def nodal_stress(out, pb, state, extend=False, integrals=None):
'''
Calculate stresses at nodal points.
'''
# Point load.
mat = pb.get_materials()['Load']
P = 2.0 * mat.get_data('special', 'val')[1]
# Calculate nodal stress.
pb.time_update()
if integrals is None: integrals = pb.get_integrals()
stress = pb.evaluate('ev_cauchy_stress.ivn.Omega(Asphalt.D, u)', mode='qp',
integrals=integrals, copy_materials=False)
sfield = Field.from_args('stress', nm.float64, (3,),
pb.domain.regions['Omega'])
svar = FieldVariable('sigma', 'parameter', sfield,
primary_var_name='(set-to-None)')
svar.set_from_qp(stress, integrals['ivn'])
print('\n==================================================================')
print('Given load = %.2f N' % -P)
print('\nAnalytical solution')
print('===================')
print('Horizontal tensile stress = %.5e MPa/mm' % (-2.*P/(nm.pi*150.)))
print('Vertical compressive stress = %.5e MPa/mm' % (-6.*P/(nm.pi*150.)))
print('\nFEM solution')
print('============')
print('Horizontal tensile stress = %.5e MPa/mm' % (svar()[0]))
print('Vertical compressive stress = %.5e MPa/mm' % (-svar()[1]))
print('==================================================================')
return out
def nodal_stress(out, pb, state, extend=False, integrals=None):
'''
Calculate stresses at nodal points.
'''
# Point load.
mat = pb.get_materials()['Load']
P = 2.0 * mat.get_data('special', 'val')[1]
# Calculate nodal stress.
pb.time_update()
if integrals is None: integrals = pb.get_integrals()
stress = pb.evaluate('ev_cauchy_stress.ivn.Omega(Asphalt.D, u)', mode='qp',
integrals=integrals, copy_materials=False)
sfield = Field.from_args('stress', nm.float64, (3,),
pb.domain.regions['Omega'])
svar = FieldVariable('sigma', 'parameter', sfield,
primary_var_name='(set-to-None)')
svar.set_from_qp(stress, integrals['ivn'])
print('\n==================================================================')
print('Given load = %.2f N' % -P)
print('\nAnalytical solution')
print('===================')
print('Horizontal tensile stress = %.5e MPa/mm' % (-2.*P/(nm.pi*150.)))
print('Vertical compressive stress = %.5e MPa/mm' % (-6.*P/(nm.pi*150.)))
print('\nFEM solution')
print('============')
print('Horizontal tensile stress = %.5e MPa/mm' % (svar()[0]))
print('Vertical compressive stress = %.5e MPa/mm' % (-svar()[1]))
print('==================================================================')
return out
def test_variables(self):
from sfepy.discrete import FieldVariable, Integral
ok = True
u = FieldVariable('u',
'parameter',
self.field,
primary_var_name='(set-to-None)')
u.set_constant(1.0)
vec = u() # Nodal values.
_ok = nm.allclose(vec, 1.0)
self.report('set constant:', _ok)
ok = _ok and ok
def fun(coors):
val = nm.empty_like(coors)
val[:, 0] = 2 * coors[:, 1] - coors[:, 0]
val[:, 1] = coors[:, 0] + 3 * coors[:, 1]
return val
u.set_from_function(fun)
coors = u.field.get_coor()
eu = u.evaluate_at(coors)
_ok = nm.allclose(eu, fun(coors), rtol=0.0, atol=1e-13)
self.report('set from function:', _ok)
ok = _ok and ok
integral = Integral('i', order=2)
gu_qp = u.evaluate(mode='grad', integral=integral)
# du_i/dx_j, i = column, j = row.
gu = nm.array([[-1., 1.], [2., 3.]])
_ok = nm.allclose(gu_qp, gu[None, None, ...], rtol=0.0, atol=1e-13)
self.report('set from function - gradient:', _ok)
ok = _ok and ok
u_qp = gu_qp[..., :, :1]
u.set_from_qp(u_qp, integral)
vu = u()
_ok = (nm.allclose(vu[::2], -1, rtol=0.0, atol=1e-13)
and nm.allclose(vu[1::2], 2, rtol=0.0, atol=1e-13))
self.report('set from qp:', _ok)
ok = _ok and ok
return ok
def test_variables(self):
from sfepy.discrete import FieldVariable, Integral
ok = True
u = FieldVariable('u', 'parameter', self.field,
primary_var_name='(set-to-None)')
u.set_constant(1.0)
vec = u() # Nodal values.
_ok = nm.allclose(vec, 1.0)
self.report('set constant:', _ok)
ok = _ok and ok
def fun(coors):
val = nm.empty_like(coors)
val[:, 0] = 2 * coors[:, 1] - coors[:, 0]
val[:, 1] = coors[:, 0] + 3 * coors[:, 1]
return val
u.set_from_function(fun)
coors = u.field.get_coor()
eu = u.evaluate_at(coors)
_ok = nm.allclose(eu, fun(coors), rtol=0.0, atol=1e-13)
self.report('set from function:', _ok)
ok = _ok and ok
integral = Integral('i', order=2)
gu_qp = u.evaluate(mode='grad', integral=integral)
# du_i/dx_j, i = column, j = row.
gu = nm.array([[-1., 1.],
[ 2., 3.]])
_ok = nm.allclose(gu_qp, gu[None, None, ...], rtol=0.0, atol=1e-13)
self.report('set from function - gradient:', _ok)
ok = _ok and ok
u_qp = gu_qp[..., :, :1]
u.set_from_qp(u_qp, integral)
vu = u()
_ok = (nm.allclose(vu[::2], -1, rtol=0.0, atol=1e-13) and
nm.allclose(vu[1::2], 2, rtol=0.0, atol=1e-13))
self.report('set from qp:', _ok)
ok = _ok and ok
return ok
