def post_process(out, pb, state, extend=False):
"""
Compute derived quantities: strain, stresses. Store also the loading
temperature.
"""
ev = pb.evaluate
strain = ev("ev_cauchy_strain.2.Omega( u )", mode="el_avg")
out["cauchy_strain"] = Struct(name="output_data", mode="cell", data=strain, dofs=None)
e_stress = ev("ev_cauchy_stress.2.Omega( solid.D, u )", mode="el_avg")
out["elastic_stress"] = Struct(name="output_data", mode="cell", data=e_stress, dofs=None)
t_stress = ev("ev_biot_stress.2.Omega( solid.alpha, T )", mode="el_avg")
out["thermal_stress"] = Struct(name="output_data", mode="cell", data=t_stress, dofs=None)
out["total_stress"] = Struct(name="output_data", mode="cell", data=e_stress + t_stress, dofs=None)
out["von_mises_stress"] = aux = out["total_stress"].copy()
vms = get_von_mises_stress(aux.data.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out["von_mises_stress"].data = vms
val = pb.get_variables()["T"]()
val.shape = (val.shape[0], 1)
out["T"] = Struct(name="output_data", mode="vertex", data=val + T0, dofs=None)
return out
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms)
return out
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def post_process(out, pb, state, extend=False):
"""
Calculate and output strain and stress for given displacements.
"""
from sfepy.base.base import Struct
ev = pb.evaluate
stress = ev('ev_cauchy_stress.2.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data',
mode='cell',
data=vms,
dofs=None)
dim = pb.domain.shape.dim
us = state().reshape((-1, dim))
field = pb.fields['displacement']
if dim == 2:
ii = field.get_dofs_in_region(pb.domain.regions['Top'])
output('top LCBC (u.0 - u.1 = 0):')
output('\n', nm.c_[us[ii], nm.diff(us[ii], 1)])
ii = field.get_dofs_in_region(pb.domain.regions['Bottom'])
output('bottom LCBC (u.0 + u.1 = -0.1):')
output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)])
ii = field.get_dofs_in_region(pb.domain.regions['Right'])
output('right LCBC (u.0 + u.1 = linspace(0, 0.1)):')
output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)])
else:
ii = field.get_dofs_in_region(pb.domain.regions['Top'])
output('top LCBC (u.0 - u.1 + u.2 = 0):')
output('\n', nm.c_[us[ii], us[ii, 0] - us[ii, 1] + us[ii, 2]])
output('top LCBC (u.0 + 0.5 u.1 + 0.1 u.2 = 0.05):')
output('\n', nm.c_[us[ii],
us[ii, 0] + 0.5 * us[ii, 1] + 0.1 * us[ii, 2]])
ii = field.get_dofs_in_region(pb.domain.regions['Bottom'])
output('bottom LCBC (u.2 - 0.1 u.1 = 0.2):')
output('\n', nm.c_[us[ii], us[ii, 2] - 0.1 * us[ii, 1]])
ii = field.get_dofs_in_region(pb.domain.regions['Right'])
output('right LCBC (u.0 + u.1 + u.2 = linspace(0, 0.1)):')
output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)])
return out
def post_process(out, pb, state, extend=False):
"""
Calculate and output strain and stress for given displacements.
"""
from sfepy.base.base import Struct
ev = pb.evaluate
stress = ev('ev_cauchy_stress.2.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms, dofs=None)
dim = pb.domain.shape.dim
us = state().reshape((-1, dim))
field = pb.fields['displacement']
if dim == 2:
ii = field.get_dofs_in_region(pb.domain.regions['Top'])
output('top LCBC (u.0 - u.1 = 0):')
output('\n', nm.c_[us[ii], nm.diff(us[ii], 1)])
ii = field.get_dofs_in_region(pb.domain.regions['Bottom'])
output('bottom LCBC (u.0 + u.1 = -0.1):')
output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)])
ii = field.get_dofs_in_region(pb.domain.regions['Right'])
output('right LCBC (u.0 + u.1 = linspace(0, 0.1)):')
output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)])
else:
ii = field.get_dofs_in_region(pb.domain.regions['Top'])
output('top LCBC (u.0 - u.1 + u.2 = 0):')
output('\n', nm.c_[us[ii], us[ii, 0] - us[ii, 1] + us[ii, 2]])
output('top LCBC (u.0 + 0.5 u.1 + 0.1 u.2 = 0.05):')
output('\n', nm.c_[us[ii],
us[ii, 0] + 0.5 * us[ii, 1] + 0.1 * us[ii, 2]])
ii = field.get_dofs_in_region(pb.domain.regions['Bottom'])
output('bottom LCBC (u.2 - 0.1 u.1 = 0.2):')
output('\n', nm.c_[us[ii], us[ii, 2] - 0.1 * us[ii, 1]])
ii = field.get_dofs_in_region(pb.domain.regions['Right'])
output('right LCBC (u.0 + u.1 + u.2 = linspace(0, 0.1)):')
output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)])
return out
def post_process(out, pb, state, extend=False):
"""
Calculate and output strain and stress for given displacements.
"""
from sfepy.base.base import Struct
ev = pb.evaluate
stress = ev('ev_cauchy_stress.2.Omega(solid.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms, dofs=None)
return out
def post_process(out, pb, state, extend=False):
"""
Calculate and output strain and stress for given displacements.
"""
from sfepy.base.base import Struct
ev = pb.evaluate
stress = ev('ev_cauchy_stress.2.Omega(solid.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms, dofs=None)
return out
def post_process(out, pb, state, extend=False):
"""
Compute derived quantities: strain, stresses. Store also the loading
temperature.
"""
ev = pb.evaluate
strain = ev('ev_cauchy_strain.2.Omega( u )', mode='el_avg')
out['cauchy_strain'] = Struct(name='output_data',
mode='cell',
data=strain,
dofs=None)
e_stress = ev('ev_cauchy_stress.2.Omega( solid.D, u )', mode='el_avg')
out['elastic_stress'] = Struct(name='output_data',
mode='cell',
data=e_stress,
dofs=None)
t_stress = ev('ev_biot_stress.2.Omega( solid.alpha, T )', mode='el_avg')
out['thermal_stress'] = Struct(name='output_data',
mode='cell',
data=t_stress,
dofs=None)
out['total_stress'] = Struct(name='output_data',
mode='cell',
data=e_stress + t_stress,
dofs=None)
out['von_mises_stress'] = aux = out['total_stress'].copy()
vms = get_von_mises_stress(aux.data.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'].data = vms
val = pb.get_variables()['T']()
val.shape = (val.shape[0], 1)
out['T'] = Struct(name='output_data',
mode='vertex',
data=val + T0,
dofs=None)
return out
def test_tensors(self):
import numpy as nm
import sfepy.mechanics.tensors as tn
ok = True
a_full = 2.0 * nm.ones((5,3,3), dtype=nm.float64)
a_sym = 2.0 * nm.ones((5,6), dtype=nm.float64)
_tr = nm.array([6.0] * 5, dtype=nm.float64)
_vt_full = 2.0 * nm.tile(nm.eye(3, dtype=nm.float64), (5,1,1))
_vt_sym = nm.tile(nm.array([2, 2, 2, 0, 0, 0], dtype=nm.float64),
(5,1,1))
_dev_full = a_full - _vt_full
_dev_sym = a_sym - _vt_sym
_vms = 6.0 * nm.ones((5,1), dtype=nm.float64)
tr = tn.get_trace(a_full, sym_storage=False)
_ok = nm.allclose(tr, _tr, rtol=0.0, atol=1e-14)
self.report('trace full: %s' % _ok)
ok = ok and _ok
tr = tn.get_trace(a_sym, sym_storage=True)
ok = ok and nm.allclose(tr, _tr, rtol=0.0, atol=1e-14)
self.report('trace sym: %s' % _ok)
ok = ok and _ok
vt = tn.get_volumetric_tensor(a_full, sym_storage=False)
_ok = nm.allclose(vt, _vt_full, rtol=0.0, atol=1e-14)
self.report('volumetric tensor full: %s' % _ok)
ok = ok and _ok
vt = tn.get_volumetric_tensor(a_sym, sym_storage=True)
_ok = nm.allclose(vt, _vt_sym, rtol=0.0, atol=1e-14)
self.report('volumetric tensor sym: %s' % _ok)
ok = ok and _ok
dev = tn.get_deviator(a_full, sym_storage=False)
_ok = nm.allclose(dev, _dev_full, rtol=0.0, atol=1e-14)
self.report('deviator full: %s' % _ok)
ok = ok and _ok
aux = (dev * nm.transpose(dev, (0, 2, 1))).sum(axis=1).sum(axis=1)
vms2 = nm.sqrt((3.0/2.0) * aux)[:,None]
dev = tn.get_deviator(a_sym, sym_storage=True)
_ok = nm.allclose(dev, _dev_sym, rtol=0.0, atol=1e-14)
self.report('deviator sym: %s' % _ok)
ok = ok and _ok
vms = tn.get_von_mises_stress(a_full, sym_storage=False)
_ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress full: %s' % _ok)
ok = ok and _ok
vms = tn.get_von_mises_stress(a_sym, sym_storage=True)
_ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress sym: %s' % _ok)
ok = ok and _ok
_ok = nm.allclose(vms2, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress via deviator: %s' % _ok)
ok = ok and _ok
return ok
def test_tensors(self):
import numpy as nm
import sfepy.mechanics.tensors as tn
ok = True
a_full = 2.0 * nm.ones((5,3,3), dtype=nm.float64)
a_sym = 2.0 * nm.ones((5,6), dtype=nm.float64)
_tr = nm.array([6.0] * 5, dtype=nm.float64)
_vt_full = 2.0 * nm.tile(nm.eye(3, dtype=nm.float64), (5,1,1))
_vt_sym = nm.tile(nm.array([2, 2, 2, 0, 0, 0], dtype=nm.float64),
(5,1,1))
_dev_full = a_full - _vt_full
_dev_sym = a_sym - _vt_sym
_vms = 6.0 * nm.ones((5,1), dtype=nm.float64)
tr = tn.get_trace(a_full, sym_storage=False)
_ok = nm.allclose(tr, _tr, rtol=0.0, atol=1e-14)
self.report('trace full: %s' % _ok)
ok = ok and _ok
tr = tn.get_trace(a_sym, sym_storage=True)
ok = ok and nm.allclose(tr, _tr, rtol=0.0, atol=1e-14)
self.report('trace sym: %s' % _ok)
ok = ok and _ok
vt = tn.get_volumetric_tensor(a_full, sym_storage=False)
_ok = nm.allclose(vt, _vt_full, rtol=0.0, atol=1e-14)
self.report('volumetric tensor full: %s' % _ok)
ok = ok and _ok
vt = tn.get_volumetric_tensor(a_sym, sym_storage=True)
_ok = nm.allclose(vt, _vt_sym, rtol=0.0, atol=1e-14)
self.report('volumetric tensor sym: %s' % _ok)
ok = ok and _ok
dev = tn.get_deviator(a_full, sym_storage=False)
_ok = nm.allclose(dev, _dev_full, rtol=0.0, atol=1e-14)
self.report('deviator full: %s' % _ok)
ok = ok and _ok
aux = (dev * nm.transpose(dev, (0, 2, 1))).sum(axis=1).sum(axis=1)
vms2 = nm.sqrt((3.0/2.0) * aux)[:,None]
dev = tn.get_deviator(a_sym, sym_storage=True)
_ok = nm.allclose(dev, _dev_sym, rtol=0.0, atol=1e-14)
self.report('deviator sym: %s' % _ok)
ok = ok and _ok
vms = tn.get_von_mises_stress(a_full, sym_storage=False)
_ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress full: %s' % _ok)
ok = ok and _ok
vms = tn.get_von_mises_stress(a_sym, sym_storage=True)
_ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress sym: %s' % _ok)
ok = ok and _ok
_ok = nm.allclose(vms2, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress via deviator: %s' % _ok)
ok = ok and _ok
t2s = nm.arange(9).reshape(3, 3)
t2s = (t2s + t2s.T) / 2
t4 = tn.get_t4_from_t2s(t2s)
expected = nm.array([[[[0, 4], [4, 2]],
[[4, 8], [8, 6]]],
[[[4, 8], [8, 6]],
[[2, 6], [6, 4]]]])
_ok = nm.allclose(t4, expected, rtol=0.0, atol=1e-14)
self.report('full 4D tensor from 2D matrix, 2D space: %s' % _ok)
ok = ok and _ok
return ok
def test_tensors(self):
import numpy as nm
import sfepy.mechanics.tensors as tn
ok = True
a_full = 2.0 * nm.ones((5,3,3), dtype=nm.float64)
a_sym = 2.0 * nm.ones((5,6), dtype=nm.float64)
_tr = nm.array([6.0] * 5, dtype=nm.float64)
_vt_full = 2.0 * nm.tile(nm.eye(3, dtype=nm.float64), (5,1,1))
_vt_sym = nm.tile(nm.array([2, 2, 2, 0, 0, 0], dtype=nm.float64),
(5,1,1))
_dev_full = a_full - _vt_full
_dev_sym = a_sym - _vt_sym
_vms = 6.0 * nm.ones((5,1), dtype=nm.float64)
tr = tn.get_trace(a_full, sym_storage=False)
_ok = nm.allclose(tr, _tr, rtol=0.0, atol=1e-14)
self.report('trace full: %s' % _ok)
ok = ok and _ok
tr = tn.get_trace(a_sym, sym_storage=True)
ok = ok and nm.allclose(tr, _tr, rtol=0.0, atol=1e-14)
self.report('trace sym: %s' % _ok)
ok = ok and _ok
vt = tn.get_volumetric_tensor(a_full, sym_storage=False)
_ok = nm.allclose(vt, _vt_full, rtol=0.0, atol=1e-14)
self.report('volumetric tensor full: %s' % _ok)
ok = ok and _ok
vt = tn.get_volumetric_tensor(a_sym, sym_storage=True)
_ok = nm.allclose(vt, _vt_sym, rtol=0.0, atol=1e-14)
self.report('volumetric tensor sym: %s' % _ok)
ok = ok and _ok
dev = tn.get_deviator(a_full, sym_storage=False)
_ok = nm.allclose(dev, _dev_full, rtol=0.0, atol=1e-14)
self.report('deviator full: %s' % _ok)
ok = ok and _ok
aux = (dev * nm.transpose(dev, (0, 2, 1))).sum(axis=1).sum(axis=1)
vms2 = nm.sqrt((3.0/2.0) * aux)[:,None]
dev = tn.get_deviator(a_sym, sym_storage=True)
_ok = nm.allclose(dev, _dev_sym, rtol=0.0, atol=1e-14)
self.report('deviator sym: %s' % _ok)
ok = ok and _ok
vms = tn.get_von_mises_stress(a_full, sym_storage=False)
_ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress full: %s' % _ok)
ok = ok and _ok
vms = tn.get_von_mises_stress(a_sym, sym_storage=True)
_ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress sym: %s' % _ok)
ok = ok and _ok
_ok = nm.allclose(vms2, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress via deviator: %s' % _ok)
ok = ok and _ok
t2s = nm.arange(9).reshape(3, 3)
t2s = (t2s + t2s.T) / 2
t4 = tn.get_t4_from_t2s(t2s)
expected = nm.array([[[[0, 4], [4, 2]],
[[4, 8], [8, 6]]],
[[[4, 8], [8, 6]],
[[2, 6], [6, 4]]]])
_ok = nm.allclose(t4, expected, rtol=0.0, atol=1e-14)
self.report('full 4D tensor from 2D matrix, 2D space: %s' % _ok)
ok = ok and _ok
return ok
pb = Problem('elasticity', equations=eqs)
pb.save_regions_as_groups('regions')
pb.set_bcs(ebcs=Conditions([fix_bot, fix_top]))
pb.set_solver(nls)
status = IndexedStruct()
state = pb.solve(status=status)
strain = pb.evaluate('ev_cauchy_strain.2.Omega(u)', u=u, mode='el_avg')
stress = pb.evaluate('ev_cauchy_stress.2.Omega(m.D, u)',
m=m,
u=u,
mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
np.savetxt('tmp_vms.dat', vms)
vms = np.loadtxt('tmp_vms.dat')
vol = mesh.cmesh.get_volumes(3)
np.savetxt('tmp_vol.dat', vol)
vol = np.loadtxt('tmp_vol.dat')
vm_stresses[i, 0] = np.sum(vms * vol) / np.sum(vol)
vm_stresses[i, 1] = np.max(vms)
pb.save_state('linear_elasticity_%f.vtk' % z_displacement, state)
# show = False
# if show:
# view = Viewer('linear_elasticity.vtk')
def test_tensors(self):
import numpy as nm
import sfepy.mechanics.tensors as tn
ok = True
a_full = 2.0 * nm.ones((5, 3, 3), dtype=nm.float64)
a_sym = 2.0 * nm.ones((5, 6), dtype=nm.float64)
_tr = nm.array([6.0] * 5, dtype=nm.float64)
_vt_full = 2.0 * nm.tile(nm.eye(3, dtype=nm.float64), (5, 1, 1))
_vt_sym = nm.tile(nm.array([2, 2, 2, 0, 0, 0], dtype=nm.float64),
(5, 1, 1))
_dev_full = a_full - _vt_full
_dev_sym = a_sym - _vt_sym
_vms = 6.0 * nm.ones((5, 1), dtype=nm.float64)
tr = tn.get_trace(a_full, sym_storage=False)
_ok = nm.allclose(tr, _tr, rtol=0.0, atol=1e-14)
self.report('trace full: %s' % _ok)
ok = ok and _ok
tr = tn.get_trace(a_sym, sym_storage=True)
ok = ok and nm.allclose(tr, _tr, rtol=0.0, atol=1e-14)
self.report('trace sym: %s' % _ok)
ok = ok and _ok
vt = tn.get_volumetric_tensor(a_full, sym_storage=False)
_ok = nm.allclose(vt, _vt_full, rtol=0.0, atol=1e-14)
self.report('volumetric tensor full: %s' % _ok)
ok = ok and _ok
vt = tn.get_volumetric_tensor(a_sym, sym_storage=True)
_ok = nm.allclose(vt, _vt_sym, rtol=0.0, atol=1e-14)
self.report('volumetric tensor sym: %s' % _ok)
ok = ok and _ok
dev = tn.get_deviator(a_full, sym_storage=False)
_ok = nm.allclose(dev, _dev_full, rtol=0.0, atol=1e-14)
self.report('deviator full: %s' % _ok)
ok = ok and _ok
aux = (dev * nm.transpose(dev, (0, 2, 1))).sum(axis=1).sum(axis=1)
vms2 = nm.sqrt((3.0 / 2.0) * aux)[:, None]
dev = tn.get_deviator(a_sym, sym_storage=True)
_ok = nm.allclose(dev, _dev_sym, rtol=0.0, atol=1e-14)
self.report('deviator sym: %s' % _ok)
ok = ok and _ok
vms = tn.get_von_mises_stress(a_full, sym_storage=False)
_ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress full: %s' % _ok)
ok = ok and _ok
vms = tn.get_von_mises_stress(a_sym, sym_storage=True)
_ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress sym: %s' % _ok)
ok = ok and _ok
_ok = nm.allclose(vms2, _vms, rtol=0.0, atol=1e-14)
self.report('von Mises stress via deviator: %s' % _ok)
ok = ok and _ok
return ok