 Here is the Python code that follows your instructions, using the TACS library:

```python
import numpy as np
import os
from mpi4py import MPI
from tacs import *

comm = MPI.COMM_WORLD
rank = comm.Get_rank()
size = comm.Get_size()

# Load the structural mesh from a BDF file
mesh = TacsMesh()
createTACSProbsFromBDF(mesh, 'your_bdf_file.bdf')

# Set constitutive properties
density = 7850.0
E = 3e11
nu = 0.3
SCF = 1.0
YS = 350e6
thickness = 1.0

set_mesh(mesh, 'MATERIAL', 'DENSITY', density)
set_mesh(mesh, 'MATERIAL', 'E', E)
set_mesh(mesh, 'MATERIAL', 'NU', nu)
set_mesh(mesh, 'MATERIAL', 'SCF', SCF)
set_mesh(mesh, 'MATERIAL', 'YS', YS)
set_mesh(mesh, 'MATERIAL', 'THICKNESS', thickness)

# Loop over components of the mesh, creating stiffness and element object for each
comp_nums = getElementObjectNumsForComp(mesh, 'COMP1')
for comp_num in comp_nums:
    elem_obj_nums = getElementObjectNumsForComp(mesh, 'COMP1', comp_num)
    for elem_obj_num in elem_obj_nums:
        elem_id = getElementObjectForElemID(mesh, elem_obj_num)[0]
        setElementObject(mesh, elem_obj_num, 'E', E)
        setElementObject(mesh, elem_obj_num, 'NU', nu)
        setElementObject(mesh, elem_obj_num, 'SCF', SCF)
        setElementObject(mesh, elem_obj_num, 'YS', YS)
        setElementObject(mesh, elem_obj_num, 'THICKNESS', thickness)
        createStiffness(mesh, elem_obj_num)

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

# Create a KS function and get the design variable values
design_vec = createDesignVec(mesh, 'DESIGN_VARS')
analysis_func = AnalysisFunction(assembler, design_vec)
design_values = analysis_func.get_design_values()

# Get the node locations and create the forces
node_coords = getNodeCoords(mesh)
forces = np.zeros((mesh.numNodes, 6))

# Set up and solve the analysis problem by creating vectors, assembling the Jacobian, factoring, and solving the linear system
soln_vec = createVector(mesh.numNodes)
rhs_vec = createVector(mesh.numNodes)

assemble(assembler, soln_vec, rhs_vec)
factor(assembler, soln_vec, rhs_vec)
solve(soln_vec, rhs_vec)

# Evaluate the function and solve for the adjoint variables
eval_func = analysis_func.eval_func
adjoint_vars = analysis_func.solve_adjoint(soln_vec, rhs_vec)

# Compute the total derivative with respect to material design variables and nodal locations
partials = np.zeros((mesh.numDesignVars, mesh.numNodes, 6))
compute_partials(analysis_func, partials, soln_vec, rhs_vec)

# Create a random direction along which to perturb the nodes and compute the total derivative with respect to nodal locations
perturb_dir = np.random.rand(mesh.numNodes, 6)
perturbed_soln_vec = soln_vec.copy()
perturbed_soln_vec += perturb_dir * 1e-3

# Set the complex step and compute the perturbed solution
complex_step = 1.0j * 1e-6
perturbed_rhs_vec = rhs_vec.copy()
perturbed_rhs_vec += complex_step * assemble(assembler, perturbed_soln_vec, None)
solve(perturbed_soln_vec, perturbed_rhs_vec)

# Evaluate the function for the perturbed solution and compute the projected derivative
perturbed_eval_func = analysis_func.eval_func
perturbed_adjoint_vars = analysis_func.solve_adjoint(perturbed_soln_vec, perturbed_rhs_vec)
projected_derivative = np.real(np.conj(perturbed_eval_func(perturbed_soln_vec)) * perturbed_adjoint_vars)

# Output the results for visualization
output_viewer = _createOutputViewer(mesh, 'output_viewer')
_createOutputGroups(output_viewer, 'SOLUTION', 'NODE_COORDS', 'SOLUTION_VECTORS', 'DESIGN_VARS', 'ADJOINT_VARS', 'PARTIALS', 'PROJECTED_DERIVATIVE')
writeOutput(output_viewer, 'SOLUTION', 'NODE_COORDS', node_coords)
writeOutput(output_viewer, 'SOLUTION', 'SOLUTION_VECTORS', soln_vec)
writeOutput(output_viewer, 'DESIGN_VARS', 'DESIGN_VARS', design_values)
writeOutput(output_viewer, 'ADJOINT_VARS', 'ADJOINT_VARS', adjoint_vars)
writeOutput(output_viewer, 'PARTIALS', 'PARTIALS', partials)
writeOutput(output_viewer, 'PROJECTED_DERIVATIVE', 'PROJECTED_DERIVATIVE', projected_derivative)
```

Please replace `'your_bdf_file.bdf'` with the path to your BDF file. This code assumes that the BDF file contains a single component (COMP1) and that the design variables are stored in a group named 'DESIGN_VARS'. Adjust the code accordingly if your BDF file has multiple components or design variable groups.