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Section 1
1-21
Complete quadratic assumed stress distribution:
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎛
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−−−−−
=
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎝
⎛
τ
σ
σ
10
3
2
1
22
2
2
xy
y
x
a
a
a
a
xyxy21x000y0
xy20y0yx1000
0xy2x0000yx1
M
a
1
through a
10
= constants of stress polynomials.
The following quadratic stress distribution is assumed for plate
bending action:
M
X
Y
Z
M
M
M
M
M
M
Q
Q
Q
Q
x
y
xy
yx
x
y
yx
x
x
y
y
M
xy
Figure 1.15
Complete quadratic assumed stress distribution:
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎛
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
−
−
−−
=
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎛
13
3
2
1
2
2
y
x
xy
y
x
a
a
a
a
yx0y010100000
x0yx100000010
xy00xyyx1000000
yxy00000yx1000
00xyx000000yx1
Q
Q
M
M
M
M
M
a
1
through a
13
= constants of stress polynomials.