def get_fargs(self,
force_pars,
normal,
anchor,
bounds,
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.cp is None:
self.cp = ContactPlane(anchor, normal, bounds)
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)
# Active points in contact change with displacements!
ii = self.cp.mask_points(coors)
k = force_pars[..., 0]
f0 = force_pars[..., 1]
k.shape = f0.shape = force.shape
ir = f0 >= 1e-14
eps = nm.where(ir, -2.0 * f0 / k, 0.0)
a = nm.zeros_like(eps)
a[ir] = k[ir]**2 / (4.0 * f0[ir])
if diff_var is None:
if ii.any():
d = self.cp.get_distance(coors[ii])
# Force in the plane normal direction.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fmode = 0
else:
if ii.any():
d = self.cp.get_distance(coors[ii])
# Force in the plane normal direction derivative.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 1)
fmode = 1
force.shape = qps.shape[ig][:2] + (1, 1)
return force, self.cp.normal, 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_planes import (ContactPlane, plot_polygon,
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*')
for name in ['cp%d' % ii for ii in range(4)]:
cpc = materials[name][0]
cp = ContactPlane(cpc['.a'], cpc['.n'], cpc['.bs'])
v1, v2 = la.get_perpendiculars(cp.normal)
ax = plot_polygon(ax, cp.bounds)
ax = plot_polygon(
ax, nm.r_[cp.anchor[None, :],
cp.anchor[None, :] + cp.normal[None, :]])
ax = plot_polygon(ax, nm.r_[cp.anchor[None, :],
cp.anchor[None, :] + v1])
ax = plot_polygon(ax, nm.r_[cp.anchor[None, :],
cp.anchor[None, :] + v2])
plt.show()
def get_fargs(self, force_pars, normal, anchor, bounds, 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.cp is None:
self.cp = ContactPlane(anchor, normal, bounds)
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)
# Active points in contact change with displacements!
ii = self.cp.mask_points(coors)
k = force_pars[..., 0]
f0 = force_pars[..., 1]
k.shape = f0.shape = force.shape
ir = f0 >= 1e-14
eps = nm.where(ir, - 2.0 * f0 / k, 0.0)
a = nm.zeros_like(eps)
a[ir] = k[ir]**2 / (4.0 * f0[ir])
if diff_var is None:
if ii.any():
d = self.cp.get_distance(coors[ii])
# Force in the plane normal direction.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fmode = 0
else:
if ii.any():
d = self.cp.get_distance(coors[ii])
# Force in the plane normal direction derivative.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 1)
fmode = 1
force.shape = qps.shape[ig][:2] + (1, 1)
return force, self.cp.normal, sg, fmode
class ContactPlaneTerm(Term):
r"""
Small deformation elastic contact plane term with penetration penalty.
The plane is given by an anchor point :math:`\ul{A}` and a normal
:math:`\ul{n}`. The contact occurs in points that orthogonally project onto
the plane into a polygon given by orthogonal projections of boundary points
:math:`\{\ul{B}_i\}`, :math:`i = 1, \dots, N_B` on the plane. In such
points, a penetration distance :math:`d(\ul{u}) = (\ul{X} + \ul{u} -
\ul{A}, \ul{n})` is computed, and a force :math:`f(d(\ul{u})) \ul{n}` is
applied. 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}
:Arguments:
- material_f : :math:`[k, f_0]`
- material_n : :math:`\ul{n}` (special)
- material_a : :math:`\ul{A}` (special)
- material_b : :math:`\{\ul{B}_i\}`, :math:`i = 1, \dots, N_B` (special)
- virtual : :math:`\ul{v}`
- state : :math:`\ul{u}`
"""
name = 'dw_contact_plane'
arg_types = ('material_f', 'material_n', 'material_a', 'material_b',
'virtual', 'state')
arg_shapes = {
'material_f': '1, 2',
'material_n': '.: D',
'material_a': '.: D',
'material_b': '.: N, D',
'virtual': ('D', 'state'),
'state': 'D'
}
geometries = ['3_4', '3_8']
integration = 'surface'
def __init__(self, *args, **kwargs):
Term.__init__(self, *args, **kwargs)
self.cp = None
@staticmethod
def function(out, force, normal, geo, fmode):
bf = geo.bf[0]
nbf = bf * normal[None, :, None]
nbf.shape = (bf.shape[0], bf.shape[2] * normal.shape[0])
if fmode == 0:
out_qp = force * nbf[None, :, :, None]
else:
nbf2 = nbf[:, :, None] * nbf[:, None, :]
out_qp = force * nbf2[None, :, :, :]
status = geo.integrate(out, nm.ascontiguousarray(out_qp))
return status
@staticmethod
def smooth_f(d, k, f0, a, eps, diff):
ii = nm.where((d > eps) & (d <= 0.0))
if not diff:
out = nm.where(d > 0.0, k * d + f0, 0.0)
if ii:
di = d[ii]
out[ii] = a[ii] * di**2 + k[ii] * di + f0[ii]
else:
out = nm.where(d > 0.0, k, 0.0)
if ii:
out[ii] = 2 * a[ii] * d[ii] + k[ii]
return out
def get_fargs(self,
force_pars,
normal,
anchor,
bounds,
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.cp is None:
self.cp = ContactPlane(anchor, normal, bounds)
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)
# Active points in contact change with displacements!
ii = self.cp.mask_points(coors)
k = force_pars[..., 0]
f0 = force_pars[..., 1]
k.shape = f0.shape = force.shape
ir = f0 >= 1e-14
eps = nm.where(ir, -2.0 * f0 / k, 0.0)
a = nm.zeros_like(eps)
a[ir] = k[ir]**2 / (4.0 * f0[ir])
if diff_var is None:
if ii.any():
d = self.cp.get_distance(coors[ii])
# Force in the plane normal direction.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fmode = 0
else:
if ii.any():
d = self.cp.get_distance(coors[ii])
# Force in the plane normal direction derivative.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 1)
fmode = 1
force.shape = qps.shape[ig][:2] + (1, 1)
return force, self.cp.normal, sg, fmode
class ContactPlaneTerm(Term):
r"""
Small deformation elastic contact plane term with penetration penalty.
The plane is given by an anchor point :math:`\ul{A}` and a normal
:math:`\ul{n}`. The contact occurs in points that orthogonally project onto
the plane into a polygon given by orthogonal projections of boundary points
:math:`\{\ul{B}_i\}`, :math:`i = 1, \dots, N_B` on the plane. In such
points, a penetration distance :math:`d(\ul{u}) = (\ul{X} + \ul{u} -
\ul{A}, \ul{n})` is computed, and a force :math:`f(d(\ul{u})) \ul{n}` is
applied. 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}
:Arguments:
- material_f : :math:`[k, f_0]`
- material_n : :math:`\ul{n}` (special)
- material_a : :math:`\ul{A}` (special)
- material_b : :math:`\{\ul{B}_i\}`, :math:`i = 1, \dots, N_B` (special)
- virtual : :math:`\ul{v}`
- state : :math:`\ul{u}`
"""
name = 'dw_contact_plane'
arg_types = ('material_f', 'material_n', 'material_a', 'material_b',
'virtual', 'state')
arg_shapes = {'material_f' : '1, 2', 'material_n' : '.: D',
'material_a' : '.: D', 'material_b' : '.: N, D',
'virtual' : ('D', 'state'), 'state' : 'D'}
geometries = ['3_4', '3_8']
integration = 'surface'
def __init__(self, *args, **kwargs):
Term.__init__(self, *args, **kwargs)
self.cp = None
@staticmethod
def function(out, force, normal, geo, fmode):
bf = geo.bf[0]
nbf = bf * normal[None, :, None]
nbf.shape = (bf.shape[0], bf.shape[2] * normal.shape[0])
if fmode == 0:
out_qp = force * nbf[None, :, :, None]
else:
nbf2 = nbf[:, :, None] * nbf[:, None, :]
out_qp = force * nbf2[None, :, :, :]
status = geo.integrate(out, nm.ascontiguousarray(out_qp))
return status
@staticmethod
def smooth_f(d, k, f0, a, eps, diff):
ii = nm.where((d > eps) & (d <= 0.0))
if not diff:
out = nm.where(d > 0.0, k * d + f0, 0.0)
if ii:
di = d[ii]
out[ii] = a[ii] * di**2 + k[ii] * di + f0[ii]
else:
out = nm.where(d > 0.0, k, 0.0)
if ii:
out[ii] = 2 * a[ii] * d[ii] + k[ii]
return out
def get_fargs(self, force_pars, normal, anchor, bounds, 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.cp is None:
self.cp = ContactPlane(anchor, normal, bounds)
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)
# Active points in contact change with displacements!
ii = self.cp.mask_points(coors)
k = force_pars[..., 0]
f0 = force_pars[..., 1]
k.shape = f0.shape = force.shape
ir = f0 >= 1e-14
eps = nm.where(ir, - 2.0 * f0 / k, 0.0)
a = nm.zeros_like(eps)
a[ir] = k[ir]**2 / (4.0 * f0[ir])
if diff_var is None:
if ii.any():
d = self.cp.get_distance(coors[ii])
# Force in the plane normal direction.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 0)
fmode = 0
else:
if ii.any():
d = self.cp.get_distance(coors[ii])
# Force in the plane normal direction derivative.
force[ii] = self.smooth_f(d, k[ii], f0[ii], a[ii], eps[ii], 1)
fmode = 1
force.shape = qps.shape[ig][:2] + (1, 1)
return force, self.cp.normal, sg, fmode