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Eiffel's Tower marks the birth of applied mechanics

I am inspired by Mike Ciavarella's recent post on the Shape of the Eiffel Tower to share a bit of my own obsession with the Tower...

The foundations of applied mechanics were laid in the late 18th and early 19th century.  During this time, many of the founders of this new field, men such as Coulomb, Lagrange, Laplace, Poisson, Coriolis, and Navier, lived and worked together in Paris.  For this reason, Paris deserves to be known as the birthplace of applied mechanics, but you won't find mention of this fact in any of the popular guidebooks. You can find, if you know where to look in the city, evidence of the influence these men had.

Of course, the Eiffel Tower is an obvious place to start.  Built in 1889, Eiffel's masterpiece exemplifies the advances made in engineering analysis and the mechanical arts during the preceding century, but there's more.  Eiffel dedicated his creation to the advance of science by inscribing on the tower's four sides the names of 72 French scientists and engineers - partisans in a revolution that transformed Paris and the world.

Here is a map that visits sites in Paris related to these men and the revolution in science and technology they created.

 

Comments

Mike Ciavarella's picture

Thanks William for your map --- that's a useful technological guide for my July visit to Paris with my students.

I just realized, last year there was this Expo Gustave Eiffel - Paris --- 'expo Gustave Eiffel,
le magicien du fer, se tient à l'Hôtel de Ville, Salle Saint Jean,
jusqu'au 29 août.
I guess it is over, what a pity, were you there?  Probably this is because last year t was 120 years anniversary Tour Eiffel, 120 ANS, Gustave Eiffel, 1889 2009, Photo:
Francisco Munoz Espejo 2009

If you prefer a documentary in spanish, see here.  Or here with some nice music. But also here old movies.

There is even a full movie about the history of the tour eiffel..  See here for the first part, and follow the links for the other 5-6 parts.  It's in french...

I am happy to see that Sarkozy is revitalizing Paris with Grand Paris : Les 10 projets architecturaux (hope you don't mind some french..).  

But my students were stimulated by Zhigang's worry that I underestimate them, so they produced a ANSYS input file for the Tour today.  Have a try, we can later discuss optimality of the Tour with various strategies before I actually make the trip in July!

/prep7
et,1,63
mp,ex,1,205000
mp,prxy,1,0.3
! DEFINIZIONE DEI KEYPINTS
k,1,,5
k,2,11.280,5
k,3,17.113,5.284
k,4,23.278,5.585
k,5,29.795,5.903
k,6,36.683,6.239
k,7,43.963,6.594
k,8,51.658,6.969
k,9,59.791,7.365
k,10,68.387,7.784
k,11,77.473,8.227
k,12,87.076,8.696
k,13,97.076,9.245
k,14,107.076,9.999
k,15,117.576,10.790
k,16,128.076,11.786
k,17,138.676,12.880
k,18,149.376,14.303
k,19,160.676,15.806
k,20,165.576,16.925
k,22,185.776,21.583
k,23,196.776,24.365
k,24,207.776,27.415
k,25,218.776,30.919
k,26,225.776,33.697
k,27,236.776,38.673
k,28,247.776,43.578
k,29,258.776,48.519
k,30,269.776,53.459
k,31,269.776
k,32,258.776
k,33,247.776
k,34,236.776
k,35,225.776
k,36,218.776
k,37,207.776
k,38,196.776
k,39,185.776
k,41,165.576
k,42,160.676
k,43,149.376
k,44,138.676
k,45,128.076
k,46,117.576
k,47,107.076
k,48,97.076
k,49,87.076
k,50,77.473
k,51,68.387
k,52,59.791
k,53,51.658
k,54,43.963
k,55,36.683
k,56,29.795
k,57,23.278
k,58,17.113
k,59,11.280
k,60
spline,1,2,3,4,5,6
spline,6,7,8,9,10,11
spline,11,12,13,14,15,16
spline,16,17,18,19,20,22
spline,22,23,24,25,26
spline,26,27,28,29,30
l,30,31
l,31,60
l,60,1
! CREAZIONE AREA
a,1,2,59,60
a,2,3,58,59
a,3,4,57,58
a,4,5,56,57
a,5,6,55,56
a,6,7,54,55
a,7,8,53,54
a,8,9,52,53
a,9,10,51,52
a,10,11,50,51
a,11,12,49,50
a,12,13,48,49
a,13,14,47,48
a,14,15,46,47
a,15,16,45,46
a,16,17,44,45
a,17,18,43,44
a,18,19,42,43
a,19,20,41,42
a,20,22,39,41
a,22,23,38,39
a,23,24,37,38
a,24,25,36,37
a,25,26,35,36
a,26,27,34,35
a,27,28,33,34
a,28,29,32,33
a,29,30,31,32

 

 
eiffel

 

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

I am very interested about the study of the Eiffel Tower. In this Ansys input file I introduce the effect of the wind along the right profile of the Tour at a pressure of 300 kg/m2 and weight of the tower. 

 

/prep7
et,1,3

mp,ex,1,205000
mp,prxy,1,0.3

!DEFINITION OF THE GRAVITY ACCELERATION
g=9.81
acel,,-g

! DEFINITION KEYPOINTS
k,1,5,269.776
k,2,5,258.776
k,3,5.284,247.776
k,4,5.585,236.776
k,5,5.903,225.776
k,6,6.239,218.776
k,7,6.594,207.776
k,8,6.969,196.776
k,9,7.365,185.776
k,10,7.784,165.576
k,11,8.227,160.676
k,12,8.696,149.376
k,13,9.245,138.676
k,14,9.999,128.076
k,15,10.790,117.576
k,16,11.786,107.076
k,17,12.880,97.076
k,18,14.303,87.076
k,19,15.806,77.473
k,20,18.925,68.387
k,21,21.583,59.791
k,22,24.365,51.658
k,23,27.415,43.963
k,24,30.919,36.683
k,25,33.697,29.795
k,26,38.673,23.278
k,27,43.578,17.113
k,28,48.519,11.280
k,29,53.459
k,30,-5,269.776
k,31,-5,258.776
k,32,-5.284,247.776
k,33,-5.585,236.776
k,34,-5.903,225.776
k,35,-6.239,218.776
k,36,-6.594,207.776
k,37,-6.969,196.776
k,38,-7.365,185.776
k,39,-7.784,165.576
k,40,-8.227,160.676
k,41,-8.696,149.376
k,42,-9.245,138.676
k,43,-9.999,128.076
k,44,-10.790,117.576
k,45,-11.786,107.076
k,46,-12.880,97.076
k,47,-14.303,87.076
k,48,-15.806,77.473
k,49,-18.925,68.387
k,50,-21.583,59.791
k,51,-24.365,51.658
k,52,-27.415,43.963
k,53,-30.919,36.683
k,54,-33.697,29.795
k,55,-38.673,23.278
k,56,-43.578,17.113
k,57,-48.519,11.280
k,58,-53.459

!GENERATION OF A SEGMENT SPLINE THROUGH A SERIES OF KEYPOINTS
spline,1,2,3,4,5,6
spline,6,7,8,9,10,11
spline,11,12,13,14,15,16
spline,16,17,18,19,20,21
spline,21,22,23,24,25
spline,25,26,27,28,29
l,29,58
spline,30,31,32,33,34,35
spline,35,36,37,38,39,40
spline,40,41,42,43,44,45
spline,45,46,47,48,49,50
spline,50,51,52,53,54,55
spline,55,56,57,58
l,1,30

! DEFINITION AREAS BY CONNECTING KEYPOINTS
a,1,2,31,30
a,2,3,32,31
a,3,4,33,32
a,4,5,34,33
a,5,6,35,34
a,6,7,36,35
a,7,8,37,36
a,8,9,38,37
a,9,10,39,38
a,10,11,40,39
a,11,12,41,40
a,12,13,42,41
a,13,14,43,42
a,14,15,44,43
a,15,16,45,44
a,16,17,46,45
a,17,18,47,46
a,18,19,48,47
a,19,20,49,48
a,20,21,50,49
a,21,22,51,50
a,22,23,52,51
a,23,24,53,52
a,24,25,54,53
a,25,26,55,54
a,26,27,56,55
a,27,28,57,56
a,28,29,58,57

!vincoli e forze

dl,29,,all
sfl,1,pres,2943
sfl,2,pres,2943
sfl,3,pres,2943
sfl,4,pres,2943
sfl,5,pres,2943
sfl,6,pres,2943
sfl,7,pres,2943
sfl,8,pres,2943
sfl,9,pres,2943
sfl,10,pres,2943
sfl,11,pres,2943
sfl,12,pres,2943
sfl,13,pres,2943
sfl,14,pres,2943
sfl,15,pres,2943
sfl,16,pres,2943
sfl,17,pres,2943
sfl,18,pres,2943
sfl,19,pres,2943
sfl,20,pres,2943
sfl,21,pres,2943
sfl,22,pres,2943
sfl,22,pres,2943
sfl,23,pres,2943
sfl,24,pres,2943
sfl,25,pres,2943
sfl,26,pres,2943
sfl,27,pres,2943
sfl,28,pres,2943

 

wind<br />
effect

Mike Ciavarella's picture

George

 I think this is a good starting point.  However

 

1) the pressure seems to be orthogonal to the elements, not constant horizontal direction

2) I would prefer to see the definition of the surfaces more "parametric" so that at later stage we can optimize, either in shape optimization (i.e. you change the coordinates of the nodes in the splines), or as a full topological optimization (see here, for example ).  See e.g. these examples

Compliance
Design Visitors Gallery

The gallery shows the last 21 computed designs using the
interactive Compliance Design program.


95-89-117-39-dynip.superkabel.
de
May 21 2010 21:08:41

166.104.65.245
May 21 2010
16:16:00

166.104.65.245
May 21 2010
16:15:30


166.104.65.245
May 21 2010
16:14:33

166.104.65.245
May 21 2010
16:13:33

166.104.65.245
May 21 2010
16:12:55


121.130.182.100
May 21 2010
10:09:31

121.130.182.100
May 21 2010
10:09:03

ip5456f079.speed.planet.nl
May 20
2010 20:22:45


ip5456f079.speed.planet.nl
May 20
2010 20:21:34

ip5456f079.speed.planet.nl
May 20
2010 20:18:35

ip5456f079.speed.planet.nl
May 20
2010 20:16:47


ip5456f079.speed.planet.nl
May 20
2010 20:15:51

ip5456f079.speed.planet.nl
May 20
2010 20:14:09

ip5456f079.speed.planet.nl
May 20
2010 20:12:35


124-171-158-150.dyn.iinet.net.
au
May 19 2010 15:11:18

csiga.gszi.bme.hu
May 19 2010
13:53:39

csiga.gszi.bme.hu
May 19 2010
13:53:34


korte.gszi.bme.hu
May 19 2010
13:14:17

korte.gszi.bme.hu
May 19 2010
13:13:48

korte.gszi.bme.hu
May 19 2010
11:51:52

 

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/

Mike Ciavarella's picture

A 99 line
topology optimization code written in MATLAB®

The Matlab code presented in this page is intended for
engineering education. Students and newcomers to the field of topology
optimization can find the code here and download it. The code may be
used in courses in structural optimization where students may be
assigned to do extensions such as multiple load-cases, alternative
mesh-independency schemes, passive areas, etc..

 

The code is here top.m
(5K, Shift+click to save). This version of the code is optimized
with respect to speed compared to the original version and was released
on May 28th, 2002.

Save the program and start Matlab in the same directory. Run the
program by writing for example:

>> top(30,10,0.5,3.0,1.5)

in the Matlab prompt.

A description of the code can be found in the paper "A 99 line topology
optimization code written in MATLAB" (PDF)
(160K) (Structural and
Multidisciplinary Optimization 21(2), 2001, pp. 120-127) by Ole Sigmund.
The
original publication is available on LINK at http://link.springer.de

 

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

CanhLe's picture

 

 More on this can be found here !

 

Canh V. Le,
PhD in Computational Mechanics
Department of Civil and Structural Engineering
The University of Sheffield
Mappin Street,
Sheffield, S1 3JD, UK.
Phone: GB +44 1142225724
http://sites.google.com/site/canhlewebpage/

Mike Ciavarella's picture

Thanks Canh V. Le,

   if you have seen our educational effort here before our trip to Paris, we want to play with Eiffel's tower design.  Do you think the 99 lines program or your LayOpt matlab code,can be adapted for our problem, or at least to something close to it?

Thanks in advance.

mike

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

CanhLe's picture

 Dear Mike,

I would recommend to use LayOut or DLO since it is in general and has been tested for large-scale performance at our group. The idea behind is that we generate nodes in working domain and make as many as possible connections which can be line (truss) elements (gridlike structures), of course the more elements are used the better solutions can be obtained. In order to reduce computational cost Matthew Gilbert and Andrew Tyas have proposed nodal adaptive to optimize the number of connections. This  procedue has also been extended to plastic limit analysis problems and implemented in a comercial software. Therefore, I believe that you can adapt this technique to your project.

Best,

Canh

 

 

 

Canh V. Le,
PhD in Computational Mechanics
Department of Civil and Structural Engineering
The University of Sheffield
Mappin Street,
Sheffield, S1 3JD, UK.
Phone: GB +44 1142225724
http://sites.google.com/site/canhlewebpage/

Mike Ciavarella's picture

I checked the link you provided but it seems to do limit analysis, not truss optimization.

I think in the classical book by Bendsoe, M.P., Sigmund, O. there is an example about Eiffel Tower, and indeed it does suggest we can both use a set of beams, or topological optimization of a continuum --- or a combination of the techniques. But I need to suggest my students something simple, like either in the software ANSYS, or a very well documented simple Matlab routine.

Book on Topology Optimization
Topology Optimization - Theory, Methods
and Applications

Bendsoe, M.P., Sigmund, O.
2nd ed. 2003. Corr. 2nd printing, 2003,
XIV, 370 p., Hardcover

ISBN: 978-3-540-42992-0

Table of
Contents
, Erata

 

Do you know what to suggest then??

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

CanhLe's picture

 

yes, the DLO is for limit analysis, but the procedure is identical to truss optimization. Have you checked this ?

Canh

Canh V. Le,
PhD in Computational Mechanics
Department of Civil and Structural Engineering
The University of Sheffield
Mappin Street,
Sheffield, S1 3JD, UK.
Phone: GB +44 1142225724
http://sites.google.com/site/canhlewebpage/

Mike Ciavarella's picture

Dear Cahn

  I am no expert in the field and about Eiffel's tower I only  have a master thesis from a student of Prof. Sacchi Landriani, whom I have been suggested to refer to from the President of the French Academy of Science, my friend Prof. Salencon of Ecole Polytechnique.  But that was not on optimal design.

Prof. Sacchi Landriani incidentally is the author of a nice paper

A
Recollection of Some Results and a Few Remarks on Structural
Optimisation

 Now, I checked briefly the paper you refer to.  It says:-

Abstract:
Computerized layout (or “topology”) optimization
was pioneered almost four decades back.
However, despite dramatic
increases in available computer power and the application of
increasingly efficient optimization algorithms, even now only relatively
modest sized problems can be tackled using the traditional “ground
structure” approach. This is because of the need, in general, for the
latter to contain every conceivable member connecting together the nodes
in a problem. A simple, but effective solution method capable of
tackling problems with large numbers of potential members (e.g.
>100,000,000) is presented. Though the method draws on the linear
programming technique of “column generation”, since layout optimization
specific heuristics are employed it is presented as an iterative “member
adding” method. The method requires a ground structure with minimal
connectivity to be used in the first iteration; members are then added
as required in subsequent iterations until the (provably) optimal
solution is found.

 

Now, the method you suggest seems "the classical sliding block upper
bound method"
( as described by Drucker and Shield, discussed in
Calladine's book and used by, for example, Ian Collins), but using some
sort of
programming method.

 

 

 Applying programming methods to
optimal design has a long history. I remember Andrew Palmer working on
the optimal design of electricity pylons using dynamic programming as
they are near serial structures - some time in the
'60. Sounds a bit like the Eifel Tower problem. I'll see if I can find
the reference.

 

 I will also scan for you a figure on the book from our Danish friends.

 

 

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

In addition to this study, I have just realized a different type of model with link8 elements, according to a colleague engineer, who has, recently, implemented a reticular trusses work on Ansys, with elements likes link8. Also, I have to complete this study with a topological analysis.

There is now a problem, in terms of deformation curve, because the postprocessing send me a message with an error about DEGREE of FREEDOM SOLUTION that is "not available"!

According to my colleague there is a constraint problem, but the processor don't give me errors in the /prep7.

Dear Canh V.Le, can you explain me any limitations about this problem, if there are?

Thanks in advance.

 commands list:

/prep7
et,1,8
mp,ex,1,205000
mp,prxy,1,0.3
mp,dens,1,1.2*10**(-3)*7874
r,1,0.001

 

 

!DEFINITION OF THE GRAVITY ACCELERATION
g=9.81
acel,,-g

!DEFINITION NODES
n,1,5,269.776
n,2,5,258.776
n,3,5.284,247.776
n,4,5.585,236.776
n,5,5.903,225.776
n,6,6.239,218.776
n,7,6.594,207.776
n,8,6.969,196.776
n,9,7.365,185.776
n,10,7.784,165.576
n,11,8.227,160.676
n,12,8.696,149.376
n,13,9.245,138.676
n,14,9.999,128.076
n,15,10.790,117.576
n,16,11.786,107.076
n,17,12.880,97.076
n,18,14.303,87.076
n,19,15.806,77.473
n,20,18.925,68.387
n,21,21.583,59.791
n,22,24.365,51.658
n,23,27.415,43.963
n,24,30.919,36.683
n,25,33.697,29.795
n,26,38.673,23.278
n,27,43.578,17.113
n,28,48.519,11.280
n,29,53.459
n,30,-5,269.776
n,31,-5,258.776
n,32,-5.284,247.776
n,33,-5.585,236.776
n,34,-5.903,225.776
n,35,-6.239,218.776
n,36,-6.594,207.776
n,37,-6.969,196.776
n,38,-7.365,185.776
n,39,-7.784,165.576
n,40,-8.227,160.676
n,41,-8.696,149.376
n,42,-9.245,138.676
n,43,-9.999,128.076
n,44,-10.790,117.576
n,45,-11.786,107.076
n,46,-12.880,97.076
n,47,-14.303,87.076
n,48,-15.806,77.473
n,49,-18.925,68.387
n,50,-21.583,59.791
n,51,-24.365,51.658
n,52,-27.415,43.963
n,53,-30.919,36.683
n,54,-33.697,29.795
n,55,-38.673,23.278
n,56,-43.578,17.113
n,57,-48.519,11.280
n,58,-53.459

n,59,,269.776
n,60,,258.776
n,61,,247.776
n,62,1,236.776
n,63,1.5,225.776
n,64,2,218.776
n,65,2.5,207.776
n,66,3,196.776
n,67,3.5,185.776
n,68,4,165.576
n,69,4.5,160.676
n,70,5,149.376
n,71,5.5,138.676
n,72,6,128.076
n,73,6,117.576
n,74,6.5,107.076
n,75,6.5,97.076
n,76,7,87.076
n,77,7.5,77.473
n,78,8,68.387
n,79,9,59.791
n,80,11,51.658
n,81,13,43.963
n,82,15,36.683
n,83,17,29.795
n,84,20,23.278
n,85,23,17.113
n,86,26,11.280
n,87,29
n,88,,269.776
n,89,,258.776
n,90,,247.776
n,91,-1,236.776
n,92,-1.5,225.776
n,93,-2,218.776
n,94,-2.5,207.776
n,95,-3,196.776
n,96,-3.5,185.776
n,97,-4,165.576
n,98,-4.5,160.676
n,99,-5,149.376
n,100,-5.5,138.676
n,101,-6,128.076
n,102,-6,117.576
n,103,-6.5,107.076
n,104,-6.5,97.076
n,105,-7,87.076
n,106,-7.5,77.473
n,107,-8,68.387
n,108,-9,59.791
n,109,-11,51.658
n,110,-13,43.963
n,111,-15,36.683
n,112,-17,29.795
n,113,-20,23.278
n,114,-23,17.113
n,115,-26,11.280
n,116,-29
n,117,41.22
n,118,37.26,11.280
n,119,33.29,17.113
n,120,29.34,23.278
n,121,25.35,29.795
n,122,22.95,36.383
n,123,20.21,43.963
n,124,17.68,51.658
n,125,-41.22
n,126,-37.26,11.280
n,127,-33.29,17.113
n,128,-29.34,23.278
n,129,-25.35,29.795
n,130,-22.95,36.383
n,131,-20.21,43.963
n,132,-17.68,51.658

 

!DEFINITION MONTANTI E CORRENTI
e,87,117
e,117,29
e,86,118
e,118,28
e,85,119
e,119,27
e,84,120
e,120,26
e,83,121
e,121,25
e,82,122
e,122,24
e,81,123
e,123,23
e,80,124
e,124,22
e,116,125
e,125,58
e,115,126
e,126,57
e,114,127
e,127,56
e,113,128
e,128,55
e,112,129
e,129,54
e,111,130
e,130,53
e,110,131
e,131,52
e,109,132
e,132,51
e,79,21
e,78,20
e,77,19
e,76,18
e,75,17
e,74,16
e,73,15
e,72,14
e,71,13
e,70,12
e,69,11
e,68,10
e,67,9
e,66,8
e,65,7
e,64,6
e,63,5
e,62,4
e,61,3
e,60,2
e,59,1
e,108,50
e,107,49
e,106,48
e,105,47
e,104,46
e,103,45
e,102,44
e,101,43
e,100,42
e,99,41
e,98,40
e,97,39
e,96,38
e,95,37
e,94,36
e,93,35
e,92,34
e,91,33
e,90,32
e,89,31
e,88,30
e,1,2
e,2,3
e,3,4
e,4,5
e,5,6
e,6,7
e,7,8
e,8,9
e,9,10
e,10,11
e,11,12
e,12,13
e,13,14
e,14,15
e,15,16
e,16,17
e,17,18
e,18,19
e,19,20
e,20,21
e,21,22
e,22,23
e,23,24
e,24,25
e,25,26
e,26,27
e,27,28
e,28,29
e,30,31
e,31,32
e,32,33
e,33,34
e,34,35
e,35,36
e,36,37
e,37,38
e,38,39
e,39,40
e,40,41
e,41,42
e,42,43
e,43,44
e,44,45
e,45,46
e,46,47
e,47,48
e,48,49
e,49,50
e,50,51
e,51,52
e,52,53
e,53,54
e,54,55
e,55,56
e,56,57
e,57,58
e,59,60
e,60,61
e,61,62
e,62,63
e,63,64
e,64,65
e,65,66
e,66,67
e,67,68
e,68,69
e,69,70
e,70,71
e,71,72
e,72,73
e,73,74
e,74,75
e,75,76
e,76,77
e,77,78
e,78,79
e,79,80
e,80,81
e,81,82
e,82,83
e,83,84
e,84,85
e,85,86
e,86,87
e,88,89
e,89,90
e,90,91
e,91,92
e,92,93
e,93,94
e,94,95
e,95,96
e,96,97
e,97,98
e,98,99
e,99,100
e,100,101
e,101,102
e,102,103
e,103,104
e,104,105
e,105,106
e,106,107
e,107,108
e,108,109
e,109,110
e,110,111
e,111,112
e,112,113
e,113,114
e,114,115
e,115,116
e,117,118
e,118,119
e,119,120
e,120,121
e,121,122
e,122,123
e,123,124
e,125,126
e,126,127
e,127,128
e,128,129
e,129,130
e,130,131
e,131,132


!DEFINITION TRAVERSI DESTRA
e,59,2
e,60,1
e,60,3
e,61,2
e,61,4
e,62,3
e,62,5
e,63,4
e,63,6
e,64,5
e,64,7
e,65,6
e,65,8
e,66,7
e,66,9
e,67,8
e,67,10
e,68,9
e,68,11
e,69,10
e,69,12
e,70,11
e,70,13
e,71,12
e,71,14
e,72,13
e,72,15
e,73,14
e,73,16
e,74,15
e,74,17
e,75,16
e,75,18
e,76,17
e,76,19
e,77,18
e,77,20
e,78,19
e,78,21
e,79,20
e,79,22
e,80,21
e,80,123
e,81,124
e,124,23
e,123,22
e,81,122
e,82,123
e,123,24
e,122,23
e,82,121
e,83,122
e,122,25
e,121,24
e,83,120
e,84,121
e,121,26
e,120,25
e,84,119
e,85,120
e,120,27
e,119,26
e,85,118
e,86,119
e,119,28
e,118,27
e,86,117
e,87,118
e,118,29
e,117,28


!DEFINITION TRAVERSI SINISTRA
e,30,89
e,31,88
e,31,90
e,32,89
e,32,91
e,33,90
e,33,92
e,34,91
e,34,93
e,35,92
e,35,94
e,36,93
e,36,95
e,37,94
e,37,96
e,38,95
e,38,97
e,39,96
e,39,98
e,40,97
e,40,99
e,41,98
e,41,100
e,42,99
e,42,101
e,43,100
e,43,102
e,44,101
e,44,103
e,45,102
e,45,104
e,46,103
e,47,104
e,46,105
e,48,105
e,47,106
e,48,107
e,49,106
e,50,107
e,49,108
e,50,109
e,51,108
e,51,131
e,52,132
e,132,110
e,131,109
e,52,130
e,53,131
e,131,111
e,130,110
e,53,129
e,54,130
e,130,112
e,129,111
e,54,128
e,55,129
e,129,113
e,128,112
e,55,127
e,56,128
e,128,114
e,127,113
e,56,126
e,57,127
e,127,115
e,126,114
e,57,125
e,58,126
e,126,116
e,125,115

 

!DEFINITION PIANI INTERMEDI
e,80,109
e,79,108
e,109,79
e,108,80
e,102,73
e,103,74
e,102,74
e,103,73

 

!DEFINITION VINCOLI INCASTRO
d,58,all
d,125,all
d,116,all
d,87,all
d,117,all
d,29,all

 

 

!DEFINITION FORZE VENTO
f,28,fx,-1188089
f,27,fx,-2335859
f,26,fx,-2822043
f,25,fx,-2886642
f,24,fx,-1938554
f,23,fx,-1691636
f,22,fx,-1505786
f,21,fx,-1107157
f,20,fx,-1040645
f,19,fx,-1022987
f,18,fx,-783132
f,17,fx,-716620
f,16,fx,-689986
f,15,fx,-456253
f,14,fx,-433503
f,13,fx,-413138
f,12,fx,-386180
f,11,fx,-360076
f,10,fx,-352571
f,9,fx,-303599
f,8,fx,-247212
f,7,fx,-233850
f,6,fx,-221254
f,5,fx,-209335
f,4,fx,-198063
f,3,fx,-187410
f,2,fx,-177286
f,1,fx,-249301


!SOLVING
finish
/solu
solve
finish
/post1
pldisp,1

 

 

 

CanhLe's picture

 Have you checked buckling condition for all elements?

 Canh V. Le,
PhD in Computational Mechanics
Department of Civil and Structural Engineering
The University of Sheffield
Mappin Street,
Sheffield, S1 3JD, UK.
Phone: GB +44 1142225724
http://sites.google.com/site/canhlewebpage/

/title,toureiffel
/filename,toureiffel
/prep7
et,1,95
mp,ex,1,205000
mp,prxy,1,0.3

! DEFINITION KEYPOINTS

k,1,5,269.776,5
k,2,5,258.776,5
k,3,5.284,247.776,5.284
k,4,5.585,236.776,5.585
k,5,5.903,225.776,5.903
k,6,6.239,218.776,6.239
k,7,6.594,207.776,6.594
k,8,6.969,196.776,6.969
k,9,7.365,185.776,7.365
k,10,7.784,165.576,7.784
k,11,8.227,160.676,8.227
k,12,8.696,149.376,8.696
k,13,9.245,138.676,9.245
k,14,9.999,128.076,9.999
k,15,10.790,117.576,10.790
k,16,11.786,107.076,11.786
k,17,12.880,97.076,12.880
k,18,14.303,87.076,14.303
k,19,16.306,77.473,16.306
k,20,18.925,68.387,18.925
k,21,21.583,59.791,21.583
k,22,24.365,51.658,24.365
k,23,27.415,43.963,27.415
k,24,30.919,36.683,30.919
k,25,34.697,29.795,34.697
k,26,38.673,23.278,38.673
k,27,43.578,17.113,43.578
k,28,48.519,11.280,48.519
k,29,57.459,0,57.459
k,30,-5,269.776,5
k,31,-5,258.776,5
k,32,-5.284,247.776,5.284
k,33,-5.585,236.776,5.585
k,34,-5.903,225.776,5.903
k,35,-6.239,218.776,6.239
k,36,-6.594,207.776,6.594
k,37,-6.969,196.776,6.969
k,38,-7.365,185.776,7.365
k,39,-7.784,165.576,7.784
k,40,-8.227,160.676,8.227
k,41,-8.696,149.376,8.696
k,42,-9.245,138.676,9.245
k,43,-9.999,128.076,9.999
k,44,-10.790,117.576,10.790
k,45,-11.786,107.076,11.786
k,46,-12.880,97.076,12.880
k,47,-14.303,87.076,14.303
k,48,-16.306,77.473,16.306
k,49,-18.925,68.387,18.925
k,50,-21.583,59.791,21.583
k,51,-24.365,51.658,24.365
k,52,-27.415,43.963,27.415
k,53,-30.919,36.683,30.919
k,54,-34.697,29.795,34.697
k,55,-38.673,23.278,38.673
k,56,-43.578,17.113,43.578
k,57,-48.519,11.280,48.519
k,58,-57.459,0,57.459

!GENERATION OF A SEGMENT !SPLINE THROUGH A ERIES OF KEYPOINTS

spline,1,2,3,4,5,6
spline,6,7,8,9,10,11
spline,11,12,13,14,15,16
spline,16,17,18,19,20,21
spline,21,22,23,24,25
spline,25,26,27,28,29

spline,30,31,32,33,34,35
spline,35,36,37,38,39,40
spline,40,41,42,43,44,45
spline,45,46,47,48,49,50
spline,50,51,52,53,54,55
spline,55,56,57,58

! DEFINIZIONE SPESSORE DELLA GAMBA dx

k,59,0.001,269.776,5
k,60,0.001,269.776,0
k,61,5,269.776,0
a,1,59,60,61
vdrag,1,,,,,,1,2,3,4,5,6
vdrag,31,,,,,,7,8,9,10,11,12
vdrag,61,,,,,,13,14,15,16,17,18
vdrag,91,,,,,,19,20,21,22,23,24
vdrag,121,,,,,,25,26,27,28

! DEFINIZIONE SPESSORE DELLA GAMBA sx

k,174,-5,269.776,0
k,175,-0.001,269.776,0
k,176,-0.001,269.776,5
a,30,174,175,176
vdrag,142,,,,,,29,30,31,32,33,34
vdrag,172,,,,,,35,36,37,38,39,40
vdrag,202,,,,,,41,42,43,44,45,46
vdrag,232,,,,,,47,48,49,50,51,52
vdrag,262,,,,,,53,54,55,56

vsymm,z,1,56,1,,0,0

! DEFINIZIONE DEL PIANO 1

a,21,370,486,50
a,24,382,498,53
a,24,21,50,53
a,24,382,370,21
a,382,370,486,498
a,498,486,50,53
va,565,566,567,568,569,570

! DEFINIZIONE DEL PIANO 2

a,15,346,462,44
a,17,354,470,46
a,17,15,44,46
a,17,354,346,15
a,354,346,462,470
a,470,462,44,46
va,571,572,573,574,575,576


!DEFINIZIONE AREA SUPERIORE

a,1,30,405,289

!DEFINIZIONE VOLUME SUPERIORE

k,521,5,270.776,5
k,522,-5,270.776,5
k,523,-5,270.776,-5
k,524,5,270.776,-5
a,521,522,523,524
a,1,30,522,521
a,30,522,523,405
a,523,524,289,405
a,1,521,524,289

va,565,566,567,568,569,570

!DEFINIZIONE VINCOLI

da,141,all
da,282,all
da,423,all
da,564,all

!DEFINIZIONE DELLA MESH

ESIZE,10,0,
MSHAPE,1,3D
MSHKEY,0
FLST,5,114,6,ORDE,2
FITEM,5,1
FITEM,5,-114
CM,_Y,VOLU
VSEL, , , ,P51X
CM,_Y1,VOLU
CHKMSH,'VOLU'
CMSEL,S,_Y
VMESH,_Y1
CMDELE,_Y
CMDELE,_Y1
CMDELE,_Y2

!DEFINIZIONE VINCOLI AREE

da,572,all
da,566,all

!DEFINIZIONE CARICHI PRIMA GAMBA

f,2413,fx,124651
f,2523,fx,88643
f,2623,fx,93705
f,2723,fx,99032
f,2814,fx,104668
f,2880,fx,110627.5
f,2980,fx,116925.5
f,3080,fx,123606
f,3186,fx,151800
f,3290,fx,176285.5
f,3356,fx,180038
f,3456,fx,193090
f,3556,fx,206569
f,3656,fx,216752
f,3756,fx,228126.5
f,3856,fx,344993
f,3956,fx,358310.5
f,4056,fx,391566
f,4153,fx,511493.5
f,4243,fx,520322.5
f,4343,fx,553578.5
f,4353,fx,752893
f,4358,fx,845818
f,4467,fx,969277
f,4523,fx,1443321
f,4579,fx,1411021.5
f,4635,fx,1167929.5
f,4700,fx,594044.5

!DEFINIZIONE CARICHI SECONDA GAMBA

f,7195,fx,124651
f,7305,fx,88643
f,7405,fx,93705
f,7505,fx,99032
f,7592,fx,104668
f,7663,fx,110627.5
f,7762,fx,116925.5
f,7862,fx,123606
f,7968,fx,151800
f,7969,fx,176285.5
f,8138,fx,180038
f,8238,fx,193090
f,8338,fx,206569
f,8438,fx,216752
f,8538,fx,228126.5
f,8638,fx,344993
f,8782,fx,358310.5
f,8739,fx,391566
f,8839,fx,511493.5
f,9025,fx,520322.5
f,9035,fx,553578.5
f,9134,fx,752893
f,9139,fx,845818
f,9249,fx,969277
f,9305,fx,1443321
f,9361,fx,1411021.5
f,9417,fx,1167929.5
f,9483,fx,594044.5

I'm going to check for a middle sectional area, because the sistem's response was really unsatisfactory, in fact the gravity effect was excessive..

However, I'm going to post  you the new command list with some important corrections, so that you can check it.

I think the  wind forces are the most probably, checking some bibliographic informations, there are about 300 Kg/m2, for variable loads on the profile of the tower.

Thanks to the availability, I'll ask you later!! 

R.C.

Dear,

I have just made some corrections on my 2D model, on real costants values and density value of Skeletal elements.

Finally, I have had some results, particularly: maximum deflection (at node 1) = 0.497997 [m]

*if we consider that it's a 2D model, with application of "3D" wind effects on nodes,  the response is largely probable. In fact, some effective data of the tower (also wikipedia..), are in the order of 0.12 [m] for the maximum deflection atop, in case of variable conditions of wind.

Below there is the commands list and the graphical response.

Thanks for your cooperation.

R.Carrieri

 

 

/prep7
et,1,8
mp,ex,1,160000*10**(6)
mp,prxy,1,0.3
mp,dens,1,7874
r,1,0.2

!DEFINITION OF THE GRAVITY ACCELERATION
g=9.81
acel,,g

!DEFINITION NODES
n,1,5,269.776
n,2,5,258.776
n,3,5.284,247.776
n,4,5.585,236.776
n,5,5.903,225.776
n,6,6.239,218.776
n,7,6.594,207.776
n,8,6.969,196.776
n,9,7.365,185.776
n,10,7.784,165.576
n,11,8.227,160.676
n,12,8.696,149.376
n,13,9.245,138.676
n,14,9.999,128.076
n,15,10.790,117.576
n,16,11.786,107.076
n,17,12.880,97.076
n,18,14.303,87.076
n,19,15.806,77.473
n,20,18.925,68.387
n,21,21.583,59.791
n,22,24.365,51.658
n,23,27.415,43.963
n,24,30.919,36.683
n,25,33.697,29.795
n,26,38.673,23.278
n,27,43.578,17.113
n,28,48.519,11.280
n,29,53.459
n,30,-5,269.776
n,31,-5,258.776
n,32,-5.284,247.776
n,33,-5.585,236.776
n,34,-5.903,225.776
n,35,-6.239,218.776
n,36,-6.594,207.776
n,37,-6.969,196.776
n,38,-7.365,185.776
n,39,-7.784,165.576
n,40,-8.227,160.676
n,41,-8.696,149.376
n,42,-9.245,138.676
n,43,-9.999,128.076
n,44,-10.790,117.576
n,45,-11.786,107.076
n,46,-12.880,97.076
n,47,-14.303,87.076
n,48,-15.806,77.473
n,49,-18.925,68.387
n,50,-21.583,59.791
n,51,-24.365,51.658
n,52,-27.415,43.963
n,53,-30.919,36.683
n,54,-33.697,29.795
n,55,-38.673,23.278
n,56,-43.578,17.113
n,57,-48.519,11.280
n,58,-53.459

n,59,,269.776
n,60,,258.776
n,61,,247.776
n,62,1,236.776
n,63,1.5,225.776
n,64,2,218.776
n,65,2.5,207.776
n,66,3,196.776
n,67,3.5,185.776
n,68,4,165.576
n,69,4.5,160.676
n,70,5,149.376
n,71,5.5,138.676
n,72,6,128.076
n,73,6,117.576
n,74,6.5,107.076
n,75,6.5,97.076
n,76,7,87.076
n,77,7.5,77.473
n,78,8,68.387
n,79,9,59.791
n,80,11,51.658
n,81,13,43.963
n,82,15,36.683
n,83,17,29.795
n,84,20,23.278
n,85,23,17.113
n,86,26,11.280
n,87,29
n,88,,269.776
n,89,,258.776
n,90,,247.776
n,91,-1,236.776
n,92,-1.5,225.776
n,93,-2,218.776
n,94,-2.5,207.776
n,95,-3,196.776
n,96,-3.5,185.776
n,97,-4,165.576
n,98,-4.5,160.676
n,99,-5,149.376
n,100,-5.5,138.676
n,101,-6,128.076
n,102,-6,117.576
n,103,-6.5,107.076
n,104,-6.5,97.076
n,105,-7,87.076
n,106,-7.5,77.473
n,107,-8,68.387
n,108,-9,59.791
n,109,-11,51.658
n,110,-13,43.963
n,111,-15,36.683
n,112,-17,29.795
n,113,-20,23.278
n,114,-23,17.113
n,115,-26,11.280
n,116,-29
n,117,41.22
n,118,37.26,11.280
n,119,33.29,17.113
n,120,29.34,23.278
n,121,25.35,29.795
n,122,22.95,36.383
n,123,20.21,43.963
n,124,17.68,51.658
n,125,-41.22
n,126,-37.26,11.280
n,127,-33.29,17.113
n,128,-29.34,23.278
n,129,-25.35,29.795
n,130,-22.95,36.383
n,131,-20.21,43.963
n,132,-17.68,51.658

!DEFINITION MONTANTI E CORRENTI
e,87,117
e,117,29
e,86,118
e,118,28
e,85,119
e,119,27
e,84,120
e,120,26
e,83,121
e,121,25
e,82,122
e,122,24
e,81,123
e,123,23
e,80,124
e,124,22
e,116,125
e,125,58
e,115,126
e,126,57
e,114,127
e,127,56
e,113,128
e,128,55
e,112,129
e,129,54
e,111,130
e,130,53
e,110,131
e,131,52
e,109,132
e,132,51
e,79,21
e,78,20
e,77,19
e,76,18
e,75,17
e,74,16
e,73,15
e,72,14
e,71,13
e,70,12
e,69,11
e,68,10
e,67,9
e,66,8
e,65,7
e,64,6
e,34,5
e,33,4
e,32,3
e,31,2
e,30,1
e,108,50
e,107,49
e,106,48
e,105,47
e,104,46
e,103,45
e,102,44
e,101,43
e,100,42
e,99,41
e,98,40
e,97,39
e,96,38
e,95,37
e,94,36
e,93,35
e,75,104
e,74,103
e,73,102
e,72,101
e,71,100
e,70,99
e,69,98
e,68,97
e,67,96
e,66,95
e,65,94
e,64,93

e,1,2
e,2,3
e,3,4
e,4,5
e,5,6
e,6,7
e,7,8
e,8,9
e,9,10
e,10,11
e,11,12
e,12,13
e,13,14
e,14,15
e,15,16
e,16,17
e,17,18
e,18,19
e,19,20
e,20,21
e,21,22
e,22,23
e,23,24
e,24,25
e,25,26
e,26,27
e,27,28
e,28,29
e,30,31
e,31,32
e,32,33
e,33,34
e,34,35
e,35,36
e,36,37
e,37,38
e,38,39
e,39,40
e,40,41
e,41,42
e,42,43
e,43,44
e,44,45
e,45,46
e,46,47
e,47,48
e,48,49
e,49,50
e,50,51
e,51,52
e,52,53
e,53,54
e,54,55
e,55,56
e,56,57
e,57,58
e,59,60
e,60,61
e,61,62
e,62,63
e,63,64
e,64,65
e,65,66
e,66,67
e,67,68
e,68,69
e,69,70
e,70,71
e,71,72
e,72,73
e,73,74
e,74,75
e,75,76
e,76,77
e,77,78
e,78,79
e,79,80
e,80,81
e,81,82
e,82,83
e,83,84
e,84,85
e,85,86
e,86,87
e,88,89
e,89,90
e,90,91
e,91,92
e,92,93
e,93,94
e,94,95
e,95,96
e,96,97
e,97,98
e,98,99
e,99,100
e,100,101
e,101,102
e,102,103
e,103,104
e,104,105
e,105,106
e,106,107
e,107,108
e,108,109
e,109,110
e,110,111
e,111,112
e,112,113
e,113,114
e,114,115
e,115,116
e,117,118
e,118,119
e,119,120
e,120,121
e,121,122
e,122,123
e,123,124
e,125,126
e,126,127
e,127,128
e,128,129
e,129,130
e,130,131
e,131,132

!DEFINITION TRAVERSI DESTRA
e,59,2
e,60,1
e,60,3
e,61,2
e,61,4
e,62,3
e,62,5
e,63,4
e,63,6
e,64,5
e,64,7
e,65,6
e,65,8
e,66,7
e,66,9
e,67,8
e,67,10
e,68,9
e,68,11
e,69,10
e,69,12
e,70,11
e,70,13
e,71,12
e,71,14
e,72,13
e,72,15
e,73,14
e,73,16
e,74,15
e,74,17
e,75,16
e,75,18
e,76,17
e,76,19
e,77,18
e,77,20
e,78,19
e,78,21
e,79,20
e,79,22
e,80,21
e,80,123
e,81,124
e,124,23
e,123,22
e,81,122
e,82,123
e,123,24
e,122,23
e,82,121
e,83,122
e,122,25
e,121,24
e,83,120
e,84,121
e,121,26
e,120,25
e,84,119
e,85,120
e,120,27
e,119,26
e,85,118
e,86,119
e,119,28
e,118,27
e,86,117
e,87,118
e,118,29
e,117,28

!DEFINITION TRAVERSI SINISTRA
e,30,89
e,31,88
e,31,90
e,32,89
e,32,91
e,33,90
e,33,92
e,34,91
e,34,93
e,35,92
e,35,94
e,36,93
e,36,95
e,37,94
e,37,96
e,38,95
e,38,97
e,39,96
e,39,98
e,40,97
e,40,99
e,41,98
e,41,100
e,42,99
e,42,101
e,43,100
e,43,102
e,44,101
e,44,103
e,45,102
e,45,104
e,46,103
e,47,104
e,46,105
e,48,105
e,47,106
e,48,107
e,49,106
e,50,107
e,49,108
e,50,109
e,51,108
e,51,131
e,52,132
e,132,110
e,131,109
e,52,130
e,53,131
e,131,111
e,130,110
e,53,129
e,54,130
e,130,112
e,129,111
e,54,128
e,55,129
e,129,113
e,128,112
e,55,127
e,56,128
e,128,114
e,127,113
e,56,126
e,57,127
e,127,115
e,126,114
e,57,125
e,58,126
e,126,116
e,125,115

!DEFINITION TRAVERSI INTERMEDI
e,75,103
e,104,74
e,74,102
e,103,73
e,73,101
e,102,72
e,72,100
e,101,71
e,71,99
e,100,70
e,70,98
e,99,69
e,69,97
e,98,68
e,68,96
e,97,67
e,67,95
e,96,66
e,66,94
e,95,65
e,65,93
e,94,64
e,64,92
e,93,63
e,63,91
e,92,62
e,91,61
e,62,90

!DEFINITION PIANI INTERMEDI
e,80,109
e,79,108
e,109,79
e,108,80

!DEFINITION VINCOLI INCASTRO
d,58,all
d,125,all
d,116,all
d,87,all
d,117,all
d,29,all

!DEFINITION FORZE VENTO
f,28,fx,-1188089
f,27,fx,-2335859
f,26,fx,-2822043
f,25,fx,-2886642
f,24,fx,-1938554
f,23,fx,-1691636
f,22,fx,-1505786
f,21,fx,-1107157
f,20,fx,-1040645
f,19,fx,-1022987
f,18,fx,-783132
f,17,fx,-716620
f,16,fx,-689986
f,15,fx,-456253
f,14,fx,-433503
f,13,fx,-413138
f,12,fx,-386180
f,11,fx,-360076
f,10,fx,-352571
f,9,fx,-303599
f,8,fx,-247212
f,7,fx,-233850
f,6,fx,-221254
f,5,fx,-209335
f,4,fx,-198063
f,3,fx,-187410
f,2,fx,-177286
f,1,fx,-249301

!SOLVING
finish
/solu
solve
finish
/post1
pldisp,1

!TABLE STAMP
prnsol,u,x
prnsol,u,y

!GRAPHIC STAMP
plnsol,u,x,1

 

 PRINT U    NODAL SOLUTION PER NODE
 
  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           
 
  LOAD STEP=     1  SUBSTEP=     1                                            
   TIME=    1.0000      LOAD CASE=   0                                        
 
  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 
 
    NODE      UX   
       1 -0.49500   
       2 -0.45798   
       3 -0.42301   
       4 -0.38814   
       5 -0.35434   
       6 -0.33278   
       7 -0.30060   
       8 -0.26939   
       9 -0.23933   
      10 -0.18576   
      11 -0.17397   
      12 -0.14805   
      13 -0.12518   
      14 -0.10419   
      15 -0.85099E-01
      16 -0.67968E-01
      17 -0.53902E-01
      18 -0.41771E-01
      19 -0.31425E-01
      20 -0.23178E-01
      21 -0.17140E-01
      22 -0.14451E-01
      23 -0.13003E-01
      24 -0.11607E-01
      25 -0.99823E-02
      26 -0.74985E-02
      27 -0.47286E-02
      28 -0.28243E-02
      29   0.0000   
      30 -0.49496   
      31 -0.45796   
      32 -0.42301   
      33 -0.38816   
      34 -0.35445   
      35 -0.33300   
      36 -0.30084   
      37 -0.26971   
 
  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           
 
  LOAD STEP=     1  SUBSTEP=     1                                            
   TIME=    1.0000      LOAD CASE=   0                                        
 
  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 
 
    NODE      UX   
      38 -0.23967   
      39 -0.18600   
      40 -0.17466   
      41 -0.14868   
      42 -0.12587   
      43 -0.10510   
      44 -0.86174E-01
      45 -0.69357E-01
      46 -0.54329E-01
      47 -0.39489E-01
      48 -0.27699E-01
      49 -0.21554E-01
      50 -0.16607E-01
      51 -0.12329E-01
      52 -0.70391E-02
      53 -0.38390E-02
      54 -0.14326E-02
      55 -0.15978E-02
      56 -0.24363E-02
      57 -0.31831E-02
      58   0.0000   
      59 -0.49379   
      60 -0.45902   
      61 -0.42287   
      62 -0.38772   
      63 -0.35341   
      64 -0.33280   
      65 -0.30057   
      66 -0.26935   
      67 -0.23928   
      68 -0.18571   
      69 -0.17391   
      70 -0.14798   
      71 -0.12511   
      72 -0.10410   
      73 -0.84994E-01
      74 -0.67758E-01
 
  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           
 
  LOAD STEP=     1  SUBSTEP=     1                                            
   TIME=    1.0000      LOAD CASE=   0                                        
 
  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 
 
    NODE      UX   
      75 -0.53651E-01
      76 -0.41634E-01
      77 -0.31346E-01
      78 -0.23221E-01
      79 -0.16489E-01
      80 -0.13231E-01
      81 -0.12666E-01
      82 -0.11416E-01
      83 -0.98516E-02
      84 -0.79083E-02
      85 -0.56977E-02
      86 -0.33031E-02
      87   0.0000   
      88 -0.49375   
      89 -0.45838   
      90 -0.42194   
      91 -0.38717   
      92 -0.35337   
      93 -0.33287   
      94 -0.30067   
      95 -0.26950   
      96 -0.23947   
      97 -0.18574   
      98 -0.17423   
      99 -0.14832   
     100 -0.12546   
     101 -0.10457   
     102 -0.85420E-01
     103 -0.68415E-01
     104 -0.53290E-01
     105 -0.37900E-01
     106 -0.26323E-01
     107 -0.19186E-01
     108 -0.15388E-01
     109 -0.10819E-01
     110 -0.61528E-02
     111 -0.17645E-02
 
  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           
 
  LOAD STEP=     1  SUBSTEP=     1                                            
   TIME=    1.0000      LOAD CASE=   0                                        
 
  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 
 
    NODE      UX   
     112  0.74992E-03
     113  0.17771E-02
     114  0.14893E-02
     115  0.15448E-03
     116   0.0000   
     117   0.0000   
     118 -0.25826E-02
     119 -0.50654E-02
     120 -0.76238E-02
     121 -0.98263E-02
     122 -0.11397E-01
     123 -0.12654E-01
     124 -0.14089E-01
     125   0.0000   
     126 -0.16234E-02
     127 -0.46720E-03
     128  0.36049E-03
     129 -0.27889E-03
     130 -0.24641E-02
     131 -0.63204E-02
     132 -0.11099E-01

 MAXIMUM ABSOLUTE VALUES
 NODE          1
 VALUE  -0.49500   
 

 

PRINT U    NODAL SOLUTION PER NODE
 
  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           
 
  LOAD STEP=     1  SUBSTEP=     1                                            
   TIME=    1.0000      LOAD CASE=   0                                        
 
  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 
 
    NODE      UY   
       1 -0.22811E-01
       2 -0.22820E-01
       3 -0.21866E-01
       4 -0.21061E-01
       5 -0.20354E-01
       6 -0.19546E-01
       7 -0.18708E-01
       8 -0.17851E-01
       9 -0.17043E-01
      10 -0.16525E-01
      11 -0.15695E-01
      12 -0.15069E-01
      13 -0.14347E-01
      14 -0.13357E-01
      15 -0.12532E-01
      16 -0.11727E-01
      17 -0.11068E-01
      18 -0.10208E-01
      19 -0.94365E-02
      20 -0.77106E-02
      21 -0.72632E-02
      22 -0.77046E-02
      23 -0.74401E-02
      24 -0.64173E-02
      25 -0.51261E-02
      26 -0.25582E-02
      27 -0.27902E-03
      28  0.56114E-03
      29   0.0000   
      30 -0.54916E-01
      31 -0.54737E-01
      32 -0.55282E-01
      33 -0.55553E-01
      34 -0.55739E-01
      35 -0.56095E-01
      36 -0.56169E-01
      37 -0.56073E-01
 
  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           
 
  LOAD STEP=     1  SUBSTEP=     1                                            
   TIME=    1.0000      LOAD CASE=   0                                        
 
  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 
 
    NODE      UY   
      38 -0.55790E-01
      39 -0.53846E-01
      40 -0.53743E-01
      41 -0.52592E-01
      42 -0.51331E-01
      43 -0.50125E-01
      44 -0.48477E-01
      45 -0.46644E-01
      46 -0.44685E-01
      47 -0.42277E-01
      48 -0.38627E-01
      49 -0.34488E-01
      50 -0.30413E-01
      51 -0.26416E-01
      52 -0.23993E-01
      53 -0.21257E-01
      54 -0.17865E-01
      55 -0.12247E-01
      56 -0.69210E-02
      57 -0.25752E-02
      58   0.0000   
      59 -0.39097E-01
      60 -0.39035E-01
      61 -0.38661E-01
      62 -0.35293E-01
      63 -0.33658E-01
      64 -0.32112E-01
      65 -0.30392E-01
      66 -0.28794E-01
      67 -0.27237E-01
      68 -0.25783E-01
      69 -0.24450E-01
      70 -0.23139E-01
      71 -0.21947E-01
      72 -0.20826E-01
      73 -0.20654E-01
      74 -0.19565E-01
 
  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           
 
  LOAD STEP=     1  SUBSTEP=     1                                            
   TIME=    1.0000      LOAD CASE=   0                                        
 
  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 
 
    NODE      UY   
      75 -0.19408E-01
      76 -0.18450E-01
      77 -0.17416E-01
      78 -0.16152E-01
      79 -0.14210E-01
      80 -0.12373E-01
      81 -0.11337E-01
      82 -0.10624E-01
      83 -0.10022E-01
      84 -0.88356E-02
      85 -0.69752E-02
      86 -0.42506E-02
      87   0.0000   
      88 -0.38471E-01
      89 -0.38410E-01
      90 -0.38403E-01
      91 -0.41432E-01
      92 -0.42577E-01
      93 -0.43636E-01
      94 -0.44578E-01
      95 -0.45230E-01
      96 -0.45629E-01
      97 -0.45079E-01
      98 -0.45261E-01
      99 -0.44708E-01
     100 -0.43959E-01
     101 -0.42893E-01
     102 -0.40641E-01
     103 -0.38819E-01
     104 -0.35800E-01
     105 -0.33239E-01
     106 -0.31016E-01
     107 -0.28228E-01
     108 -0.24488E-01
     109 -0.21157E-01
     110 -0.18622E-01
     111 -0.17771E-01
 
  ***** POST1 NODAL DEGREE OF FREEDOM LISTING *****                           
 
  LOAD STEP=     1  SUBSTEP=     1                                            
   TIME=    1.0000      LOAD CASE=   0                                        
 
  THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM 
 
    NODE      UY   
     112 -0.16618E-01
     113 -0.14742E-01
     114 -0.11371E-01
     115 -0.64371E-02
     116   0.0000   
     117   0.0000   
     118 -0.13447E-02
     119 -0.37708E-02
     120 -0.60390E-02
     121 -0.77530E-02
     122 -0.86270E-02
     123 -0.93988E-02
     124 -0.99885E-02
     125   0.0000   
     126 -0.40912E-02
     127 -0.96613E-02
     128 -0.14650E-01
     129 -0.17879E-01
     130 -0.20105E-01
     131 -0.21397E-01
     132 -0.20392E-01

 MAXIMUM ABSOLUTE VALUES
 NODE         36
 VALUE  -0.56169E-01
 

Narasimham's picture

Interesting Cauchy and Lame stayed on Paris outskirts  maybe for their undisturbed researches?...

Narasimham's picture

Using an ANSYS model for same height and load bearing functionality (as a visitors' monument) with self weight,wind and earthquake resistance etc., can one optimize/redesign for another structural configuration using only a fraction of weight of steel originally used? What such lighter re-designs have been made so far?

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