Analytical and Numerical Methods of Structural Analysis (1)
-
Upload
luis-montoya -
Category
Documents
-
view
220 -
download
0
Transcript of Analytical and Numerical Methods of Structural Analysis (1)
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 1/50
Lecture #4Analytical and Numerical Methodsof Structural Analysis
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 2/50
FLOWCHART OF STRCTRALANAL!S"S
Real object
Structural
layout
Design model
Only load-carrying structureis kept
Assumptions and simplifications
are applied, loads are calculatedaccording to the problem
Results of analysis
Implementation
on real object
This step is beyond the scope
of structural analysis
Structural analysis
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 3/50
FLOWCHART OF STRCTRALANAL!S"S
$
Real object
Structural
layout
Design model
Results of analysis
Implementation
on real object
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 4/50
FLOWCHART OF STRCTRALANAL!S"S
4
Real object
Structural
layout
Design model
Results of analysis
Implementation
on real object
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 5/50
FLOWCHART OF STRCTRALANAL!S"S
%
Real object
Structural
layout
Design model
Results of analysis
Implementation
on real object
Depending on the kind of
problem which is solved, thedesign model could be either as
detailed as structural layout, or
as generalized as below
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 6/50
M&THO'S OF STRCTRAL ANAL!S"S
Analytical methods Numerical methods
!est for designingcalculations, suit for
checking calculations with
certain limitations
!est for checkingcalculations, practically
effete for designing
calculations
Solutions e"ist for partialcases #specific ob$ects%
&ersatile and fle"ible
'eed much work to bedeveloped, but onlysimple software for
application
'eed e"pensive andcomple" software and
hardware
(
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 7/50
ANAL!T"CAL M&THO'S OFSTRCTRAL ANAL!S"S
)
Widely used nowadays:( methods of )echanics of )aterials*( methods for statically indeterminate structures
( method of forces*
( method of displacements*( beam theory for thin-walled structures*( method of reduction coefficients+
Rarely used nowadays #mostly due to the progressof numerical methods%( methods based on alculus of &ariations*( methods of Theory of lasticity+
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 8/50
&*AM+L& TO COM+AR& ANAL!T"CALAN' NM&R"CAL M&THO'S
,
Aim:
Design the steelbracket to minimize
the self-weight
displacement of the
load+
Gien data:
D./01 mm*
2./311 mm*
24/.11 mm*
mload/1+3 kg+
!bjecties:D4, δ4, δ.+ load
"#$ D#$ #
"%$ D%$ %
base
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 9/50
-AS"C &.AT"ONS OF SOL"'M&CHAN"CS
/
&'uilibrium
e'uations
(onstitutie
e'uations
(ompatibility
e'uations
This is not only the sum of
forces or moments, but appliesfor elementary volume as well
5hysical law, e"pressesthe relation between
stress and strain
Solid body should
remain continuous
while being deformed
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 10/50
-AS"C &.AT"ONS OF SOL"'M&CHAN"CS
01
&'uilibrium
e'uations
(onstitutie
e'uations
(ompatibility
e'uations
This is not only the sum of forces
or moments, but applies for elementary volume as well+
0
0
0
xy x xz
xy y yz
yz xz z
X ,
x y z
Y , x y z
Z , x y z
where X ,Y ,Z external forces.
τ σ τ
τ σ τ
τ τ σ
∂∂ ∂+ + + =
∂ ∂ ∂∂ ∂ ∂
+ + + =∂ ∂ ∂
∂∂ ∂+ + + =
∂ ∂ ∂
−
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 11/50
-AS"C &.AT"ONS OF SOL"'M&CHAN"CS
00
&'uilibrium
e'uations
(onstitutie
e'uations
(ompatibility
e'uations
5hysical law, e"presses the
relation between stress and strain+
( )( )
( )( )
( )( )
1
1
1
x x y z
y y x z
z z x y
xy yz xz xy xz yz
, E
, E
, E
, ,G G G
ε σ ν σ σ
ε σ ν σ σ
ε σ ν σ σ
τ τ τ γ γ γ
= − +
= − +
= − +
= = =
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 12/50
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 13/50
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 14/50
WA!S TO SOL2& A SOL"' M&CHAN"CS
+RO-L&M
04
Displacements
are set asun*nowns
Strains are
deried
Stresses are
deried
ompatibility
e6uations
onstitutive
e6uations
&'uilibrium
e'uations are
soled
6uilibriume6uations
Stresses are
set asun*nowns
Strains arederied
onstitutive
e6uations
6uilibrium
e6uations
(ompatibility
e'uations are
soled
ompatibilitye6uations
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 15/50
&*AM+L& TO COM+AR& ANAL!T"CALAN' NM&R"CAL M&THO'S
0%
Analytical methods
used:( )ethods of
)echanics of
)aterials*
( )ohr8s integral tocalculate
displacements+
Software used:
)athAD &49+1
load
"#$ D#$ #
"%$ D%$ %
base
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 16/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
0(
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 17/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
0)
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 18/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
0,
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 19/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
0/
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 20/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
1
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 21/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
0
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 22/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 23/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
$
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 24/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
4
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 25/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
%
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 26/50
M&THO'S OF STRCTRAL ANAL!S"S
Analytical methods Numerical methods
!est for designingcalculations, suit for
checking calculations with
certain limitations
!est for checkingcalculations, practically
effete for designing
calculations
Solutions e"ist for partialcases #specific ob$ects%
&ersatile and fle"ible
'eed much work to bedeveloped, but onlysimple software for
application
'eed e"pensive andcomple" software and
hardware
(
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 27/50
NM&R"CAL M&THO'S OFSTRCTRAL ANAL!S"S
)
)ost widely used nowadays is+inite &lement ,ethod -+&,./
The structural analysis using 7) is called finite
element analysis #7A%+
Generally$ +&, is just a method to sole
differential e'uations/The physical background of 7) is the same as in
analytical methods+
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 28/50
F"N"T& &L&M&NT M&THO'
,
The smooth field of stresses is calculated using the combination
of basic functions, which are constructed on a mesh+
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 29/50
F"N"T& &L&M&NT M&THO'
/
Software work on principle :;:O <garbage in = garbage out>?
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 30/50
F"N"T& &L&M&NT M&THO'
$1
Software work on principle :;:O <garbage in = garbage out>?
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 31/50
F"N"T& &L&M&NT M&THO'
$0
Software work on principle :;:O <garbage in = garbage out>?
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 32/50
F"N"T& &L&M&NT M&THO'
$
ven if the result is realistic,
you should always check it+
;t8s not a big problem
to create a <nice picture> using 7A+
The problem is to get the reliable and verified result+
That8s a difference between professional and
beginner+
7A is a way to find a stress state,
but not the way to design or to check the strength@
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 33/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
$$load
base
!bject +&, model
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 34/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
$4
Assignment
of parameters
O CO C
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 35/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
$%
Deformed
shape
3 finite elements
in model
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 36/50
&*AM+L& TO COM+AR& ANAL!T"CAL AN'
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 37/50
Analytical method +inite element analysis
Displacement is B+CC µm
#or 0+1B µm in 7A%
Displacement is B+04 µm
#or 0+.. µm in 7A%
D4/CB µm, δ4/. µm,
δ./ 44+. mm
D4/30 µm, δ4/. µm,
δ./ 4 mm
'eed only simplesoftware for application
'eed e"pensive andcomple" software
$)
&*AM+L& TO COM+AR& ANAL!T"CAL AN'NM&R"CAL M&THO'S
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 38/50
M&THO'S OF STRCTRAL ANAL!S"S
Analytical methods Numerical methods
!est for designingcalculations, suit for
checking calculations with
certain limitations
!est for checkingcalculations, practically
effete for designing
calculations
Solutions e"ist for partialcases #specific ob$ects%
&ersatile and fle"ible
'eed much work to bedeveloped, but onlysimple software for
application
'eed e"pensive andcomple" software and
hardware
$,
&*AM+L& "LLSTRAT"N3 TH& '&S"3N OF F"N"T&
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 39/50
&*AM+L& "LLSTRAT"N3 TH& '&S"3N OF F"N"T&&L&M&NT MO'&L
$/
Shell model+
4. elements inmodel, around 3
minutes to solve
on poor office 5
&*AM+L& "LLSTRAT"N3 TH& '&S"3N OF F"N"T&
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 40/50
&*AM+L& "LLSTRAT"N3 TH& '&S"3N OF F"N"T&&L&M&NT MO'&L
41
Solid model+
.31 elements, around .1
minutes to solve on powerful 5#9"9+.:Ez processor,
4C :! memory%+
&*AM+L& "LLSTRAT"N3 TH& '&S"3N OF F"N"T&
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 41/50
&*AM+L& "LLSTRAT"N3 TH& '&S"3N OF F"N"T&&L&M&NT MO'&L
40
Difference5ertain there is a difference, but for some results it is negligible+
Thus, the model should be built according to problem,as in analytical methods
F"N"T& &L&M&NT SOFTWAR&
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 42/50
F"N"T& &L&M&NT SOFTWAR&
4
Widely used nowadays:
( A'SFS*( 5atranG'astran*( A!AHIS*( Solidworks Simulation #former OS)OS%*
And many-many others, freeware and proprietary?
Any difference5 :enerally, no difference+ 7A
packages are often customized to be more convenientfor some specific problems+ !ut for most cases,
differences between packages and limitations have
marketing but not the technical reason+
F"N"T& &L&M&NT M&THO' H"STOR"CAL
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 43/50
4J91Theoretical aspects were developed for the
first time
4J31,4JC1
Theoretical background was developed, therise of computer power allowed to make first
specific software
4JB12arge general-purpose packages appeared
#A'SFS, 'ASTKA'%
4J01 :raphical pre- and post-processing
4JJ1Kise of the role of automatic meshing, and
thus the model scale
.111 )ulti-disciplinary and large-scale problems 4$
F"N"T& &L&M&NT M&THO' H"STOR"CAL+RO3R&SS
+R"NC"+AL COM+ON&NTS OF F&A
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 44/50
+R"NC"+AL COM+ON&NTS OF F&ASOTWAR&
44
2re6processor
Soler
2ost6precessor
onstruction of the model, setting
the properties, loads, constraintsetc+
Solution itself+ Two main types of
solvers are iterative or sparse +
2ooking on results, processing of
results, generating <nice figures>
F"N"T& &L&M&NT M&THO' OL'
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 45/50
4%
F"N"T& &L&M&NT M&THO' OL'"NT&RFAC&
F"N"T& &L&M&NT M&THO' MO'&RN
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 46/50
4(
F"N"T& &L&M&NT M&THO' MO'&RN"NT&RFAC&
CONCLS"ONS
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 47/50
CONCLS"ONS
( <Analytical method> does not mean <by hand> or <on
paper>, modern software can give large benefits+
( 'umerical methods are very e"acting in terms of
software and hardware+
( 7A is not a magic key that opens every door+ ;t8s $ust a versatile and effective tool to calculate stresses+
( Deep insight is re6uired for successful structural
analysis, no matter is it analytics of 7A+
( :enerally, analytical methods are good for
designing, 7A = for checking+ Eowever, in many
cases both of methods can be used for both phases of
analysis+ 4)
CONCLS"ONS
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 48/50
CONCLS"ONS
Lhat does it mean to be a professional in structuralanalysisM
nowledge of comple" formulasM Isage of modern
softwareM
'either of it is an answer+ Answer is a deep
understanding of how the structure wor*s, and
application of proper methods according to the given
problem+
Analytical and numerical methods loss their
disadvantages when they are combined together+
4,
WH&R& TO F"N' MOR& "NFORMAT"ON5
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 49/50
WH&R& TO F"N' MOR& "NFORMAT"ON5-OO6S AN' S&FL L"N6S
4/
:ood book about structural analysis and Ansys isE. Madenci, I.Guven. The Finite Element Method and Applications inEngineering Using ANSYS, !!"
&ery useful links are
Official website resource library ansys+com
Kesourse for Ansys users ansys+net
5erfect forum #not for beginners, though% "ansys+org
Foutube #it8s not a $oke, search <Ansys> for amazing training
videos% youtube+com
? ;nternet is boundless ?
7/23/2019 Analytical and Numerical Methods of Structural Analysis (1)
http://slidepdf.com/reader/full/analytical-and-numerical-methods-of-structural-analysis-1 50/50
TO+"C OF TH& N&*T L&CTR&
Statically determinate trusses
All materials of our course are available
at department website k41.+khai+edu
4+ :o to the page <NPQRUV>
.+ 5ress <Structural )echanics #lecturer &akulenko S+&+%>