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
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