A first course on solid mechanics

% stress tensor which satisfies equilibrium conditions
syms q 'real';
sig = [0 0; 0 -q];

% small strain tensor
syms b s 'real';
e11 = 2*s/(2*s+b);
syms e22 'real';
eps = [e11 0; 0 e22];

% imposing elastic constitutive law
syms E ni 'real';
eq1 = sig(1,1)/E -ni*sig(2,2)/E == eps(1,1);
eq2 = sig(2,2)/E -ni*sig(1,1)/E == eps(2,2);

% the equations can be solved with respect the unknowns q and e22
sol = solve([eq1 eq2],[q e22]);
q = sol.q
e22 = sol.e22

% integration of the vertical strain component
syms u_2 X_2 'real';
syms u_2(X_2);
ode = diff(u_2, X_2, 1) == e22;
cond = u_2(0) == 0;
sol = dsolve(ode,cond);
u_2(X_2) = sol;

% vertical lowering of the panel's top
syms h 'real';
w = -u_2(h)