```python
import numpy as np
from fealpy.mesh import MeshFactory as MF
from fealpy.functionspace import LagrangeFiniteElementSpace
from fealpy.boundarycondition import DirichletBC
from fealpy.timeintegratoralg import solve_linear_system
from fealpy.linear_elasticity_model import LinearElasticityModel
import time
import matplotlib.pyplot as plt

class BoxDomain:
    def __init__(self, lx, ly, lz, nx, ny, nz):
        self.mesh = MF.boxmesh3d([0, lx, 0, ly, 0, lz], nx, ny, nz)

    def is_on_dirichlet_boundary(self, p):
        # Implement your logic here
        pass

    def is_on_neumann_boundary(self, p):
        # Implement your logic here
        pass

    def is_on_fracture_boundary(self, p):
        # Implement your logic here
        pass

    def displacement(self, p):
        # Define displacement function
        pass

    def strain(self, p):
        # Define strain function
        pass

    def stress(self, p):
        # Define stress function
        pass

    def source(self, p):
        # Define source function
        pass

    def dirichlet_condition(self, p):
        # Define Dirichlet boundary condition
        pass

    def neumann_condition(self, p):
        # Define Neumann boundary condition
        pass

class IterationCounter:
    def __init__(self):
        self.count = 0

    def increment(self):
        self.count += 1

    def get_count(self):
        return self.count

class LinearElasticitySolver:
    def __init__(self, mesh, p=1):
        self.space = LagrangeFiniteElementSpace(mesh, p=p)
        self.A = None
        self.f = None

    def precondition(self):
        # Implement preconditioning here
        pass

    def solve(self):
        # Implement solver here
        pass

# Main part
lx, ly, lz = 1.0, 1.0, 1.0
nx, ny, nz = 10, 10, 10
box_domain = BoxDomain(lx, ly, lz, nx, ny, nz)
mesh = box_domain.mesh

# Define finite element space
space = LagrangeFiniteElementSpace(mesh, p=2)

# Set up boundary conditions
dbc = DirichletBC(space, box_domain.dirichlet_condition)

# Define source function
f = lambda p: box_domain.source(p)

# Compute stiffness matrix and linear elasticity matrix
A = space.stiff_matrix()
b = space.source_vector(f)

# Apply boundary conditions
A, b = dbc.apply(A, b)

print("Shape of the matrix:", A.shape)

# Solve the system
solver = LinearElasticitySolver(mesh)
start_time = time.time()
solver.solve()
end_time = time.time()

print("Time to solve the system:", end_time - start_time)

# Plot the mesh
fig = plt.figure()
axes = fig.gca(projection='3d')
mesh.add_plot(axes)
plt.show()
```