# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
# INITIAL AUTHORS - API and implementation and/or documentation
# :author: Simone Coniglio
# OTHER AUTHORS - MACROSCOPIC CHANGES
"""Generation of the design space and disciplines of the topology optimization
problems."""
from __future__ import annotations
from numpy import arange
from numpy import concatenate
from numpy import fix
from numpy import full
from numpy import kron
from numpy import logical_and
from numpy import ones
from numpy import where
from numpy import zeros
from gemseo.algos.design_space import DesignSpace
from gemseo.core.discipline import MDODiscipline
from gemseo.problems.topo_opt.density_filter_disc import DensityFilter
from gemseo.problems.topo_opt.fea_disc import FininiteElementAnalysis
from gemseo.problems.topo_opt.material_model_interpolation_disc import (
MaterialModelInterpolation,
)
from gemseo.problems.topo_opt.volume_fraction_disc import VolumeFraction
[docs]def initialize_design_space_and_discipline_to(
problem: str,
n_x: int,
n_y: int,
e0: float,
nu: float,
penalty: float,
min_member_size: float,
vf0: float,
) -> tuple[DesignSpace, list[MDODiscipline]]:
"""Initialize design space and disciplines for 2D topology optimization problems.
Args:
problem: The problem name, one of "MBB", "L-Shape", "Short_Cantilever".
n_x: The number of elements in the x-direction.
n_y: The number of elements in the y-direction.
e0: The full material Young's modulus.
nu: The material Poisson's ratio.
penalty: The SIMP penalty coefficient.
min_member_size: The minimum structural member size.
vf0: The minimum structural element dimension
imposed in the topology optimization solution.
Returns:
- The design space.
- The disciplines.
"""
# Define the nodal coordinates
x = 0
yy = zeros((n_x + 1) * (n_y + 1))
xx = zeros((n_x + 1) * (n_y + 1))
for i in range(1, n_x + 2):
for j in range(1, n_y + 2):
yy[x] = j
xx[x] = i
x += 1
yy = n_y + 1 - yy
xx -= 1
# Compute the centroid coordinates
xc = zeros(n_x * n_y)
yc = zeros(n_x * n_y)
for xi in range(n_x):
xc[xi * n_y : (xi + 1) * n_y] = xi + 0.5
for yi in range(n_y):
yc[arange(yi, n_x * n_y, n_y)] = yi + 0.5
yc = n_y - yc
# DEFINE LOADS AND SUPPORTS
if "MBB" == problem:
excitation_node = 0 # Node where the force is applied
excitation_direction = 1 # 0 for x and 1 for y
amplitude = -1 # Amplitude of the force
fixednodes = concatenate(
([[where(xx == min(xx))], [(n_x + 1) * (n_y + 1) - 1]]), axis=None
) # Fixed nodes
fixed_dir = concatenate(([[ones(n_y + 1)], [2]]), axis=None) - 1
emptyelts = [] # Mandatory empty elements
fullelts = [] # Mandatory full elements
elif "Short_Cantilever" == problem:
excitation_node = where(
logical_and((xx == max(xx)), (yy == fix(0.5 * min(yy) + 0.5 * max(yy))))
)[0][
0
] # Nodes where the force is applied
excitation_direction = 1 # 0 for x and 1 for y
amplitude = -1 # Amplitude of the force
fixednodes = kron([1, 1], where(xx == min(xx))[0]) # Fixed nodes
fixed_dir = concatenate([[ones(n_y + 1)], [2 * ones(n_y + 1)]]).flatten() - 1
emptyelts = [] # Mandatory empty elements
fullelts = [] # Mandatory full elements
elif "L-Shape" == problem:
excitation_node = where(
logical_and((xx == max(xx)), (yy == fix(0.5 * min(yy) + 0.5 * max(yy))))
)[0][
0
] # Nodes where the force is applied
excitation_direction = 1 # 0 for x and 1 for y
amplitude = -1 # Amplitude of the force
fixednodes = kron([1, 1], where(yy == max(yy))[0]) # Fixed nodes
fixed_dir = concatenate([[ones(n_x + 1)], [2 * ones(n_x + 1)]]).flatten()
emptyelts = where(
logical_and(xc >= (max(xx) + min(xx)) / 2, yc >= ((max(yy) + min(yy)) / 2))
)[
0
] # Mandatory empty elements
fullelts = [] # Mandatory full element
else:
msg = "The examples covered by this function are MBB, L-Shape and Short_Cantilever."
raise NotImplementedError(msg)
initial_point = full((n_x * n_y,), vf0)
initial_point[emptyelts] = 0
initial_point[fullelts] = 1
ds = DesignSpace()
ds.add_variable(
"x",
size=n_x * n_y,
l_b=zeros((n_x * n_y,)),
u_b=ones((n_x * n_y,)),
value=initial_point,
)
df = DensityFilter(n_x=n_x, n_y=n_y, min_member_size=min_member_size)
mmi = MaterialModelInterpolation(
e0=e0,
penalty=penalty,
n_x=n_x,
n_y=n_y,
empty_elements=emptyelts,
full_elements=fullelts,
)
fea = FininiteElementAnalysis(
nu=nu,
n_x=n_x,
n_y=n_y,
f_node=excitation_node,
f_direction=excitation_direction,
f_amplitude=amplitude,
fixed_nodes=fixednodes,
fixed_dir=fixed_dir,
)
vf = VolumeFraction(
n_x=n_x, n_y=n_y, empty_elements=emptyelts, full_elements=fullelts
)
disciplines = [df, mmi, fea, vf]
return ds, disciplines
