def main():
import os
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.fem import MeshIO
import sfepy.linalg as la
from sfepy.mechanics.contact_bodies import ContactSphere, plot_points
conf_dir = os.path.dirname(__file__)
io = MeshIO.any_from_filename(filename_mesh, prefix_dir=conf_dir)
bb = io.read_bounding_box()
outline = [vv for vv in la.combine(zip(*bb))]
ax = plot_points(None, nm.array(outline), 'r*')
csc = materials['cs'][0]
cs = ContactSphere(csc['.c'], csc['.r'])
pps = (bb[1] - bb[0]) * nm.random.rand(5000, 3) + bb[0]
mask = cs.mask_points(pps, 0.0)
ax = plot_points(ax, cs.centre[None, :], 'b*', ms=30)
ax = plot_points(ax, pps[mask], 'kv')
ax = plot_points(ax, pps[~mask], 'r.')
plt.show()
def get_fargs(self,
force_pars,
centre,
radius,
virtual,
state,
mode=None,
term_mode=None,
diff_var=None,
**kwargs):
sg, _ = self.get_mapping(virtual)
assert_((force_pars >= 0.0).all(),
'force parameters must be non-negative!')
if self.cs is None:
self.cs = ContactSphere(centre, radius)
ig = self.char_fun.ig
qps = self.get_physical_qps()
qp_coors = qps.values[ig]
u_qp = self.get(state, 'val').reshape(qp_coors.shape)
# Deformed QP coordinates.
coors = u_qp + qp_coors
force = nm.zeros(coors.shape[0], dtype=nm.float64)
normals = nm.zeros((coors.shape[0], 3), dtype=nm.float64)
fd = None
k, f0, eps, a = self._get_force_pars(force_pars, force.shape)
# Active points in contact change with displacements!
ii = self.cs.mask_points(coors, nm.abs(eps.min()))
if diff_var is None:
if ii.any():
d, normals[ii] = self.cs.get_distance(coors[ii])
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fmode = 0
else:
if ii.any():
d, normals[ii] = self.cs.get_distance(coors[ii])
# Force derivative.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 1)
# Force / (R - d).
aux = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fd = nm.zeros_like(force)
fd[ii] = aux / (self.cs.radius - d)
fd.shape = qps.shape[ig][:2] + (1, 1)
fmode = 1
force.shape = qps.shape[ig][:2] + (1, 1)
normals.shape = qps.shape[ig][:2] + (3, 1)
return force, normals, fd, sg, fmode
def main():
import os
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.fem import MeshIO
import sfepy.linalg as la
from sfepy.mechanics.contact_bodies import ContactSphere, plot_points
conf_dir = os.path.dirname(__file__)
io = MeshIO.any_from_filename(filename_mesh, prefix_dir=conf_dir)
bb = io.read_bounding_box()
outline = [vv for vv in la.combine(zip(*bb))]
ax = plot_points(None, nm.array(outline), 'r*')
csc = materials['cs'][0]
cs = ContactSphere(csc['.c'], csc['.r'])
pps = (bb[1] - bb[0]) * nm.random.rand(5000, 3) + bb[0]
mask = cs.mask_points(pps, 0.0)
ax = plot_points(ax, cs.centre[None, :], 'b*', ms=30)
ax = plot_points(ax, pps[mask], 'kv')
ax = plot_points(ax, pps[~mask], 'r.')
plt.show()
def get_fargs(self, force_pars, centre, radius, virtual, state,
mode=None, term_mode=None, diff_var=None, **kwargs):
sg, _ = self.get_mapping(virtual)
assert_((force_pars >= 0.0).all(),
'force parameters must be non-negative!')
if self.cs is None:
self.cs = ContactSphere(centre, radius)
ig = self.char_fun.ig
qps = self.get_physical_qps()
qp_coors = qps.values[ig]
u_qp = self.get(state, 'val').reshape(qp_coors.shape)
# Deformed QP coordinates.
coors = u_qp + qp_coors
force = nm.zeros(coors.shape[0], dtype=nm.float64)
normals = nm.zeros((coors.shape[0], 3), dtype=nm.float64)
fd = None
k, f0, eps, a = self._get_force_pars(force_pars, force.shape)
# Active points in contact change with displacements!
ii = self.cs.mask_points(coors, nm.abs(eps.min()))
if diff_var is None:
if ii.any():
d, normals[ii] = self.cs.get_distance(coors[ii])
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fmode = 0
else:
if ii.any():
d, normals[ii] = self.cs.get_distance(coors[ii])
# Force derivative.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 1)
# Force / (R - d).
aux = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fd = nm.zeros_like(force)
fd[ii] = aux / (self.cs.radius - d)
fd.shape = qps.shape[ig][:2] + (1, 1)
fmode = 1
force.shape = qps.shape[ig][:2] + (1, 1)
normals.shape = qps.shape[ig][:2] + (3, 1)
return force, normals, fd, sg, fmode
class ContactSphereTerm(ContactPlaneTerm):
r"""
Small deformation elastic contact sphere term with penetration penalty.
The sphere is given by a centre point :math:`\ul{C}` and a radius
:math:`R`. The contact occurs in points that are closer to :math:`\ul{C}`
than :math:`R`. In such points, a penetration distance :math:`d(\ul{u}) =
R - ||\ul{X} + \ul{u} - \ul{C}||` is computed, and a force
:math:`f(d(\ul{u})) \ul{n}(\ul{u})` is applied, where :math:`\ul{n}(\ul{u})
= (\ul{X} + \ul{u} - \ul{C}) / ||\ul{X} + \ul{u} - \ul{C}||`. The force
depends on the non-negative parameters :math:`k` (stiffness) and
:math:`f_0` (force at zero penetration):
- If :math:`f_0 = 0`:
.. math::
f(d) = 0 \mbox{ for } d \leq 0 \;, \\
f(d) = k d \mbox{ for } d > 0 \;.
- If :math:`f_0 > 0`:
.. math::
f(d) = 0 \mbox{ for } d \leq -\frac{2 r_0}{k} \;, \\
f(d) = \frac{k^2}{4 r_0} d^2 + k d + r_0
\mbox{ for } -\frac{2 r_0}{k} < d \leq 0 \;, \\
f(d) = k d + f_0 \mbox{ for } d > 0 \;.
In this case the dependence :math:`f(d)` is smooth, and a (small) force
is applied even for (small) negative penetrations: :math:`-\frac{2
r_0}{k} < d \leq 0`.
:Definition:
.. math::
\int_{\Gamma} \ul{v} \cdot f(d(\ul{u})) \ul{n}(\ul{u})
:Arguments:
- material_f : :math:`[k, f_0]`
- material_c : :math:`\ul{C}` (special)
- material_r : :math:`R` (special)
- virtual : :math:`\ul{v}`
- state : :math:`\ul{u}`
"""
name = 'dw_contact_sphere'
arg_types = ('material_f', 'material_c', 'material_r', 'virtual', 'state')
arg_shapes = {'material_f' : '1, 2', 'material_c' : '.: D',
'material_r' : '.: 1',
'virtual' : ('D', 'state'), 'state' : 'D'}
geometries = ['3_4', '3_8']
integration = 'surface'
def __init__(self, *args, **kwargs):
Term.__init__(self, *args, **kwargs)
self.cs = None
@staticmethod
def function(out, force, normals, fd, geo, fmode):
bf = geo.bf[0]
nbf = bf * normals
nbf.shape = (normals.shape[0], normals.shape[1],
bf.shape[2] * normals.shape[2])
if fmode == 0:
out_qp = force * nbf[..., None]
else:
nbf2 = nbf[..., None] * nbf[..., None, :]
dim = normals.shape[2]
n_ep = bf.shape[2]
bb = bf[:, 0]
vb = nm.zeros((bf.shape[0], dim, dim * n_ep))
for ii in range(dim):
vb[:, ii, ii*n_ep:(ii+1)*n_ep] = bb
ee = nm.eye(3)[None, ...]
eebf2 = dot_sequences(vb, dot_sequences(ee, vb), 'ATB')
out_qp = force * nbf2
if fd is not None:
out_qp -= fd * (eebf2[None, :, :, :] - nbf2)
status = geo.integrate(out, nm.ascontiguousarray(out_qp))
return status
def get_fargs(self, force_pars, centre, radius, virtual, state,
mode=None, term_mode=None, diff_var=None, **kwargs):
sg, _ = self.get_mapping(virtual)
assert_((force_pars >= 0.0).all(),
'force parameters must be non-negative!')
if self.cs is None:
self.cs = ContactSphere(centre, radius)
ig = self.char_fun.ig
qps = self.get_physical_qps()
qp_coors = qps.values[ig]
u_qp = self.get(state, 'val').reshape(qp_coors.shape)
# Deformed QP coordinates.
coors = u_qp + qp_coors
force = nm.zeros(coors.shape[0], dtype=nm.float64)
normals = nm.zeros((coors.shape[0], 3), dtype=nm.float64)
fd = None
k, f0, eps, a = self._get_force_pars(force_pars, force.shape)
# Active points in contact change with displacements!
ii = self.cs.mask_points(coors, nm.abs(eps.min()))
if diff_var is None:
if ii.any():
d, normals[ii] = self.cs.get_distance(coors[ii])
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fmode = 0
else:
if ii.any():
d, normals[ii] = self.cs.get_distance(coors[ii])
# Force derivative.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 1)
# Force / (R - d).
aux = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fd = nm.zeros_like(force)
fd[ii] = aux / (self.cs.radius - d)
fd.shape = qps.shape[ig][:2] + (1, 1)
fmode = 1
force.shape = qps.shape[ig][:2] + (1, 1)
normals.shape = qps.shape[ig][:2] + (3, 1)
return force, normals, fd, sg, fmode
class ContactSphereTerm(ContactPlaneTerm):
r"""
Small deformation elastic contact sphere term with penetration penalty.
The sphere is given by a centre point :math:`\ul{C}` and a radius
:math:`R`. The contact occurs in points that are closer to :math:`\ul{C}`
than :math:`R`. In such points, a penetration distance :math:`d(\ul{u}) =
R - ||\ul{X} + \ul{u} - \ul{C}||` is computed, and a force
:math:`f(d(\ul{u})) \ul{n}(\ul{u})` is applied, where :math:`\ul{n}(\ul{u})
= (\ul{X} + \ul{u} - \ul{C}) / ||\ul{X} + \ul{u} - \ul{C}||`. The force
depends on the non-negative parameters :math:`k` (stiffness) and
:math:`f_0` (force at zero penetration):
- If :math:`f_0 = 0`:
.. math::
f(d) = 0 \mbox{ for } d \leq 0 \;, \\
f(d) = k d \mbox{ for } d > 0 \;.
- If :math:`f_0 > 0`:
.. math::
f(d) = 0 \mbox{ for } d \leq -\frac{2 r_0}{k} \;, \\
f(d) = \frac{k^2}{4 r_0} d^2 + k d + r_0
\mbox{ for } -\frac{2 r_0}{k} < d \leq 0 \;, \\
f(d) = k d + f_0 \mbox{ for } d > 0 \;.
In this case the dependence :math:`f(d)` is smooth, and a (small) force
is applied even for (small) negative penetrations: :math:`-\frac{2
r_0}{k} < d \leq 0`.
:Definition:
.. math::
\int_{\Gamma} \ul{v} \cdot f(d(\ul{u})) \ul{n}(\ul{u})
:Arguments:
- material_f : :math:`[k, f_0]`
- material_c : :math:`\ul{C}` (special)
- material_r : :math:`R` (special)
- virtual : :math:`\ul{v}`
- state : :math:`\ul{u}`
"""
name = 'dw_contact_sphere'
arg_types = ('material_f', 'material_c', 'material_r', 'virtual', 'state')
arg_shapes = {
'material_f': '1, 2',
'material_c': '.: D',
'material_r': '.: 1',
'virtual': ('D', 'state'),
'state': 'D'
}
geometries = ['3_4', '3_8']
integration = 'surface'
def __init__(self, *args, **kwargs):
Term.__init__(self, *args, **kwargs)
self.cs = None
@staticmethod
def function(out, force, normals, fd, geo, fmode):
bf = geo.bf[0]
nbf = bf * normals
nbf.shape = (normals.shape[0], normals.shape[1],
bf.shape[2] * normals.shape[2])
if fmode == 0:
out_qp = force * nbf[..., None]
else:
nbf2 = nbf[..., None] * nbf[..., None, :]
dim = normals.shape[2]
n_ep = bf.shape[2]
bb = bf[:, 0]
vb = nm.zeros((bf.shape[0], dim, dim * n_ep))
for ii in range(dim):
vb[:, ii, ii * n_ep:(ii + 1) * n_ep] = bb
ee = nm.eye(3)[None, ...]
eebf2 = dot_sequences(vb, dot_sequences(ee, vb), 'ATB')
out_qp = force * nbf2
if fd is not None:
out_qp -= fd * (eebf2[None, :, :, :] - nbf2)
status = geo.integrate(out, nm.ascontiguousarray(out_qp))
return status
def get_fargs(self,
force_pars,
centre,
radius,
virtual,
state,
mode=None,
term_mode=None,
diff_var=None,
**kwargs):
sg, _ = self.get_mapping(virtual)
assert_((force_pars >= 0.0).all(),
'force parameters must be non-negative!')
if self.cs is None:
self.cs = ContactSphere(centre, radius)
ig = self.char_fun.ig
qps = self.get_physical_qps()
qp_coors = qps.values[ig]
u_qp = self.get(state, 'val').reshape(qp_coors.shape)
# Deformed QP coordinates.
coors = u_qp + qp_coors
force = nm.zeros(coors.shape[0], dtype=nm.float64)
normals = nm.zeros((coors.shape[0], 3), dtype=nm.float64)
fd = None
k, f0, eps, a = self._get_force_pars(force_pars, force.shape)
# Active points in contact change with displacements!
ii = self.cs.mask_points(coors, nm.abs(eps.min()))
if diff_var is None:
if ii.any():
d, normals[ii] = self.cs.get_distance(coors[ii])
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fmode = 0
else:
if ii.any():
d, normals[ii] = self.cs.get_distance(coors[ii])
# Force derivative.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 1)
# Force / (R - d).
aux = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fd = nm.zeros_like(force)
fd[ii] = aux / (self.cs.radius - d)
fd.shape = qps.shape[ig][:2] + (1, 1)
fmode = 1
force.shape = qps.shape[ig][:2] + (1, 1)
normals.shape = qps.shape[ig][:2] + (3, 1)
return force, normals, fd, sg, fmode