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Clear["Global`*"]
Di = 1.98;
tc = 0.01;
Ri = 1.99;
hs = 0.01;
ts = 0.01;
p = 1.6 10^6;
nu = 0.3;
r = 0.5*(Di + tc);
R = Ri + 0.5*hs;
nfy = ArcSin[r/R];
kc = Power[3 (1 - nu^2), (4)^-1]/Sqrt[r*tc];
nlam = Power[3 (1 - nu^2), (4)^-1] Sqrt[R/hs];
k21 = 1 - (1 - 2 nu)/(2 Power[3 (1 - nu^2), (4)^-1]) Sqrt[hs/R]
     Cot[nfy];
k22 = 1 - (1 + 2 nu)/(2 Power[3 (1 - nu^2), (4)^-1]) Sqrt[hs/R]
     Cot[nfy];
k2d = 1 -
   nu/Power[3 (1 - nu^2), (4)^-1] Sqrt[hs/R] Cot[nfy] + (1 - 2 nu)^2/(
    8 Sqrt[3 (1 - nu^2)]) hs/R (Cot[nfy])^2;
k23 = 1 + (2 - nu)/(2 nu Power[3 (1 - nu^2), (4)^-1]) hs/R Cot[nfy];

a11 = Sqrt[r/tc]*(1 + Sqrt[Sin[nfy]]*k2d);
a12 = (1 - tc^2/(k21*hs^2)) ;
a21 = (1 - tc^2/(k21*hs^2));
a22 = 2 ((3 (1 - nu^2))^0.75)*Sqrt[tc/
   r] (1 + 1/(k21 Sqrt[Sin[nfy]]) (tc/hs)^2.5);
a10 = 1/4 ((1 - nu)/Sin[nfy] tc/hs -
     2 Power[3 (1 - nu^2), (4)^-1] Sqrt[R/hs] tc/hs k2d*
      Cos[nfy] - (2 - nu));
a20 = (p*r)/(2.0*k21)*Cot[nfy];
Solve[{a11 x + a12 y == a10, a21 x + a22 y == a20}, {x, y}]
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