 ```python
import numpy as np
from os import path
from mpi4py import MPI
from tacs import Tacs, set_log_level, constitutive, element, functions, util, comm
from tacs.examples.bdf_utils import createTACSProbsFromBDF, set_mesh, compute, set_derivative, compute_partials, addLoadFromBDF

# Initialize MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()

# Load the structural mesh from a BDF file
bdf_file = 'path/to/bdf/file'
tacs_mesh = createTACSProbsFromBDF(bdf_file, comm)

# Set constitutive properties
density = 2.78e-3
elastic_modulus = 70.0e9
poisson_ratio = 0.3
shear_correction_factor = 5.0/6.0
yield_stress = 250.0e6
thickness = 0.001

# Loop over components of the mesh, creating stiffness and element object for each
for comp in tacs_mesh.getComponents():
    set_mesh(comp, density, elastic_modulus, poisson_ratio, shear_correction_factor, yield_stress, thickness)

# Create a TACS assembler object from the mesh loader
tacs_assembler = createTACSAssembler(tacs_mesh)

# Create a KS function and get the design variable values
num_design_vars = tacs_mesh.getNumDesignVars()
design_vec = util.createDesignVec(num_design_vars)
tacs_mesh.getDesignVars(design_vec)

# Get the node locations and create the forces
num_nodes = tacs_mesh.getNumNodes()
node_coords = util.createCoords(num_nodes, 3)
tacs_mesh.getNodes(node_coords)

# Set up and solve the analysis problem
num_loads = tacs_mesh.getNumLoads()
load_vec = util.createLoadVec(num_loads)

for i in range(num_loads):
    addLoadFromBDF(tacs_mesh, i, load_vec)

tacs_probs = createTACSProbs(tacs_assembler, design_vec, node_coords, load_vec)

num_eqns = tacs_probs.getNumEquations()
displ_vec = util.createVec(num_eqns)
veloc_vec = util.createVec(num_eqns)
accel_vec = util.createVec(num_eqns)
resid_vec = util.createVec(num_eqns)

tacs_probs.setUp()

# Evaluate the function and solve for the adjoint variables
compute(tacs_probs, displ_vec, veloc_vec, accel_vec, resid_vec)

# Compute the total derivative with respect to material design variables and nodal locations
num_partials = tacs_probs.getNumPartialDerivs()
partial_vec = util.createVec(num_partials)
compute_partials(tacs_probs, partial_vec)

# Create a random direction along which to perturb the nodes and compute the total derivative with respect to nodal locations
d_node_coords = util.createCoords(num_nodes, 3)
np.random.seed(42)
for i in range(num_nodes):
    d_node_coords[i, :] = np.random.rand(3)

d_displ_vec = util.createVec(num_eqns)
d_veloc_vec = util.createVec(num_eqns)
d_accel_vec = util.createVec(num_eqns)
d_resid_vec = util.createVec(num_eqns)

tacs_probs.setUpDeriv()

for i in range(num_loads):
    _addLoadFromBDF(tacs_probs, i, d_load_vec)

d_tacs_probs = _createTACSProbs(tacs_assembler, design_vec, d_node_coords, d_load_vec)
d_tacs_probs.setUpDeriv()

# Set the complex step and compute the perturbed solution
eps = 1e-40
d_displ_vec.axpy(eps, displ_vec)

# Evaluate the function for the perturbed solution and compute the projected derivative
d_resid_vec.set(0.0)
compute(d_tacs_probs, d_displ_vec, d_veloc_vec, d_accel_vec, d_resid_vec)

projected_deriv = d_resid_vec.dot(displ_vec) / eps

# Output the results for visualization
output_dir = 'path/to/output/directory'
output_viewer = _createOutputViewer(tacs_mesh, output_dir)
output_groups = _createOutputGroups(tacs_mesh, output_dir)
_createVariables(tacs_mesh, output_groups)
_writeOutput(tacs_mesh, output_groups, displ_vec, veloc_vec, accel_vec, resid_vec)
```