def Dif_basic_F(S, Coords):
E = Element("Q4")
N = E.N()
G_map = E.G_map()
F = np.zeros((len(Coords), 1))
#print(F)
x_ip = [-np.sqrt(3) / 3, np.sqrt(3) / 3]
W_ip = [1, 1]
for i in range(len(x_ip)):
N_l = N(x_ip[i], x_ip[i]) #N local
N_T = np.transpose(N_l)
B, Jdet = G_map(x_ip[i], x_ip[i], Coords)
#print("N_T is ",N_T)
S_val = S(x_ip[i], x_ip[i])
#print(S_val)
F = F + N_T * S_val * Jdet * W_ip[i] * W_ip[i]
#print(F)
#reference file
file = open('../outputs/f_elemental.txt', 'w')
for i in range(4):
if i != 0:
file.write('\n')
file.write(str(F[i]))
file.write(" ")
file.close()
return F
def Dif_basic_K(Coords, k=1): #let k be an optional arguement
num_nodes = 4 # number of nodes
E = Element("Q4")
# K = np.zeros((num_nodes,num_nodes))
# Now to step through K_mat and integrate each element
Ke = np.zeros((len(Coords), len(Coords)))
x_ip = [-np.sqrt(3) / 3, np.sqrt(3) / 3]
W_ip = [1, 1]
for i in range(len(x_ip)):
for j in range(len(x_ip)): # now ready to integrate
G_m = E.G_map()
B, Jdet = G_m(x_ip[i], x_ip[j], Coords)
B_T = np.transpose(B)
Ke = Ke + B_T.dot(B) * k * Jdet * W_ip[i] * W_ip[j]
#print(Ke)
#Ke = Ke + ((np.transpose(B)) * k * B * Jdet * W_ip[i] * W_ip[j])
#Ke = Ke + (np.dot(np.transpose(B_val), k*B_val) * abs(J_d_val)*w_ip[i]*w_ip[j])
#file = open('../outputs/K_elemental.txt', 'w')
#for i in range(4):
# if i != 0:
# file.write('\n')
# for j in range(4):
# file.write(str(K[i, j]))
# file.write(" ")
#file.close()
return Ke
def calcStressStrainElemental(d, A, NodalCoord, Connectivity):
#calculate strains in center of element!
E = Element("Q4")
stress = np.zeros((3, len(Connectivity)))
strain = np.zeros((3, len(Connectivity)))
for e in range(0, len(Connectivity)):
Coord_mat_el = getElementCoordinates(e, NodalCoord, Connectivity)
Elemental_disp = getElementDisplacements(e, d, A)
gradN, detJ = E.G_map(0, 0, Coord_mat_el)
B = get_B_plane_stress(gradN)
strain[:, e] = np.dot(B, Elemental_disp)[:, 0]
stress[:, e] = strain[:, e]
return strain, stress
def ES_K(Coords):
num_nodes = 4 # number of nodes
E = Element("Q4")
# Now to step through K_mat and integrate each element
Ke = np.zeros((len(Coords), len(Coords)))
x_ip = [-np.sqrt(3) / 3, np.sqrt(3) / 3]
print(len(Coords))
W_ip = [1, 1]
for i in range(len(x_ip)):
for j in range(len(x_ip)): # now ready to integrate
G_m = E.G_map()
B, Jdet = G_m(x_ip[i], x_ip[j], Coords)
def getInternalForces(Coord_mat_el,sigma):
E = Element("Q4")
weights = [1, 1]
xIP = [-np.sqrt(3) / 3, np.sqrt(3) / 3]
fint_pre = np.zeros((1,8))
count = 0
for i in range(len(xIP)):
for j in range(len(xIP)):
gradN, detJ = E.G_map(xIP[i], xIP[j], Coord_mat_el)
B = get_B_plane_stress(gradN)
fint_pre += np.dot(np.transpose(B),sigma[:,count]) * detJ * weights[i] * weights[j]
count += 1
return np.transpose(fint_pre)
def getStrainElement(Coord_mat_el, d):
E = Element("Q4")
xIP = [-np.sqrt(3) / 3, np.sqrt(3) / 3]
epsilon = np.zeros((3, 4))
count = 0
for i in range(len(xIP)):
for j in range(len(xIP)):
gradN, detJ = E.G_map(xIP[i], xIP[j], Coord_mat_el)
B = get_B_plane_stress(gradN)
val = np.dot(B, d)
for k in range(3):
epsilon[k, count] = val[k]
count += 1
return epsilon
def Dif_basic_K(Coords, k=1): #let k be an optional arguement
E = Element("Q4")
Ke = np.zeros((len(Coords), len(Coords)))
x_ip = [-np.sqrt(3) / 3, np.sqrt(3) / 3]
W_ip = [1, 1]
for i in range(len(x_ip)):
for j in range(len(x_ip)): # now ready to integrate
G_m = E.G_map()
B, Jdet = G_m(x_ip[i], x_ip[j], Coords)
B_T = np.transpose(B)
Ke = Ke + B_T.dot(B) * k * Jdet * W_ip[i] * W_ip[j]
return Ke
