114 FUNDAMENTAL SOLUTIONS
Assume now that the boundary conditions for our problem are,
atx = 0->w = 0
atx=l->w=l
Equation (f) can be written at the two points as,
q
0
B cos
1
+ (q
x
- l)e"
1/2
[A sin (^3/2) + B cos (^3/2)] = q*
r- r- (h)
^
0
e"
1/2
[i4sin(
N
/3/2) + Bcos(
N
/3/2)] + (g
1
-l)Bcosl = q[
where
+
q* =
-j—
= -^e
x/2
A sin l^z-x
)
+ £cos(^—x
dx * V 2 / V 2
_|_
e
x/2 A jv__
COS
I
->L_
x
) _
[^cos(-^x)
RV3 . Λ/3
ß
T-
sin
V
x
(i)
4.9 EXPLICIT FORMS FOR THE FUNDAMENTAL SOLUTION
In this section we present some explicit forms for the fundamental
solution for some commonly occurring problems. These are pre-
sented in Table 4.1.
We have reverted to the simpler notation for the delta function
explained in Chapter 2 and have taken our source point to be at the
origin by a simple coordinate transformation.
The Mindlin solution is given in Section 4.6.