Structural Optimization

OpenAeroStruct can also handle structural-only optimization problems. Here we prescribe a load on the spar and allow the optimizer to vary the structural thickness to minimize weight subject to failure constraints. Although doing structural-only optimizations is relatively rare, this is a building block towards aerostructural optimization.

For more details about mesh_dict and surf_dict in the following script, see Mesh and Surface Dictionaries.

import numpy as np

from openaerostruct.geometry.utils import generate_mesh
from openaerostruct.structures.struct_groups import SpatialBeamAlone

import openmdao.api as om

# Create a dictionary to store options about the surface
mesh_dict = {"num_y": 7, "wing_type": "CRM", "symmetry": True, "num_twist_cp": 5}

mesh, twist_cp = generate_mesh(mesh_dict)

surf_dict = {
    # Wing definition
    "name": "wing",  # name of the surface
    "symmetry": True,  # if true, model one half of wing
    # reflected across the plane y = 0
    "fem_model_type": "tube",
    "mesh": mesh,
    # Structural values are based on aluminum 7075
    "E": 70.0e9,  # [Pa] Young's modulus of the spar
    "G": 30.0e9,  # [Pa] shear modulus of the spar
    "yield": 500.0e6 / 2.5,  # [Pa] yield stress divided by 2.5 for limiting case
    "mrho": 3.0e3,  # [kg/m^3] material density
    "fem_origin": 0.35,  # normalized chordwise location of the spar
    "t_over_c_cp": np.array([0.15]),  # maximum airfoil thickness
    "thickness_cp": np.ones((3)) * 0.1,
    "wing_weight_ratio": 2.0,
    "struct_weight_relief": False,  # True to add the weight of the structure to the loads on the structure
    "distributed_fuel_weight": False,
    "exact_failure_constraint": False,
}

# Create the problem and assign the model group
prob = om.Problem()

ny = surf_dict["mesh"].shape[1]

indep_var_comp = om.IndepVarComp()
indep_var_comp.add_output("loads", val=np.ones((ny, 6)) * 2e5, units="N")
indep_var_comp.add_output("load_factor", val=1.0)

struct_group = SpatialBeamAlone(surface=surf_dict)

# Add indep_vars to the structural group
struct_group.add_subsystem("indep_vars", indep_var_comp, promotes=["*"])

prob.model.add_subsystem(surf_dict["name"], struct_group)

prob.driver = om.ScipyOptimizeDriver()
prob.driver.options["disp"] = True
prob.driver.options["tol"] = 1e-9

# Setup problem and add design variables, constraint, and objective
prob.model.add_design_var("wing.thickness_cp", lower=0.01, upper=0.5, ref=1e-1)
prob.model.add_constraint("wing.failure", upper=0.0)
prob.model.add_constraint("wing.thickness_intersects", upper=0.0)

# Add design variables, constraisnt, and objective on the problem
prob.model.add_objective("wing.structural_mass", scaler=1e-5)

# Set up the problem
prob.setup(force_alloc_complex=False)

prob.run_driver()
Optimization terminated successfully    (Exit mode 0)
            Current function value: [0.71088468]
            Iterations: 14
            Function evaluations: 22
            Gradient evaluations: 14
Optimization Complete
-----------------------------------
print(prob["wing.structural_mass"][0])
71088.46823994313