def test_plastic_centroid():
## Test created in response to #114
# Since the section being tested is a compound geometry with two different
# materials, this tests that the plastic centroid takes into account the
# correct "center" of the original section which is affected by EA of each
# of the constituent geometries.
steel = Material(
name="Steel",
elastic_modulus=200e3,
poissons_ratio=0.3,
density=7.85e-6,
yield_strength=500,
color="grey",
)
timber = Material(
name="Timber",
elastic_modulus=5e3,
poissons_ratio=0.35,
density=6.5e-7,
yield_strength=20,
color="burlywood",
)
# create 310UB40.4
ub = i_section(d=304,
b=165,
t_f=10.2,
t_w=6.1,
r=11.4,
n_r=8,
material=steel)
# create timber panel on top of the UB
panel = rectangular_section(d=50, b=600, material=timber)
panel = panel.align_center(ub).align_to(ub, on="top")
# merge the two sections into one geometry object
geometry = CompoundGeometry([ub, panel])
# create a mesh - use a mesh size of 5 for the UB, 20 for the panel
geometry.create_mesh(mesh_sizes=[100, 100])
# create a Section object
section = Section(geometry)
# perform a geometric, warping and plastic analysis
section.calculate_geometric_properties()
section.calculate_plastic_properties()
x_pc, y_pc = section.get_pc()
assert x_pc == pytest.approx(82.5)
assert y_pc == pytest.approx(250.360654576)
def test_rectangle():
fy = 500
E = 200e3
b = 50
d = 100
steel = Material(
name="Steel",
elastic_modulus=E,
poissons_ratio=0.3,
yield_strength=fy,
density=8.05e-6,
color="grey",
)
Sx = b * d * d / 4
Mp = Sx * fy
geom_mat = sections.rectangular_section(d=d, b=b, material=steel)
geom_nomat = sections.rectangular_section(d=d, b=b)
geom_mat.create_mesh(mesh_sizes=[2.5])
geom_nomat.create_mesh(mesh_sizes=[2.5])
sec_mat = Section(geom_mat)
sec_nomat = Section(geom_nomat)
sec_mat.calculate_geometric_properties()
sec_mat.calculate_plastic_properties()
sec_nomat.calculate_geometric_properties()
sec_nomat.calculate_plastic_properties()
assert sec_nomat.get_s()[0] == pytest.approx(Sx)
assert sec_mat.get_s()[0] == pytest.approx(Mp)
assert sec_mat.get_s()[0] / fy == sec_nomat.get_s()[0]
def test_multi_nested_compound_geometry_from_points():
"""
Testing a multi-nested section. This section contains three nested materials in concentric
square rings with a hole going through the center of the whole section. This test confirms
that the section can be successfully built using .from_points, that the control_points
and hole nodes persist in the right locations, and that the plastic section calculation
raises a warning because the nested regions overlap.
"""
points = [
[-50.0, 50.0],
[50.0, 50.0],
[50.0, -50.0],
[-50.0, -50.0],
[37.5, -37.5],
[37.5, 37.5],
[-37.5, 37.5],
[-37.5, -37.5],
[25.0, -25.0],
[25.0, 25.0],
[-25.0, 25.0],
[-25.0, -25.0],
[12.5, -12.5],
[12.5, 12.5],
[-12.5, 12.5],
[-12.5, -12.5],
]
facets = [
[0, 1],
[1, 2],
[2, 3],
[3, 0],
[4, 5],
[5, 6],
[6, 7],
[7, 4],
[8, 9],
[9, 10],
[10, 11],
[11, 8],
[12, 13],
[13, 14],
[14, 15],
[15, 12],
]
control_points = [[-43.75, 0.0], [-31.25, 0.0], [-18.75, 0.0]]
holes = [[0, 0]]
mat1 = Material(
name="mat1",
elastic_modulus=2,
poissons_ratio=0.3,
density=1e-6,
yield_strength=5,
color="grey",
)
mat2 = Material(
name="mat2",
elastic_modulus=5,
poissons_ratio=0.2,
density=2e-6,
yield_strength=10,
color="blue",
)
mat3 = Material(
name="mat3",
elastic_modulus=1,
poissons_ratio=0.25,
density=1.5e-6,
yield_strength=3,
color="green",
)
materials = [mat1, mat2, mat3]
nested_compound = CompoundGeometry.from_points(
points=points,
facets=facets,
control_points=control_points,
holes=holes,
materials=materials,
)
wkt_test_geom = shapely.wkt.loads(
"MULTIPOLYGON (((50 50, 50 -50, -50 -50, -50 50, 50 50), (12.5 12.5, -12.5 12.5, -12.5 -12.5, 12.5 -12.5, 12.5 12.5)), ((-37.5 -37.5, -37.5 37.5, 37.5 37.5, 37.5 -37.5, -37.5 -37.5), (12.5 12.5, -12.5 12.5, -12.5 -12.5, 12.5 -12.5, 12.5 12.5)), ((-25 -25, -25 25, 25 25, 25 -25, -25 -25), (12.5 12.5, -12.5 12.5, -12.5 -12.5, 12.5 -12.5, 12.5 12.5)))"
)
assert (nested_compound.geom - wkt_test_geom) == Polygon()
assert nested_compound.control_points == [
(-43.75, 0.0),
(-31.25, 0.0),
(-18.75, 0.0),
]
assert nested_compound.holes == [(0, 0)]
# test materials
for idx, geom in enumerate(nested_compound.geoms):
assert geom.material == materials[idx]
# Section contains overlapping geometries which will result in potentially incorrect
# plastic properties calculation (depends on user intent and geometry).
# Test to ensure a warning is raised about this to notify the user.
nested_compound.create_mesh([25, 30, 35])
nested_compound_sec = Section(nested_compound)
nested_compound_sec.calculate_geometric_properties()
with pytest.warns(UserWarning):
nested_compound_sec.calculate_plastic_properties()
)
from shapely import wkt
import json
big_sq = rectangular_section(d=300, b=250)
small_sq = rectangular_section(d=100, b=75)
small_hole = rectangular_section(d=40, b=30).align_center(small_sq)
i_sec = i_section(d=200, b=100, t_f=20, t_w=10, r=12, n_r=12)
small_sq_w_hole = small_sq - small_hole
composite = (big_sq + small_sq_w_hole.align_to(
big_sq, on="top", inner=True).align_to(big_sq, on="top") + i_sec.align_to(
big_sq, on="bottom", inner=True).align_to(big_sq, on="right"))
composite.create_mesh([200])
comp_sec = Section(composite)
comp_sec.calculate_geometric_properties()
comp_sec.calculate_plastic_properties()
# Subtractive modelling
nested_geom = (small_sq - small_hole) + small_hole
nested_geom.create_mesh([50])
nested_sec = Section(nested_geom)
# Overlapped modelling
overlay_geom = small_sq + small_hole
overlay_geom.create_mesh([50])
overlay_sec = Section(overlay_geom)
steel = Material("steel", 200e3, 0.3, 7.85e-6, 400, "grey")
def test_material_persistence():
# %% # Mirror the 200 PFC about the y-axis pfc1 = pfc1.mirror_section(axis="y", mirror_point=[0, 0]) # %% # Merge the pfc sections geometry = ((pfc1 - pfc2) | pfc1) + pfc2 # %% # Rotate the geometry counter-clockwise by 30 degrees geometry = geometry.rotate_section(angle=30) geometry.plot_geometry() # %% # Create a mesh and section. For the mesh, use a mesh size of 5 for the 200PFC # and 4 for the 150PFC geometry.create_mesh(mesh_sizes=[5, 4]) section = Section(geometry, time_info=True) section.display_mesh_info() # display the mesh information section.plot_mesh() # plot the generated mesh # %% # Perform a geometric, warping and plastic analysis, displaying the time info # and the iteration info for the plastic analysis section.calculate_geometric_properties() section.calculate_warping_properties() section.calculate_plastic_properties(verbose=True) section.plot_centroids()
# %%
# Create a 50 diameter circle discretised by 64 points
geometry = sections.circular_section(d=50, n=64)
geometry.plot_geometry()
# %%
# Create a mesh with a mesh size of 2.5 and display information about it
geometry.create_mesh(mesh_sizes=[2.5])
section = Section(geometry, time_info=True)
section.display_mesh_info()
section.plot_mesh()
# %%
# perform a geometric, warping and plastic analysis, displaying the time info
section.calculate_geometric_properties()
section.calculate_warping_properties()
section.calculate_plastic_properties()
# %%
# Print the results to the terminal
section.display_results()
# %%
# Get and print the second moments of area and the torsion constant
(ixx_c, iyy_c, ixy_c) = section.get_ic()
j = section.get_j()
print("Ixx + Iyy = {0:.3f}".format(ixx_c + iyy_c))
print("J = {0:.3f}".format(j))
import pytest_check as check
from shapely.geometry import Polygon
from sectionproperties.pre.geometry import Geometry
import sectionproperties.pre.library.primitive_sections as sections
import sectionproperties.pre.library.steel_sections as steel_sections
from sectionproperties.analysis.section import Section
from sectionproperties.tests.helper_functions import validate_properties
# Setup for angle section
angle = steel_sections.angle_section(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
angle.create_mesh(mesh_sizes=2.5)
angle_section = Section(angle)
angle_section.calculate_geometric_properties()
angle_section.calculate_plastic_properties()
angle_section.calculate_warping_properties()
def test_angle_all_properties():
check.almost_equal(angle_section.section_props.area, 2747.059)
check.almost_equal(angle_section.section_props.perimeter, 471.3501)
check.almost_equal(angle_section.section_props.cx, 2.122282e1)
check.almost_equal(angle_section.section_props.cy, 5.098127e1)
check.almost_equal(angle_section.section_props.ixx_g, 1.342632e7)
check.almost_equal(angle_section.section_props.iyy_g, 2.955753e6)
check.almost_equal(angle_section.section_props.ixy_g, 1.086603e6)
check.almost_equal(angle_section.section_props.ixx_c, 6.286470e6)
check.almost_equal(angle_section.section_props.iyy_c, 1.718455e6)
check.almost_equal(angle_section.section_props.ixy_c, -1.885622e6)
check.almost_equal(angle_section.section_props.zxx_plus, 6.348769e4)
check.almost_equal(angle_section.section_props.zxx_minus, 1.233094e5)
# import unittest
import sectionproperties.pre.library.primitive_sections as primitive_sections
import sectionproperties.pre.pre as pre
from sectionproperties.analysis.section import Section
from sectionproperties.tests.helper_functions import validate_properties
import sectionproperties.analysis.section as file
# Rectangle section setup
rectangle_geometry = primitive_sections.rectangular_section(b=50, d=100)
rectangle_geometry.create_mesh(mesh_sizes=100)
rectangle_section = Section(rectangle_geometry)
rectangle_section.calculate_geometric_properties()
rectangle_section.calculate_warping_properties()
rectangle_section.calculate_plastic_properties()
tol = 1e-6
warp_tol = 1e-4
def test_rectangular_section_geometric():
check.almost_equal(rectangle_section.section_props.area, 100 * 50, rel=tol)
check.almost_equal(rectangle_section.section_props.perimeter,
2 * 100 + 2 * 50,
rel=tol)
check.almost_equal(rectangle_section.section_props.mass,
1 * 100 * 50,
rel=tol)
check.almost_equal(rectangle_section.section_props.ea,
1 * 100 * 50,