User-Provided Mesh Example
Here is an example script with a custom mesh provided as an array of coordinates. This should help you understand how meshes are defined in OpenAeroStruct and how to create them for your own custom planform shapes. This is an alternative to the helper-function approach described in Aerodynamic Optimization.
The following shows the portion of the example script in which the user provides the coordinates for the mesh. This example is for a wing with a kink and two distinct trapezoidal segments.
# -----------------------------------------------------------------------------
# CUSTOM MESH: Example mesh for a 2-segment wing with sweep
# -----------------------------------------------------------------------------
# Planform specifications
half_span = 12.0 # wing half-span in m
kink_location = 4.0 # spanwise location of the kink in m
root_chord = 6.0 # root chord in m
kink_chord = 3.0 # kink chord in m
tip_chord = 2.0 # tip chord in m
inboard_LE_sweep = 10.0 # inboard leading-edge sweep angle in deg
outboard_LE_sweep = -10.0 # outboard leading-edge sweep angle in deg
# Mesh specifications
nx = 5 # number of chordwise nodal points (should be odd)
ny_outboard = 9 # number of spanwise nodal points for the outboard segment
ny_inboard = 7 # number of spanwise nodal points for the inboard segment
# Initialize the 3-D mesh object. Indexing: Chordwise, spanwise, then the 3-D coordinates.
# We use ny_inboard+ny_outboard-1 because the 2 segments share the nodes where they connect.
mesh = np.zeros((nx, ny_inboard + ny_outboard - 1, 3))
# The form of this 3-D array can be confusing initially.
# For each node, we are providing the x, y, and z coordinates.
# x is streamwise, y is spanwise, and z is up.
# For example, the node for the leading edge at the tip would be specified as mesh[0, 0, :] = np.array([x, y, z]).
# And the node at the trailing edge at the root would be mesh[nx-1, ny-1, :] = np.array([x, y, z]).
# We only provide the right half of the wing here because we use symmetry.
# Print elements of the mesh to better understand the form.
####### THE Z-COORDINATES ######
# Assume no dihedral, so set the z-coordinate for all the points to 0.
mesh[:, :, 2] = 0.0
####### THE Y-COORDINATES ######
# Using uniform spacing for the spanwise locations of all the nodes within each of the two trapezoidal segments:
# Outboard
mesh[:, :ny_outboard, 1] = np.linspace(half_span, kink_location, ny_outboard)
# Inboard
mesh[:, ny_outboard : ny_outboard + ny_inboard, 1] = np.linspace(kink_location, 0, ny_inboard)[1:]
###### THE X-COORDINATES ######
# Start with the leading edge and create some intermediate arrays that we will use
x_LE = np.zeros(ny_inboard + ny_outboard - 1)
array_for_inboard_leading_edge_x_coord = np.linspace(0, kink_location, ny_inboard) * np.tan(
inboard_LE_sweep / 180.0 * np.pi
)
array_for_outboard_leading_edge_x_coord = (
np.linspace(0, half_span - kink_location, ny_outboard) * np.tan(outboard_LE_sweep / 180.0 * np.pi)
+ np.ones(ny_outboard) * array_for_inboard_leading_edge_x_coord[-1]
)
x_LE[:ny_inboard] = array_for_inboard_leading_edge_x_coord
x_LE[ny_inboard : ny_inboard + ny_outboard] = array_for_outboard_leading_edge_x_coord[1:]
# Then the trailing edge
x_TE = np.zeros(ny_inboard + ny_outboard - 1)
array_for_inboard_trailing_edge_x_coord = np.linspace(
array_for_inboard_leading_edge_x_coord[0] + root_chord,
array_for_inboard_leading_edge_x_coord[-1] + kink_chord,
ny_inboard,
)
array_for_outboard_trailing_edge_x_coord = np.linspace(
array_for_outboard_leading_edge_x_coord[0] + kink_chord,
array_for_outboard_leading_edge_x_coord[-1] + tip_chord,
ny_outboard,
)
x_TE[:ny_inboard] = array_for_inboard_trailing_edge_x_coord
x_TE[ny_inboard : ny_inboard + ny_outboard] = array_for_outboard_trailing_edge_x_coord[1:]
# # Quick plot to check leading and trailing edge x-coords
# plt.plot(x_LE, np.arange(0, ny_inboard+ny_outboard-1), marker='*')
# plt.plot(x_TE, np.arange(0, ny_inboard+ny_outboard-1), marker='*')
# plt.show()
# exit()
for i in range(0, ny_inboard + ny_outboard - 1):
mesh[:, i, 0] = np.linspace(np.flip(x_LE)[i], np.flip(x_TE)[i], nx)
# -----------------------------------------------------------------------------
# END MESH
# -----------------------------------------------------------------------------
The following shows a visualization of the mesh.
The complete script for the optimization is as follows. Make sure you go through the Aerostructural Optimization with Wingbox before trying to understand this setup.
import warnings
import matplotlib
warnings.filterwarnings('ignore')
matplotlib.use('Agg')
"""
This example script can be used to run a multipoint aerostructural (w/ wingbox) optimization for a custom user-provided mesh.
The fuel burn from the cruise flight-point is the objective function and a 2.5g
maneuver flight-point is used for the structural sizing.
After running the optimization, use the 'plot_wingbox.py' script in the utils/
directory (e.g., as 'python ../utils/plot_wingbox.py aerostruct.db' if running
from this directory) to visualize the results.
'plot_wingbox.py' is still under development and will probably not work as it is for other types of cases for now.
"""
import numpy as np
from openaerostruct.integration.aerostruct_groups import AerostructGeometry, AerostructPoint
from openaerostruct.structures.wingbox_fuel_vol_delta import WingboxFuelVolDelta
import openmdao.api as om
# docs checkpoint 0
# -----------------------------------------------------------------------------
# CUSTOM MESH: Example mesh for a 2-segment wing with sweep
# -----------------------------------------------------------------------------
# Planform specifications
half_span = 12.0 # wing half-span in m
kink_location = 4.0 # spanwise location of the kink in m
root_chord = 6.0 # root chord in m
kink_chord = 3.0 # kink chord in m
tip_chord = 2.0 # tip chord in m
inboard_LE_sweep = 10.0 # inboard leading-edge sweep angle in deg
outboard_LE_sweep = -10.0 # outboard leading-edge sweep angle in deg
# Mesh specifications
nx = 5 # number of chordwise nodal points (should be odd)
ny_outboard = 9 # number of spanwise nodal points for the outboard segment
ny_inboard = 7 # number of spanwise nodal points for the inboard segment
# Initialize the 3-D mesh object. Indexing: Chordwise, spanwise, then the 3-D coordinates.
# We use ny_inboard+ny_outboard-1 because the 2 segments share the nodes where they connect.
mesh = np.zeros((nx, ny_inboard + ny_outboard - 1, 3))
# The form of this 3-D array can be confusing initially.
# For each node, we are providing the x, y, and z coordinates.
# x is streamwise, y is spanwise, and z is up.
# For example, the node for the leading edge at the tip would be specified as mesh[0, 0, :] = np.array([x, y, z]).
# And the node at the trailing edge at the root would be mesh[nx-1, ny-1, :] = np.array([x, y, z]).
# We only provide the right half of the wing here because we use symmetry.
# Print elements of the mesh to better understand the form.
####### THE Z-COORDINATES ######
# Assume no dihedral, so set the z-coordinate for all the points to 0.
mesh[:, :, 2] = 0.0
####### THE Y-COORDINATES ######
# Using uniform spacing for the spanwise locations of all the nodes within each of the two trapezoidal segments:
# Outboard
mesh[:, :ny_outboard, 1] = np.linspace(half_span, kink_location, ny_outboard)
# Inboard
mesh[:, ny_outboard : ny_outboard + ny_inboard, 1] = np.linspace(kink_location, 0, ny_inboard)[1:]
###### THE X-COORDINATES ######
# Start with the leading edge and create some intermediate arrays that we will use
x_LE = np.zeros(ny_inboard + ny_outboard - 1)
array_for_inboard_leading_edge_x_coord = np.linspace(0, kink_location, ny_inboard) * np.tan(
inboard_LE_sweep / 180.0 * np.pi
)
array_for_outboard_leading_edge_x_coord = (
np.linspace(0, half_span - kink_location, ny_outboard) * np.tan(outboard_LE_sweep / 180.0 * np.pi)
+ np.ones(ny_outboard) * array_for_inboard_leading_edge_x_coord[-1]
)
x_LE[:ny_inboard] = array_for_inboard_leading_edge_x_coord
x_LE[ny_inboard : ny_inboard + ny_outboard] = array_for_outboard_leading_edge_x_coord[1:]
# Then the trailing edge
x_TE = np.zeros(ny_inboard + ny_outboard - 1)
array_for_inboard_trailing_edge_x_coord = np.linspace(
array_for_inboard_leading_edge_x_coord[0] + root_chord,
array_for_inboard_leading_edge_x_coord[-1] + kink_chord,
ny_inboard,
)
array_for_outboard_trailing_edge_x_coord = np.linspace(
array_for_outboard_leading_edge_x_coord[0] + kink_chord,
array_for_outboard_leading_edge_x_coord[-1] + tip_chord,
ny_outboard,
)
x_TE[:ny_inboard] = array_for_inboard_trailing_edge_x_coord
x_TE[ny_inboard : ny_inboard + ny_outboard] = array_for_outboard_trailing_edge_x_coord[1:]
# # Quick plot to check leading and trailing edge x-coords
# plt.plot(x_LE, np.arange(0, ny_inboard+ny_outboard-1), marker='*')
# plt.plot(x_TE, np.arange(0, ny_inboard+ny_outboard-1), marker='*')
# plt.show()
# exit()
for i in range(0, ny_inboard + ny_outboard - 1):
mesh[:, i, 0] = np.linspace(np.flip(x_LE)[i], np.flip(x_TE)[i], nx)
# -----------------------------------------------------------------------------
# END MESH
# -----------------------------------------------------------------------------
# docs checkpoint 1
# -----------------------------------------------------------------------------
# On to the problem setup (this is the same setup used for the Q400 example)
# -----------------------------------------------------------------------------
# Provide coordinates for a portion of an airfoil for the wingbox cross-section as an nparray with dtype=complex (to work with the complex-step approximation for derivatives).
# These should be for an airfoil with the chord scaled to 1.
# We use the 10% to 60% portion of the NASA SC2-0612 airfoil for this case
# We use the coordinates available from airfoiltools.com. Using such a large number of coordinates is not necessary.
# The first and last x-coordinates of the upper and lower surfaces must be the same
# fmt: off
upper_x = np.array([0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6], dtype="complex128")
lower_x = np.array([0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6], dtype="complex128")
upper_y = np.array([ 0.0447, 0.046, 0.0472, 0.0484, 0.0495, 0.0505, 0.0514, 0.0523, 0.0531, 0.0538, 0.0545, 0.0551, 0.0557, 0.0563, 0.0568, 0.0573, 0.0577, 0.0581, 0.0585, 0.0588, 0.0591, 0.0593, 0.0595, 0.0597, 0.0599, 0.06, 0.0601, 0.0602, 0.0602, 0.0602, 0.0602, 0.0602, 0.0601, 0.06, 0.0599, 0.0598, 0.0596, 0.0594, 0.0592, 0.0589, 0.0586, 0.0583, 0.058, 0.0576, 0.0572, 0.0568, 0.0563, 0.0558, 0.0553, 0.0547, 0.0541], dtype="complex128") # noqa: E201, E241
lower_y = np.array([-0.0447, -0.046, -0.0473, -0.0485, -0.0496, -0.0506, -0.0515, -0.0524, -0.0532, -0.054, -0.0547, -0.0554, -0.056, -0.0565, -0.057, -0.0575, -0.0579, -0.0583, -0.0586, -0.0589, -0.0592, -0.0594, -0.0595, -0.0596, -0.0597, -0.0598, -0.0598, -0.0598, -0.0598, -0.0597, -0.0596, -0.0594, -0.0592, -0.0589, -0.0586, -0.0582, -0.0578, -0.0573, -0.0567, -0.0561, -0.0554, -0.0546, -0.0538, -0.0529, -0.0519, -0.0509, -0.0497, -0.0485, -0.0472, -0.0458, -0.0444], dtype="complex128")
# fmt: on
surf_dict = {
# Wing definition
"name": "wing", # name of the surface
"symmetry": True, # if true, model one half of wing
"S_ref_type": "wetted", # how we compute the wing area,
# can be 'wetted' or 'projected'
"mesh": mesh,
"twist_cp": np.array([6.0, 7.0, 7.0, 7.0]),
"fem_model_type": "wingbox",
"data_x_upper": upper_x,
"data_x_lower": lower_x,
"data_y_upper": upper_y,
"data_y_lower": lower_y,
"spar_thickness_cp": np.array([0.004, 0.004, 0.004, 0.004]), # [m]
"skin_thickness_cp": np.array([0.003, 0.006, 0.010, 0.012]), # [m]
"original_wingbox_airfoil_t_over_c": 0.12,
# Aerodynamic deltas.
# These CL0 and CD0 values are added to the CL and CD
# obtained from aerodynamic analysis of the surface to get
# the total CL and CD.
# These CL0 and CD0 values do not vary wrt alpha.
# They can be used to account for things that are not included, such as contributions from the fuselage, nacelles, tail surfaces, etc.
"CL0": 0.0,
"CD0": 0.0142,
"with_viscous": True, # if true, compute viscous drag
"with_wave": True, # if true, compute wave drag
# Airfoil properties for viscous drag calculation
"k_lam": 0.05, # percentage of chord with laminar
# flow, used for viscous drag
"c_max_t": 0.38, # chordwise location of maximum thickness
"t_over_c_cp": np.array([0.1, 0.1, 0.15, 0.15]),
# Structural values are based on aluminum 7075
"E": 73.1e9, # [Pa] Young's modulus
"G": (73.1e9 / 2 / 1.33), # [Pa] shear modulus (calculated using E and the Poisson's ratio here)
"yield": (420.0e6 / 1.5), # [Pa] allowable yield stress
"mrho": 2.78e3, # [kg/m^3] material density
"strength_factor_for_upper_skin": 1.0, # the yield stress is multiplied by this factor for the upper skin
"wing_weight_ratio": 1.25,
"exact_failure_constraint": False, # if false, use KS function
"struct_weight_relief": True,
"distributed_fuel_weight": True,
"fuel_density": 803.0, # [kg/m^3] fuel density (only needed if the fuel-in-wing volume constraint is used)
"Wf_reserve": 500.0, # [kg] reserve fuel mass
}
surfaces = [surf_dict]
# Create the problem and assign the model group
prob = om.Problem()
# Add problem information as an independent variables component
indep_var_comp = om.IndepVarComp()
indep_var_comp.add_output("v", val=np.array([0.5 * 310.95, 0.3 * 340.294]), units="m/s")
indep_var_comp.add_output("alpha", val=0.0, units="deg")
indep_var_comp.add_output("alpha_maneuver", val=0.0, units="deg")
indep_var_comp.add_output("Mach_number", val=np.array([0.5, 0.3]))
indep_var_comp.add_output(
"re",
val=np.array([0.569 * 310.95 * 0.5 * 1.0 / (1.56 * 1e-5), 1.225 * 340.294 * 0.3 * 1.0 / (1.81206 * 1e-5)]),
units="1/m",
)
indep_var_comp.add_output("rho", val=np.array([0.569, 1.225]), units="kg/m**3")
indep_var_comp.add_output("CT", val=0.43 / 3600, units="1/s")
indep_var_comp.add_output("R", val=2e6, units="m")
indep_var_comp.add_output("W0", val=25400 + surf_dict["Wf_reserve"], units="kg")
indep_var_comp.add_output("speed_of_sound", val=np.array([310.95, 340.294]), units="m/s")
indep_var_comp.add_output("load_factor", val=np.array([1.0, 2.5]))
indep_var_comp.add_output("empty_cg", val=np.zeros((3)), units="m")
indep_var_comp.add_output("fuel_mass", val=3000.0, units="kg")
prob.model.add_subsystem("prob_vars", indep_var_comp, promotes=["*"])
# Loop over each surface in the surfaces list
for surface in surfaces:
# Get the surface name and create a group to contain components
# only for this surface
name = surface["name"]
aerostruct_group = AerostructGeometry(surface=surface)
# Add group to the problem with the name of the surface.
prob.model.add_subsystem(name, aerostruct_group)
# Loop through and add a certain number of aerostruct points
for i in range(2):
point_name = "AS_point_{}".format(i)
# Connect the parameters within the model for each aerostruct point
# Create the aero point group and add it to the model
AS_point = AerostructPoint(surfaces=surfaces, internally_connect_fuelburn=False)
prob.model.add_subsystem(point_name, AS_point)
# Connect flow properties to the analysis point
prob.model.connect("v", point_name + ".v", src_indices=[i])
prob.model.connect("Mach_number", point_name + ".Mach_number", src_indices=[i])
prob.model.connect("re", point_name + ".re", src_indices=[i])
prob.model.connect("rho", point_name + ".rho", src_indices=[i])
prob.model.connect("CT", point_name + ".CT")
prob.model.connect("R", point_name + ".R")
prob.model.connect("W0", point_name + ".W0")
prob.model.connect("speed_of_sound", point_name + ".speed_of_sound", src_indices=[i])
prob.model.connect("empty_cg", point_name + ".empty_cg")
prob.model.connect("load_factor", point_name + ".load_factor", src_indices=[i])
prob.model.connect("fuel_mass", point_name + ".total_perf.L_equals_W.fuelburn")
prob.model.connect("fuel_mass", point_name + ".total_perf.CG.fuelburn")
for surface in surfaces:
name = surface["name"]
if surf_dict["distributed_fuel_weight"]:
prob.model.connect("load_factor", point_name + ".coupled.load_factor", src_indices=[i])
com_name = point_name + "." + name + "_perf."
prob.model.connect(
name + ".local_stiff_transformed", point_name + ".coupled." + name + ".local_stiff_transformed"
)
prob.model.connect(name + ".nodes", point_name + ".coupled." + name + ".nodes")
# Connect aerodynamic mesh to coupled group mesh
prob.model.connect(name + ".mesh", point_name + ".coupled." + name + ".mesh")
if surf_dict["struct_weight_relief"]:
prob.model.connect(name + ".element_mass", point_name + ".coupled." + name + ".element_mass")
# Connect performance calculation variables
prob.model.connect(name + ".nodes", com_name + "nodes")
prob.model.connect(name + ".cg_location", point_name + "." + "total_perf." + name + "_cg_location")
prob.model.connect(name + ".structural_mass", point_name + "." + "total_perf." + name + "_structural_mass")
# Connect wingbox properties to von Mises stress calcs
prob.model.connect(name + ".Qz", com_name + "Qz")
prob.model.connect(name + ".J", com_name + "J")
prob.model.connect(name + ".A_enc", com_name + "A_enc")
prob.model.connect(name + ".htop", com_name + "htop")
prob.model.connect(name + ".hbottom", com_name + "hbottom")
prob.model.connect(name + ".hfront", com_name + "hfront")
prob.model.connect(name + ".hrear", com_name + "hrear")
prob.model.connect(name + ".spar_thickness", com_name + "spar_thickness")
prob.model.connect(name + ".t_over_c", com_name + "t_over_c")
prob.model.connect("alpha", "AS_point_0" + ".alpha")
prob.model.connect("alpha_maneuver", "AS_point_1" + ".alpha")
# Here we add the fuel volume constraint componenet to the model
prob.model.add_subsystem("fuel_vol_delta", WingboxFuelVolDelta(surface=surface))
prob.model.connect("wing.struct_setup.fuel_vols", "fuel_vol_delta.fuel_vols")
prob.model.connect("AS_point_0.fuelburn", "fuel_vol_delta.fuelburn")
if surf_dict["distributed_fuel_weight"]:
prob.model.connect("wing.struct_setup.fuel_vols", "AS_point_0.coupled.wing.struct_states.fuel_vols")
prob.model.connect("fuel_mass", "AS_point_0.coupled.wing.struct_states.fuel_mass")
prob.model.connect("wing.struct_setup.fuel_vols", "AS_point_1.coupled.wing.struct_states.fuel_vols")
prob.model.connect("fuel_mass", "AS_point_1.coupled.wing.struct_states.fuel_mass")
comp = om.ExecComp("fuel_diff = (fuel_mass - fuelburn) / fuelburn", units="kg")
prob.model.add_subsystem("fuel_diff", comp, promotes_inputs=["fuel_mass"], promotes_outputs=["fuel_diff"])
prob.model.connect("AS_point_0.fuelburn", "fuel_diff.fuelburn")
## Use these settings if you do not have pyOptSparse or SNOPT
prob.driver = om.ScipyOptimizeDriver()
prob.driver.options["optimizer"] = "SLSQP"
prob.driver.options["tol"] = 1e-4
recorder = om.SqliteRecorder("aerostruct.db")
prob.driver.add_recorder(recorder)
# We could also just use prob.driver.recording_options['includes']=['*'] here, but for large meshes the database file becomes extremely large. So we just select the variables we need.
prob.driver.recording_options["includes"] = [
"alpha",
"rho",
"v",
"cg",
"AS_point_1.cg",
"AS_point_0.cg",
"AS_point_0.coupled.wing_loads.loads",
"AS_point_1.coupled.wing_loads.loads",
"AS_point_0.coupled.wing.normals",
"AS_point_1.coupled.wing.normals",
"AS_point_0.coupled.wing.widths",
"AS_point_1.coupled.wing.widths",
"AS_point_0.coupled.aero_states.wing_sec_forces",
"AS_point_1.coupled.aero_states.wing_sec_forces",
"AS_point_0.wing_perf.CL1",
"AS_point_1.wing_perf.CL1",
"AS_point_0.coupled.wing.S_ref",
"AS_point_1.coupled.wing.S_ref",
"wing.geometry.twist",
"wing.mesh",
"wing.skin_thickness",
"wing.spar_thickness",
"wing.t_over_c",
"wing.structural_mass",
"AS_point_0.wing_perf.vonmises",
"AS_point_1.wing_perf.vonmises",
"AS_point_0.coupled.wing.def_mesh",
"AS_point_1.coupled.wing.def_mesh",
]
prob.driver.recording_options["record_objectives"] = True
prob.driver.recording_options["record_constraints"] = True
prob.driver.recording_options["record_desvars"] = True
prob.driver.recording_options["record_inputs"] = True
prob.model.add_objective("AS_point_0.fuelburn", scaler=1e-5)
prob.model.add_design_var("wing.twist_cp", lower=-15.0, upper=15.0, scaler=0.1)
prob.model.add_design_var("wing.spar_thickness_cp", lower=0.003, upper=0.1, scaler=1e2)
prob.model.add_design_var("wing.skin_thickness_cp", lower=0.003, upper=0.1, scaler=1e2)
prob.model.add_design_var("wing.geometry.t_over_c_cp", lower=0.07, upper=0.2, scaler=10.0)
prob.model.add_design_var("fuel_mass", lower=0.0, upper=2e5, scaler=1e-5)
prob.model.add_design_var("alpha_maneuver", lower=-15.0, upper=15)
prob.model.add_constraint("AS_point_0.CL", equals=0.6)
prob.model.add_constraint("AS_point_1.L_equals_W", equals=0.0)
prob.model.add_constraint("AS_point_1.wing_perf.failure", upper=0.0)
prob.model.add_constraint("fuel_vol_delta.fuel_vol_delta", lower=0.0)
prob.model.add_constraint("fuel_diff", equals=0.0)
# Set up the problem
prob.setup()
/home/docs/checkouts/readthedocs.org/user_builds/mdolab-openaerostruct/envs/latest/lib/python3.11/site-packages/openmdao/core/system.py:2422: PromotionWarning:'AS_point_0.coupled.wing.struct_states' <class SpatialBeamStates>: input variable 'load_factor', promoted using 'load_factor', was already promoted using 'load_factor'. /home/docs/checkouts/readthedocs.org/user_builds/mdolab-openaerostruct/envs/latest/lib/python3.11/site-packages/openmdao/core/system.py:2422: PromotionWarning:'AS_point_0.coupled.wing.struct_states' <class SpatialBeamStates>: input variable 'nodes', promoted using 'nodes', was already promoted using 'nodes'. /home/docs/checkouts/readthedocs.org/user_builds/mdolab-openaerostruct/envs/latest/lib/python3.11/site-packages/openmdao/core/system.py:2422: PromotionWarning:'AS_point_1.coupled.wing.struct_states' <class SpatialBeamStates>: input variable 'load_factor', promoted using 'load_factor', was already promoted using 'load_factor'. /home/docs/checkouts/readthedocs.org/user_builds/mdolab-openaerostruct/envs/latest/lib/python3.11/site-packages/openmdao/core/system.py:2422: PromotionWarning:'AS_point_1.coupled.wing.struct_states' <class SpatialBeamStates>: input variable 'nodes', promoted using 'nodes', was already promoted using 'nodes'. /home/docs/checkouts/readthedocs.org/user_builds/mdolab-openaerostruct/envs/latest/lib/python3.11/site-packages/openmdao/core/driver.py:743: OpenMDAOWarning:ScipyOptimizeDriver: No matches for pattern 'cg' in recording_options['includes'].
# change linear solver for aerostructural coupled adjoint
prob.model.AS_point_0.coupled.linear_solver = om.LinearBlockGS(iprint=0, maxiter=30, use_aitken=True)
prob.model.AS_point_1.coupled.linear_solver = om.LinearBlockGS(iprint=0, maxiter=30, use_aitken=True)
# om.view_model(prob)
# prob.check_partials(form='central', compact_print=True)
prob.run_driver()
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 59819.4728 1
NL: NLBGS 2 ; 59187.3066 0.9894321
NL: NLBGS 3 ; 1879.7489 0.0314236956
NL: NLBGS 4 ; 47.0388256 0.000786346375
NL: NLBGS 5 ; 0.117150412 1.95839927e-06
NL: NLBGS 6 ; 0.00466493664 7.798358e-08
NL: NLBGS 7 ; 3.90004533e-05 6.51969192e-10
NL: NLBGS 8 ; 4.64470169e-08 7.7645313e-13
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 63961.0672 1
NL: NLBGS 2 ; 54760.1129 0.85614758
NL: NLBGS 3 ; 1601.08786 0.0250322256
NL: NLBGS 4 ; 37.0946936 0.00057995739
NL: NLBGS 5 ; 0.0861602861 1.34707393e-06
NL: NLBGS 6 ; 0.00311660643 4.8726617e-08
NL: NLBGS 7 ; 2.72242833e-05 4.25638353e-10
NL: NLBGS 8 ; 2.65633562e-08 4.15305082e-13
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 1.27431151e-09 1
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 7.73898743e-10 1
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 13182.9265 1
NL: NLBGS 2 ; 12203.3035 0.925690025
NL: NLBGS 3 ; 1931.43789 0.146510556
NL: NLBGS 4 ; 81.7125596 0.0061983627
NL: NLBGS 5 ; 0.938797863 7.12131609e-05
NL: NLBGS 6 ; 0.0805607708 6.11099296e-06
NL: NLBGS 7 ; 0.00202640221 1.5371414e-07
NL: NLBGS 8 ; 2.40681435e-05 1.82570567e-09
NL: NLBGS 9 ; 1.55115374e-06 1.1766384e-10
NL: NLBGS 10 ; 1.21665613e-07 9.22902919e-12
NL: NLBGS 11 ; 4.41000751e-09 3.34524169e-13
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 100627.776 1
NL: NLBGS 2 ; 98695.2584 0.980795387
NL: NLBGS 3 ; 16329.0591 0.162271887
NL: NLBGS 4 ; 876.928461 0.0087145766
NL: NLBGS 5 ; 32.6985144 0.000324945216
NL: NLBGS 6 ; 1.59196514 1.58203352e-05
NL: NLBGS 7 ; 0.0535616814 5.32275318e-07
NL: NLBGS 8 ; 0.00288506466 2.86706592e-08
NL: NLBGS 9 ; 4.41671969e-05 4.38916557e-10
NL: NLBGS 10 ; 9.39914238e-06 9.34050494e-11
NL: NLBGS 11 ; 1.61676089e-06 1.60667457e-11
NL: NLBGS 12 ; 3.87733381e-08 3.8531447e-13
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 4455.4879 1
NL: NLBGS 2 ; 4346.71715 0.975587242
NL: NLBGS 3 ; 496.589363 0.111455664
NL: NLBGS 4 ; 16.0643834 0.00360552733
NL: NLBGS 5 ; 0.127301542 2.85718522e-05
NL: NLBGS 6 ; 0.0094779491 2.1272528e-06
NL: NLBGS 7 ; 0.000111216458 2.4961679e-08
NL: NLBGS 8 ; 6.99317961e-07 1.56956539e-10
NL: NLBGS 9 ; 5.52767667e-08 1.24064453e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 12363.017 1
NL: NLBGS 2 ; 11539.1768 0.933362523
NL: NLBGS 3 ; 1673.26519 0.135344405
NL: NLBGS 4 ; 45.9036559 0.00371298169
NL: NLBGS 5 ; 0.266990112 2.15958702e-05
NL: NLBGS 6 ; 0.0298712644 2.41617918e-06
NL: NLBGS 7 ; 0.000491091982 3.97226648e-08
NL: NLBGS 8 ; 7.73339501e-06 6.25526519e-10
NL: NLBGS 9 ; 4.25276941e-07 3.43991228e-11
NL: NLBGS 10 ; 1.32346513e-08 1.07050337e-12
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 7428.56475 1
NL: NLBGS 2 ; 7454.23582 1.00345573
NL: NLBGS 3 ; 561.08328 0.0755305095
NL: NLBGS 4 ; 41.8942523 0.00563961595
NL: NLBGS 5 ; 0.153419528 2.06526474e-05
NL: NLBGS 6 ; 0.00375465043 5.05434167e-07
NL: NLBGS 7 ; 0.000229436244 3.08856761e-08
NL: NLBGS 8 ; 6.63641617e-07 8.93364519e-11
NL: NLBGS 9 ; 1.19693845e-08 1.61126475e-12
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 7417.14914 1
NL: NLBGS 2 ; 6934.96737 0.934990957
NL: NLBGS 3 ; 797.988861 0.107587005
NL: NLBGS 4 ; 45.6094678 0.00614919115
NL: NLBGS 5 ; 0.363661014 4.90297562e-05
NL: NLBGS 6 ; 0.0135853845 1.83161808e-06
NL: NLBGS 7 ; 0.000577758607 7.78949697e-08
NL: NLBGS 8 ; 3.2215825e-06 4.34342419e-10
NL: NLBGS 9 ; 1.2331219e-07 1.66252811e-11
NL: NLBGS 10 ; 7.50454455e-09 1.01178288e-12
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 6235.14415 1
NL: NLBGS 2 ; 6252.50818 1.00278486
NL: NLBGS 3 ; 431.866279 0.0692632388
NL: NLBGS 4 ; 34.2799289 0.00549785668
NL: NLBGS 5 ; 0.131774704 2.11341872e-05
NL: NLBGS 6 ; 0.00202154181 3.24217333e-07
NL: NLBGS 7 ; 0.000139764864 2.24156588e-08
NL: NLBGS 8 ; 3.3480034e-07 5.36956855e-11
NL: NLBGS 9 ; 4.9678542e-09 7.96750496e-13
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 6251.91828 1
NL: NLBGS 2 ; 5823.80919 0.931523563
NL: NLBGS 3 ; 458.363403 0.0733156421
NL: NLBGS 4 ; 41.1887122 0.00658817188
NL: NLBGS 5 ; 0.258966219 4.14218817e-05
NL: NLBGS 6 ; 0.00167739156 2.68300302e-07
NL: NLBGS 7 ; 0.000125295775 2.00411729e-08
NL: NLBGS 8 ; 2.59673786e-07 4.15350576e-11
NL: NLBGS 9 ; 1.97211551e-09 3.15441664e-13
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 1678.44974 1
NL: NLBGS 2 ; 1658.03274 0.987835798
NL: NLBGS 3 ; 116.719706 0.0695401852
NL: NLBGS 4 ; 9.16697922 0.00546157504
NL: NLBGS 5 ; 0.0377886482 2.25140183e-05
NL: NLBGS 6 ; 0.000617224893 3.67735105e-07
NL: NLBGS 7 ; 4.201249e-05 2.5030532e-08
NL: NLBGS 8 ; 9.08534933e-08 5.41294095e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 1831.45166 1
NL: NLBGS 2 ; 1583.994 0.864884413
NL: NLBGS 3 ; 112.379987 0.0613611537
NL: NLBGS 4 ; 10.5961848 0.00578567539
NL: NLBGS 5 ; 0.0718780393 3.92464845e-05
NL: NLBGS 6 ; 0.000717753499 3.91904146e-07
NL: NLBGS 7 ; 5.491392e-05 2.99838216e-08
NL: NLBGS 8 ; 4.89494171e-08 2.67271139e-11
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 177.930154 1
NL: NLBGS 2 ; 178.434393 1.00283391
NL: NLBGS 3 ; 11.4530251 0.0643680952
NL: NLBGS 4 ; 0.946669241 0.00532045423
NL: NLBGS 5 ; 0.00351967743 1.97812307e-05
NL: NLBGS 6 ; 3.35837686e-05 1.8874692e-07
NL: NLBGS 7 ; 2.51116352e-06 1.41131982e-08
NL: NLBGS 8 ; 5.46876943e-09 3.07354841e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 177.908069 1
NL: NLBGS 2 ; 163.75034 0.920421095
NL: NLBGS 3 ; 12.9869972 0.0729983595
NL: NLBGS 4 ; 1.24994707 0.00702580316
NL: NLBGS 5 ; 0.00743786787 4.18073666e-05
NL: NLBGS 6 ; 9.6816413e-05 5.4419349e-07
NL: NLBGS 7 ; 7.66561369e-06 4.30874987e-08
NL: NLBGS 8 ; 1.40097173e-08 7.87469469e-11
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 1019.56826 1
NL: NLBGS 2 ; 1024.03283 1.00437888
NL: NLBGS 3 ; 68.3257349 0.0670143802
NL: NLBGS 4 ; 5.51147411 0.00540569409
NL: NLBGS 5 ; 0.0213857463 2.09752963e-05
NL: NLBGS 6 ; 0.000256983853 2.52051641e-07
NL: NLBGS 7 ; 1.84332724e-05 1.80794883e-08
NL: NLBGS 8 ; 4.09302621e-08 4.01447002e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 1015.33539 1
NL: NLBGS 2 ; 951.447887 0.93707744
NL: NLBGS 3 ; 71.9974815 0.0709100483
NL: NLBGS 4 ; 6.86553257 0.00676183716
NL: NLBGS 5 ; 0.0439640206 4.32999983e-05
NL: NLBGS 6 ; 0.000522836787 5.14939982e-07
NL: NLBGS 7 ; 4.08338884e-05 4.02171428e-08
NL: NLBGS 8 ; 6.54140493e-08 6.44260508e-11
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 4551.01002 1
NL: NLBGS 2 ; 4576.00784 1.00549281
NL: NLBGS 3 ; 306.11985 0.0672641566
NL: NLBGS 4 ; 24.2794342 0.00533495512
NL: NLBGS 5 ; 0.0928297501 2.0397615e-05
NL: NLBGS 6 ; 0.00109083731 2.39691257e-07
NL: NLBGS 7 ; 7.69361035e-05 1.69052811e-08
NL: NLBGS 8 ; 1.83501525e-07 4.0321055e-11
NL: NLBGS 9 ; 2.05485995e-09 4.51517343e-13
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 4503.59894 1
NL: NLBGS 2 ; 4234.91448 0.940340056
NL: NLBGS 3 ; 326.67644 0.0725367521
NL: NLBGS 4 ; 30.4250772 0.00675572529
NL: NLBGS 5 ; 0.202973049 4.50690774e-05
NL: NLBGS 6 ; 0.00203719361 4.52347919e-07
NL: NLBGS 7 ; 0.000155687463 3.45695665e-08
NL: NLBGS 8 ; 2.92297744e-07 6.49031471e-11
NL: NLBGS 9 ; 1.74593807e-09 3.87676188e-13
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 3359.11605 1
NL: NLBGS 2 ; 3377.85822 1.00557949
NL: NLBGS 3 ; 225.013885 0.066986041
NL: NLBGS 4 ; 18.0166534 0.00536351027
NL: NLBGS 5 ; 0.0658387616 1.96000259e-05
NL: NLBGS 6 ; 0.000837425599 2.49299395e-07
NL: NLBGS 7 ; 5.9477678e-05 1.77063481e-08
NL: NLBGS 8 ; 1.45142203e-07 4.32084516e-11
NL: NLBGS 9 ; 1.78190163e-09 5.3046742e-13
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 3323.72812 1
NL: NLBGS 2 ; 3126.0042 0.940511405
NL: NLBGS 3 ; 239.791305 0.0721452827
NL: NLBGS 4 ; 22.4651391 0.00675901829
NL: NLBGS 5 ; 0.138156923 4.15668545e-05
NL: NLBGS 6 ; 0.0014815623 4.45753157e-07
NL: NLBGS 7 ; 0.000113000827 3.3998216e-08
NL: NLBGS 8 ; 1.48328177e-07 4.46270488e-11
NL: NLBGS 9 ; 1.53465784e-09 4.61727852e-13
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 2601.22546 1
NL: NLBGS 2 ; 2617.1098 1.00610648
NL: NLBGS 3 ; 173.279214 0.0666144541
NL: NLBGS 4 ; 13.7046073 0.00526851961
NL: NLBGS 5 ; 0.0501319066 1.92724189e-05
NL: NLBGS 6 ; 0.000603949289 2.32178755e-07
NL: NLBGS 7 ; 4.25489211e-05 1.635726e-08
NL: NLBGS 8 ; 1.01842791e-07 3.91518508e-11
NL: NLBGS 9 ; 1.14522167e-09 4.40262364e-13
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 2550.86864 1
NL: NLBGS 2 ; 2401.74168 0.941538752
NL: NLBGS 3 ; 189.445917 0.0742672179
NL: NLBGS 4 ; 17.6187306 0.00690695332
NL: NLBGS 5 ; 0.111872837 4.38567613e-05
NL: NLBGS 6 ; 0.00115028288 4.50937716e-07
NL: NLBGS 7 ; 8.78614957e-05 3.44437554e-08
NL: NLBGS 8 ; 1.68576492e-07 6.60859165e-11
NL: NLBGS 9 ; 1.10019461e-09 4.31301945e-13
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 1681.10361 1
NL: NLBGS 2 ; 1691.57222 1.00622722
NL: NLBGS 3 ; 111.958257 0.0665980708
NL: NLBGS 4 ; 8.92973623 0.00531182979
NL: NLBGS 5 ; 0.0320292429 1.90525098e-05
NL: NLBGS 6 ; 0.000398077407 2.36795284e-07
NL: NLBGS 7 ; 2.82479523e-05 1.68032191e-08
NL: NLBGS 8 ; 6.91927109e-08 4.11590996e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 1647.82691 1
NL: NLBGS 2 ; 1552.03497 0.941867715
NL: NLBGS 3 ; 122.353976 0.074251716
NL: NLBGS 4 ; 11.4468683 0.00694664482
NL: NLBGS 5 ; 0.0697258954 4.23138467e-05
NL: NLBGS 6 ; 0.0007521354 4.56440779e-07
NL: NLBGS 7 ; 5.75020147e-05 3.48956642e-08
NL: NLBGS 8 ; 9.47556755e-08 5.75034154e-11
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 534.807124 1
NL: NLBGS 2 ; 536.319268 1.00282746
NL: NLBGS 3 ; 36.1026048 0.0675058411
NL: NLBGS 4 ; 2.86199037 0.00535144399
NL: NLBGS 5 ; 0.0110913874 2.0739042e-05
NL: NLBGS 6 ; 0.000143843779 2.68963842e-07
NL: NLBGS 7 ; 1.00670291e-05 1.8823663e-08
NL: NLBGS 8 ; 2.34205986e-08 4.37926078e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 544.086815 1
NL: NLBGS 2 ; 506.103644 0.930189134
NL: NLBGS 3 ; 37.66376 0.0692238057
NL: NLBGS 4 ; 3.42327333 0.00629177777
NL: NLBGS 5 ; 0.0225600466 4.14640567e-05
NL: NLBGS 6 ; 0.00017040105 3.13187243e-07
NL: NLBGS 7 ; 1.26074273e-05 2.317172e-08
NL: NLBGS 8 ; 1.2239101e-08 2.24947575e-11
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 256.046847 1
NL: NLBGS 2 ; 258.25441 1.00862171
NL: NLBGS 3 ; 16.580322 0.0647550329
NL: NLBGS 4 ; 1.32368588 0.00516970193
NL: NLBGS 5 ; 0.00444365411 1.7354848e-05
NL: NLBGS 6 ; 5.11339102e-05 1.99705291e-07
NL: NLBGS 7 ; 3.67408039e-06 1.43492507e-08
NL: NLBGS 8 ; 8.50899586e-09 3.32321837e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 242.884616 1
NL: NLBGS 2 ; 231.209128 0.951929899
NL: NLBGS 3 ; 18.4819744 0.0760936394
NL: NLBGS 4 ; 1.80708245 0.0074400861
NL: NLBGS 5 ; 0.0103592258 4.2650811e-05
NL: NLBGS 6 ; 0.000168916716 6.95460744e-07
NL: NLBGS 7 ; 1.36439626e-05 5.61746678e-08
NL: NLBGS 8 ; 4.06312665e-08 1.67286291e-10
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 1199.91089 1
NL: NLBGS 2 ; 1210.59169 1.00890133
NL: NLBGS 3 ; 76.8135009 0.0640160044
NL: NLBGS 4 ; 6.00240793 0.00500237808
NL: NLBGS 5 ; 0.0198460018 1.6539563e-05
NL: NLBGS 6 ; 0.000229705135 1.91435161e-07
NL: NLBGS 7 ; 1.61641755e-05 1.34711466e-08
NL: NLBGS 8 ; 3.78466263e-08 3.15411974e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 1135.42777 1
NL: NLBGS 2 ; 1082.45119 0.953342184
NL: NLBGS 3 ; 85.3180484 0.0751417666
NL: NLBGS 4 ; 8.17111519 0.00719650815
NL: NLBGS 5 ; 0.0471581836 4.1533407e-05
NL: NLBGS 6 ; 0.000726707871 6.40030032e-07
NL: NLBGS 7 ; 5.76826634e-05 5.0802583e-08
NL: NLBGS 8 ; 1.74531489e-07 1.53714304e-10
NL: NLBGS 9 ; 6.82561981e-10 6.01149629e-13
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 4596.81178 1
NL: NLBGS 2 ; 4641.85188 1.00979812
NL: NLBGS 3 ; 279.234386 0.0607452294
NL: NLBGS 4 ; 20.1376016 0.00438077575
NL: NLBGS 5 ; 0.0620977592 1.35088757e-05
NL: NLBGS 6 ; 0.000713256539 1.55163312e-07
NL: NLBGS 7 ; 4.65843017e-05 1.01340459e-08
NL: NLBGS 8 ; 1.14411129e-07 2.4889235e-11
NL: NLBGS 9 ; 1.12890979e-09 2.45585384e-13
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 4308.78922 1
NL: NLBGS 2 ; 4117.60132 0.955628394
NL: NLBGS 3 ; 314.553802 0.0730028288
NL: NLBGS 4 ; 27.6516442 0.00641749753
NL: NLBGS 5 ; 0.15997835 3.71283769e-05
NL: NLBGS 6 ; 0.00191439922 4.44300968e-07
NL: NLBGS 7 ; 0.000141273497 3.27872844e-08
NL: NLBGS 8 ; 4.49498065e-07 1.04321201e-10
NL: NLBGS 9 ; 1.58721633e-09 3.68367133e-13
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 1850.75175 1
NL: NLBGS 2 ; 1869.85962 1.01032438
NL: NLBGS 3 ; 108.757532 0.0587639762
NL: NLBGS 4 ; 7.56926922 0.00408983497
NL: NLBGS 5 ; 0.0205768277 1.11180917e-05
NL: NLBGS 6 ; 0.000252720273 1.36550066e-07
NL: NLBGS 7 ; 1.59834641e-05 8.63620103e-09
NL: NLBGS 8 ; 4.30560242e-08 2.32640733e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 1711.81232 1
NL: NLBGS 2 ; 1625.55671 0.949611523
NL: NLBGS 3 ; 133.246795 0.0778396051
NL: NLBGS 4 ; 10.8407644 0.00633291641
NL: NLBGS 5 ; 0.0580616025 3.39182057e-05
NL: NLBGS 6 ; 0.000422830525 2.47007525e-07
NL: NLBGS 7 ; 2.86318498e-05 1.67260449e-08
NL: NLBGS 8 ; 7.76875846e-08 4.53832371e-11
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 590.116582 1
NL: NLBGS 2 ; 596.89267 1.01148263
NL: NLBGS 3 ; 34.4002045 0.0582939126
NL: NLBGS 4 ; 2.3738814 0.00402273292
NL: NLBGS 5 ; 0.00633527682 1.0735636e-05
NL: NLBGS 6 ; 7.72042085e-05 1.30828739e-07
NL: NLBGS 7 ; 4.84775969e-06 8.2149186e-09
NL: NLBGS 8 ; 1.37059963e-08 2.32259128e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 541.871381 1
NL: NLBGS 2 ; 518.324852 0.956545907
NL: NLBGS 3 ; 41.3292465 0.0762713219
NL: NLBGS 4 ; 3.34458795 0.0061722912
NL: NLBGS 5 ; 0.0178849541 3.30059027e-05
NL: NLBGS 6 ; 0.000134842332 2.48845642e-07
NL: NLBGS 7 ; 9.08207474e-06 1.67605728e-08
NL: NLBGS 8 ; 2.61182972e-08 4.82001783e-11
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 527.343524 1
NL: NLBGS 2 ; 533.529294 1.01173006
NL: NLBGS 3 ; 30.6151043 0.0580553338
NL: NLBGS 4 ; 2.09085512 0.00396488253
NL: NLBGS 5 ; 0.00554487896 1.05147379e-05
NL: NLBGS 6 ; 6.81810211e-05 1.29291473e-07
NL: NLBGS 7 ; 4.23555666e-06 8.03187385e-09
NL: NLBGS 8 ; 1.21785713e-08 2.30941896e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 483.576294 1
NL: NLBGS 2 ; 463.501984 0.95848781
NL: NLBGS 3 ; 36.4040597 0.0752809021
NL: NLBGS 4 ; 2.92183708 0.0060421429
NL: NLBGS 5 ; 0.0157103881 3.24879202e-05
NL: NLBGS 6 ; 0.00011698578 2.41917937e-07
NL: NLBGS 7 ; 7.8150022e-06 1.61608464e-08
NL: NLBGS 8 ; 2.28400154e-08 4.7231462e-11
NL: NLBGS Converged
==================
AS_point_0.coupled
==================
NL: NLBGS 1 ; 316.194523 1
NL: NLBGS 2 ; 320.009443 1.0120651
NL: NLBGS 3 ; 18.1819581 0.0575024449
NL: NLBGS 4 ; 1.23493104 0.00390560542
NL: NLBGS 5 ; 0.00318279267 1.00659323e-05
NL: NLBGS 6 ; 3.92858171e-05 1.24245723e-07
NL: NLBGS 7 ; 2.43074681e-06 7.68750448e-09
NL: NLBGS 8 ; 7.00756213e-09 2.21621869e-11
NL: NLBGS Converged
==================
AS_point_1.coupled
==================
NL: NLBGS 1 ; 288.84284 1
NL: NLBGS 2 ; 276.826267 0.958397538
NL: NLBGS 3 ; 21.7740483 0.0753837216
NL: NLBGS 4 ; 1.72779277 0.0059817746
NL: NLBGS 5 ; 0.0091697294 3.17464313e-05
NL: NLBGS 6 ; 6.34805872e-05 2.19775526e-07
NL: NLBGS 7 ; 4.18425019e-06 1.4486252e-08
NL: NLBGS 8 ; 1.20817589e-08 4.18281404e-11
NL: NLBGS Converged
Optimization terminated successfully (Exit mode 0)
Current function value: 0.026596816564823787
Iterations: 17
Function evaluations: 20
Gradient evaluations: 17
Optimization Complete
-----------------------------------# prob.run_model()
print("The fuel burn value is", prob["AS_point_0.fuelburn"][0], "[kg]")
The fuel burn value is 2659.6816564823785 [kg]
print(
"The wingbox mass (excluding the wing_weight_ratio) is",
prob["wing.structural_mass"][0] / surf_dict["wing_weight_ratio"],
"[kg]",
)
The wingbox mass (excluding the wing_weight_ratio) is 1119.5523503688187 [kg]
There is plenty of room for improvement. A finer mesh and a tighter optimization tolerance should be used.