Consider an infinitely long hollow cylinder made of a homogeneous isotropic material, of radii R₁, R2, R₁ > R₂. Assume c

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Consider An Infinitely Long Hollow Cylinder Made Of A Homogeneous Isotropic Material Of Radii R R2 R R Assume C 1 (95.17 KiB) Viewed 41 times

Consider an infinitely long hollow cylinder made of a homogeneous isotropic material, of radii R₁, R2, R₁ > R₂. Assume cylindrical coordinates, with the z-axis parallel to the symmetry axis of the cylinder. The cylinder is subject to external and internal pressures P₁ and P₂ respectively. The free energy density is given by 2 K 2 F = == /14₁²³ + μ • (uz - 18un) ². Uij 2 d) Express σij as a function of Wij. e) State the boundary conditions for orr. f) Considering the symmetries of the system, integrate the force balance equation, . µV²u + (K + ! ) ▼ (▼ · u) + ƒ = 0. g) Use the displacement vector from part f) to compute the diagonal components of the stress tensor. h) Finally, use the boundary conditions of part e) to determine the integration con- stants.