Question: How to apply Newton-Raphson method?

Hello Everybody,

I was trying to apply the Newton-Raphon method("Newton" in maple) for the following problem to obtain the constants (c1...cM) without success.

eq[1] := -0.0139687 c[2] - 0.0132951 c[1] = 0
eq[2] := 24806.4 c[2] - 0.0139687 c[1] = 0

If anybody has experience with it or knows how to use it I would really appreciate your help.

Just to introduce the previous steps of calculations leading to the problem:To calculate the critical buckling force N and the shape of a rectangular uniformly loaded plate the governing diff. equation is the following

D11*w''''(x)+(2*D12+4*D66)*w''(x)''(y)+D22*w''''(y)+N*w''(x)=0

For the follwing solution of a boundary value problem(Boundary conditions:clamped-clamped: w(x=0,x=a)=0 & w'(x=0,x=a)=0) I applied the Ritz method:

w:=sum(c[i]*(cos(2*i*Pi*x/a)-1)),i=1..M)

Thus the Potential Energy P is:

P:=16537.6*c[2]^2-0.0139687*c[2]*c[1]+1033,60*c[1]^2-9.86960*N*c[2]^2-2.46740*N*c[1]^2

 deriving P to each constant c and setting them =0 leads to:

eq[1] := -0.0139687 c[2] + 2067.20 c[1] - 4.93480 N c[1] = 0
eq[2] := 33075.2 c[2] - 0.0139687 c[1] - 19.7392 N c[2] = 0

After calculating N=418,902  and feeding eq1 and eq 2,the follwing equations if two terms are considered:

eq[1] := -0.0139687 c[2] - 0.0132951 c[1] = 0
eq[2] := 24806.4 c[2] - 0.0139687 c[1] = 0

Everything I tried resulted in any c1 = c2 = 0 which is not  realistic. Maybe I made a mistake earlier.

Thanks a lot in advance.

Sam

 Plate_Buckling.mw