"i" will always equal 4 because your for loop has no condition that will stop it from going to the end. Because "i" will always be 4 at the end of the loop, QbarA, QbarB, QbarC will never get set and therefore, when you get to the line where "A" is being set, you will get an error.
The following code is probably closer to what you want, but your output function will return an array mismatch error because A, B, and D are 3x3 arrays, N and M are 1x3 arrays. Would need background on your algorithm to help further.
clc, close all, clear variables
E1 = 40;
E2 = 1.8;
V12 = 0.25;
V21 = 0.01125;
G12 = 0.7;
t = 0.005;
z0 = -t*2;
z1 = -t;
z2 = 0;
z3 = t;
z4 = t*2;
theta = [0,15,90,-30];
Q11 = E1/(1-V12*V21);
Q12 = (V21*E2)/(1-V12*V21);
Q22 = E2/(1-V12*V21);
Q66 = G12;
Nx = 1200*4*t;
Ny = -600*4*t;
Nxy = 600*4*t;
My = 36/12;
Mx = -18/18;
Mxy = 0;
N = [Nx;Ny;Nxy];
M = [Mx;My;Mxy];
for i = 1:4
m = cosd(theta(i));
n = sind(theta(i));
Qbar11 = Q11.*m^4+2.*(Q12+2*Q66).*m^2.*n^2+Q22*n^4;
Qbar12 = (Q11+Q22-4*Q66)*m^2*n^2+Q12*(m^4+n^4);
Qbar16 = (Q11-Q12-2*Q66)*m^3*n+(Q12-Q22+2*Q66)*m*n^3;
Qbar22 = Q11.*n^4+2.*(Q12+2*Q66).*m^2.*n^2+Q22*m^4;
Qbar26 = (Q11-Q12-2*Q66)*m*n^3+(Q12-Q22+2*Q66)*m^3*n;
Qbar66 = (Q11+Q22-2*Q12-2*Q66)*m^2*n^2+Q66*(m^4+n^4);
Qbar = [Qbar11 Qbar12 Qbar16
Qbar12 Qbar22 Qbar26
Qbar16 Qbar26 Qbar66];
A = Qbar*t+Qbar*t+Qbar*t+Qbar*t;
B = 1/2*(Qbar*(z1^2-z0^2)+Qbar*(z2^2-z1^2)+Qbar*(z3^2-z2^2)+Qbar*(z4^2-z3^2));
D = 1/3*(Qbar*(z1^3-z0^3)+Qbar*(z2^3-z1^3)+Qbar*(z3^3-z2^3)+Qbar*(z4^3-z3^3));
Output = [A,B;B,D]^-1.*[N,M]
end
