kill(all);

D:
E/(1-nu^2)*
matrix(
[ 1,nu,       0],
[nu, 1,       0],
[ 0, 0,(1-nu)/2]
);

A: integrate(D,z,-h/2,h/2);

B: integrate(D*z,z,-h/2,h/2);

C: integrate(D*z^2,z,-h/2,h/2);

e:matrix([ex],[ey],[gxy])$
k:matrix([kx],[ky],[kxy]);
q:matrix([qx],[qy],[qxy])$
m:matrix([mx],[my],[mxy])$

m - B.e - C.k;
eqns:list_matrix_entries(%);

momenti e curvature nominali di riferimento

mref:F*l/b;

kref:12*F*l/E/b/h^3;

caso a curvatura ky imposta

null_ky:[mx=mref,ky=0,mxy=0];

null_ky:append(
    null_ky,
    linsolve(ev(eqns,null_ky),[kx,my,kxy])
);

risultati

fullratsimp( 
    ev( 
[mx,my,mxy]/mref, null_ky));%,nu=0.3;

fullratsimp( 
    ev( 
[kx,ky,kxy]/kref, null_ky));%,nu=0.3;

caso a curvatura ky libera, my nullo

null_ky:[mx=mref,my=0,mxy=0];

null_ky:append(
    null_ky,
    linsolve(ev(eqns,null_ky),[kx,ky,kxy])
);

risultati

fullratsimp( 
    ev( 
[mx,my,mxy]/mref   , null_ky));%,nu=0.3;

fullratsimp( 
    ev( 
[kx,ky,kxy]/kref   , null_ky));%,nu=0.3;