def Moment_z(x):
return float(x_matrix[0] * positive(x - x1, 1) -
x_matrix[2] * np.sin(theta) * positive(x - (xI), 1) +
x_matrix[3] * positive(x - x2, 1) -
P * np.sin(theta) * positive(x - (xII), 1) +
x_matrix[5] * positive(x - x3, 1) - doubleintegrate_spline(
coor_x, find_interpolant(coor_x, Area_chord), x))
def w(x):
return float(-(1 / (6 * E * Iyy)) *
(x_matrix[1] * positive(x - x1, 3) -
x_matrix[2] * np.cos(theta) * positive(x - (xI), 3) +
x_matrix[4] * positive(x - x2, 3) - P * np.cos(theta) *
positive(x - (xII), 3) + x_matrix[6] * positive(x - x3, 3)) +
x_matrix[7] * x + x_matrix[8])
def Sy(x):
return float(
x_matrix[0] * positive(x - x1, 0) -
x_matrix[2] * np.sin(theta) * positive(x - (xI), 0) +
x_matrix[3] * positive(x - x2, 0) -
P * np.sin(theta) * positive(x - (xII), 0) +
x_matrix[5] * positive(x - x3, 0) -
integrate_spline(coor_x, find_interpolant(coor_x, Area_chord), x))
def v(x):
return float(
-(1 / (6 * E * Izz)) *
(x_matrix[0] * positive(x - x1, 3) - x_matrix[2] * np.sin(theta) *
positive(x - (xI), 3) + x_matrix[3] * positive(x - x2, 3) -
P * np.sin(theta) * positive(x - (xII), 3) +
x_matrix[5] * positive(x - x3, 3) - 6 * quadrupleintegrate_spline(
coor_x, find_interpolant(coor_x, Area_chord), x)) +
x_matrix[9] * x + x_matrix[10])
def T(x):
return float(
-x_matrix[0] * (np.abs(z_hat) - ha / 2) * positive(x - x1, 0) +
x_matrix[2] *
(np.sin(theta) * np.abs(z_hat) - np.cos(theta) * ha / 2) *
positive(x - (xI), 0) - x_matrix[3] *
(np.abs(z_hat) - ha / 2) * positive(x - x2, 0) + P *
(np.sin(theta) * np.abs(z_hat) - np.cos(theta) * ha / 2) *
positive(x - (xII), 0) - x_matrix[5] *
(np.abs(z_hat) - ha / 2) * positive(x - x3, 0) -
integrate_spline(coor_x, find_interpolant(coor_x, torque_chord), x))
def Twist(x):
return float(
(1 / (G * J)) *
(-x_matrix[0] *
(np.abs(z_hat) - ha / 2) * positive(x - x1, 1) + x_matrix[2] *
(np.sin(theta) * np.abs(z_hat) - np.cos(theta) * ha / 2) *
positive(x - (xI), 1) - x_matrix[3] *
(np.abs(z_hat) - ha / 2) * positive(x - x2, 1) + P *
(np.sin(theta) * np.abs(z_hat) - np.cos(theta) * ha / 2) *
positive(x - (xII), 1) - x_matrix[5] *
(np.abs(z_hat) - ha / 2) * positive(x - x3, 1) -
doubleintegrate_spline(coor_x, find_interpolant(coor_x, torque_chord),
x)) - x_matrix[11])
def Moment_y(x):
return float(x_matrix[1] * positive(x - x1, 1) -
x_matrix[2] * np.cos(theta) * positive(x - (xI), 1) +
x_matrix[4] * positive(x - x2, 1) -
P * np.cos(theta) * positive(x - (xII), 1) +
x_matrix[6] * positive(x - x3, 1))
def Sz(x):
return float(x_matrix[1] * positive(x - x1, 0) -
x_matrix[2] * np.cos(theta) * positive(x - (xI), 0) +
x_matrix[4] * positive(x - x2, 0) -
P * np.cos(theta) * positive(x - (xII), 0) +
x_matrix[6] * positive(x - x3, 0))