def get_properties():
# build the lists of points, facets, holes and control points
points = request.json['points']
facets = request.json['facets']
holes = request.json['holes']
control_points = request.json['controls']
# create the custom geometry object
geometry = sections.CustomSection(points, facets, holes, control_points)
geometry.clean_geometry() # clean the geometry
# create the mesh - use a smaller refinement for the angle region
mesh = geometry.create_mesh(mesh_sizes=[0.0005, 0.001])
# create a CrossSection object
section = CrossSection(geometry, mesh)
# perform a geometric, warping and plastic analysis
section.calculate_geometric_properties()
section.calculate_warping_properties()
section.calculate_plastic_properties()
properties = section.display_results()
return jsonify({'properties': properties})
# create a mesh - use a mesh size of 5 for the UB, 20 for the panel
mesh = geometry.create_mesh(mesh_sizes=[5, 20])
# create a CrossSection object - take care to list the materials in the same order as entered into
# the MergedSection
section = CrossSection(geometry, mesh, materials=[steel, timber])
section.display_mesh_info() # display the mesh information
# plot the mesh with coloured materials and a line transparency of 0.5
section.plot_mesh(materials=True, alpha=0.5)
# perform a geometric, warping and plastic analysis
section.calculate_geometric_properties(time_info=True)
section.calculate_warping_properties(time_info=True)
section.calculate_plastic_properties(time_info=True, verbose=True)
# perform a stress analysis with N = 100 kN, Mxx = 120 kN.m and Vy = 75 kN
stress_post = section.calculate_stress(N=-100e3,
Mxx=-120e6,
Vy=-75e3,
time_info=True)
# print the results to the terminal
section.display_results()
# plot the centroids
section.plot_centroids()
stress_post.plot_stress_n_zz(pause=False) # plot the axial stress
stress_post.plot_stress_m_zz(pause=False) # plot the bending stress
def test_angle(self):
"""Section properties are validated against results from the Strand7
beam section utility."""
geometry = sections.AngleSection(d=150,
b=90,
t=12,
r_r=10,
r_t=5,
n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)
val_list = []
val_list.append({"prop": "area", "val": 2746.73, "tol": 2e-4})
val_list.append({"prop": "perimeter", "val": 471, "tol": 1e-3})
val_list.append({"prop": "cx", "val": 21.2255, "tol": 2e-4})
val_list.append({"prop": "cy", "val": 50.9893, "tol": 2e-4})
val_list.append({"prop": "ixx_g", "val": 1.3428e7, "tol": 2e-4})
val_list.append({"prop": "iyy_g", "val": 2.95629e6, "tol": 2e-4})
val_list.append({"prop": "ixy_g", "val": 1.08669e6, "tol": 2e-4})
val_list.append({"prop": "ixx_c", "val": 6.28678e6, "tol": 2e-4})
val_list.append({"prop": "iyy_c", "val": 1.71882e6, "tol": 3e-4})
val_list.append({"prop": "ixy_c", "val": -1.88603e6, "tol": 3e-4})
val_list.append({"prop": "zxx_plus", "val": 63496.0, "tol": 2e-4})
val_list.append({"prop": "zxx_minus", "val": 123296, "tol": 2e-4})
val_list.append({"prop": "zyy_plus", "val": 24992.1, "tol": 3e-4})
val_list.append({"prop": "zyy_minus", "val": 80979.0, "tol": 2e-4})
val_list.append({"prop": "rx", "val": 47.8416, "tol": 2e-4})
val_list.append({"prop": "ry", "val": 25.0154, "tol": 2e-4})
val_list.append({"prop": "i11_c", "val": 6.96484e6, "tol": 2e-4})
val_list.append({"prop": "i22_c", "val": 1.04076e6, "tol": 2e-4})
val_list.append({"prop": "phi", "val": 19.7744 - 180, "tol": 2e-4})
val_list.append({"prop": "z11_plus", "val": 97751.9, "tol": 2e-4})
val_list.append({"prop": "z11_minus", "val": 69403.3, "tol": 2e-4})
val_list.append({"prop": "z22_plus", "val": 27959.0, "tol": 2e-4})
val_list.append({"prop": "z22_minus", "val": 20761.6, "tol": 3e-4})
val_list.append({"prop": "r11", "val": 50.3556, "tol": 2e-4})
val_list.append({"prop": "r22", "val": 19.4656, "tol": 2e-4})
val_list.append({"prop": "sxx", "val": 113541, "tol": 2e-4})
val_list.append({"prop": "syy", "val": 45724.6, "tol": 2e-4})
val_list.append({
"prop": "sf_xx_plus",
"val": 113541 / 63496.0,
"tol": 2e-4
})
val_list.append({
"prop": "sf_xx_minus",
"val": 113541 / 123296,
"tol": 2e-4
})
val_list.append({
"prop": "sf_yy_plus",
"val": 45724.6 / 24992.1,
"tol": 3e-4
})
val_list.append({
"prop": "sf_yy_minus",
"val": 45724.6 / 80979.0,
"tol": 2e-4
})
val_list.append({"prop": "s11", "val": 121030, "tol": 2e-4})
val_list.append({"prop": "s22", "val": 43760.6, "tol": 2e-4})
val_list.append({
"prop": "sf_11_plus",
"val": 121030 / 97751.9,
"tol": 2e-4
})
val_list.append({
"prop": "sf_11_minus",
"val": 121030 / 69403.3,
"tol": 2e-4
})
val_list.append({
"prop": "sf_22_plus",
"val": 43760.6 / 27959.0,
"tol": 2e-4
})
val_list.append({
"prop": "sf_22_minus",
"val": 43760.6 / 20761.6,
"tol": 3e-4
})
val_list.append({"prop": "j", "val": 135333, "tol": 1e-3})
val_list.append({"prop": "gamma", "val": 1.62288e8, "tol": 5e-4})
val_list.append({"prop": "A_s11", "val": 885.444, "tol": 2e-4})
val_list.append({"prop": "A_s22", "val": 1459.72, "tol": 4e-4})
val_list.append({"prop": "x11_se", "val": 28.719, "tol": 1e-3})
val_list.append({"prop": "y22_se", "val": 35.2348, "tol": 5e-4})
section.calculate_geometric_properties()
section.calculate_plastic_properties()
section.calculate_warping_properties()
validate_properties(self, val_list, section)
def test_custom(self):
"""Section properties are validated against results from the Strand7
beam section utility."""
points = [[-10, 0], [110, 0], [100, 10], [55, 10], [55, 90], [100, 90],
[110, 100], [110, 110], [-10, 110], [-10, 100], [0, 90],
[45, 90], [45, 10], [-10, 10]]
facets = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6,
7], [7, 8],
[8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 0]]
holes = []
control_points = [[0, 5]]
geometry = sections.CustomSection(points, facets, holes,
control_points)
mesh = geometry.create_mesh(mesh_sizes=[5])
section = CrossSection(geometry, mesh)
val_list = []
val_list.append({"prop": "area", "val": 4250, "tol": None})
val_list.append({"prop": "cx", "val": 49.3333, "tol": None})
val_list.append({"prop": "cy", "val": 65.0196, "tol": None})
val_list.append({"prop": "ixx_g", "val": 2.56725e7, "tol": None})
val_list.append({"prop": "iyy_g", "val": 1.41858e7, "tol": None})
val_list.append({"prop": "ixy_g", "val": 1.37979e7, "tol": None})
val_list.append({"prop": "ixx_c", "val": 7.70542e6, "tol": None})
val_list.append({"prop": "iyy_c", "val": 3.84228e6, "tol": None})
val_list.append({"prop": "ixy_c", "val": 165472, "tol": None})
val_list.append({"prop": "zxx_plus", "val": 171306, "tol": None})
val_list.append({"prop": "zxx_minus", "val": 118509, "tol": None})
val_list.append({"prop": "zyy_plus", "val": 63334.2, "tol": None})
val_list.append({"prop": "zyy_minus", "val": 64757.5, "tol": None})
val_list.append({"prop": "rx", "val": 42.5798, "tol": None})
val_list.append({"prop": "ry", "val": 30.0677, "tol": None})
val_list.append({"prop": "phi", "val": 177.552 - 180, "tol": 1e-4})
val_list.append({"prop": "i11_c", "val": 7.71249e6, "tol": None})
val_list.append({"prop": "i22_c", "val": 3.8352e6, "tol": None})
val_list.append({"prop": "z11_plus", "val": 162263, "tol": None})
val_list.append({"prop": "z11_minus", "val": 114268, "tol": None})
val_list.append({"prop": "z22_plus", "val": 60503.0, "tol": None})
val_list.append({"prop": "z22_minus", "val": 62666.1, "tol": None})
val_list.append({"prop": "r11", "val": 42.5993, "tol": None})
val_list.append({"prop": "r22", "val": 30.04, "tol": None})
val_list.append({"prop": "sxx", "val": 153196, "tol": None})
val_list.append({"prop": "syy", "val": 101494, "tol": None})
val_list.append({
"prop": "sf_xx_plus",
"val": 153196 / 171306,
"tol": None
})
val_list.append({
"prop": "sf_xx_minus",
"val": 153196 / 118509,
"tol": None
})
val_list.append({
"prop": "sf_yy_plus",
"val": 101494 / 63334.2,
"tol": None
})
val_list.append({
"prop": "sf_yy_minus",
"val": 101494 / 64757.5,
"tol": None
})
val_list.append({"prop": "s11", "val": 153347, "tol": None})
val_list.append({"prop": "s22", "val": 101501, "tol": None})
val_list.append({
"prop": "sf_11_plus",
"val": 153347 / 162263,
"tol": None
})
val_list.append({
"prop": "sf_11_minus",
"val": 153347 / 114268,
"tol": None
})
val_list.append({
"prop": "sf_22_plus",
"val": 101501 / 60503.0,
"tol": None
})
val_list.append({
"prop": "sf_22_minus",
"val": 101501 / 62666.1,
"tol": None
})
val_list.append({"prop": "j", "val": 347040, "tol": 5e-3})
val_list.append({"prop": "gamma", "val": 7.53539e9, "tol": 1e-3})
val_list.append({"prop": "A_s11", "val": 2945.53, "tol": 5e-4})
val_list.append({"prop": "A_s22", "val": 956.014, "tol": 5e-4})
val_list.append({"prop": "x11_se", "val": 1.9134, "tol": 5e-3})
val_list.append({"prop": "y22_se", "val": 3.02028, "tol": 5e-3})
section.calculate_geometric_properties()
section.calculate_plastic_properties()
section.calculate_warping_properties()
validate_properties(self, val_list, section)
class TestRectangle(unittest.TestCase):
"""Section properties are mostly validated against hand calcs. Results from
Strand7 and Roark's Formulas for Stress and Strain are used for some
warping properties."""
def setUp(self):
self.geometry = sections.RectangularSection(d=100, b=50)
self.mesh = self.geometry.create_mesh(mesh_sizes=[10])
self.section = CrossSection(self.geometry, self.mesh)
def test_geometric(self):
self.section.calculate_geometric_properties()
val_list = []
val_list.append({"prop": "area", "val": 100 * 50, "tol": None})
val_list.append({
"prop": "perimeter",
"val": 100 * 2 + 50 * 2,
"tol": None
})
val_list.append({"prop": "ea", "val": 1 * 100 * 50, "tol": None})
val_list.append({"prop": "qx", "val": 100 * 50 * 50, "tol": None})
val_list.append({"prop": "qy", "val": 100 * 50 * 25, "tol": None})
val_list.append({"prop": "ixx_g", "val": 50 * 100**3 / 3, "tol": None})
val_list.append({"prop": "iyy_g", "val": 100 * 50**3 / 3, "tol": None})
val_list.append({
"prop": "ixy_g",
"val": 100 * 50 * 50 * 25,
"tol": None
})
val_list.append({"prop": "cx", "val": 50 / 2, "tol": None})
val_list.append({"prop": "cy", "val": 100 / 2, "tol": None})
val_list.append({
"prop": "ixx_c",
"val": 50 * 100**3 / 12,
"tol": None
})
val_list.append({
"prop": "iyy_c",
"val": 100 * 50**3 / 12,
"tol": None
})
val_list.append({"prop": "ixy_c", "val": 0, "tol": None})
val_list.append({
"prop": "zxx_plus",
"val": 50 * 100**2 / 6,
"tol": None
})
val_list.append({
"prop": "zxx_minus",
"val": 50 * 100**2 / 6,
"tol": None
})
val_list.append({
"prop": "zyy_plus",
"val": 100 * 50**2 / 6,
"tol": None
})
val_list.append({
"prop": "zyy_minus",
"val": 100 * 50**2 / 6,
"tol": None
})
val_list.append({
"prop": "rx",
"val": (50 * 100**3 / 12 / 100 / 50)**0.5,
"tol": None
})
val_list.append({
"prop": "ry",
"val": (100 * 50**3 / 12 / 100 / 50)**0.5,
"tol": None
})
val_list.append({
"prop": "i11_c",
"val": 50 * 100**3 / 12,
"tol": None
})
val_list.append({
"prop": "i22_c",
"val": 100 * 50**3 / 12,
"tol": None
})
val_list.append({"prop": "phi", "val": 0, "tol": None})
val_list.append({
"prop": "z11_plus",
"val": 50 * 100**2 / 6,
"tol": None
})
val_list.append({
"prop": "z11_minus",
"val": 50 * 100**2 / 6,
"tol": None
})
val_list.append({
"prop": "z22_plus",
"val": 100 * 50**2 / 6,
"tol": None
})
val_list.append({
"prop": "z22_minus",
"val": 100 * 50**2 / 6,
"tol": None
})
val_list.append({
"prop": "r11",
"val": (50 * 100**3 / 12 / 100 / 50)**0.5,
"tol": None
})
val_list.append({
"prop": "r22",
"val": (100 * 50**3 / 12 / 100 / 50)**0.5,
"tol": None
})
validate_properties(self, val_list, self.section)
def test_plastic(self):
self.section.calculate_geometric_properties()
self.section.calculate_plastic_properties()
val_list = []
val_list.append({"prop": "x_pc", "val": 50 / 2, "tol": None})
val_list.append({"prop": "y_pc", "val": 100 / 2, "tol": None})
val_list.append({"prop": "x11_pc", "val": 50 / 2, "tol": None})
val_list.append({"prop": "y22_pc", "val": 100 / 2, "tol": None})
val_list.append({"prop": "sxx", "val": 50 * 100**2 / 4, "tol": None})
val_list.append({"prop": "syy", "val": 100 * 50**2 / 4, "tol": None})
val_list.append({"prop": "s11", "val": 50 * 100**2 / 4, "tol": None})
val_list.append({"prop": "s22", "val": 100 * 50**2 / 4, "tol": None})
val_list.append({"prop": "sf_xx_plus", "val": 1.5, "tol": None})
val_list.append({"prop": "sf_xx_minus", "val": 1.5, "tol": None})
val_list.append({"prop": "sf_yy_plus", "val": 1.5, "tol": None})
val_list.append({"prop": "sf_yy_minus", "val": 1.5, "tol": None})
val_list.append({"prop": "sf_11_plus", "val": 1.5, "tol": None})
val_list.append({"prop": "sf_11_minus", "val": 1.5, "tol": None})
val_list.append({"prop": "sf_22_plus", "val": 1.5, "tol": None})
val_list.append({"prop": "sf_22_minus", "val": 1.5, "tol": None})
validate_properties(self, val_list, self.section)
def test_warping(self):
self.section.calculate_geometric_properties()
self.section.calculate_warping_properties()
val_list = []
val_list.append({"prop": "j", "val": 2861002, "tol": 0.04}) # roark's
val_list.append({"prop": "j", "val": 2.85852e6, "tol": 2e-5}) # st7
val_list.append({
"prop": "gamma",
"val": 3.17542e8,
"tol": None
}) # st7
val_list.append({"prop": "x_se", "val": 50 / 2, "tol": None})
val_list.append({"prop": "y_se", "val": 100 / 2, "tol": None})
val_list.append({"prop": "x11_se", "val": 0, "tol": None})
val_list.append({"prop": "y22_se", "val": 0, "tol": None})
val_list.append({"prop": "x_st", "val": 50 / 2, "tol": None})
val_list.append({"prop": "y_st", "val": 100 / 2, "tol": None})
val_list.append({"prop": "A_sx", "val": 5 / 6 * 100 * 50, "tol": None})
val_list.append({"prop": "A_sy", "val": 5 / 6 * 100 * 50, "tol": None})
val_list.append({
"prop": "A_s11",
"val": 5 / 6 * 100 * 50,
"tol": None
})
val_list.append({
"prop": "A_s22",
"val": 5 / 6 * 100 * 50,
"tol": None
})
t = 0.1
# build the lists of points, facets, holes and control points
points = [
[-t / 2, -2 * a], [t / 2, -2 * a], [t / 2, -t / 2], [a, -t / 2], [a, t / 2], [-t / 2, t / 2],
[-b / 2, -2 * a], [b / 2, -2 * a], [b / 2, -2 * a - t], [-b / 2, -2 * a - t]
]
facets = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 0], [6, 7], [7, 8], [8, 9], [9, 6]]
holes = []
control_points = [[0, 0], [0, -2 * a - t / 2]]
# create the custom geometry object
geometry = sections.CustomSection(points, facets, holes, control_points)
geometry.clean_geometry() # clean the geometry
geometry.plot_geometry() # plot the geometry
# create the mesh - use a smaller refinement for the angle region
mesh = geometry.create_mesh(mesh_sizes=[0.0005, 0.001])
# create a CrossSection object
section = CrossSection(geometry, mesh)
section.plot_mesh() # plot the generated mesh
# perform a geometric, warping and plastic analysis
section.calculate_geometric_properties()
section.calculate_warping_properties()
section.calculate_plastic_properties()
# plot the centroids
section.plot_centroids()
def process_geometry(geometry, mesh_sizes, loadcases):
# update this to receive the geometry, mesh info, material and loads
# generate a finite element mesh
mesh = geometry.create_mesh(mesh_sizes=mesh_sizes)
# generate material - can be overwritten if needed --all in N and cm
# create a CrossSection object for analysis
section = CrossSection(geometry, mesh)
# calculate various cross-section properties
section.calculate_geometric_properties()
section.calculate_warping_properties()
section.calculate_plastic_properties()
# Area
area = section.get_area()
sheararea = section.get_As()
asx = sheararea[0]
asy = sheararea[1]
# Second Moment of Area about centroid
(ixx, iyy, ixy) = section.get_ic()
# Centroid
(xg, yg) = section.get_c()
# Radii of Gyration
(rxx, ryy) = section.get_rc()
# Principal bending axis angle
phi = section.get_phi()
# St. Venant torsion constant
ipp = section.get_j()
# Warping Constant
cw = section.get_gamma()
# Elastic Section Moduli
(welx_top, welx_bottom, wely_top, wely_bottom) = section.get_z()
# Plastic Section Moduli
(wplx, wply) = section.get_s()
# plot centroid to image
section.plot_centroids(pause=False)
buf = io.BytesIO()
plt.savefig(buf, format='png', bbox_inches='tight')
buf.seek(0)
plot_centroid = base64.b64encode(buf.getvalue()).decode()
plt.close()
# calculate torsion resistance from stress and torque
#from the below can also return torsional stress if wanted
stress_post = section.calculate_stress(Mzz=10)
unit_mzz_zxy = []
maxstress = []
for group in stress_post.material_groups:
maxstress.append(max(group.stress_result.sig_zxy_mzz))
unit_mzz_zxy.append(group.stress_result.sig_zxy_mzz.tolist())
#there should be only one maxstress value therefore:
wt = 10 / maxstress[0]
#plot this image
stress_post.plot_stress_mzz_zxy(pause=False)
buf = io.BytesIO()
plt.savefig(buf, format='png', bbox_inches='tight')
buf.seek(0)
plot_unittorsionstress = base64.b64encode(buf.getvalue()).decode()
plt.close()
#foreach load case submitted calculate vm stress state and create image
vmStressImages = {}
vmStressStates = {}
for loadcase in loadcases:
lc_name = loadcase[0]
s_n = loadcase[1]
s_vx = loadcase[2]
s_vy = loadcase[3]
s_mxx = loadcase[4]
s_myy = loadcase[5]
s_mzz = loadcase[6]
stress_post = section.calculate_stress(N=s_n,
Vx=s_vx,
Vy=s_vy,
Mxx=s_mxx,
Myy=s_myy,
Mzz=s_mzz)
stress_state = []
for group in stress_post.material_groups:
stress_state.append(group.stress_result.sig_vm.tolist())
vmStressStates['lc_' + str(lc_name) + '_vm_stress'] = stress_state
#plot this image
stress_post.plot_stress_vm(pause=False)
buf = io.BytesIO()
plt.savefig(buf, format='png', bbox_inches='tight')
buf.seek(0)
vmStressImages['lc_' + str(lc_name) + '_vm_stress'] = base64.b64encode(
buf.getvalue()).decode()
plt.close()
# create rhino mesh
rmesh = rhino_mesh_from_meshpy(mesh)
# return send_file(path, as_attachment=True)
# get some of the calculated section properties
return_data = {}
return_data['properties'] = {
'area': area,
'Avx': asx,
'Avy': asy,
'xg': xg,
'yg': yg,
'rxx': rxx,
'ryy': ryy,
'phi': phi,
'ixx': ixx,
'iyy': iyy,
'ipp': ipp,
'cw': cw,
'welx+': welx_top,
'welx-': welx_bottom,
'wely+': wely_top,
'wely-': wely_bottom,
'wplx': wplx,
'wply': wply,
'wt': wt,
}
return_data['geometry'] = {
'mesh': rhino.CommonObject.Encode(rmesh),
}
return_data['images'] = {
'centroids': plot_centroid,
'unittorsion_vxy_stress': plot_unittorsionstress,
}
return_data['images'].update(vmStressImages)
return_data['stress_results'] = {
'unittorsion_vxy_stress': unit_mzz_zxy,
}
return_data['stress_results'].update(vmStressStates)
return return_data
