Consider two long cylinders of two different materials where one cylinder just fits inside the other. The inner radius of the inner cylinder is a, and its outer radius is b. The inner radius of the outer cylinder is also b, and its outer radius is c. The Young's modu- lus and Poisson ratio of the inner cylinder are E₁ and v₁, respectively, and those of the outer cylinder are E2 and v2, respectively. The radial stress σ, hoop stress or, and radi- al displacement u, are given, respectively, by, A σm(r) = + B₁ σου (1) = A + B₁ i=1,2 -(1 + v) u, (r) (1-v) A, + rB rE E₁ (a) where i = 1 refers to the inner cylinder and i = 2 to the outer cylinder. If the outer surface of the outer cylinder is subjected to a compressive radial dis- placement U, and the inner surface of the inner cylinder has no radial stress, then the following four boundary conditions can be used to determine A, and B, i = 1,2: σm(a) = 0 σm(b) =σ(b) u1(b) = u(b) u2(c)=-U。 (b) Substituting Eqs. (a) into (b), the following system of equations in matrix form is obtained: 1 a² 0 0 A₁ 0 b² -1 -b² B₁ 0 (1+2) E/E₂ B₁₂ -UE₂c -(1+) (1)b² 0 -(1 +12) Determine the hoop stress in the V₁ =v2 0.4, E₁ =2.1 x 10° N/m², E2 b = 6.4 mm, and c = 8 mm (Answer: -1.179 x 10' N/m²) -(1-2)bE/E2A2 (1-v2)c² inner and outer cylinders at rb when 0.21 x 10° N/m², U, 0.25 mm, a 5 mm, 1(b) = -6.301 x 10' N/m² and σ2(b) = Write a MATLAB script that determines the hoop stresses and states the results in command window.