def test_transform_data(self):
import numpy as nm
from sfepy.mechanics.tensors import transform_data
ok = True
coors = nm.eye(3)
data = nm.eye(3)
expected = nm.zeros((3, 3))
expected[[0, 1, 2], [0, 0, 2]] = 1.0
out = transform_data(data, coors)
_ok = nm.allclose(out, expected, rtol=0.0, atol=1e-14)
self.report('vectors in cylindrical coordinates: %s' % _ok)
ok = ok and _ok
data = nm.zeros((3, 6))
data[:, :3] = [[1, 2, 3]]
expected = data.copy()
expected[1, [0, 1]] = expected[1, [1, 0]]
out = transform_data(data, coors)
_ok = nm.allclose(out, expected, rtol=0.0, atol=1e-14)
self.report('sym. tensors in cylindrical coordinates: %s' % _ok)
ok = ok and _ok
return ok
def test_transform_data(self):
import numpy as nm
from sfepy.mechanics.tensors import transform_data
ok = True
coors = nm.eye(3)
data = nm.eye(3)
expected = nm.zeros((3, 3))
expected[[0, 1, 2], [0, 0, 2]] = 1.0
out = transform_data(data, coors)
_ok = nm.allclose(out, expected, rtol=0.0, atol=1e-14)
self.report('vectors in cylindrical coordinates: %s' % _ok)
ok = ok and _ok
data = nm.zeros((3, 6))
data[:, :3] = [[1, 2, 3]]
expected = data.copy()
expected[1, [0, 1]] = expected[1, [1, 0]]
out = transform_data(data, coors)
_ok = nm.allclose(out, expected, rtol=0.0, atol=1e-14)
self.report('sym. tensors in cylindrical coordinates: %s' % _ok)
ok = ok and _ok
return ok
def test_transform_data4(self):
import numpy as nm
import sfepy.mechanics.tensors as tn
ok = True
if not hasattr(nm, 'einsum'):
self.report('no numpy.einsum(), skipping!')
return ok
expected = nm.zeros((6, 6), dtype=nm.float64)
expected[0, 0] = expected[1, 1] = 1.0
phi = nm.deg2rad(30.)
dr, v1, v2, om1, om2 = get_ortho_d(phi, phi + nm.deg2rad(90.))
# Rotate coordinate system by phi.
mtx = tn.make_axis_rotation_matrix([0., 0., 1.], phi)
do = tn.transform_data(dr[None, ...], mtx=mtx[None, ...])
_ok = nm.allclose(do, expected, rtol=0.0, atol=1e-14)
self.report('sym. 4th-th order tensor rotation: %s' % _ok)
ok = ok and _ok
dt, vt1, vt2, omt1, omt2 = get_ortho_d(0, nm.deg2rad(90.))
expected1 = nm.zeros((3, 3), dtype=nm.float64)
expected1[0, 0] = 1.0
expected2 = nm.zeros((3, 3), dtype=nm.float64)
expected2[1, 1] = 1.0
omr1 = nm.einsum('pq,ip,jq->ij', om1, mtx, mtx)
omr2 = nm.einsum('pq,ip,jq->ij', om2, mtx, mtx)
ii = tn.get_sym_indices(3)
jj = tn.get_full_indices(3)
o1 = om1.flat[ii]
o2 = om2.flat[ii]
omr12 = tn.transform_data(o1[None,...], mtx=mtx[None, ...])[0, jj]
omr22 = tn.transform_data(o2[None,...], mtx=mtx[None, ...])[0, jj]
_ok1 = nm.allclose(omr1, expected1, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr12, expected1, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 1: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
_ok1 = nm.allclose(omr2, expected2, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr22, expected2, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 2: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
return ok
def test_transform_data4(self):
import numpy as nm
import sfepy.mechanics.tensors as tn
ok = True
if not hasattr(nm, 'einsum'):
self.report('no numpy.einsum(), skipping!')
return ok
expected = nm.zeros((6, 6), dtype=nm.float64)
expected[0, 0] = expected[1, 1] = 1.0
phi = nm.deg2rad(30.)
dr, v1, v2, om1, om2 = get_ortho_d(phi, phi + nm.deg2rad(90.))
# Rotate coordinate system by phi.
mtx = tn.make_axis_rotation_matrix([0., 0., 1.], phi)
do = tn.transform_data(dr[None, ...], mtx=mtx[None, ...])
_ok = nm.allclose(do, expected, rtol=0.0, atol=1e-14)
self.report('sym. 4th-th order tensor rotation: %s' % _ok)
ok = ok and _ok
dt, vt1, vt2, omt1, omt2 = get_ortho_d(0, nm.deg2rad(90.))
expected1 = nm.zeros((3, 3), dtype=nm.float64)
expected1[0, 0] = 1.0
expected2 = nm.zeros((3, 3), dtype=nm.float64)
expected2[1, 1] = 1.0
omr1 = nm.einsum('pq,ip,jq->ij', om1, mtx, mtx)
omr2 = nm.einsum('pq,ip,jq->ij', om2, mtx, mtx)
ii = tn.get_sym_indices(3)
jj = tn.get_full_indices(3)
o1 = om1.flat[ii]
o2 = om2.flat[ii]
omr12 = tn.transform_data(o1[None,...], mtx=mtx[None, ...])[0, jj]
omr22 = tn.transform_data(o2[None,...], mtx=mtx[None, ...])[0, jj]
_ok1 = nm.allclose(omr1, expected1, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr12, expected1, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 1: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
_ok1 = nm.allclose(omr2, expected2, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr22, expected2, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 2: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
return ok
def make_mesh(dims, shape, transform=None):
"""
Generate a 2D rectangle mesh in 3D space, and optionally apply a coordinate
transform.
"""
_mesh = gen_block_mesh(dims, shape, [0, 0], name='shell10x', verbose=False)
coors = nm.c_[_mesh.coors, nm.zeros(_mesh.n_nod, dtype=nm.float64)]
coors = nm.ascontiguousarray(coors)
conns = [_mesh.get_conn(_mesh.descs[0])]
mesh = Mesh.from_data(_mesh.name, coors, _mesh.cmesh.vertex_groups, conns,
[_mesh.cmesh.cell_groups], _mesh.descs)
if transform == 'bend':
bbox = mesh.get_bounding_box()
x0, x1 = bbox[:, 0]
angles = 0.5 * nm.pi * (coors[:, 0] - x0) / (x1 - x0)
mtx = make_axis_rotation_matrix([0, -1, 0], angles[:, None, None])
coors = mesh.coors.copy()
coors[:, 0] = 0
coors[:, 2] = (x1 - x0)
mesh.coors[:] = transform_data(coors, mtx=mtx)
mesh.coors[:, 0] -= 0.5 * (x1 - x0)
elif transform == 'twist':
bbox = mesh.get_bounding_box()
x0, x1 = bbox[:, 0]
angles = 0.5 * nm.pi * (coors[:, 0] - x0) / (x1 - x0)
mtx = make_axis_rotation_matrix([-1, 0, 0], angles[:, None, None])
mesh.coors[:] = transform_data(mesh.coors, mtx=mtx)
return mesh
def make_mesh(dims, shape, transform=None):
"""
Generate a 2D rectangle mesh in 3D space, and optionally apply a coordinate
transform.
"""
_mesh = gen_block_mesh(dims, shape, [0, 0], name='shell10x', verbose=False)
coors = nm.c_[_mesh.coors, nm.zeros(_mesh.n_nod, dtype=nm.float64)]
coors = nm.ascontiguousarray(coors)
conns = [_mesh.get_conn(_mesh.descs[0])]
mesh = Mesh.from_data(_mesh.name, coors, _mesh.cmesh.vertex_groups, conns,
[_mesh.cmesh.cell_groups], _mesh.descs)
if transform == 'bend':
bbox = mesh.get_bounding_box()
x0, x1 = bbox[:, 0]
angles = 0.5 * nm.pi * (coors[:, 0] - x0) / (x1 - x0)
mtx = make_axis_rotation_matrix([0, -1, 0], angles[:, None, None])
coors = mesh.coors.copy()
coors[:, 0] = 0
coors[:, 2] = (x1 - x0)
mesh.coors[:] = transform_data(coors, mtx=mtx)
mesh.coors[:, 0] -= 0.5 * (x1 - x0)
elif transform == 'twist':
bbox = mesh.get_bounding_box()
x0, x1 = bbox[:, 0]
angles = 0.5 * nm.pi * (coors[:, 0] - x0) / (x1 - x0)
mtx = make_axis_rotation_matrix([-1, 0, 0], angles[:, None, None])
mesh.coors[:] = transform_data(mesh.coors, mtx=mtx)
return mesh
def eval_function(out, a1, a2, h0, mtx_c, c33, mtx_b, mtx_t, geo,
term_mode, fmode):
if term_mode == 'strain':
out_qp = membranes.get_green_strain_sym3d(mtx_c, c33)
elif term_mode == 'stress':
n_el, n_qp, dm, _ = mtx_c.shape
dim = dm + 1
sym = dim2sym(dim)
out_qp = nm.zeros((n_el, n_qp, sym, 1), dtype=mtx_c.dtype)
stress = eval_membrane_mooney_rivlin(a1, a2, mtx_c, c33, 0)
out_qp[..., 0:2, 0] = stress[..., 0:2, 0]
out_qp[..., 3, 0] = stress[..., 2, 0]
status = geo.integrate(out, out_qp, fmode)
out[:, 0, :, 0] = transform_data(out.squeeze(), mtx=mtx_t)
return status
def eval_function(out, a1, a2, h0, mtx_c, c33, mtx_b, mtx_t, geo,
term_mode, fmode):
if term_mode == 'strain':
out_qp = membranes.get_green_strain_sym3d(mtx_c, c33)
elif term_mode == 'stress':
n_el, n_qp, dm, _ = mtx_c.shape
dim = dm + 1
sym = dim2sym(dim)
out_qp = nm.zeros((n_el, n_qp, sym, 1), dtype=mtx_c.dtype)
stress = eval_membrane_mooney_rivlin(a1, a2, mtx_c, c33, 0)
out_qp[..., 0:2, 0] = stress[..., 0:2, 0]
out_qp[..., 3, 0] = stress[..., 2, 0]
status = geo.integrate(out, out_qp, fmode)
out[:, 0, :, 0] = transform_data(out.squeeze(), mtx=mtx_t)
return status