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@C_R sir...i just want to find buckling load of thin composite square plate under shear loading..do u have any code or idea about this..i understand theory...but to apply in maple...i have a problem ..like this is eigen value problem for example problem in this photo ...i don't know how to apply in maple..i have all value of D and R..so i want to find S...but i dont' know how to start..A(mn) also depend on m and n...(eg m,n = form 1..10) ...can u please advise me?

 

@tomleslie sir..i want to integrate..this eqations for all values in X and Y.....like for X(1) and Y(1) we got 1 answer...for X(1),Y(2) and...like that....X and Y have each 100 values/ how can i get it..please help me sir


 

restart

iteration := [seq(a, a = 1 .. 10)];

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

(1)

lambda[i] := evalf([seq((1/2)*(2*i+1)*Pi, `in`(i, iteration))]);

[4.712388981, 7.853981635, 10.99557429, 14.13716694, 17.27875960, 20.42035225, 23.56194490, 26.70353756, 29.84513021, 32.98672287]

(2)

alpha[i] := evalf([seq((cosh(i)-cos(i))/(sinh(i)+sin(i)), `in`(i, lambda[i]))]);

[1.018461155, .9992244968, 1.000033553, .9999985501, 1.000000063, .9999999973, 1.000000000, 1.000000000, 1.000000000, 1.000000000]

(3)

eq_x := sin(i*x/a)-sinh(i*x/a)+j*(cosh(i*x/a)-cos(i*x/a));

sin(i*x/a)-sinh(i*x/a)+j*(cosh(i*x/a)-cos(i*x/a))

(4)

X := [seq(seq(eq_x, `in`(i, lambda[i])), `in`(j, alpha[i]))]:

eq_y := sin(i*y/b)-sinh(i*y/b)+j*(cosh(i*y/b)-cos(i*y/b)):

Y := [seq(seq(eq_y, `in`(i, lambda[i])), `in`(j, alpha[i]))]:

eq_1 := D__11*((diff(A(x), x, x))*B(y)*((diff(A(x), x, x))*B(y)))+(2*(D__12+2*D__66))*(diff(A(x), x))*((diff(B(y), y))*((diff(A(x), x))*(diff(B(y), y))))+D__22*A(x)*((diff(B(y), y, y))*A(x)*(diff(B(y), y, y)))-N__xy((diff(A(x), x))*B(y)*A(x)*(diff(B(y), y))+(diff(A(x), x))*B(y)*A(x)*(diff(B(y), y)));

D__11*(diff(diff(A(x), x), x))^2*B(y)^2+2*(D__12+2*D__66)*(diff(A(x), x))^2*(diff(B(y), y))^2+D__22*A(x)^2*(diff(diff(B(y), y), y))^2-N__xy(2*(diff(A(x), x))*B(y)*A(x)*(diff(B(y), y)))

(5)

"(∫)[0]^(b)(∫)[0]^(a)eq_1 ⅆx ⅆy, A(x) in X), B(y) in Y"

Error, unable to match delimiters

"(∫)[0]^b(∫)[0]^aeq_1 ⅆx ⅆy, A(x) in X), B(y) in Y"

 

``


 

Download approximate_function.mw

@Carl Love  i dont' get it...sir...if my (m,n,i,j) values are sereis.....like (1..10)...how can i get...M[i,j]....can u please..write code for this...i honestly just didn't see by myself

@Carl Love hello sir.
actually my equations is like that and ..it eigen value buckling problem .....how to get M value ...i dont' know how to ask question...i want M(ij) value...for ..like (i,j,m,n= 1 to 10)...can u help me this..?..o

hi my (m,n,i,j) values...are all...from 1 to 20....;please...help me guys

@acer yes those depend on i...here is..my new file..with i=1....but what if...i= 1 t0 20 with odd number.
w depend on i and..t_pe depend on w..so...for example ..if i used.. i = 1,3,5,7....we gonna have..4 w values depend on w and...4 t_pe equations..depend on  w...form t_pe equations (as shown in my file..i want c(i))....like...if i =1...i gonna get w(1) and t_pe(1) ..from t_pe1...i cant c(1)...as shown in figure..but..if i used  = 1,3,5,7.....how can i get..c(i) value.....

my questions will be messsed..please..look at my file...
thak u so much sir..u put too much time for me

 Pi.mw

@acer i gonna put another file....in this file i used only one value...(so it's clear)...here is my  file .

..Pi.mw...

.in this file i only use i= 1.....so it's easily...but in my real calculation...(i value)  may be like (1,3.5.to ..anyvalue..all will be odd number..)..so ...if i use...(i form 1 to...20...) how to get...derivative..each respective .to each......

(it is Ritz solution to plate bending) ..by the way);
thak u very much..sir...

how to take derivative of ...two list....like i want to derivative of....soltion(1) with respect to appro_function(1) and 2 with 2 and 3 with 3...here is my mfile..sir

partial_derivative_form_2_list.mw

restart

appro_function := [seq(w[2*i-1], i = 1 .. 10)];

[w[1], w[3], w[5], w[7], w[9], w[11], w[13], w[15], w[17], w[19]]

(1)

solution := [(1/128)*c[1]*(3*D__11*Pi^4*b^4*c[1]+2*D__12*Pi^4*a^2*b^2*c[1]+3*D__22*Pi^4*a^4*c[1]+4*D__66*Pi^4*a^2*b^2*c[1]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[3]*(243*D__11*Pi^4*b^4*c[3]+162*D__12*Pi^4*a^2*b^2*c[3]+243*D__22*Pi^4*a^4*c[3]+324*D__66*Pi^4*a^2*b^2*c[3]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[5]*(1875*D__11*Pi^4*b^4*c[5]+1250*D__12*Pi^4*a^2*b^2*c[5]+1875*D__22*Pi^4*a^4*c[5]+2500*D__66*Pi^4*a^2*b^2*c[5]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[7]*(7203*D__11*Pi^4*b^4*c[7]+4802*D__12*Pi^4*a^2*b^2*c[7]+7203*D__22*Pi^4*a^4*c[7]+9604*D__66*Pi^4*a^2*b^2*c[7]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[9]*(19683*D__11*Pi^4*b^4*c[9]+13122*D__12*Pi^4*a^2*b^2*c[9]+19683*D__22*Pi^4*a^4*c[9]+26244*D__66*Pi^4*a^2*b^2*c[9]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[11]*(43923*D__11*Pi^4*b^4*c[11]+29282*D__12*Pi^4*a^2*b^2*c[11]+43923*D__22*Pi^4*a^4*c[11]+58564*D__66*Pi^4*a^2*b^2*c[11]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[13]*(85683*D__11*Pi^4*b^4*c[13]+57122*D__12*Pi^4*a^2*b^2*c[13]+85683*D__22*Pi^4*a^4*c[13]+114244*D__66*Pi^4*a^2*b^2*c[13]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[15]*(151875*D__11*Pi^4*b^4*c[15]+101250*D__12*Pi^4*a^2*b^2*c[15]+151875*D__22*Pi^4*a^4*c[15]+202500*D__66*Pi^4*a^2*b^2*c[15]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[17]*(250563*D__11*Pi^4*b^4*c[17]+167042*D__12*Pi^4*a^2*b^2*c[17]+250563*D__22*Pi^4*a^4*c[17]+334084*D__66*Pi^4*a^2*b^2*c[17]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[19]*(390963*D__11*Pi^4*b^4*c[19]+260642*D__12*Pi^4*a^2*b^2*c[19]+390963*D__22*Pi^4*a^4*c[19]+521284*D__66*Pi^4*a^2*b^2*c[19]-32*a^4*b^4*q__0)/(a^3*b^3)];

[(1/128)*c[1]*(3*D__11*Pi^4*b^4*c[1]+2*D__12*Pi^4*a^2*b^2*c[1]+3*D__22*Pi^4*a^4*c[1]+4*D__66*Pi^4*a^2*b^2*c[1]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[3]*(243*D__11*Pi^4*b^4*c[3]+162*D__12*Pi^4*a^2*b^2*c[3]+243*D__22*Pi^4*a^4*c[3]+324*D__66*Pi^4*a^2*b^2*c[3]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[5]*(1875*D__11*Pi^4*b^4*c[5]+1250*D__12*Pi^4*a^2*b^2*c[5]+1875*D__22*Pi^4*a^4*c[5]+2500*D__66*Pi^4*a^2*b^2*c[5]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[7]*(7203*D__11*Pi^4*b^4*c[7]+4802*D__12*Pi^4*a^2*b^2*c[7]+7203*D__22*Pi^4*a^4*c[7]+9604*D__66*Pi^4*a^2*b^2*c[7]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[9]*(19683*D__11*Pi^4*b^4*c[9]+13122*D__12*Pi^4*a^2*b^2*c[9]+19683*D__22*Pi^4*a^4*c[9]+26244*D__66*Pi^4*a^2*b^2*c[9]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[11]*(43923*D__11*Pi^4*b^4*c[11]+29282*D__12*Pi^4*a^2*b^2*c[11]+43923*D__22*Pi^4*a^4*c[11]+58564*D__66*Pi^4*a^2*b^2*c[11]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[13]*(85683*D__11*Pi^4*b^4*c[13]+57122*D__12*Pi^4*a^2*b^2*c[13]+85683*D__22*Pi^4*a^4*c[13]+114244*D__66*Pi^4*a^2*b^2*c[13]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[15]*(151875*D__11*Pi^4*b^4*c[15]+101250*D__12*Pi^4*a^2*b^2*c[15]+151875*D__22*Pi^4*a^4*c[15]+202500*D__66*Pi^4*a^2*b^2*c[15]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[17]*(250563*D__11*Pi^4*b^4*c[17]+167042*D__12*Pi^4*a^2*b^2*c[17]+250563*D__22*Pi^4*a^4*c[17]+334084*D__66*Pi^4*a^2*b^2*c[17]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[19]*(390963*D__11*Pi^4*b^4*c[19]+260642*D__12*Pi^4*a^2*b^2*c[19]+390963*D__22*Pi^4*a^4*c[19]+521284*D__66*Pi^4*a^2*b^2*c[19]-32*a^4*b^4*q__0)/(a^3*b^3)]

(2)

``

Download partial_derivative_form_2_list.mw

i think i'm assign wrong...here is my new one..i want to do partial derivative of...solution(1) by appro_function(1) ..and 2 for 2..and 3 or 3 like that
 

restart

appro_function := [seq(w[2*i-1], i = 1 .. 10)];

[w[1], w[3], w[5], w[7], w[9], w[11], w[13], w[15], w[17], w[19]]

(1)

solution := [(1/128)*c[1]*(3*D__11*Pi^4*b^4*c[1]+2*D__12*Pi^4*a^2*b^2*c[1]+3*D__22*Pi^4*a^4*c[1]+4*D__66*Pi^4*a^2*b^2*c[1]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[3]*(243*D__11*Pi^4*b^4*c[3]+162*D__12*Pi^4*a^2*b^2*c[3]+243*D__22*Pi^4*a^4*c[3]+324*D__66*Pi^4*a^2*b^2*c[3]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[5]*(1875*D__11*Pi^4*b^4*c[5]+1250*D__12*Pi^4*a^2*b^2*c[5]+1875*D__22*Pi^4*a^4*c[5]+2500*D__66*Pi^4*a^2*b^2*c[5]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[7]*(7203*D__11*Pi^4*b^4*c[7]+4802*D__12*Pi^4*a^2*b^2*c[7]+7203*D__22*Pi^4*a^4*c[7]+9604*D__66*Pi^4*a^2*b^2*c[7]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[9]*(19683*D__11*Pi^4*b^4*c[9]+13122*D__12*Pi^4*a^2*b^2*c[9]+19683*D__22*Pi^4*a^4*c[9]+26244*D__66*Pi^4*a^2*b^2*c[9]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[11]*(43923*D__11*Pi^4*b^4*c[11]+29282*D__12*Pi^4*a^2*b^2*c[11]+43923*D__22*Pi^4*a^4*c[11]+58564*D__66*Pi^4*a^2*b^2*c[11]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[13]*(85683*D__11*Pi^4*b^4*c[13]+57122*D__12*Pi^4*a^2*b^2*c[13]+85683*D__22*Pi^4*a^4*c[13]+114244*D__66*Pi^4*a^2*b^2*c[13]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[15]*(151875*D__11*Pi^4*b^4*c[15]+101250*D__12*Pi^4*a^2*b^2*c[15]+151875*D__22*Pi^4*a^4*c[15]+202500*D__66*Pi^4*a^2*b^2*c[15]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[17]*(250563*D__11*Pi^4*b^4*c[17]+167042*D__12*Pi^4*a^2*b^2*c[17]+250563*D__22*Pi^4*a^4*c[17]+334084*D__66*Pi^4*a^2*b^2*c[17]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[19]*(390963*D__11*Pi^4*b^4*c[19]+260642*D__12*Pi^4*a^2*b^2*c[19]+390963*D__22*Pi^4*a^4*c[19]+521284*D__66*Pi^4*a^2*b^2*c[19]-32*a^4*b^4*q__0)/(a^3*b^3)];

[(1/128)*c[1]*(3*D__11*Pi^4*b^4*c[1]+2*D__12*Pi^4*a^2*b^2*c[1]+3*D__22*Pi^4*a^4*c[1]+4*D__66*Pi^4*a^2*b^2*c[1]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[3]*(243*D__11*Pi^4*b^4*c[3]+162*D__12*Pi^4*a^2*b^2*c[3]+243*D__22*Pi^4*a^4*c[3]+324*D__66*Pi^4*a^2*b^2*c[3]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[5]*(1875*D__11*Pi^4*b^4*c[5]+1250*D__12*Pi^4*a^2*b^2*c[5]+1875*D__22*Pi^4*a^4*c[5]+2500*D__66*Pi^4*a^2*b^2*c[5]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[7]*(7203*D__11*Pi^4*b^4*c[7]+4802*D__12*Pi^4*a^2*b^2*c[7]+7203*D__22*Pi^4*a^4*c[7]+9604*D__66*Pi^4*a^2*b^2*c[7]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[9]*(19683*D__11*Pi^4*b^4*c[9]+13122*D__12*Pi^4*a^2*b^2*c[9]+19683*D__22*Pi^4*a^4*c[9]+26244*D__66*Pi^4*a^2*b^2*c[9]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[11]*(43923*D__11*Pi^4*b^4*c[11]+29282*D__12*Pi^4*a^2*b^2*c[11]+43923*D__22*Pi^4*a^4*c[11]+58564*D__66*Pi^4*a^2*b^2*c[11]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[13]*(85683*D__11*Pi^4*b^4*c[13]+57122*D__12*Pi^4*a^2*b^2*c[13]+85683*D__22*Pi^4*a^4*c[13]+114244*D__66*Pi^4*a^2*b^2*c[13]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[15]*(151875*D__11*Pi^4*b^4*c[15]+101250*D__12*Pi^4*a^2*b^2*c[15]+151875*D__22*Pi^4*a^4*c[15]+202500*D__66*Pi^4*a^2*b^2*c[15]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[17]*(250563*D__11*Pi^4*b^4*c[17]+167042*D__12*Pi^4*a^2*b^2*c[17]+250563*D__22*Pi^4*a^4*c[17]+334084*D__66*Pi^4*a^2*b^2*c[17]-32*a^4*b^4*q__0)/(a^3*b^3), (1/128)*c[19]*(390963*D__11*Pi^4*b^4*c[19]+260642*D__12*Pi^4*a^2*b^2*c[19]+390963*D__22*Pi^4*a^4*c[19]+521284*D__66*Pi^4*a^2*b^2*c[19]-32*a^4*b^4*q__0)/(a^3*b^3)]

(2)

``

``


 

Download partial_derivative_form_2_list.mw

@mmcdara  sir....why it can't get lately..it actually solved...if i go assumptions..i dont' know i can go futher calculations...can u tell me why my style of sovling doesn't worked.

Here is the worksheet.

i want to put table all the value of w

stiffnessmatrixcal.mw

@acer sir ..please how to decide the proper range of that kind of equations?

@tomleslie  sir ..please how to decide the proper range of that kind of equations?

hello Sir,
i think my plot should be ellipse..but it show like this and it show like this..please check 
with respect

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