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Copy pathglobal_load_vector_uniform_largedef.py
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global_load_vector_uniform_largedef.py
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import numpy as np
import time
from geomdl import exchange
import surface_geom_SEM as sgs
import element_stiff_matrix_small as esmsml
import global_stiff_matrix_small as gsmsml
# For test
# uniform_load_x = 0
# uniform_load_y = 0
# uniform_load_z = 1
def shape_function_2d(lobatto_pw, xi1, xi2):
"""
In this function the matrix N_2D in
(u1, u2, u3) = N_2D (u1_node, u2_node, u3_node, β1, β2) at each
integration point xi1 and xi2 is claculated.
The conincidence of integration and nodal points is included to make
the generation of N_2D fast.
-Output
a 3x3, 5 * len**
"""
len = lobatto_pw.shape[0]
shp_func = np.zeros((3, 5 * len**2))
xi1_index = np.where(lobatto_pw == xi1)[0]
xi2_index = np.where(lobatto_pw == xi2)[0]
n_index = 5 * (xi2_index[0]*len + xi1_index[0])
shp_func[0, n_index] = 1
shp_func[1, n_index + 1] = 1
shp_func[2, n_index + 2] = 1
return shp_func
def shape_function_2d_general(lobatto_pw, lag_xi1, lag_xi2): #in a case that xi1 and xi2 are not coincided with SEM nodes
len = lobatto_pw.shape[0]
shp_func = np.zeros((3, 5 * len**2))
len = lobatto_pw.shape[0]
num = 0
for i in range(len):
for j in range(len):
shp_func[:, num:num+5] = np.array([[lag_xi1[j] * lag_xi2[i], 0, 0, 0, 0],
[0, lag_xi1[j] * lag_xi2[i], 0, 0, 0],\
[0, 0, lag_xi1[j] * lag_xi2[i], 0, 0]])
num += 5
return shp_func
def element_load_vector(lobatto_pw, elem_jacobian_all,\
uniform_load_x, uniform_load_y, uniform_load_z):
'''
-Output:
Element load vector which is a numpy 1D array.
'''
len = lobatto_pw.shape[0]
elem_load_v = np.zeros(5 * len**2) # 5 DOF at each node
for i in range(len):
# print(i, '\n')
xi2 = lobatto_pw[i, 0]
w2 = lobatto_pw[i, 1]
for j in range(len):
xi1 = lobatto_pw[j, 0]
w1 = lobatto_pw[j, 1]
jac_mtx = elem_jacobian_all[i, j]
# print("jac2 and w1 and w2 is", jac2,' ',w1,' ',w2, '\n')
elem_load_v_var =\
np.transpose(shape_function_2d(lobatto_pw, xi1, xi2))\
@ np.transpose((uniform_load_x, uniform_load_y, uniform_load_z))
elem_load_v = elem_load_v + elem_load_v_var *\
np.linalg.det(jac_mtx) * w1 * w2
return elem_load_v
def global_load_vector(lobatto_pw, jacobian_all, element_boundaries_u, element_boundaries_v,\
uniform_load_x, uniform_load_y, uniform_load_z):
number_element_u = len(element_boundaries_u) - 1
number_element_v = len(element_boundaries_v) - 1
number_lobatto_node = lobatto_pw.shape[0]
number_node_one_row = number_element_u*(number_lobatto_node - 1) + 1
node_global_3 = number_element_v * (number_lobatto_node-1) * number_node_one_row +\
number_node_one_row #This is the node equal to u = v = 1 in IGA parametric space
global_load_v = np.zeros((5*node_global_3))
for i_main in range(number_element_v):
for j_main in range(number_element_u):
# print('row {} out of {}'.format(i_main, number_element_v-1))
# node_1_u = element_boundaries_u[j_main]
# node_1_v = element_boundaries_v[i_main]
# node_3_u = element_boundaries_u[j_main+1]
# node_3_v = element_boundaries_v[i_main+1]
elem_jacobian_all = jacobian_all[i_main, j_main]
elem_load_v = element_load_vector( lobatto_pw, elem_jacobian_all,\
uniform_load_x, uniform_load_y, uniform_load_z)
# print('element load vector is : ', elem_load_v,'\n')
node_1_number = i_main * (number_lobatto_node - 1) * number_node_one_row +\
j_main * (number_lobatto_node - 1) + 1
# node_2_number = i_main * (number_lobatto_node-1) * number_node_one_row +\
# (j_main+1) * (number_lobatto_node-1) + 1
# node_3_number = node_1_number + (number_lobatto_node-1) * number_node_one_row
# node_4_number = node_2_number + (number_lobatto_node-1) * number_node_one_row
number_dof_element = 5 * number_lobatto_node**2
connectivity = np.zeros(number_dof_element)
p = 0
for i in range(number_lobatto_node):
for j in range(number_lobatto_node):
h = 5*i*number_lobatto_node + 5*j
connectivity[h] = (5*(node_1_number + p + j) - 5)
connectivity[h+1] = (5*(node_1_number + p + j) - 4)
connectivity[h+2] = (5*(node_1_number + p + j) - 3)
connectivity[h+3] = (5*(node_1_number + p + j) - 2)
connectivity[h+4] = (5*(node_1_number + p + j) - 1)
p = p + number_node_one_row
connectivity = connectivity.astype(int)
for i in range(number_dof_element):
global_load_v[connectivity[i]] = \
global_load_v[connectivity[i]] + elem_load_v[i]
return global_load_v
def load_vector_bc_applied(load_vector, bc):
load_v = np.delete(load_vector, bc, 0)
return load_v
# def element_load_vector(surface, lobatto_pw, uniform_load_x, uniform_load_y,\
# uniform_load_z, node_1_u, node_1_v, node_3_u,\
# node_3_v):
# '''
# -Output:
# Element load vector which is a numpy 1D array.
# '''
# len = lobatto_pw.shape[0]
# jac1_mtx = np.array(np.array([[(node_3_u - node_1_u)/2, 0],\
# [0, (node_3_v - node_1_v)/2]]))
# # xi1 = 0.5
# # xi2 = 0.0
# # second_surf_der = surface.derivatives(xi1, xi2, order=2)
# # ders = surface.ders_uvt(0, second_surf_der)
# # vector_1 = ders[0,:]
# # vector_2 = ders[1,:]
# # jac2 = np.linalg.norm((np.cross(vector_1,vector_2)))
# # print("jac2 is", jac2, '\n')
# elem_load_v = np.zeros(5 * len**2) # 5 DOF at each node
# for i in range(len):
# # print(i, '\n')
# xi2 = lobatto_pw[i, 0]
# w2 = lobatto_pw[i, 1]
# for j in range(len):
# xi1 = lobatto_pw[j, 0]
# w1 = lobatto_pw[j, 1]
# uv_var = esmsml.xi_to_uv(xi1, xi2, node_1_u,\
# node_1_v, node_3_u, node_3_v)
# # print(surfs.physical_crd(uv_var[0], uv_var[1]))
# second_surf_der = surface.derivatives(uv_var[0], uv_var[1], order=2)
# ders = surface.ders_uvt(0, second_surf_der)
# vector_1 = ders[0,:]
# vector_2 = ders[1,:]
# jac2 = np.linalg.norm((np.cross(vector_1,vector_2)))
# # print("jac2 and w1 and w2 is", jac2,' ',w1,' ',w2, '\n')
# elem_load_v_var =\
# np.transpose(shape_function_2d(lobatto_pw, xi1, xi2))\
# @ np.transpose((uniform_load_x, uniform_load_y, uniform_load_z))
# elem_load_v = elem_load_v + elem_load_v_var *\
# np.linalg.det(jac1_mtx) * jac2 * \
# w1 * w2
# return elem_load_v
# def global_load_vector(surface, lobatto_pw, element_boundaries_u, element_boundaries_v,\
# uniform_load_x, uniform_load_y, uniform_load_z):
# number_element_u = len(element_boundaries_u) - 1
# number_element_v = len(element_boundaries_v) - 1
# number_lobatto_node = lobatto_pw.shape[0]
# number_node_one_row = number_element_u*(number_lobatto_node - 1) + 1
# node_global_3 = number_element_v * (number_lobatto_node-1) * number_node_one_row +\
# number_node_one_row #This is the node equal to u = v = 1 in IGA parametric space
# global_load_v = np.zeros((5*node_global_3))
# for i_main in range(number_element_v):
# for j_main in range(number_element_u):
# # print('row {} out of {}'.format(i_main, number_element_v-1))
# node_1_u = element_boundaries_u[j_main]
# node_1_v = element_boundaries_v[i_main]
# node_3_u = element_boundaries_u[j_main+1]
# node_3_v = element_boundaries_v[i_main+1]
# elem_load_v = element_load_vector(surface, lobatto_pw, \
# uniform_load_x, uniform_load_y,\
# uniform_load_z, node_1_u, node_1_v,\
# node_3_u, node_3_v)
# # print('element load vector is : ', elem_load_v,'\n')
# node_1_number = i_main * (number_lobatto_node-1) * number_node_one_row +\
# j_main * (number_lobatto_node-1) + 1
# # node_2_number = i_main * (number_lobatto_node-1) * number_node_one_row +\
# # (j_main+1) * (number_lobatto_node-1) + 1
# # node_3_number = node_1_number + (number_lobatto_node-1) * number_node_one_row
# # node_4_number = node_2_number + (number_lobatto_node-1) * number_node_one_row
# number_dof_element = 5*number_lobatto_node**2
# connectivity = np.zeros(number_dof_element)
# p = 0
# for i in range(number_lobatto_node):
# for j in range(number_lobatto_node):
# h = 5*i*number_lobatto_node + 5*j
# connectivity[h] = (5*(node_1_number + p + j) - 5)
# connectivity[h+1] = (5*(node_1_number + p + j) - 4)
# connectivity[h+2] = (5*(node_1_number + p + j) - 3)
# connectivity[h+3] = (5*(node_1_number + p + j) - 2)
# connectivity[h+4] = (5*(node_1_number + p + j) - 1)
# p = p + number_node_one_row
# connectivity = connectivity.astype(int)
# for i in range(number_dof_element):
# global_load_v[connectivity[i]] = \
# global_load_v[connectivity[i]] + elem_load_v[i]
# return global_load_v
if __name__ == '__main__':
lobatto_pw = esmsml.lbto_pw("node_weight.dat")
# lag_xi1 = esm.lagfunc(lobatto_pw, lobatto_pw[1, 0])
# lag_xi2 = esm.lagfunc(lobatto_pw, lobatto_pw[2, 0])
# sh1 = shape_function_2d(lobatto_pw, lobatto_pw[1, 0], lobatto_pw[2, 0])[0]
# sh2 = shape_function_2d(lobatto_pw, lobatto_pw[1, 0], lobatto_pw[2, 0])[0]
data = exchange.import_json("pinched_shell.json") # pinched_shell_kninsertion_changedeg.json pinched_shell.json pinched_shell_half.json rectangle_cantilever square square_kninsertion generic_shell_kninsertion foursided_curved_kninsertion foursided_curved_kninsertion2 rectangle_kninsertion
# gsm.visualization(data)
surfs = sgs.SurfaceGeo(data, 0, 3)
# load = element_load_vector(surfs, lobatto_pw, 0, 0,\
# 10, 0, 0, 1,\
# 1)
bc_h_bott = [1, 0, 1, 0, 1] #pinched shell. zero means clamped DOF
bc_h_top = [0, 1, 0, 1, 0]
bc_v_left = [1, 1, 0, 1, 0]
bc_v_right = [0, 1, 1, 1, 0]
time1 = time.time()
u_manual = [0, 0.5, 1]
v_manual = [0, 1]
mesh = gsmsml.mesh_func(surfs, u_manual, v_manual)
# mesh = gsm.mesh_func(surfs)
element_boundaries_u = mesh[0]
element_boundaries_v = mesh[1]
bc1 = gsmsml.global_boundary_condition(lobatto_pw, bc_h_bott, bc_h_top,\
bc_v_left, bc_v_right, element_boundaries_u,\
element_boundaries_v)
global_load = global_load_vector(surfs, lobatto_pw, element_boundaries_u, element_boundaries_v)
print(global_load)
print("End")