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Solve Block Problem - "S" Shaped Catenary

Forum|Forum|13 years ago
February 3, 2013
7 replies
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I have a boat which is supporting an umbilical (cable) - which is supplying the electrical power and communications to an ROV (remote operated vehicle) which is several hundred metres below the surface of the water. There is a bit of a twist to the problem - because the ROV operator wants to attach weights to the umbilical (at location number A - over maybe 50m of umbilical length) - and he also wants to add small buoyancy modules (at location number B - over maybe 50m of umbilical length). The ROV operator wants to do this - in order to isolate the ships motion from the ROV - so the shape of the umbilical will be an "S" shape (rotated through 90 degrees) - when looked on side ways.

I decided to approach this problem as a "chain" - with a series of links (with each link having its own individual weight to allow for the situation where the umbilical has additional weight - location A (lead weights) - or buoyancy blocks - at location B). I then sought to get equilibrium at each end of each link. I then set out the equations for 16 links - and used the Find function to solve for the 50 unknowns. The equations are non linear as they have sin and cos functions - so using the Find function appeared the only option. So apart from the spreadsheet being - not very slick - I noticed that if I had more than 16 elements - which generated 50 unknowns - the Find function would not work with more than 50 unknowns.

As you can perhaps appreciate - if the umbilical is 2000m long - dividing this up into 16 links - is very rough indeed. Additionally, I would like to input the drag forces on the umbilical - but that is just going to add more unknowns - as this varies with the inclination of each link.

So I am looking for any ideas on how I could

add more links to get a more "accurate" representation of the "S" shape (rotated through 90 degrees) - when looked on side ways
how to resolve the 50 unknown apparent limit on the Find function

Many thanks in advance - to positive contributors.

1_Catenary-Analysis-Sixteen-Element-xmcd.zip

Other

Best answer by RichardJ

I just realized there's a better approach. New stuff highlighted in green.

Note: Worksheet edited 8:30 pm EST.

V

ValeryOchkov

24-Ruby IV

May be this help you

V

ValeryOchkov

24-Ruby IV

And a video: http://communities.ptc.com/videos/1549

V

ValeryOchkov

24-Ruby IV

Gordon Durward wrote:
how to resolve the 50 unknown apparent limit on the Find function

Find(x) where x is a vector

V

ValeryOchkov

24-Ruby IV

Valery Ochkov wrote:
Gordon Durward wrote:
how to resolve the 50 unknown apparent limit on the Find function
Find(x) where x is a vector

I have check it

1_51x-xmcd.zip

F

Fred_Kohlhepp

23-Emerald I

Search this forum for "finite element", there is a matrix solution capability.

V

ValeryOchkov

24-Ruby IV

One picture for the first step of the problem solution:

T

tietjee

15-Moonstone

gordon,

you have picked a very diffcult problem to solve. i did solve a similar problem for anchoring a barge. the catenary was a length of chain and then some wire rope. depending on the force of the barge determined the lenght of the catenary and whether the chain was lifted off the bottom. i divided the problem into parts to define functions. using the functions, wrote several programs to get the different answers. our company has since purchased several programs to solve this problem. our designs involve multiple cables, sizes, lengths,current, waves, etc. attached is the mathcad file for the single cable. good luck.

D

DenisJaunin

15-Moonstone

Hello,

If I may, I enclose two links that deal a little off topic.

It's in French, but with an automatic translator, you should be out.

Cordially.

Denis.

http://www.univ-brest.fr/lpo/mouillages/visualiser/m01.htm

http://fred.elie.free.fr/corps_remorque.pdf

P

ptc-4853592

Author

1-Visitor

Hi Everyone,

I would just like to respond to the recent replies that I have received:-

Thanks Fred for reminding me about the "introduction to FEA beginnings" that Mathcad do - though I have to confess I am struggling with the way it is presented - I would say it should be presented in a better way - as Mathcad is meant to be for engineers - applying mathematics - to solve engineering problems - but thanks anyway.

Thanks Valery for your suggestion in which you appear to be implying that there is a very precise mathematical solution to this "s" shaped catenary problem - and if that is the case - then there is no need for a numerical approach to the problem. Your suggestion revolves around the derivation of a "standard" "u" shaped catenary curve - because as I recal that is the standard technique for deriving the mathematical expression for a "standard" "u" shaped catenary curve. With respect - I have some reservations - since if the amount of buoyancy that is fitted to the "top hump" of the "s" shaped catenary - is not sufficient - then the "top hump" might not exist (or only just) - therefore I feel it might not be a very general solution - and may invalidate some of the assumtions made in linking the "various parts" of the catenary together - like the paper you posted on the 3rd of February.

Thanks David for your thoughts on this problem and the problem you had to try and find a solution too with your chain and wire rope for the barge - but I would like to see the Mathcad spreadsheets that you refer to - which I didn't see in your posting?

Thanks Denis for posting the links to what appears to be a dynamic situation affecting a catenary cable. I will see if there is anything in there that might be of use.