- , (. 1.10). 1, 2
. , C - .
C Rc Mc (. 1.10).
. Rc Mc Cxyz, .
:
( 1, 2, R, Mc) ~ 0
:
å C = 0; å U = 0; å Z = 0; å Mx = 0; å My = 0; å Mz = 0,
.
:
Qx = - Rcx = å Ci; Mx = å Mx (Ri); ü
Qy = - Rcy = å Ui ; My = å My (Ri); ý (1.1)
Nz = Rcz = - å Zi; Mz = - å Mz (Ri). þ
:
Qx, Qy - ;
Nz - ;
Mx, My - ;
Mz - .
(1.1), F:
Qx = t zxdF; Mx = - s z × ydF; Qy = t zydF; My = - s z × xdF; Nz = s z dF; Mz = (t zx y - t zy x) dF. |
(1.2)
, (1.2) , . , (1.1) .
- (), .
1. () , Nz ¹ 0, . , () , (. 1.11).
2. , Mx ( My). , (. 1.11).
3. , Qy ¹ 0, Mx ¹ 0, . , , , (. 1.11).
.
:
1. - . .
|
|
2. , , , , Nz , (1.11).
2.
2.1.
. F .
(. 1.11). s z, Nz = .
, F, :
Nz = s z dF = s z × F,
:
s z = Nz / F (2.1)
. : s z > 0, Nz > 0; s z < 0, Nz < 0.
. l , l +D l, D l - .
e = D l/l. (2.2)
. : D l > 0, e > 0; : D l < 0, e < 0.
Nz . , . (2.2) .
, (2.2) , .
A (x, y, z) - '.
AA' (u, v, w) .
x, y, z.
l Oxyz, , , Oyz , z .
, , z (. 2.1).
, z, , AA'. , : w (0) = 0, w (z) = AA ¢, w (l) = D l (.2.1).
z z+ D z . w (z +D z) = w (z) + D w, , w (z) D w (. 2.1). , D z, (2.2) . (2.2) D l = D w, l = D z , z:
|
|
e z = . (2.3)
, w (z) e z (z), e z (2.3) w:
e zdz,
w (z) = w 0 + e zdz. (2.4)