Gentleman, Thank you for the support and assistance in using Maple to work with elliptic integrals. My motivation for studying this problem is to develop an understanding of the analytical approach to the structural stability of confined cylinders and compare the results to a finite element formulation. At the time of the paper there was a difference of opinion among designers as to why the buckling load produced in testing machines was significantly less than the load predicted by the closed form solution. The difference is generally thought to be the result of imperfections in the material and geometry of the cylinder. As regards the reason for using an elliptic integral in the solution of the problem, I would call your attention to Figure 4 of the Lo paper. Download 4865_Lo_p693.pdf
View file details As noted on page 692, the angle phi starts out equal to 0 at the origin, decreases along the curve to a maximum negative value at the inflection point, and then becomes positive from there on. To solve equation (8) the author introduces the transformation of phi shown in (9) to eliminate the change of sign. It is my understanding that this substitution is what suggests the use of the ellipic integrals to solve the equation, subject to the boundary conditions given in (11). After developing a function, f(x,y) for equation (14), I'm going to work on solving the case of ring buckling under an end compressive load (pp. 694-695) and compare the critical end compressive load as shown in Figure 9 with a FEA solution given by ANSYS. I'm sure I will have questions... Download 4865_Lo_p694.pdf
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View file details I look forward to developing my analytical skills and the use of Maple. Thank you again for your assistance. Respectfully, Wayne

The attached files present the solution to a buckling problem of a circular ring restrained circumferentially by a rigid, frictionless boundary. I am attempting to recreate the solution using Maple, with the goal of creating a VBA routine to allow evaluation of the critical load, viz., buckling load, for different diameters and thicknesses of the ring. Download 4865_Lo_p691.pdf
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