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Using superposition of the stress field (8.4.15) given in Example 8.7, show that the problem of equal

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Using superposition of the stress field (8.4.15) given in Example 8.7, show that the problem of equal biaxial tension loading on a stress-free hole as shown in the figure is given by Eq. (8.4.9).

T T T T

Equation 8.4.15

Or T - 1 (1 - ) + 7 (1+34 - 44) T T ** = (1+)-(1+34) 08 20 de cos --7(1-34+24) sin Tre= T cos 20 sin 20

Equation 8.4.9

- T(1-1). or = T de T1+-

Data from example 8.7

Consider now an infinite medium with a circular stress-free hole subjected to a uniform far-field tension in

T a X T

where the far-field conditions have been determined using the transformation laws established in Exercise 3.3

The stresses corresponding to this Airy function are 0,= a3 (1+2 log r) +2a2- de a3(3+2 log r) + 2a2 a1 +9/17

aT 2 2a2 + 2a21 + a2 2021 2021 6a23 4024 + a 2024 a T 4 6023 4 a T == 2 T 2a2 2 This system is easily solved

T * = (1-7)+7 (1+4 44) cus 28 2 T *-(+)-(+)006 20 7) de = T T Tro = 1+ 3a T - 7(1-34 +24) s sin 20 cos

150, 180 210 120 240 90 3 2 270 60 (a,0)/T -1.30 -(a,0)/T 10 300 330Dimensionless Stress,/T 32 2.8 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 2 3 4 6 Dimensionless Distance, rla 5 7 8 9 10

Transcribed Image Text:

T T T T

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