pmodalshell!db

Soltion4Processingsee Solution-rocessing chap! 1!

Post4Processingsee ost-rocessing chap! 1!


13/13

Example /: 'rianglar )ea- Spring A/%!

/%! Mo0al anal,sis reslts: 'rianglar lea- spring with -inite shell elements

Fig% /%/: 1steigenmo0e /%"? 9

Fig% /%!: /n0eigenmo0e 1?@%56! 9

Fig% /%: !r0eigenmo0e 1%56! 9

prac1+2-clamped beam and plate

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