Компьютерная обработка информации (в пакете MathCAD). Мартьянова А.Е. - 99 стр.

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Мартьянова А.Е. Компьютерная обработка информации
99
Расчет нормальной силы
Nx() E
h
R
⋅ e
kx⋅
C1 sin k x⋅()⋅ C2 cos k x⋅()⋅+()⋅ e
k− x⋅
C3 sin k x⋅()⋅ C4 cos k x⋅()⋅+()⋅+
γ
Lx−()R
2
⋅
Eh⋅
⋅+
...
⎡
⎢
⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎦
⋅:=
Расчет угла поворота оболочки
φ x( ) k exp k x⋅()⋅ C1 sin k x⋅()⋅ C2 cos k x⋅()⋅+()⋅
exp k x⋅( ) C1 cos k x⋅()⋅ k⋅ C2 sin k x⋅()⋅ k⋅−()⋅+
...
k− exp k− x⋅()⋅ C3 sin k x⋅()⋅ C4 cos k x⋅()⋅+()⋅+
...
exp k− x⋅( ) C3 cos k x⋅()⋅ k⋅ C4 sin k x⋅()⋅ k⋅−()⋅
γ R
2
⋅
Eh⋅()
−+
...
⎡
⎢
⎢
⎢
⎢
⎣
⎤
⎥
⎥
⎥
⎥
⎦
:=
Расчет изгибающего момента
Mx() 2− D⋅ k
2
⋅ exp k x⋅()⋅ C1⋅ cos k x⋅()⋅ 2D⋅ k
2
⋅ exp k x⋅()⋅ C2⋅ sin k x⋅()⋅+
2D⋅ k
2
⋅ exp k− x⋅()⋅ C3⋅ cos k x⋅()⋅ 2D⋅ k
2
⋅ exp k− x⋅()⋅ C4⋅ sin k x⋅()⋅−+
...
⎛
⎜
⎝
⎞
⎠
:=
Расчет поперечной силы
Qx() 2D⋅ k
3
⋅ exp k x⋅()⋅ C1⋅ sin k x⋅()⋅ 2D⋅ k
3
⋅ exp k x⋅()⋅ C1⋅ cos k x⋅()⋅−
2− D⋅ k
3
⋅ exp k− x⋅()⋅ C3⋅ cos k x⋅()⋅+
...
2D⋅ k
3
⋅ exp k x⋅()⋅ C2⋅ sin k x⋅()⋅ 2D⋅ k
3
⋅ exp k− x⋅()⋅ C3⋅ sin k x⋅()⋅−+
...
2− D⋅ k
3
⋅ exp k− x⋅()⋅ C4⋅ cos k x⋅()⋅+
...
2D⋅ k
3
⋅ exp k− x⋅()⋅ C4⋅ sin k x⋅()⋅ 2D⋅ k
3
⋅ exp k x⋅()⋅ C2⋅ cos k x⋅()⋅++
...
⎛
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎠
:=
Численное решение краевой задачи для ОДУ IV порядка
4
x
ω
d
d
4
E
h
DR
2
⋅
⋅ω⋅+
q
D
Краевые (граничные) условия
ω 0() 0
Mx L() D−
2
x
ω L()
d
d
2
⋅ 0
x
ω 0()
d
d
φ
0
Qx L() D−
3
x
ω L()
d
d
3
⋅ 0
Мартьянова А.Е. Компьютерная обработка информации                                                                        99

     Расчет нормальной силы
               h ⎡ k⋅ x                                              − k⋅ x
N ( x) := E⋅     ⋅ ⎢ e ⋅ ( C1⋅ sin ( k ⋅ x) + C2⋅ cos ( k ⋅ x) ) + e        ⋅ ( C3⋅ sin ( k ⋅ x) + C4⋅ cos ( k ⋅ x) ) ... ⎥⎤
               R                         2
                   ⎢        ( L − x) ⋅ R                                                                                  ⎥
                   ⎢⎣ + γ ⋅                                                                                               ⎥⎦
                                E⋅ h


     Расчет угла поворота оболочки

φ ( x) := ⎡ k ⋅ exp ( k ⋅ x) ⋅ ( C1⋅ sin ( k ⋅ x) + C2⋅ cos ( k ⋅ x) ) ...              ⎤
          ⎢ + exp ( k ⋅ x) ⋅ ( C1⋅ cos ( k ⋅ x) ⋅ k − C2⋅ sin ( k ⋅ x) ⋅ k) ...         ⎥
          ⎢ + −k ⋅ exp ( −k ⋅ x) ⋅ ( C3⋅ sin ( k ⋅ x) + C4⋅ cos ( k ⋅ x) ) ...          ⎥
           ⎢                                                                    γ⋅R
                                                                                      2 ⎥
           ⎢ + exp ( −k ⋅ x) ⋅ ( C3⋅ cos ( k ⋅ x) ⋅ k − C4⋅ sin ( k ⋅ x) ⋅ k) −         ⎥
           ⎣                                                                    ( E⋅ h) ⎦


     Расчет изгибающего момента

M( x) := ⎛ −2⋅ D⋅ k ⋅ exp ( k ⋅ x) ⋅ C1⋅ cos ( k ⋅ x) + 2⋅ D⋅ k ⋅ exp ( k ⋅ x) ⋅ C2⋅ sin ( k ⋅ x) ...   ⎞
                   2                                           2
            ⎜          2                                            2
            ⎝ + 2⋅ D⋅ k ⋅ exp ( −k ⋅ x) ⋅ C3⋅ cos ( k ⋅ x) − 2⋅ D⋅ k ⋅ exp ( −k ⋅ x) ⋅ C4⋅ sin ( k ⋅ x) ⎠

     Расчет поперечной силы

Q ( x) := ⎛ 2⋅ D⋅ k ⋅ exp ( k ⋅ x) ⋅ C1⋅ sin ( k ⋅ x) − 2⋅ D⋅ k ⋅ exp ( k ⋅ x) ⋅ C1⋅ cos ( k ⋅ x) ...        ⎞
                   3                                           3
           ⎜             3
           ⎜ + −2⋅ D⋅ k ⋅ exp ( −k ⋅ x) ⋅ C3⋅ cos ( k ⋅ x) ...                                               ⎟
           ⎜ + 2⋅ D⋅ k 3 ⋅ exp ( k ⋅ x) ⋅ C2⋅ sin ( k ⋅ x) − 2⋅ D⋅ k 3 ⋅ exp ( −k ⋅ x) ⋅ C3⋅ sin ( k ⋅ x) ...⎟
           ⎜ + −2⋅ D⋅ k 3 ⋅ exp ( −k ⋅ x) ⋅ C4⋅ cos ( k ⋅ x) ...                                             ⎟
           ⎜           3                                               3
           ⎝ + 2⋅ D⋅ k ⋅ exp ( −k ⋅ x) ⋅ C4⋅ sin ( k ⋅ x) + 2⋅ D⋅ k ⋅ exp ( k ⋅ x) ⋅ C2⋅ cos ( k ⋅ x) ⎠


            Численное решение краевой задачи для ОДУ IV порядка

                 d4                 h              q
                         ω + E⋅              ⋅ω
                     4                   2         D
                dx                D⋅ R
             Краевые (граничные) условия

                      ω ( 0)      0                                                           d2
                                                                       Mx( L)         −D⋅             ω ( L)     0
                                                                                                  2
                                                                                             dx
                      d                                                                      d3
                         ω ( 0)         φ     0                        Qx ( L)        −D⋅             ω ( L)     0
                      dx                                                                          3
                                                                                             dx

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