Acer,

Thank you for the assistance - the contributors to this site are the most valuable asset to the product.

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

Acer,

Thank you for the assistance - the contributors to this site are the most valuable asset to the product.

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

Thank you all for the suggestions. As Doug suggested, I will dynamically stretch the plot; although the changes are lost with each execution of the plot() command, it is a minor inconvenience.

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

Thank you all for the suggestions. As Doug suggested, I will dynamically stretch the plot; although the changes are lost with each execution of the plot() command, it is a minor inconvenience.

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

Thank you, David for the assistance. I ended up assigning each plot to a variable and then displaying the set, e.g., display({plot1, plot2, plot3,...})

This allowed me to vary the constants that were used in each solution before plotting.

Does anyone know of a way to stretch one axis more than the other when plotting?

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

Thank you, David for the assistance. I ended up assigning each plot to a variable and then displaying the set, e.g., display({plot1, plot2, plot3,...})

This allowed me to vary the constants that were used in each solution before plotting.

Does anyone know of a way to stretch one axis more than the other when plotting?

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

Thank you, acer for the suggestion. I will try it this evening.
Wayne J. Bell
AREVA NP, Inc.
Charlotte, North Carolina

Thank you, acer for the suggestion. I will try it this evening.
Wayne J. Bell
AREVA NP, Inc.
Charlotte, North Carolina

Thank you Dr. Israel for your investigation and deciphering the representation of elliptic integrals in the paper. Can you recommend any texts or papers that would give one a starting point on how these functions are developed and their applications in engineering? The paper that I am currently investigating uses them to describe the buckled shape of a constrained ring.
Have a Merry Christmas!

I have attached a worksheet which solves for beta and k, given N = 180. Page 693 of the journal article indicates that if one of the three parameters (beta, k, and, N) is given, then equations (15) and (16) can be used to solve for the other two. As I noted earlier, I have been able to solve the set of equations using the Solver in Excel and get a value of beta = 4.4919 radians (257 deg 22 min) and k = 0.1710. This is in good agreement with the article which indicates a value of beta = 257 degrees 25 minutes. Maple yields a solution of beta = 4.675064704, k = .9987187227, which is a 'correct' solution; however, it is not in agreement with the article's value. I am simply trying to use Maple as a tool to reestablish the development of an engineering analysis and I do not yet understand how to properly evaluate elliptic integrals. That said, I still think Maple should be able to verify/duplicate this original work. I have tried to contact some of original authors of the article to learn what they did to evaluate the equations, but most of them have passed away. Any thoughts on how to set it up in Maple would be appreciated. Also if anyone knows of references/articles on the applications of elliptic integrals in engineering analysis I would be very grateful. Thank you all for your thoughts and suggestions.
Excerpt from journal article:

Download 4865_Lo_p693.pdfView file details
Maple worksheet:

View 4865_Elliptic Equations.mw on MapleNet or

Download 4865_Elliptic Equations.mwView file details

Mariner,
Thank you for checking the EllipticF command; it also sounds like I should be careful using earlier references and tables to check Maple. There is still a problem with elliptic integrals however, and this goes back to the earlier "Plot This! - Elliptic Integrals" post, which Dr. Israel answered previously. The implicit plot command applied as shown below yields a value of beta equal to approx. 277 degrees for a range of k from 0 to 1. However, when the expression below is evaluated at k = 0, the correct answer should be beta = tan (beta), which yields beta equal to 257 degrees 27 minutes. I am trying to verify if the EllipticF and EllipticE commands are yielding correct results, which is critical for the analysis I am working on. I will try to get hold of the table you referenced and verify Maple's results for the entire range of values.
If you enter the Maple input below you'll see the discrepancy.
> with(plots): Digits = 15:
> implicitplot(2*EllipticE(sin(beta),k)-EllipticF(sin(beta),k)=tan(beta)*sqrt(1-k^2*sin(beta)^2),
k=0..1, beta = 3.5..5.5, view = [0..1, 3.5..5.5]);
Please note that the plot generated does not agree with the expected value of 257 degrees 27 minutes at k = 0. This discrepancy is the sole reason for the discussion on elliptic integrals. Thank you for your help.

Mariner,
Thank you for checking the EllipticF command; it also sounds like I should be careful using earlier references and tables to check Maple. There is still a problem with elliptic integrals however, and this goes back to the earlier "Plot This! - Elliptic Integrals" post, which Dr. Israel answered previously. The implicit plot command applied as shown below yields a value of beta equal to approx. 277 degrees for a range of k from 0 to 1. However, when the expression below is evaluated at k = 0, the correct answer should be beta = tan (beta), which yields beta equal to 257 degrees 27 minutes. I am trying to verify if the EllipticF and EllipticE commands are yielding correct results, which is critical for the analysis I am working on. I will try to get hold of the table you referenced and verify Maple's results for the entire range of values.
If you enter the Maple input below you'll see the discrepancy.
> with(plots): Digits = 15:
> implicitplot(2*EllipticE(sin(beta),k)-EllipticF(sin(beta),k)=tan(beta)*sqrt(1-k^2*sin(beta)^2),
k=0..1, beta = 3.5..5.5, view = [0..1, 3.5..5.5]);
Please note that the plot generated does not agree with the expected value of 257 degrees 27 minutes at k = 0. This discrepancy is the sole reason for the discussion on elliptic integrals. Thank you for your help.

Dr. Israel,
I have posted the entire article which includes the development of the transcendental equation (16) posted yesterday. Thank you for your assistance. I am attempting to work through the entire solution of the buckling analysis as presented in the paper using Maple, with the intent of developing a VBA routine that will calculate the critical load for various combinations of ring diameter and thickness.
Equation (16) is one of several transcendental equations (see equation (14)) used in the analysis and I am working through paper, hoping to develop plots that match the figures shown in the paper (see Figures 6, 7, and 9).
This effort is part of a paper on buckling of cylinders under circumferential loads, which compares the results of analytical solutions (of which the Lo paper is one) and finite element methods using ANSYS. The paper is a requirement for completing the Master of Science in Civil Engineering degree at the University of North Carolina at Charlotte. I am also employed full time at AREVA, Inc., a nuclear services company and have chosen the topic of ring buckling because it applies to the work we are involved with in the design of containment structures for nuclear reactors. If you are interested, I would be willing to offer compensation for your efforts.
Respectfully,
Wayne J. Bell

Dr. Israel,
I have posted the entire article which includes the development of the transcendental equation (16) posted yesterday. Thank you for your assistance. I am attempting to work through the entire solution of the buckling analysis as presented in the paper using Maple, with the intent of developing a VBA routine that will calculate the critical load for various combinations of ring diameter and thickness.
Equation (16) is one of several transcendental equations (see equation (14)) used in the analysis and I am working through paper, hoping to develop plots that match the figures shown in the paper (see Figures 6, 7, and 9).
This effort is part of a paper on buckling of cylinders under circumferential loads, which compares the results of analytical solutions (of which the Lo paper is one) and finite element methods using ANSYS. The paper is a requirement for completing the Master of Science in Civil Engineering degree at the University of North Carolina at Charlotte. I am also employed full time at AREVA, Inc., a nuclear services company and have chosen the topic of ring buckling because it applies to the work we are involved with in the design of containment structures for nuclear reactors. If you are interested, I would be willing to offer compensation for your efforts.
Respectfully,
Wayne J. Bell