Following procedures similar to those for the homogeneous problem (see Section 8.4.1), develop the following stress field

Question:

Following procedures similar to those for the homogeneous problem (see Section 8.4.1), develop the following stress field for a pressurized hole in an infinite nonhomogeneous medium with moduli variation given by (14.2.3)

Or-Pil = -Pi() 00 Te (2+k-n)/2 2-kv-nv k+n-2v Pi- (2+k-n)/2

Plot the dimensionless stress fields for this case using the same parameters n and n used in Figs. 14.7 and 14.8.

Data from section 8.4.1

Consider the problem of a hole under uniform pressure in an infinite medium, as shown in Fig. 8.10. The

Dimensionless Stress 2 1.5 0.5H 0 -0.5 -1 0.5 0.6 og/p or/p 1/2=0.5 0.7 0.8 Dimensionless Distance, r/r 0.9 1

image

Although both the stress and displacement fields decrease to zero as  , there is a fundamental difference in

Equation 14.2.3

n E(r) = E. (-)"

Fig 14.7

Dimensionless Stress, a, lp 0.1 0 -0.1- -0.2- -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 n = 0 (Homogeneous Case) 1.5

Fig 14.8

Dimensionless Stress, P 0.8 0.6 0.4 0.2 n = 0 (Homogeneous Case) n = 1/2 1.5 n=1 2 n = 2 2.5 3 Distance, r/a

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question
Question Posted: