AIRY STRESS FUNCTION FOR TWO DIMENSIONAL INCLUSION ...

dislocation which does not exist in this case as it is an elastic plate and
σ x
∞ ∞ ∞ ∞
= S ,σ = σ = τ = 0 .
ψ ** ( z ) , we get
y z xy
Figure 3-2 Infinite Plate with a Hole Subjected to Tensile Loading.
Substituting the power series for the arbitrary analytic functionsγ ** ( z) and
∞
S −n
γ ( z)
= z + ∑ an z ,
4
∞
S −n
ψ ( z)
= − z + ∑ bnz .
2
The number of terms to be taken into consideration for the summation is
determined by the boundary condition. Therefore, taking the first three terms for the
above condition, we get
20
n=
1
n=
1
Sz a1
a2
a3
γ ( z)
= + + 2 + 3 ,
4 z z z
Sz b b b
ψ ( z)
= .
z z z
− 1 2 3
+ + 2 + 3
2
Integrating the second potential function, we can obtain χ (z) as:
Y
a
X
S
(3.2.1)