弹性力学数值方法：混合元法：有限元法基础.docx

import numpy as np

from scipy.sparse import lil_matrix

from scipy.sparse.linalg import spsolve

E = 200e9 #

nu = 0.3 #

#

return np.sum(u**2) + np.sum(s**2)

def solve_mixed_fem():

#

u = np.zeros((num_nodes, 2)) #

s = np.zeros((num_elements, 3)) #

#

grad_u = lil_matrix((num_nodes*2, num_nodes*2))

grad_s = lil_matrix((num_elements*3, num_elements*3))

#

K = lil_matrix((num_nodes*2 + num_elements*3, num_nodes*2 + num_elements*3))

K[:num_nodes*2, :num_nodes*2] = grad_u

K[num_nodes*2:, num_nodes*2:] = grad_s

#

#

K[0, :] = 0

K[1, :] = 0

K[0, 0] = 1

K[1, 1] = 1

s = x[num_nodes*2:].reshape((num_elements, 3))

return u, s

num_nodes = 10

num_elements = 5

u, s = solve_mixed_fem()