§5-2 Complex-variable representation of stress and displacement One Complex-variable representation of stress component According to the relation between stress component and stress function, t O2 2 Ox 2 =一 Oxo 21
21 §5-2 Complex-variable representation of stress and displacement According to the relation between stress component and stress function, x y x y xy y x = − = = 2 2 2 2 2 One Complex-variable representation of stress component
§5-2应力和位移的复变函数表示 应力分量的复变函数表示 根据应力分量和应力函数的关系 2 ax 2 Oxo 22
22 §5-2 应力和位移的复变函数表示 根据应力分量和应力函数的关系 x y x y xy y x = − = = 2 2 2 2 2 一 应力分量的复变函数表示
We find Complex-variable representation of stress compone nt y R+ + 2 2 aza for p=(E0(=)+z0()+x()+()) 2 yields +0,=20()+(2)=4Re0 hence. for
23 We find Complex-variable representation of stress component, y x z z x y = + + = 2 4 2 2 2 2 ( ( ) ( ) ( ) ( )) 2 1 = z z + z z + z + z for 2[ '(z) '(z)] 4Re '(z) x + y = + = yields hence, for
可得到应力分量的复变函数表示 y R+ + 2 2 aza 由 p=(E0()+-0()+(2)+() 2 可得 0+=20(x)+y(x)=4Reg() 而由 24
24 可得到应力分量的复变函数表示 y x z z x y = + + = 2 4 2 2 2 2 ( ( ) ( ) ( ) ( )) 2 1 = z z + z z + z + z 由 2[ '(z) '(z)] 4Re '(z) x + y = + = 可得 而由
:-0.+2iT 02b r-21 2 Oy- Okay 0.0 i|φ ax a 2 z yeds,x+21=220"(2)+x(z) or yx+2ry=2[0"(2)+v(z) 25
25 22 4 i 2 2i 22 22 2i 2 zx y x y x y y x xy = − = − − − + = 2i 2[z ''( z ) ''( z)] yields y − x + xy = + 2i 2[z ''( z ) '( z)] or y − x + xy = +