def get_fargs(self,
mtx_d,
drill,
virtual,
state,
mode=None,
term_mode=None,
diff_var=None,
**kwargs):
from sfepy.discrete.variables import create_adof_conn
vv, vu = virtual, state
geo, _ = self.get_mapping(vv)
# Displacements of element nodes.
vec_u = vu()
econn = vu.field.get_econn('volume', self.region)
adc = create_adof_conn(nm.arange(vu.n_dof, dtype=nm.int32), econn, 6,
0)
el_u = vec_u[adc]
qp_coors = geo.qp.vals
dsg = shell10x.get_dsg_strain(geo.coors_loc, geo.qp.vals)
mtx_b = shell10x.create_strain_matrix(geo.bfgm, geo.dxidx, dsg)
mtx_be = shell10x.add_eas_dofs(mtx_b, qp_coors, geo.det, geo.det0,
geo.dxidx0)
mtx_dr = shell10x.rotate_elastic_tensor(mtx_d, geo.bfu, geo.ebs)
mtx_k_qp = ddot(ddot(mtx_be, mtx_dr, 'ATB'), mtx_be, 'AB')
# Integrate.
mtx_k = (mtx_k_qp * (geo.det * geo.qp.weights)[..., None, None]).sum(1)
# Static condensation.
k11 = mtx_k[:, :24, :24]
k12 = mtx_k[:, :24, 24:]
k22 = mtx_k[:, 24:, 24:]
mtx_k = k11 - ddot(ddot(k12, nm.linalg.inv(k22)), k12.transpose(
0, 2, 1))
if drill != 0.0:
coefs = mtx_dr[..., 3, 3].mean(1) * geo.volume * drill
mtx_k = shell10x.lock_drilling_rotations(mtx_k, geo.ebs, coefs)
# DOFs in mtx_k are DOF-by-DOF. Transform is u and phi node-by-node.
blocks = nm.arange(24).reshape(2, 3, 4)
blocks = blocks.transpose((0, 2, 1)).reshape((-1, 3))
shell10x.transform_asm_matrices(mtx_k[:, None, ...], geo.mtx_t, blocks)
fmode = diff_var is not None
return (mtx_k, el_u, fmode)
def lock_drilling_rotations(mtx, ebs, coefs):
"""
Lock the drilling rotations in the stiffness matrix.
"""
mtx_drl = create_drl_transform(ebs)
mtx_idrl = nm.linalg.inv(mtx_drl)
mtx_tr = ddot(ddot(mtx_drl, mtx), mtx_idrl)
idrl = nm.arange(20, 24)
mtx_tr[:, idrl, idrl] = coefs[:, None]
mtx2 = ddot(ddot(mtx_idrl, mtx_tr), mtx_drl)
return mtx2
def lock_drilling_rotations(mtx, ebs, coefs):
"""
Lock the drilling rotations in the stiffness matrix.
"""
mtx_drl = create_drl_transform(ebs)
mtx_idrl = nm.linalg.inv(mtx_drl)
mtx_tr = ddot(ddot(mtx_drl, mtx), mtx_idrl)
idrl = nm.arange(20, 24)
mtx_tr[:, idrl, idrl] = coefs[:, None]
mtx2 = ddot(ddot(mtx_idrl, mtx_tr), mtx_drl)
return mtx2
def rotate_elastic_tensor(mtx_d, bfu, ebs):
"""
Rotate the elastic tensor into the local coordinate system of each cell.
The local coordinate system results from interpolation of `ebs` with the
bilinear basis.
"""
# ! mtx_ts is not orthonormal for non-planar cells!
mtx_ts = nm.einsum('qi,cijk->cqjk', bfu[:, 0, :], ebs)
# print nm.einsum('cqji,cqjk->cqik', mtx_ts, mtx_ts)
# ? double entries here?
tt = create_strain_transform(mtx_ts)
mtx_dr = ddot(ddot(tt, mtx_d, 'ATB'), tt, 'AB')
return mtx_dr
def rotate_elastic_tensor(mtx_d, bfu, ebs):
"""
Rotate the elastic tensor into the local coordinate system of each cell.
The local coordinate system results from interpolation of `ebs` with the
bilinear basis.
"""
# ! mtx_ts is not orthonormal for non-planar cells!
mtx_ts = nm.einsum('qi,cijk->cqjk', bfu[:, 0, :], ebs)
# print nm.einsum('cqji,cqjk->cqik', mtx_ts, mtx_ts)
# ? double entries here?
tt = create_strain_transform(mtx_ts)
mtx_dr = ddot(ddot(tt, mtx_d, 'ATB'), tt, 'AB')
return mtx_dr
def function(out, mtx_k, el_u, fmode):
if fmode == 0:
out[:, 0, ...] = ddot(mtx_k, el_u[..., None], 'AB')
else:
out[:, 0, ...] = mtx_k
return 0
def get_fargs(self, mtx_d, drill, virtual, state,
mode=None, term_mode=None, diff_var=None, **kwargs):
from sfepy.discrete.variables import create_adof_conn
vv, vu = virtual, state
geo, _ = self.get_mapping(vv)
# Displacements of element nodes.
vec_u = vu()
econn = vu.field.get_econn('volume', self.region)
adc = create_adof_conn(nm.arange(vu.n_dof, dtype=nm.int32), econn, 6, 0)
el_u = vec_u[adc]
qp_coors = geo.qp.vals
dsg = shell10x.get_dsg_strain(geo.coors_loc, geo.qp.vals)
mtx_b = shell10x.create_strain_matrix(geo.bfgm, geo.dxidx, dsg)
mtx_be = shell10x.add_eas_dofs(mtx_b, qp_coors, geo.det,
geo.det0, geo.dxidx0)
mtx_dr = shell10x.rotate_elastic_tensor(mtx_d, geo.bfu, geo.ebs)
mtx_k_qp = ddot(ddot(mtx_be, mtx_dr, 'ATB'), mtx_be, 'AB')
# Integrate.
mtx_k = (mtx_k_qp * (geo.det * geo.qp.weights)[..., None, None]).sum(1)
# Static condensation.
k11 = mtx_k[:, :24, :24]
k12 = mtx_k[:, :24, 24:]
k22 = mtx_k[:, 24:, 24:]
mtx_k = k11 - ddot(ddot(k12, nm.linalg.inv(k22)),
k12.transpose(0, 2, 1))
if drill != 0.0:
coefs = mtx_dr[..., 3, 3].mean(1) * geo.volume * drill
mtx_k = shell10x.lock_drilling_rotations(mtx_k, geo.ebs, coefs)
# DOFs in mtx_k are DOF-by-DOF. Transform is u and phi node-by-node.
blocks = nm.arange(24).reshape(2, 3, 4)
blocks = blocks.transpose((0, 2, 1)).reshape((-1, 3))
shell10x.transform_asm_matrices(mtx_k[:, None, ...], geo.mtx_t, blocks)
fmode = diff_var is not None
return (mtx_k, el_u, fmode)
def function(out, mtx_k, el_u, fmode):
if fmode == 0:
out[:, 0, ...] = ddot(mtx_k, el_u[..., None], 'AB')
else:
out[:, 0, ...] = mtx_k
return 0
def transform_asm_matrices(out, mtx_t, blocks):
"""
Transform matrix assembling contributions to global coordinate system, one
node at a time.
Parameters
----------
out : array
The array of matrices, transformed in-place.
mtx_t : array
The array of transposed transformation matrices :math:`T`, see
:func:`create_transformation_matrix`.
blocks : array
The DOF blocks that are
"""
for ir in blocks:
ir = ir[:, None]
for ic in blocks:
fn = out[:, 0, ir, ic]
out[:, 0, ir, ic] = ddot(ddot(mtx_t, fn, 'AB'), mtx_t, 'ABT')
def transform_asm_matrices(out, mtx_t, blocks):
"""
Transform matrix assembling contributions to global coordinate system, one
node at a time.
Parameters
----------
out : array
The array of matrices, transformed in-place.
mtx_t : array
The array of transposed transformation matrices :math:`T`, see
:func:`create_transformation_matrix`.
blocks : array
The DOF blocks that are
"""
for ir in blocks:
ir = ir[:, None]
for ic in blocks:
fn = out[:, 0, ir, ic]
out[:, 0, ir, ic] = ddot(ddot(mtx_t, fn, 'AB'), mtx_t, 'ABT')
def get_mapping(self, qp_coors, weights):
"""
Get the mapping for given quadrature points and weights.
"""
domain = self.region.domain
mesh = domain.mesh
iels = self.region.get_cells()
conn = nm.take(domain.get_conn(), iels.astype(nm.int32), axis=0)
e_coors = mesh.coors[conn]
mtx_t = shell10x.create_transformation_matrix(e_coors)
e_centres = mesh.cmesh.get_centroids(2)[iels]
coors_loc = ddot((e_coors - e_centres[:, None, :]), mtx_t)
ebs = shell10x.create_local_bases(coors_loc)
rops = shell10x.create_rotation_ops(ebs)
ps = self.field.poly_space
qp_coors0 = nm.array([[0.5, 0.5, 0.5]])
# Should be thickness, but not used anywhere.
qp_weights0 = nm.array([0.0])
dxidx0, det0 = shell10x.get_mapping_data(ebs, rops, ps, coors_loc,
qp_coors0, qp_weights0,
special_dx3=True)
aux = shell10x.get_mapping_data(ebs, rops, ps, coors_loc,
qp_coors, weights)
coors_loc_3d, bfu, bfgm, dxidx, det = aux
self.coors_loc = coors_loc
self.e_centres = e_centres
self.mtx_t = mtx_t
self.ebs = ebs
self.rops = rops
self.dxidx0 = dxidx0
self.det0 = det0
self.coors_loc_3d = coors_loc_3d
self.bfu = bfu
self.bfgm = bfgm
self.dxidx = dxidx
self.det = det
self.volume = (det * weights).sum(1)
return self
