Wayne J. Bell AREVA NP, Inc. Charlotte, North Carolina

The initial posting was not clear in that I am trying to plot the harmonic (i.e., sinusoidal) distribution of a force around the rim of a circle (pipe). The radius is constant as well as the total force input; however, the force is distributed around the circumference using the cosine function as shown below so that the force distribution is maximum at 0 degrees and 180 degrees. This will model the pure bending moment applied to a pipe about an axis in the plane of the pipe cross section. I would like to be able to plot this distribution of the force around the rim of the pipe. Any suggestions / comments are appreciated.

fy :=FORCE/(2*Pi*R)*COS(PHI), PHI=0..2*Pi, R = CONSTANT

Wayne J. Bell AREVA NP, Inc. Charlotte, North Carolina

To all,

Thank you for the comments; this is one of the strong points of Maple - a dedicated user community.

Dr. Israel,

I think your solution may be what I am looking for, which is the intermediate step in the solution of the ODE.

Acer,

The units are now being carried correctly after I added the following two commands:

Units[UseSystem]('FPS'); with(Units[Standard]):

If I did not specify the 'FPS' system, the results were converted to SI. The help file is not much help either.

Now that the units are being carried through, is there a way to change the primary label? For example, can I force the length to be listed in inches and not feet? (See attached, improved file).

View 4865_Kent_ASME_Appl_Mech_V53_P17_1931.mw on MapleNet or Download 4865_Kent_ASME_Appl_Mech_V53_P17_1931.mw

View file details

Thank you for your help ... I'm getting there!

Wayne J. Bell AREVA NP, Inc. Charlotte, North Carolina

Doug,

You are exactly right, I was not reading the plotted results correctly; however, assuming I did want to plot (or otherwise use the value of P_bar in an expression), does the fact that I have declared it as a global variable mean that it retains it's value outside of the procedure?

Thank you for your comments (and patience).

Wayne J. Bell AREVA NP, Inc. Charlotte, North Carolina

Thank you for the assistance; I will make the suggested changes.

Wayne J. Bell AREVA NP, Inc. Charlotte, North Carolina

Thank you Scott for the help, I can now populate the spreadsheet with the results of the fsolve() command; however, because the solution is for two unknowns, I would like to separate the solution given by Maple into separate cells. Is there a way to get at solutions in a fashion similar to specifying RHS and LHS for equations?
Wayne J. Bell
AREVA NP, Inc.
Charlotte, North Carolina

J. Tarr,
Thank you, that was it exactly.
Wayne J. Bell
AREVA NP, Inc.
Charlotte, North Carolina

Scott,
The result of entering the expression was:
Maple 11, IBM INTELNT, Jun 8 2007, Build ID 296069
After carefully entering the expression below in the cell of the spreadsheet that is using the Maple Add-In I am getting the correct values for beta, given the value of &1 assigned to cell I14.
=Maple("fsolve(2*(2*EllipticE(&1)-EllipticE(sin(beta), &1))-2*EllipticK(&1)+EllipticF(sin(beta), &1) = tan(beta)*sqrt(1-&1^2*sin(beta)^2),beta,Pi/2..3*Pi/2);",I14)
Finally, Dr. Israel provided some valuable insight into the correct syntax for evaluating Elliptic integrals in the range I am interested in; however, in his reply (see posting titled "Elliptic Integrals") he uses fsolve() to get a value of (k=0.1703382972, beta = 4.491817834) to the equation given above. How can you fsolve() for an equation that contains tow unknowns? If you would read through the posting and respond I would be very grateful.
The more familiar I am becoming with Maple, the more impressed I am with it's computational capacity. I believe that any software developed to handle complex and computationally intensive problems will initially have a steep learning curve, with the promise of large increments in productivity later. Thank you for your help and have a Merry Christmas.

Scott,
I am trying to call Maple to fsolve() the equation given the variable pointed to by &1. Oddly enough, only the first expression is evaluated [EllipticE(&1)] and the other calls to elliptic integrals are simply listed in the cell as characters. I may be better of creating a column vector within Maple that has a solution over the range of interest and exporting that to the spreadsheet.
I am using Excel 2003 and Maple 11 for this problem. Thank you for your assistance.

Thank you for the help; this is a great site for learning. The following code generates a 45X10 matrix to allow me to compare the EllipticF and EllipticE commands in Maple, which by the way are in perfect agreement with published tables.
> deg2rad := (1/180)*Pi;
> for i to 45 do count := 1;
for j from 0 by 5 to 45 do A[i, count] := evalf(EllipticF(sin(i*deg2rad), sin(j*deg2rad)));
count := count+1;
end do;
end do:

I have checked the settings under my profile and everything looks OK, but I got the same message when I tried to send myself a message.

Please accept my apology Jaques, but crashing Maple was not my intention. As I mentioned in the original request, Dr. Israel provided the Maple commands (I can't take credit for the effects) which seem to work, in that the implicitplot() command generates a plot similar to Figure 5 of the attached article, however the values are wrong for the specified range. The Maple staff is looking into the issue as well, but any help provided is appreciated.
Perhaps Dr. Israel could offer some insight.

Georgios,
Thank you for the clarification; I was using the **Sum** form of the command vs. **sum** which you suggested. I am now able to specify the number of terms for evaluation. I will investigate the difference in implementation of the two forms of the command as you suggested.

Assuming the expression below represents the trigonometric sine series for the deflection of a curved bar (see initial post), I would like to expand the summation in a way that would allow me to specify the number of terms.
s := Sum(a[k]*sin(k*Pi*x/l), k = 1 .. infinity)
For example, to see the effect of using the first three terms, I would like to generate the expression:
y := a[1]*sin(Pi*x/l)+a[2]*sin(2*Pi*x/l)+a[3]*sin(3*Pi*x/l)
Any suggestions/guidance would be appreciated.

After reviewing the SUM() command, I think this is what represents the sine series given above.
Sum(a[k]*sin(k*Pi*x/l), k = 1 .. infinity);