For the axisymmetric problem of Example 8.6, explicitly develop the displacement solution given by relation (8.4.5). Data

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For the axisymmetric problem of Example 8.6, explicitly develop the displacement solution given by relation (8.4.5).

Data from example 8.6

The first example to be investigated involves a hollow thick-walled cylinder under the action of uniform

1/2

Applying the boundary conditions () = P, 0(1) = p2 creates two equations for the two unknown constants A and

From plane strain theory, the out-of-plane longitudinal stress is given by ripi - rp2 22-1 U = 0 = v(or -08)

For the case of only internal pressure (p = 0 and p = p) with rj/r = 0.5, the nondimensional stress

Equation 8.4.5

=  + vr [(1 - 2v) B- Up  1+v (P2 - P1) - 1 + - | =] E  1) 12 + (1-20)  - 132, r (8.4.5)


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