Matlab don't show calculated variables.

I wrote this:

syms C0 C1 C2 C3 X L P EI1 EI2
Y(X)=C0+C1*X+C2*X^2+C3*X^3;

dY(X)=diff(Y(X),X);
d2Y(X)=diff(dY(X),X);

f0 = Y(0) == 0;
f1 = Y(L) == 0;
R=solve([f0,f1],[C0,C1]);
C0 = R.C0;
C1 = R.C1;

U=(EI1/2)*int(d2Y(X)^2,[0 L/2])+(EI2/2)*int(d2Y(X)^2,[L/2 L]);
V=-P*Y(L/2);

PI(C2,C3)=U+V;
dPIdC2=diff(PI(C2,C3),C2);
dPIdC3=diff(PI(C2,C3),C3);

f2 = dPIdC2 == 0;
f3 = dPIdC3 == 0;
S=solve([f2,f3],[C2,C3]);
C2 = S.C2;
C3 = S.C3;
C= ([C0;C1;C2;C3]);
disp(C);
Y(X)=C0+C1*X+C2*X^2+C3*X^3;
disp Y(X);
disp (Y(X));
FLECHA = Y(L/2)

But Matlab returns:

C =

0

- C3*L^2 - C2*L

(P*(EI1*L + 11*EI2*L))/(4*(EI1^2 + 14*EI1*EI2 + EI2^2))

-(P*(EI1 + 7*EI2))/(6*(EI1^2 + 14*EI1*EI2 + EI2^2))

______________________________________________

Y(X)

C3*X^3 + C2*X^2 + C1*X + C0

FLECHA

(C3*L^3)/8 + (C2*L^2)/4 + (C1*L)/2 + C0

It dont show Y(X) in terms of calculated values of C0, C1, C2 and C3.

I Want the Y(x) in function of P, L, EI1, EI2, (...), with this script these variables C0, C1... are calculateds but MATLAB dont write Y(X) em terms of them.

Answer 1

[Tiago Araujo]

I fixed doing:

syms C0 C1 C2 C3 X L P EI1 EI2
Y(X)=C0+C1*X+C2*X^2+C3*X^3;
dY(X)=diff(Y(X),X);
d2Y(X)=diff(dY(X),X);
f0 = Y(0) == 0;
f1 = Y(L) == 0;
U=(EI1/2)*int(d2Y(X)^2,[0 L/2])+(EI2/2)*int(d2Y(X)^2,[L/2 L]);
V=-P*Y(L/2);
PI(C2,C3)=U+V;
dPIdC2=diff(PI(C2,C3),C2);
dPIdC3=diff(PI(C2,C3),C3);
f2 = dPIdC2 == 0;
f3 = dPIdC3 == 0;
S=solve([f0,f1,f2,f3],[C0,C1,C2,C3]);
C0=S.C0;
C1=S.C1;
C2 = S.C2;
C3 = S.C3;
C= ([C0;C1;C2;C3]);
disp(C);
Y(X)=C0+C1*X+C2*X^2+C3*X^3;
disp Y(X);
disp (Y(X));
FLECHA = Y(L/2)

Answer 2

[Jan]

I get a dfifferent output than you:

syms C0 C1 C2 C3 X L P EI1 EI2
Y(X)=C0+C1*X+C2*X^2+C3*X^3;
dY(X)=diff(Y(X),X);
d2Y(X)=diff(dY(X),X);
f0 = Y(0) == 0;
f1 = Y(L) == 0;
R=solve([f0,f1],[C0,C1]);
C0 = R.C0;
C1 = R.C1;
U=(EI1/2)*int(d2Y(X)^2,[0 L/2])+(EI2/2)*int(d2Y(X)^2,[L/2 L]);
V=-P*Y(L/2);
PI(C2,C3)=U+V;
dPIdC2=diff(PI(C2,C3),C2);
dPIdC3=diff(PI(C2,C3),C3);
f2 = dPIdC2 == 0;
f3 = dPIdC3 == 0;
S=solve([f2,f3],[C2,C3]);
C2 = S.C2;
C3 = S.C3;
C= ([C0;C1;C2;C3]);
disp(C);

Y(X)=C0+C1*X+C2*X^2+C3*X^3;
disp Y(X);

Y(X)

disp (Y(X));

FLECHA = Y(L/2)

FLECHA = 

[Tiago Araujo]

Hi! Thanks!

But, have you seen that the C3 and C2 are still present in the Y(X) instead of their value in function of EI, P and L... ?

I need Y(X) only in function of EI1 EI2 P and L...