Hi guys,
Anyone have found a way forward?
Just to summarize what I have tried so far:
Attempting to solve for a/b = 1, and with t1 and k1 to k7 determinants as a 1st trial like Levy did in Table 2, the K solution should be 10.047.
These determinants means that n = 1 and m = 1, 3, 5 and 7...
Hi cent,
I am looking for a closed-form solution to the above stated problem. Hence, why I want to solve this Levy equation. This method is also industry accepted.
Regarding what you mentioned about its convergence, I do agree, but in a physical practical sense, I think it is accurate enough...
Hi Stress_Eng,
It's not that I'm not open to other methods. It's just that the trusted values are from Levy's paper (referenced by Timoshenko) for this special case of the plate (CCCC with uniaxial compression). Although most engineers simply go to Bruhn without actually realizing Bruhn is...
Hi SW,
I just tried it and it doesn't work. I hope I am doing it right.
Assuming aspect ratio = 1, and K = 10 (for illustration purposes only), I get the following equations:
Equation 8a; n = 1, m = 1, 3, 5, 7
(-1/6)k1-(1/6)t1+(3/10)k3+(9/10)t1+(5/426)k5+(25/426)t1+(7/2010)k7+(49/2010)t1=0...
I get what you are saying. The problem is, all the coefficients of the km and tn variables must be set in a square matrix and solved simultaneously (determinate = 0) to determine the K. What makes things even more interesting is Levy solved with n = 1 and managed to get rapid convergence with...
In Levy's paper, he stated that for the first calculations, he used t1, k1, k3, k5, and k7.
This means he used n = 1 and m = 1 to 7.
If I assume aspect ratio = 1, then the equations will be this:
(k1 + t1)/(4-K) + (3k3 + 9t1)/(100-9K) + (5k5 + 25t1)/(676-25K) + (7k7 + 49t1)/(2500-49K) = 0...
Hi SW,
My issue is I can't figure out how to set up the matrix itself.
I have never attempted to solve a simultaneous infinite series before.
Are you suggesting something like this?
Taking the first equation of Equation 8:
Below are the coefficients of km for m,n (lets say I only go up to 5)...
Hi Stress_Eng,
I get what you mean, but I am not looking to go down a new mathematical path for now.
I was hoping to just solve the equation provided by Levy. The convergence should also be quick and with today's computational power, should take just a fraction of a second.
Thanks,
Prathik
Hi All,
For a rectangular plate buckling with all sides built-in, Levy has solved this problem in his 1942 paper: "BUCKLING OF RECTANGULAR PLATES WITH BUILT-IN EDGES", S. LEVY, JOURNAL OF APPLIED MECHANICS, VOL. 9, PG. 171, 1942.
In his paper, the buckling coefficient, K is determined by...
