5. 点Dのy方向変位
x
y
B
CD
dx
dy
A
v(x, y)
A (x, y)
u(x, y)
A’(x+u(x, y), y+v(x, y))
B’
A’
C’
D’
y’
x’
D (x, y+dy)
v (x, y+dy) D’’
D’’(x+u(x, y),
y+dy+v(x, y+dy))
5/13
6. y軸方向の垂直ひずみ
DAD’’A’ −
DA
εy =
=
D’’A’ = −
DA = dy
(y+dy+v(x, y+dy)) (y+v(x, y))
εy =
dy
v(x, y+dy) − v(x, y)
= ∂
∂
y
v(x, y)
dy → 0
6/13
v(x, y+dy) − v(x, y) +dy
11. 3次元空間の変位とひずみの関係
変位ベクトル:
u
v
w
垂直ひずみ
εx = ∂
∂
x
u(x, y, z)
εy = ∂
∂
y
v(x, y, z)
εz = ∂
∂
z
w(x, y, z)
せん断ひずみ
γxy = +
∂
∂
x
v(x, y, z)
∂
∂
y
u(x, y, z)
γzx = +
∂
∂
x
w(x, y, z)
∂
∂
z
u(x, y, z)
γyz = +
∂
∂
y
w(x, y, z)
∂
∂
z
v(x, y, z)
11/13