def _x3_CST(self, x1, diff=None):
N1 = 1.
N2 = 1.
A0 = self.tip_displacement / max(x1)
A = [A0] + list(self.D)
if diff is None:
return (CST(x1,
max(x1),
deltasz=self.tip_displacement,
Au=A,
N1=N1,
N2=N2))
elif diff == 'x1':
psi = x1 / max(x1)
return (dxi_u(psi, A, delta_xi, N1=N1, N2=N2))
elif diff == 'x11':
return (ddxi_u(psi, A, N1=N1, N2=N2))
elif diff == 'theta3':
return (np.zeros(len(x1)))
def integrand(psi, Au, delta_xi):
return np.sqrt(1 + dxi_u(psi, Au, delta_xi, N1, N2)**2)
def generate_geometries(length_0,
A,
TE_displacement,
N1,
N2,
thickness,
x_to_track=[]):
# new chord
current_chord = calculate_c(length_0, A, TE_displacement, N1, N2)
# Get coordinates for specific points in the neutral line
tracked = {'x': [], 'y': []}
for x in x_to_track:
tracked['y'].append(current_chord * calculate_deformed_psi(
x / length_0, length_0, current_chord, A, TE_displacement)[0])
tracked['x'] = CST(tracked['y'],
current_chord,
TE_displacement,
Au=A,
N1=N1,
N2=N2)
# Get offset values for left side
left_tracked = {'x': [], 'y': []}
for i in range(len(x_to_track)):
dxi = dxi_u(tracked['y'][i] / current_chord, A,
TE_displacement / current_chord, N1, N2)
xi_component = -dxi / (dxi**2 + 1)**.5
psi_component = 1 / (dxi**2 + 1)**.5
left_tracked['x'].append(tracked['x'][i] -
thickness / 2 * psi_component)
left_tracked['y'].append(tracked['y'][i] -
thickness / 2 * xi_component)
# Get offset values for right side
right_tracked = {'x': [], 'y': []}
for i in range(len(x_to_track)):
dxi = dxi_u(tracked['y'][i] / current_chord, A,
TE_displacement / current_chord, N1, N2)
xi_component = -dxi / (dxi**2 + 1)**.5
psi_component = 1 / (dxi**2 + 1)**.5
right_tracked['x'].append(tracked['x'][i] +
thickness / 2 * psi_component)
right_tracked['y'].append(tracked['y'][i] +
thickness / 2 * xi_component)
# non-dimensional y coordinates (extend it a little on the bottom to guarantee nice shape)
psi = np.linspace(-.1, current_chord, 1000)
# non-dimensional x coordinates
xi = CST(psi, current_chord, TE_displacement, Au=A, N1=N1, N2=N2)
fig = plt.figure(1, figsize=SIZE, dpi=90)
ax = fig.add_subplot(111)
ax.set_aspect('equal')
# Genrate neutral line
line = LineString(zip(xi, psi))
# Create offsets to neutral line
offset_left = line.parallel_offset(thickness / 2., 'left', join_style=1)
offset_right = line.parallel_offset(thickness / 2., 'right', join_style=1)
# Create baffle
coords = (offset_left.coords[:] + offset_right.coords[::] +
[offset_left.coords[0]])
main = Polygon(coords)
# Remove base material
coords = ((-1, 0), (-1, -1), (1, -1), (1, 0), (-1, 0))
root = Polygon(coords)
main = main.difference(root)
# Plot tracked points
plt.scatter(right_tracked['x'], right_tracked['y'], c='c')
plt.scatter(left_tracked['x'], left_tracked['y'], c='g')
plt.scatter([0] * len(x_to_track), x_to_track, c='b')
plt.scatter(tracked['x'], tracked['y'], c='r')
# Plot geometry
skin_patch = PolygonPatch(main,
facecolor='#808080',
edgecolor='#808080',
alpha=0.5,
zorder=2)
ax.add_patch(skin_patch)
plt.xlabel('x', fontsize=14)
plt.ylabel('y', fontsize=14)
plt.grid()
plt.show()
# Get the flag
flags = []
x, y = find_point_inside(main)
flags.append((x, y))
# Export data
data_main = extract_poly_coords(main)
data = {
'model': data_main,
'flags': flags,
'left': left_tracked,
'right': right_tracked
}
output_file = 'curves.p'
fileObject = open(output_file, 'wb')
pickle.dump(data, fileObject)
fileObject.close()
def generate_geometries_animate(length_0,
A,
TE_displacement,
N1,
N2,
thickness,
x_to_track=[]):
# new chord
current_chord = calculate_c(length_0, A, TE_displacement, N1, N2)
# Get coordinates for specific points in the neutral line
tracked = {'x': [], 'y': []}
for x in x_to_track:
tracked['y'].append(current_chord * calculate_deformed_psi(
x / length_0, length_0, current_chord, A, TE_displacement)[0])
tracked['x'] = CST(tracked['y'],
current_chord,
TE_displacement,
Au=A,
N1=N1,
N2=N2)
# Get offset values for left side
left_tracked = {'x': [], 'y': []}
for i in range(len(x_to_track)):
dxi = dxi_u(tracked['y'][i] / current_chord, A,
TE_displacement / current_chord)
xi_component = -dxi / (dxi**2 + 1)**.5
psi_component = 1 / (dxi**2 + 1)**.5
left_tracked['x'].append(tracked['x'][i] -
thickness / 2 * psi_component)
left_tracked['y'].append(tracked['y'][i] -
thickness / 2 * xi_component)
# Get offset values for right side
right_tracked = {'x': [], 'y': []}
for i in range(len(x_to_track)):
dxi = dxi_u(tracked['y'][i] / current_chord, A,
TE_displacement / current_chord)
xi_component = -dxi / (dxi**2 + 1)**.5
psi_component = 1 / (dxi**2 + 1)**.5
right_tracked['x'].append(tracked['x'][i] +
thickness / 2 * psi_component)
right_tracked['y'].append(tracked['y'][i] +
thickness / 2 * xi_component)
# non-dimensional y coordinates (extend it a little on the bottom to guarantee nice shape)
psi = np.linspace(-.1, current_chord, 1000)
# non-dimensional x coordinates
xi = CST(psi, current_chord, TE_displacement, Au=A, N1=N1, N2=N2)
# Genrate neutral line
line = LineString(zip(xi, psi))
# Create offsets to neutral line
offset_left = line.parallel_offset(thickness / 2., 'left', join_style=1)
offset_right = line.parallel_offset(thickness / 2., 'right', join_style=1)
# Create baffle
coords = (offset_left.coords[:] + offset_right.coords[::] +
[offset_left.coords[0]])
main = Polygon(coords)
# Remove base material
coords = ((-1, 0), (-1, -1), (1, -1), (1, 0), (-1, 0))
root = Polygon(coords)
main = main.difference(root)
# 3Plot tracked points
# plt.scatter(right_tracked['x'],right_tracked['y'],c='c')
# plt.scatter(left_tracked['x'],left_tracked['y'],c='g')
# plt.scatter([0]*len(x_to_track),x_to_track, c='b')
# plt.scatter(tracked['x'],tracked['y'], c='r')
# Plot geometry
skin_patch = PolygonPatch(main,
facecolor='#909090',
edgecolor='#909090',
alpha=0.5,
zorder=2)
return skin_patch
# Shape coefficients
A = [-TE_displacement, 0.2]
# new chord
current_chord = calculate_c(length_0, A, TE_displacement, N1, N2)
#current_chord = 1
# non-dimensional y coordinates
y = np.linspace(0, current_chord)
# non-dimensional x coordinates
x = CST(y, current_chord, TE_displacement, Au=A, N1=N1, N2=N2)
dxi = dxi_u(psi=np.array(y) / current_chord,
Au=A,
delta_xi=TE_displacement / current_chord,
N1=N1,
N2=N2)
# Plotting
plt.plot(x, y, label='A = ' + str(A[0]))
plt.plot(dxi, y, label='dxi')
plt.axis('equal')
plt.legend()
plt.grid()
plt.xlabel(r'$x$', fontsize=14.)
plt.ylabel('$y$', fontsize=14.)
plt.show()
length_0 = 1.
for TE_displacement in np.linspace(0, 0.4, 3):