Issue 41
Ch. F. Markides et alii, Frattura ed Integrità Strutturale, 41 (2017) 396-411; DOI: 10.3221/IGF-ESIS.41.51
In addition, with m =3,5,7,9,…, 2 2 1 m t
m
m
m
2
a
t
b
t
a
t
b
1
1
1
m
m
m
m
2
2
2
A
i
1
1
m
m
m
m
m
m
m
m
m
2
2
t
t
t
t
t
t
t
t
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
(12)
m
m
m
m
1
1
t
a
t
b
t
a
t
b
1 m
1
1
1
m
m
m
m
1
1
1
1
B
i
1
1
m
m
m
m
m
m
m
m
2
2
t
t
t
t
t
t
t
t
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
where
1
t
i
i
1
(13)
1,2
1,2
1,2
and , , m m m m a b a b are the real and imaginary parts of the following constants (as coefficients of the Fourier series representation of the boundary conditions on L ): ,
1
a b
sin 2 cos 2
o
o
P R
sin 4
1
3
o
i
2
c
o
6 i
o
e
sin 2
sin 2
o
o
2
2
4
2sin sin 4 2cos 2 sin 4 sin 2 cos4 2 3 o o o o o
3
2 i o
o
e
o
i
2
e
2
o
2sin
1 i
a b
o
sin 1 m
sin 1 m
o
P R
1
m
c
(14)
2
m m
m
2
1
1
o
2sin
m
o
1 o
1 cos 2 sin 1 m
2sin 2 cos
m
m
1 i m
o
o
o
1 cos
m e
2
m
4
1
1 c P R
sin 1 m
o
o
sin 1 m
1
m
5,7,...
2
i
m m
m
2
1
1
o
2sin
o
1 o
1 cos 2 sin 1 m
2sin 2 cos
m
m
i m
1 o
m e
o
o
1 cos
2
m
4
1
What is more, and again for m =3,5,7,9,…,
m
m
1
2
2
2
2
2
2
1,2 z R 1
1,2 1,2 z R 1 z
(15)
P z
z
1 ,2 1,2 m m
1,2
1,2
1,2
m
m
1 R i
1,2
Finally,
0 x
0
0 xy
1 1 b b Ri
1 1 a a R
1 1 a a Ri
1 1 b b R
(16)
,
,
y
indicate constant stresses throughout the disc cross-section [20], where the respective coefficients of Fourier series representation of the boundary conditions on L read as [14]:
2 i o
1
a b
2 sin 2
o
sin 2 cos 2
o
c P R
e
1
o
i
2
o
o
o
o
2 i
(17)
e
2
sin 2
sin 2
o
o
2
2
2
o
o
2sin
2sin
1
400
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