Numerically generate and plot the fields of stress ( r , ) and displacement (u

Numerically generate and plot the fields of stress (σ_r, σ_θ) and displacement (u_r) within the composite cylinder of Exercise 8.20 for the specific case with material (1) = steel and material (2) = aluminum. Use Table 4.2 for elastic moduli values. Explore and discuss the continuity issues for these field quantities at the interface r = r₁.

Table 4.2

Data from exercise 8.20

A long composite cylinder is subjected to the external pressure loading as shown in the following figure. Assuming idealized perfect bonding between the two materials, the normal stress and displacement will be continuous across the interface r = r₁ (see Section 5.2). Under these conditions, determine the stress and displacement fields in each material.

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Table 4.2 Typical values of elastic moduli for common engineering materials. (GPa) (GPa) k(GPa) Aluminum Concrete Copper Glass Nylon Rubber Steel E(GPa) 68.9 27.6 89.6 68.9 28.3 0.0019 207 P 0.34 0.20 0.34 0.25 0.40 0.499 0.29 25.7 11.5 33.4 27.6 10.1 0.654 x 10-3 80.2 54.6 7.7 71 27.6 4.04 0.326 111 71.8 15.3 93.3 45.9 47.2 0.326 164 a(10-6PC) 25.5 11 18 8.8 102 200 13.5