Exemplo -- Sage

import numpy as np from math import pow def grelha(EI, GJt, L, angle): alpha = np.radians(angle) kl = np.zeros((6,6)) T = np.zeros((6,6)) kl[0,0] = 12.0*EI/pow(L,3) kl[1,0] = 0.0 kl[2,0] = -6.0*EI/pow(L,2) kl[3,0] = -12.0*EI/pow(L,3) kl[4,0] = 0.0 kl[5,0] = -6.0*EI/pow(L,2) kl[0,1] = 0.0 kl[1,1] = GJt/L kl[2,1] = 0.0 kl[3,1] = 0.0 kl[4,1] = -GJt/L kl[5,1] = 0.0 kl[0,2] = -6.0*EI/pow(L,2) kl[1,2] = 0.0 kl[2,2] = 4.0*EI/L kl[3,2] = 6.0*EI/pow(L,2) kl[4,2] = 0.0 kl[5,2] = 2.0*EI/L kl[0,3] = -12.0*EI/pow(L,3) kl[1,3] = 0.0 kl[2,3] = 6.0*EI/pow(L,2) kl[3,3] = 12.0*EI/pow(L,3) kl[4,3] = 0.0 kl[5,3] = 6.0*EI/pow(L,2) kl[0,4] = 0.0 kl[1,4] = -GJt/L kl[2,4] = 0.0 kl[3,4] = 0.0 kl[4,4] = GJt/L kl[5,4] = 0.0 kl[0,5] = -6.0*EI/pow(L,2) kl[1,5] = 0.0 kl[2,5] = 2.0*EI/L kl[3,5] = 6.0*EI/pow(L,2) kl[4,5] = 0.0 kl[5,5] = 4.0*EI/L T[0,0] = 1.0 T[1,1] = np.cos(alpha) T[1,2] = np.sin(alpha) T[2,1] = -np.sin(alpha) T[2,2] = np.cos(alpha) T[3,3] = 1.0 T[4,4] = np.cos(alpha) T[4,5] = np.sin(alpha) T[5,4] = -np.sin(alpha) T[5,5] = np.cos(alpha) kg = np.dot(np.dot(T.T,kl),T) return kl, T, kg

K=grelha(100e3,20e3,4,45)

K

(array([[  18750.,       0.,  -37500.,  -18750.,       0.,  -37500.],
       [      0.,    5000.,       0.,       0.,   -5000.,       0.],
       [ -37500.,       0.,  100000.,   37500.,       0.,   50000.],
       [ -18750.,       0.,   37500.,   18750.,       0.,   37500.],
       [      0.,   -5000.,       0.,       0.,    5000.,       0.],
       [ -37500.,       0.,   50000.,   37500.,       0.,  100000.]]),
array([[ 1.        ,  0.        ,  0.        ,  0.        ,  0.        ,
         0.        ],
       [ 0.        ,  0.70710678,  0.70710678,  0.        ,  0.        ,
         0.        ],
       [ 0.        , -0.70710678,  0.70710678,  0.        ,  0.        ,
         0.        ],
       [ 0.        ,  0.        ,  0.        ,  1.        ,  0.        ,
         0.        ],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.70710678,
         0.70710678],
       [ 0.        ,  0.        ,  0.        ,  0.        , -0.70710678,
         0.70710678]]), array([[ 18750.       ,  26516.5042945,
-26516.5042945, -18750.       ,
         26516.5042945, -26516.5042945],
       [ 26516.5042945,  52500.       , -47500.       , -26516.5042945,
         22500.       , -27500.       ],
       [-26516.5042945, -47500.       ,  52500.       ,  26516.5042945,
        -27500.       ,  22500.       ],
       [-18750.       , -26516.5042945,  26516.5042945,  18750.       ,
        -26516.5042945,  26516.5042945],
       [ 26516.5042945,  22500.       , -27500.       , -26516.5042945,
         52500.       , -47500.       ],
       [-26516.5042945, -27500.       ,  22500.       ,  26516.5042945,
        -47500.       ,  52500.       ]]))

(array([[  18750.,       0.,  -37500.,  -18750.,       0.,  -37500.],
       [      0.,    5000.,       0.,       0.,   -5000.,       0.],
       [ -37500.,       0.,  100000.,   37500.,       0.,   50000.],
       [ -18750.,       0.,   37500.,   18750.,       0.,   37500.],
       [      0.,   -5000.,       0.,       0.,    5000.,       0.],
       [ -37500.,       0.,   50000.,   37500.,       0.,  100000.]]), array([[ 1.        ,  0.        ,  0.        ,  0.        ,  0.        ,
         0.        ],
       [ 0.        ,  0.70710678,  0.70710678,  0.        ,  0.        ,
         0.        ],
       [ 0.        , -0.70710678,  0.70710678,  0.        ,  0.        ,
         0.        ],
       [ 0.        ,  0.        ,  0.        ,  1.        ,  0.        ,
         0.        ],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.70710678,
         0.70710678],
       [ 0.        ,  0.        ,  0.        ,  0.        , -0.70710678,
         0.70710678]]), array([[ 18750.       ,  26516.5042945, -26516.5042945, -18750.       ,
         26516.5042945, -26516.5042945],
       [ 26516.5042945,  52500.       , -47500.       , -26516.5042945,
         22500.       , -27500.       ],
       [-26516.5042945, -47500.       ,  52500.       ,  26516.5042945,
        -27500.       ,  22500.       ],
       [-18750.       , -26516.5042945,  26516.5042945,  18750.       ,
        -26516.5042945,  26516.5042945],
       [ 26516.5042945,  22500.       , -27500.       , -26516.5042945,
         52500.       , -47500.       ],
       [-26516.5042945, -27500.       ,  22500.       ,  26516.5042945,
        -47500.       ,  52500.       ]]))

Exemplo

434 days ago by jmcastro