AbstractFirst, we calculate, in a heuristic manner, the Green function of an orthotropic plate in a half-plane which is clamped along the boundary. We then justify the solution and generalize our approach to operators of the form $$(Q(\partial ')-a^2\partial _n^2)(Q(\partial ')-b^2\partial _n^2)$$
(
Q
(
∂
′
)
-
a
2
∂
n
2
)
(
Q
(
∂
′
)
-
b
2
∂
n
2
)
(where $$\partial '=(\partial _1,\dots ,\partial _{n-1})$$
∂
′
=
(
∂
1
,
⋯
,
∂
n
-
1
)
and $$a>0,b>0,a\ne b)$$
a
>
0
,
b
>
0
,
a
≠
b
)
with respect to Dirichlet boundary conditions at $$x_n=0.$$
x
n
=
0
.
The Green function $$G_\xi $$
G
ξ
is represented by a linear combination of fundamental solutions $$E^c$$
E
c
of $$Q(\partial ')(Q(\partial ')-c^2\partial _n^2),$$
Q
(
∂
′
)
(
Q
(
∂
′
)
-
c
2
∂
n
2
)
,
$$c\in \{a,b\},$$
c
∈
{
a
,
b
}
,
that are shifted to the source point $$\xi ,$$
ξ
,
to the mirror point $$-\xi ,$$
-
ξ
,
and to the two additional points $$-\frac{a}{b}\xi $$
-
a
b
ξ
and $$-\frac{b}{a}\xi ,$$
-
b
a
ξ
,
respectively.
Stress analysis of a circular hole in an orthotropic plate with finite width using complex potential method
