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create/src/Mod/Fem/femresult/resulttools.py
Uwe b73b8e32d9 [FEM] use proper histogram titles 
- use for the histogram titles the same as in the CCX dialog and not our internal abbreviations
- in the CCX dialog don't use the term PEEQ but the common wording that also gives the user the info what this is about
2022-06-03 13:09:32 +02:00

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# ***************************************************************************
# * Copyright (c) 2017 Bernd Hahnebach <bernd@bimstatik.org> *
# * *
# * This program is free software; you can redistribute it and/or modify *
# * it under the terms of the GNU Lesser General Public License (LGPL) *
# * as published by the Free Software Foundation; either version 2 of *
# * the License, or (at your option) any later version. *
# * for detail see the LICENCE text file. *
# * *
# * 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 Library General Public License for more details. *
# * *
# * You should have received a copy of the GNU Library General Public *
# * License along with this program; if not, write to the Free Software *
# * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
# * USA *
# * *
# ***************************************************************************
__title__ = "Fem Tools for results"
__author__ = "Bernd Hahnebach"
__url__ = "https://www.freecadweb.org"
## \addtogroup FEM
# @{
import numpy as np
from math import isnan
import FreeCAD
from femtools.femutils import is_of_type
def purge_results(analysis):
"""Removes all result objects and result meshes from an analysis group
Parameters
----------
analysis : Fem::FemAnalysis
analysis group as a container for all objects needed for the analysis
"""
# if analysis typ check is used result mesh
# without result obj is created in the analysis
# we could run into trouble in one loop because
# we will delete objects and try to access them later
# result object
for m in analysis.Group:
if m.isDerivedFrom("Fem::FemResultObject"):
if m.Mesh and is_of_type(m.Mesh, "Fem::MeshResult"):
analysis.Document.removeObject(m.Mesh.Name)
analysis.Document.removeObject(m.Name)
analysis.Document.recompute()
# result mesh
for m in analysis.Group:
if is_of_type(m, "Fem::MeshResult"):
analysis.Document.removeObject(m.Name)
analysis.Document.recompute()
# dat text object
for m in analysis.Group:
if is_of_type(m, "App::TextDocument") and m.Name.startswith("ccx_dat_file"):
analysis.Document.removeObject(m.Name)
analysis.Document.recompute()
def reset_mesh_deformation(resultobj):
"""Resets result mesh deformation
Parameters
----------
resultobj : Fem::ResultMechanical
FreeCAD FEM mechanical result object
"""
if FreeCAD.GuiUp:
if resultobj.Mesh:
resultobj.Mesh.ViewObject.applyDisplacement(0.0)
def reset_mesh_color(resultobj):
"""Resets result mesh color
Parameters
----------
resultobj : Fem::ResultMechanical
FreeCAD FEM mechanical result object
"""
if FreeCAD.GuiUp:
if resultobj.Mesh:
resultobj.Mesh.ViewObject.NodeColor = {}
resultobj.Mesh.ViewObject.ElementColor = {}
node_numbers = resultobj.Mesh.FemMesh.Nodes.keys()
zero_values = [0] * len(node_numbers)
resultobj.Mesh.ViewObject.setNodeColorByScalars(node_numbers, zero_values)
def show_displacement(resultobj, displacement_factor=0.0):
if FreeCAD.GuiUp:
if resultobj.Mesh.ViewObject.Visibility is False:
resultobj.Mesh.ViewObject.Visibility = True
resultobj.Mesh.ViewObject.setNodeDisplacementByVectors(
resultobj.NodeNumbers, resultobj.DisplacementVectors
)
resultobj.Mesh.ViewObject.applyDisplacement(displacement_factor)
def show_result(resultobj, result_type="Sabs", limit=None):
"""Sets mesh color using selected type of results
Parameters
----------
resultobj : Fem::ResultMechanical
FreeCAD FEM mechanical result object
result_type : str, optional
default is Sabs
FreeCAD FEM mechanical result object
- U1, U2, U3 - deformation
- Uabs - absolute deformation
- Sabs - Von Mises stress
limit : float
limit cutoff value. All values over the limit are treated
as equal to the limit. Useful for filtering out hotspots.
"""
if result_type == "None":
reset_mesh_color(resultobj.Mesh)
return
if resultobj:
if result_type == "Sabs":
values = resultobj.vonMises
elif result_type == "Uabs":
values = resultobj.DisplacementLengths
# TODO: the result object does have more result types to show, implement them
else:
match = {"U1": 0, "U2": 1, "U3": 2}
d = zip(*resultobj.DisplacementVectors)
values = list(d[match[result_type]])
show_color_by_scalar_with_cutoff(resultobj, values, limit)
else:
FreeCAD.Console.PrintError("Error, No result object given.\n")
def show_color_by_scalar_with_cutoff(resultobj, values, limit=None):
"""Sets mesh color using list of values. Internally used by show_result function.
Parameters
----------
resultobj : Fem::ResultMechanical
FreeCAD FEM mechanical result object
values : list of floats
the values to be colored and cutoff
has to be the same length as resultobj.NodeNumbers
resultobj.NodeNumbers has to be present in the resultobj
limit : float
limit cutoff value. All values over the limit are treated
as equal to the limit. Useful for filtering out hotspots.
"""
if limit:
filtered_values = []
for v in values:
if v > limit:
filtered_values.append(limit)
else:
filtered_values.append(v)
else:
filtered_values = values
if FreeCAD.GuiUp:
if resultobj.Mesh.ViewObject.Visibility is False:
resultobj.Mesh.ViewObject.Visibility = True
resultobj.Mesh.ViewObject.setNodeColorByScalars(
resultobj.NodeNumbers, filtered_values
)
def get_stats(res_obj, result_type):
"""Returns minimum and maximum value for provided result type
Parameters
----------
resultobj : Fem::ResultMechanical
FreeCAD FEM mechanical result object
result_type : str
type of FEM result
allowed are: see dict keys in def get_all_stats()
None - always return (0.0, 0.0)
"""
match_table = get_all_stats(res_obj)
match_table["None"] = (0.0, 0.0)
stats = ()
if result_type in match_table:
stats = match_table[result_type]
return stats
# - U1, U2, U3 - deformation
# - Uabs - absolute deformation
# - Sabs - Von Mises stress
# - Prin1 - Principal stress 1
# - Prin2 - Principal stress 2
# - Prin3 - Principal stress 3
# - MaxSear - maximum shear stress
# - Peeq - Equivalent plastic strain
# - Temp - Temperature
# - MFlow - MassFlowRate
# - NPress - NetworkPressure
def get_all_stats(res_obj):
"""Returns all stats for provided result type
- U1, U2, U3 - deformation
- Uabs - absolute deformation
- Sabs - Von Mises stress
- MaxPrin - Principal stress 1
- MidPrin - Principal stress 2
- MinPrin - Principal stress 3
- MaxShear - maximum shear stress
- Peeq - peeq strain
- Temp - Temperature
- MFlow - MassFlowRate
- NPress - NetworkPressure
for more information on result types and names
see in code file src/Mod/Fem/App/FemVTKTools.cpp
the methods _getFreeCADMechResultVectorProperties()
and _getFreeCADMechResultScalarProperties()
as well as forum topic
https://forum.freecadweb.org/viewtopic.php?f=18&t=33106&start=30#p277434
Parameters
----------
resultobj : Fem::ResultMechanical
FreeCAD FEM mechanical result object
"""
m = res_obj.Stats
stats_dict = {
"U1": (m[0], m[1]),
"U2": (m[2], m[3]),
"U3": (m[4], m[5]),
"Uabs": (m[6], m[7]),
"Sabs": (m[8], m[9]),
"MaxPrin": (m[10], m[11]),
"MidPrin": (m[12], m[13]),
"MinPrin": (m[14], m[15]),
"MaxShear": (m[16], m[17]),
"Peeq": (m[18], m[19]),
"Temp": (m[20], m[21]),
"MFlow": (m[22], m[23]),
"NPress": (m[24], m[25])
}
return stats_dict
def fill_femresult_stats(res_obj):
"""Fills a FreeCAD FEM mechanical result object with stats data
Parameters
----------
resultobj : Fem::ResultMechanical
FreeCAD FEM mechanical result object
"""
FreeCAD.Console.PrintLog(
"Calculate stats list for result obj: " + res_obj.Name + "\n"
)
# set stats values to 0, they may not exist in res_obj
x_min = y_min = z_min = x_max = y_max = z_max = 0
a_max = a_min = s_max = s_min = 0
p1_min = p1_max = p2_min = p2_max = p3_min = p3_max = 0
ms_min = ms_max = peeq_min = peeq_max = 0
temp_min = temp_max = 0
mflow_min = mflow_max = npress_min = npress_max = 0
if res_obj.DisplacementVectors:
x_max, y_max, z_max = map(max, zip(*res_obj.DisplacementVectors))
x_min, y_min, z_min = map(min, zip(*res_obj.DisplacementVectors))
if res_obj.DisplacementLengths:
a_min = min(res_obj.DisplacementLengths)
a_max = max(res_obj.DisplacementLengths)
if res_obj.vonMises:
s_min = min(res_obj.vonMises)
s_max = max(res_obj.vonMises)
if res_obj.PrincipalMax:
p1_min = min(res_obj.PrincipalMax)
p1_max = max(res_obj.PrincipalMax)
if res_obj.PrincipalMed:
p2_min = min(res_obj.PrincipalMed)
p2_max = max(res_obj.PrincipalMed)
if res_obj.PrincipalMin:
p3_min = min(res_obj.PrincipalMin)
p3_max = max(res_obj.PrincipalMin)
if res_obj.MaxShear:
ms_min = min(res_obj.MaxShear)
ms_max = max(res_obj.MaxShear)
if res_obj.Peeq:
peeq_min = min(res_obj.Peeq)
peeq_max = max(res_obj.Peeq)
if res_obj.Temperature:
temp_min = min(res_obj.Temperature)
temp_max = max(res_obj.Temperature)
if res_obj.MassFlowRate:
# DisplacementVectors is empty, no_of_values needs to be set
mflow_min = min(res_obj.MassFlowRate)
mflow_max = max(res_obj.MassFlowRate)
if res_obj.NetworkPressure:
npress_min = min(res_obj.NetworkPressure)
npress_max = max(res_obj.NetworkPressure)
res_obj.Stats = [x_min, x_max,
y_min, y_max,
z_min, z_max,
a_min, a_max,
s_min, s_max,
p1_min, p1_max,
p2_min, p2_max,
p3_min, p3_max,
ms_min, ms_max,
peeq_min, peeq_max,
temp_min, temp_max,
mflow_min, mflow_max,
npress_min, npress_max]
"""
stat_types = [
"U1",
"U2",
"U3",
"Uabs",
"Sabs",
"MaxPrin",
"MidPrin",
"MinPrin",
"MaxShear",
"Peeq",
"Temp",
"MFlow",
"NPress"
]
"""
# len(stat_types) == 13*3 == 39
# do not forget to adapt initialization of all Stats items in modules:
# - module femobjects/_FemResultMechanical.py
# do not forget to adapt the def get_stats in:
# - get_stats in module femresult/resulttools.py
# - module femtest/testccxtools.py
# TODO: all stats stuff should be reimplemented
# maybe a dictionary would be far more robust than a list
FreeCAD.Console.PrintLog("Stats list for result obj: " + res_obj.Name + " calculated\n")
return res_obj
def add_disp_apps(res_obj):
res_obj.DisplacementLengths = calculate_disp_abs(res_obj.DisplacementVectors)
FreeCAD.Console.PrintLog("Added DisplacementLengths.\n")
return res_obj
def add_von_mises(res_obj):
mstress = []
iterator = zip(
res_obj.NodeStressXX,
res_obj.NodeStressYY,
res_obj.NodeStressZZ,
res_obj.NodeStressXY,
res_obj.NodeStressXZ,
res_obj.NodeStressYZ
)
for Sxx, Syy, Szz, Sxy, Sxz, Syz in iterator:
mstress.append(calculate_von_mises((Sxx, Syy, Szz, Sxy, Sxz, Syz)))
res_obj.vonMises = mstress
FreeCAD.Console.PrintLog("Added von Mises stress.\n")
return res_obj
def add_principal_stress_std(res_obj):
# saved into PrincipalMax, PrincipalMed, PrincipalMin
# TODO may be use only one container for principal stresses in result object
# https://forum.freecadweb.org/viewtopic.php?f=18&t=33106&p=416006#p416006
# but which one is better
prinstress1 = []
prinstress2 = []
prinstress3 = []
shearstress = []
iterator = zip(
res_obj.NodeStressXX,
res_obj.NodeStressYY,
res_obj.NodeStressZZ,
res_obj.NodeStressXY,
res_obj.NodeStressXZ,
res_obj.NodeStressYZ
)
for Sxx, Syy, Szz, Sxy, Sxz, Syz in iterator:
prin1, prin2, prin3, shear = calculate_principal_stress_std((Sxx, Syy, Szz, Sxy, Sxz, Syz))
prinstress1.append(prin1)
prinstress2.append(prin2)
prinstress3.append(prin3)
shearstress.append(shear)
res_obj.PrincipalMax = prinstress1
res_obj.PrincipalMed = prinstress2
res_obj.PrincipalMin = prinstress3
res_obj.MaxShear = shearstress
FreeCAD.Console.PrintLog("Added standard principal stresses and max shear values.\n")
return res_obj
def get_concrete_nodes(res_obj):
#
# HarryvL: determine concrete / non-concrete nodes
#
from femmesh.meshtools import get_femnodes_by_refshape
femmesh = res_obj.Mesh.FemMesh
nsr = femmesh.NodeCount # nsr number of stress results
# ic[iic]:
# ic = flag for material type; iic = node number
# ic = 0: NOT ASSIGNED
# ic = 1: ReinforcedMaterial
# ic = 2: NOT ReinforcedMaterial
ic = np.zeros(nsr)
for obj in res_obj.getParentGroup().Group:
if obj.isDerivedFrom("App::MaterialObjectPython") \
and is_of_type(obj, "Fem::MaterialReinforced"):
FreeCAD.Console.PrintMessage("ReinforcedMaterial\n")
if obj.References == []:
for iic in range(nsr):
if ic[iic] == 0:
ic[iic] = 1
else:
for ref in obj.References:
concrete_nodes = get_femnodes_by_refshape(femmesh, ref)
for cn in concrete_nodes:
ic[cn - 1] = 1
elif obj.isDerivedFrom("App::MaterialObjectPython") \
and is_of_type(obj, "Fem::MaterialCommon"):
FreeCAD.Console.PrintMessage("No ReinforcedMaterial\n")
if obj.References == []:
for iic in range(nsr):
if ic[iic] == 0:
ic[iic] = 2
else:
for ref in obj.References:
non_concrete_nodes = get_femnodes_by_refshape(femmesh, ref)
for ncn in non_concrete_nodes:
ic[ncn - 1] = 2
return ic
def add_principal_stress_reinforced(res_obj):
#
# HarryvL: determine concrete / non-concrete nodes
#
ic = get_concrete_nodes(res_obj)
#
# calculate principal and max Shear and fill them in res_obj
#
# saved into PS1Vector, PS2Vector, PS3Vector
# TODO may be use only one container for principal stresses in result object
# https://forum.freecadweb.org/viewtopic.php?f=18&t=33106&p=416006#p416006
# but which one is better
prinstress1 = []
prinstress2 = []
prinstress3 = []
shearstress = []
ps1v = []
ps2v = []
ps3v = []
#
# HarryvL: additional arrays to hold reinforcement ratios
# and mohr coulomb stress
#
rhx = []
rhy = []
rhz = []
moc = []
# material parameter
for obj in res_obj.getParentGroup().Group:
if is_of_type(obj, "Fem::MaterialReinforced"):
matrix_af = float(
FreeCAD.Units.Quantity(obj.Material["AngleOfFriction"]).getValueAs("rad")
)
matrix_cs = float(
FreeCAD.Units.Quantity(obj.Material["CompressiveStrength"]).getValueAs("MPa")
)
reinforce_yield = float(
FreeCAD.Units.Quantity(obj.Reinforcement["YieldStrength"]).getValueAs("MPa")
)
# print(matrix_af)
# print(matrix_cs)
# print(reinforce_yield)
iterator = zip(
res_obj.NodeStressXX,
res_obj.NodeStressYY,
res_obj.NodeStressZZ,
res_obj.NodeStressXY,
res_obj.NodeStressXZ,
res_obj.NodeStressYZ
)
for isv, stress_tensor in enumerate(iterator):
rhox = 0.
rhoy = 0.
rhoz = 0.
mc = 0.
if ic[isv] == 1:
#
# HarryvL: for concrete scxx etc. are affected by
# reinforcement (see calculate_rho(stress_tensor)). for all other
# materials scxx etc. are the original stresses
#
rhox, rhoy, rhoz = calculate_rho(
stress_tensor,
reinforce_yield
)
prin1, prin2, prin3, shear, psv = calculate_principal_stress_reinforced(
stress_tensor
)
prinstress1.append(prin1)
prinstress2.append(prin2)
prinstress3.append(prin3)
shearstress.append(shear)
ps1v.append(psv[0])
ps2v.append(psv[1])
ps3v.append(psv[2])
#
# reinforcement ratios and mohr coulomb criterion
#
rhx.append(rhox)
rhy.append(rhoy)
rhz.append(rhoz)
if ic[isv] == 1:
mc = calculate_mohr_coulomb(prin1, prin3, matrix_af, matrix_cs)
moc.append(mc)
res_obj.PrincipalMax = prinstress1
res_obj.PrincipalMed = prinstress2
res_obj.PrincipalMin = prinstress3
res_obj.MaxShear = shearstress
#
# HarryvL: additional concrete and principal stress plot
# results for use in _ViewProviderFemResultMechanical
#
res_obj.ReinforcementRatio_x = rhx
res_obj.ReinforcementRatio_y = rhy
res_obj.ReinforcementRatio_z = rhz
res_obj.MohrCoulomb = moc
res_obj.PS1Vector = ps1v
res_obj.PS2Vector = ps2v
res_obj.PS3Vector = ps3v
FreeCAD.Console.PrintLog(
"Added reinforcement principal stresses and max shear values as well as "
"reinforcment ratios, Mohr Coloumb values.\n"
)
return res_obj
def compact_result(res_obj):
"""
compacts result.Mesh and appropriate result.NodeNumbers
"""
# as workaround for https://www.freecadweb.org/tracker/view.php?id=2873
# get compact mesh data
from femmesh.meshtools import compact_mesh
compact_femmesh_data = compact_mesh(res_obj.Mesh.FemMesh)
compact_femmesh = compact_femmesh_data[0]
node_map = compact_femmesh_data[1]
# FreeCAD result obj does not support elem results ATM
# elem_map = compact_femmesh_data[2]
# set result mesh
res_obj.Mesh.FemMesh = compact_femmesh
# set result node numbers
new_node_numbers = []
for old_node_id in res_obj.NodeNumbers:
new_node_numbers.append(node_map[old_node_id])
res_obj.NodeNumbers = new_node_numbers
return res_obj
def calculate_von_mises(stress_tensor):
# Von mises stress: http://en.wikipedia.org/wiki/Von_Mises_yield_criterion
# simplification: https://forum.freecadweb.org/viewtopic.php?f=18&t=33974&p=296542#p296542
# stress_tensor ... (Sxx, Syy, Szz, Sxy, Sxz, Syz)
normal = stress_tensor[:3]
shear = stress_tensor[3:]
pressure = np.average(normal)
return np.sqrt(1.5 * np.linalg.norm(normal - pressure)**2 + 3.0 * np.linalg.norm(shear)**2)
def calculate_principal_stress_std(
stress_tensor
):
# if NaN is inside the array, which can happen on Calculix frd result files return NaN
# https://forum.freecadweb.org/viewtopic.php?f=22&t=33911&start=10#p284229
# https://forum.freecadweb.org/viewtopic.php?f=18&t=32649#p274291
for s in stress_tensor:
if isnan(s) is True:
return (float("NaN"), float("NaN"), float("NaN"), float("NaN"))
s11 = stress_tensor[0] # Sxx
s22 = stress_tensor[1] # Syy
s33 = stress_tensor[2] # Szz
s12 = stress_tensor[3] # Sxy
s31 = stress_tensor[4] # Sxz
s23 = stress_tensor[5] # Syz
sigma = np.array([
[s11, s12, s31],
[s12, s22, s23],
[s31, s23, s33]
]) # https://forum.freecadweb.org/viewtopic.php?f=18&t=24637&start=10#p240408
eigvals = list(np.linalg.eigvalsh(sigma))
eigvals.sort()
eigvals.reverse()
maxshear = (eigvals[0] - eigvals[2]) / 2.0
return (eigvals[0], eigvals[1], eigvals[2], maxshear)
def calculate_principal_stress_reinforced(stress_tensor):
#
# HarryvL - calculate principal stress vectors and values
# - for total stresses use stress_tensor[0], stress_tensor[1], stress_tensor[2]
# on the diagonal of the stress tensor
#
# difference to the original method:
# https://forum.freecadweb.org/viewtopic.php?f=18&t=33106&start=90#p296539
#
s11 = stress_tensor[0] # Sxx
s22 = stress_tensor[1] # Syy
s33 = stress_tensor[2] # Szz
s12 = stress_tensor[3] # Sxy
s31 = stress_tensor[4] # Sxz
s23 = stress_tensor[5] # Syz
sigma = np.array([
[s11, s12, s31],
[s12, s22, s23],
[s31, s23, s33]
]) # https://forum.freecadweb.org/viewtopic.php?f=18&t=24637&start=10#p240408
eigenvalues, eigenvectors = np.linalg.eig(sigma)
#
# HarryvL: suppress complex eigenvalue and vectors that may occur for
# near-zero (numerical noise) stress fields
#
eigenvalues = eigenvalues.real
eigenvectors = eigenvectors.real
eigenvectors[:, 0] = eigenvalues[0] * eigenvectors[:, 0]
eigenvectors[:, 1] = eigenvalues[1] * eigenvectors[:, 1]
eigenvectors[:, 2] = eigenvalues[2] * eigenvectors[:, 2]
idx = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[idx]
eigenvectors = eigenvectors[:, idx]
maxshear = (eigenvalues[0] - eigenvalues[2]) / 2.0
return (eigenvalues[0], eigenvalues[1], eigenvalues[2], maxshear,
tuple([tuple(row) for row in eigenvectors.T]))
def calculate_rho(stress_tensor, fy):
#
# HarryvL - Calculation of Reinforcement Ratios and
# Concrete Stresses according to http://heronjournal.nl/53-4/3.pdf
# - See post:
# https://forum.freecadweb.org/viewtopic.php?f=18&t=28821
# fy: factored yield strength of reinforcement bars
#
rmin = 1.0e9
eqmin = 14
sxx = stress_tensor[0]
syy = stress_tensor[1]
szz = stress_tensor[2]
sxy = stress_tensor[3]
syz = stress_tensor[5]
sxz = stress_tensor[4]
rhox = np.zeros(15)
rhoy = np.zeros(15)
rhoz = np.zeros(15)
# i1=sxx+syy+szz NOT USED
# i2=sxx*syy+syy*szz+szz*sxx-sxy**2-sxz**2-syz**2 NOT USED
i3 = (sxx * syy * szz + 2 * sxy * sxz * syz - sxx * syz**2
- syy * sxz**2 - szz * sxy**2)
# Solution (5)
d = (sxx * syy - sxy**2)
if d != 0.:
rhoz[0] = i3 / d / fy
# Solution (6)
d = (sxx * szz - sxz**2)
if d != 0.:
rhoy[1] = i3 / d / fy
# Solution (7)
d = (syy * szz - syz**2)
if d != 0.:
rhox[2] = i3 / d / fy
# Solution (9)
if sxx != 0.:
fc = sxz * sxy / sxx - syz
fxy = sxy**2 / sxx
fxz = sxz**2 / sxx
# Solution (9+)
rhoy[3] = syy - fxy + fc
rhoy[3] /= fy
rhoz[3] = szz - fxz + fc
rhoz[3] /= fy
# Solution (9-)
rhoy[4] = syy - fxy - fc
rhoy[4] /= fy
rhoz[4] = szz - fxz - fc
rhoz[4] /= fy
# Solution (10)
if syy != 0.:
fc = syz * sxy / syy - sxz
fxy = sxy**2 / syy
fyz = syz**2 / syy
# Solution (10+)
rhox[5] = sxx - fxy + fc
rhox[5] /= fy
rhoz[5] = szz - fyz + fc
rhoz[5] /= fy
# Solution (10-)vm
rhox[6] = sxx - fxy - fc
rhox[6] /= fy
rhoz[6] = szz - fyz - fc
rhoz[6] /= fy
# Solution (11)
if szz != 0.:
fc = sxz * syz / szz - sxy
fxz = sxz**2 / szz
fyz = syz**2 / szz
# Solution (11+)
rhox[7] = sxx - fxz + fc
rhox[7] /= fy
rhoy[7] = syy - fyz + fc
rhoy[7] /= fy
# Solution (11-)
rhox[8] = sxx - fxz - fc
rhox[8] /= fy
rhoy[8] = syy - fyz - fc
rhoy[8] /= fy
# Solution (13)
rhox[9] = (sxx + sxy + sxz) / fy
rhoy[9] = (syy + sxy + syz) / fy
rhoz[9] = (szz + sxz + syz) / fy
# Solution (14)
rhox[10] = (sxx + sxy - sxz) / fy
rhoy[10] = (syy + sxy - syz) / fy
rhoz[10] = (szz - sxz - syz) / fy
# Solution (15)
rhox[11] = (sxx - sxy - sxz) / fy
rhoy[11] = (syy - sxy + syz) / fy
rhoz[11] = (szz - sxz + syz) / fy
# Solution (16)
rhox[12] = (sxx - sxy + sxz) / fy
rhoy[12] = (syy - sxy - syz) / fy
rhoz[12] = (szz + sxz - syz) / fy
# Solution (17)
if syz != 0.:
rhox[13] = (sxx - sxy * sxz / syz) / fy
if sxz != 0.:
rhoy[13] = (syy - sxy * syz / sxz) / fy
if sxy != 0.:
rhoz[13] = (szz - sxz * syz / sxy) / fy
for ir in range(0, rhox.size):
if rhox[ir] >= -1.e-10 and rhoy[ir] >= -1.e-10 and rhoz[ir] > -1.e-10:
# Concrete Stresses
scxx = sxx - rhox[ir] * fy
scyy = syy - rhoy[ir] * fy
sczz = szz - rhoz[ir] * fy
ic1 = (scxx + scyy + sczz)
ic2 = (scxx * scyy + scyy * sczz + sczz * scxx - sxy**2
- sxz**2 - syz**2)
ic3 = (scxx * scyy * sczz + 2 * sxy * sxz * syz - scxx * syz**2
- scyy * sxz**2 - sczz * sxy**2)
if ic1 <= 1.e-6 and ic2 >= -1.e-6 and ic3 <= 1.0e-6:
rsum = rhox[ir] + rhoy[ir] + rhoz[ir]
if rsum < rmin and rsum > 0.:
rmin = rsum
eqmin = ir
return rhox[eqmin], rhoy[eqmin], rhoz[eqmin]
def calculate_mohr_coulomb(prin1, prin3, phi, fck):
#
# HarryvL - Calculation of Mohr Coulomb yield criterion to judge
# concrete curshing and shear failure
# phi: angle of internal friction
# fck: factored compressive strength of the matrix material (usually concrete)
#
coh = fck * (1 - np.sin(phi)) / 2 / np.cos(phi)
mc_stress = ((prin1 - prin3) + (prin1 + prin3) * np.sin(phi)
- 2. * coh * np.cos(phi))
if mc_stress < 0.:
mc_stress = 0.
return mc_stress
def calculate_disp_abs(displacements):
# see https://forum.freecadweb.org/viewtopic.php?f=18&t=33106&start=100#p296657
return [np.linalg.norm(nd) for nd in displacements]
## @}
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