#
##
## This file is part of pyFormex 1.0.7 (Mon Jun 17 12:20:39 CEST 2019)
## pyFormex is a tool for generating, manipulating and transforming 3D
## geometrical models by sequences of mathematical operations.
## Home page: http://pyformex.org
## Project page: http://savannah.nongnu.org/projects/pyformex/
## Copyright 2004-2019 (C) Benedict Verhegghe (benedict.verhegghe@ugent.be)
## Distributed under the GNU General Public License version 3 or later.
##
## This program is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program. If not, see http://www.gnu.org/licenses/.
##
"""Finite Element Models in pyFormex.
Finite element models are geometrical models that consist of a unique
set of nodal coordinates and one of more sets of elements.
"""
from __future__ import absolute_import, division, print_function
import numpy as np
import pyformex as pf
from pyformex import zip
from pyformex import arraytools as at
from pyformex.coords import Coords
from pyformex.connectivity import Connectivity
from pyformex.geometry import Geometry
from pyformex.mesh import Mesh, mergeMeshes
######################## Finite Element Model ##########################
[docs]class Model(Geometry):
"""Contains all FE model data."""
_set_coords = Geometry._set_coords_inplace
def __init__(self, coords=None, elems=None, meshes=None, fuse=True):
"""Create new model data.
coords is an array with nodal coordinates
elems is either a single element connectivity array, or a list of such.
In a simple case, coords and elems can be the arrays obtained by
``coords, elems = F.feModel()``.
This is however limited to a model where all elements have the same
number of nodes. Then you can use the list of elems arrays. The 'fe'
plugin has a helper function to create this list. E.g., if ``FL`` is a
list of Formices (possibly with different plexitude), then
``fe.mergeModels([Fi.feModel() for Fi in FL])``
will return the (coords,elems) tuple to create the Model.
The model can have node and element property numbers.
"""
Geometry.__init__(self)
if meshes is not None:
if coords is not None or elems is not None:
raise ValueError("You can not use nodes/elems together with meshes")
for M in meshes:
if M.prop is None:
M.setProp(0)
self.coords, self.elems = mergeMeshes(meshes, fuse=fuse)
self.prop = np.concatenate([M.prop for M in meshes])
else:
if not isinstance(elems, list):
elems = [elems]
self.coords = Coords(coords)
self.elems = [Connectivity(e) for e in elems]
self.prop = None
meshes = self.meshes()
nnodes = [m.nnodes() for m in meshes]
nelems = [m.nelems() for m in meshes]
nplex = [m.nplex() for m in meshes]
self.cnodes = np.cumsum([0]+nnodes)
self.celems = np.cumsum([0]+nelems)
print("Finite Element Model")
print("Number of nodes: %s" % self.coords.shape[0])
print("Number of elements: %s" % self.celems[-1])
print("Number of element groups: %s" % len(nelems))
#print("Number of nodes per group: %s" % nnodes)
print("Number of elements per group: %s" % nelems)
print("Plexitude of each group: %s" % nplex)
def _select(self, sel, compact=False):
return self
[docs] def meshes(self):
"""Return the parts as a list of meshes"""
return [Mesh(self.coords, e) for e in self.elems]
[docs] def nnodes(self):
"""Return the number of nodes in the model."""
return self.coords.shape[0]
[docs] def nelems(self):
"""Return the number of elements in the model."""
return self.celems[-1]
[docs] def ngroups(self):
"""Return the number of element groups in the model."""
return len(self.elems)
[docs] def mplex(self):
"""Return the plexitude of all the element groups in the model.
Returns a list of integers.
"""
return [e.nplex() for e in self.elems]
[docs] def splitElems(self, elems):
"""Splits a set of element numbers over the element groups.
Parameters:
- `elems`: a list of element numbers in the range 0..self.nelems()
Returns two lists of element sets, the first in global numbering,
the second in group numbering.
Each item contains the element numbers from the given set that
belong to the corresponding group.
"""
elems = np.unique(elems)
split = []
n = 0
for e in self.celems[1:]:
i = elems.searchsorted(e)
split.append(elems[n:i])
n = i
return split, [np.asarray(s) - ofs for s, ofs in zip(split, self.celems)]
[docs] def elemNrs(self, group, elems=None):
"""Return the global element numbers for elements in group
Parameters:
- `group`: group number
- `elems`: list of local element numbers. If omitted, the list of all
the elements in that group is used.
Returns a list with corresponding global element numbers.
"""
if elems is None:
elems = np.arange(len(self.elems[group]))
return self.celems[group] + elems
[docs] def getElems(self, sets):
"""Return the definitions of the elements in sets.
sets should be a list of element sets with length equal to the
number of element groups. Each set contains element numbers local
to that group.
As the elements can be grouped according to plexitude,
this function returns a list of element arrays matching
the element groups in self.elems. Some of these arrays may
be empty.
"""
return [e[s] for e, s in zip(self.elems, sets)]
[docs] def renumber(self, old=None, new=None):
"""Renumber a set of nodes.
old and new are equally sized lists with unique node numbers, all
smaller than the number of nodes in the model.
The old numbers will be renumbered to the new numbers.
If one of the lists is None, a range with the length of the
other is used.
If the lists are shorter than the number of nodes, the remaining
nodes will be numbered in an unspecified order.
If both lists are None, the nodes are renumbered randomly.
This function returns a tuple (old,new) with the full renumbering
vectors used. The first gives the old node numbers of the current
numbers, the second gives the new numbers corresponding with the
old ones.
"""
nnodes = self.nnodes()
if old is None and new is None:
old = np.unique(np.random.randint(0, nnodes-1, nnodes))
new = np.unique(np.random.randint(0, nnodes-1, nnodes))
nn = max(old.size, new.size)
old = old[:nn]
new = new[:nn]
elif old is None:
new = np.asarray(new).reshape(-1)
at.checkUniqueNumbers(new, 0, nnodes)
old = np.arange(new.size)
elif new is None:
old = np.asarray(old).reshape(-1)
at.checkUniqueNumbers(old, 0, nnodes)
new = np.arange(old.size)
all = np.arange(nnodes)
old = np.concatenate([old, np.setdiff1d(all, old)])
new = np.concatenate([new, np.setdiff1d(all, new)])
oldnew = old[new]
newold = np.argsort(oldnew)
self.coords = self.coords[oldnew]
self.elems = [Connectivity(newold[e], eltype=e.eltype) for e in self.elems]
return oldnew, newold
[docs]class FEModel(Geometry):
"""A Finite Element Model.
This class is intended to collect all data concerning a Finite Element
Model. In due time it may replace the Model class. Currently it only
holds geometrical data, but will probably be expanded later to include
a property database holding material data, boundary conditions, loading
conditions and simulation step data.
While the Model class stores the geometry in a single coords block
and multiple elems blocks, the new FEModel class uses a list of Meshes.
The Meshes do not have to be compact though, and thus all Meshes in the
FEModel could used the same coords block, resulting in an equivalent
model as the old Model class. But the Meshes may also use different
coords blocks, allowing to accomodate better to versatile applications.
"""
_set_coords = Geometry._set_coords_inplace
def __init__(self, meshes):
"""Create a new FEModel."""
Geometry.__init__(self)
if not isinstance(meshes, list):
meshes = [meshes]
for m in meshes:
if not isinstance(m, Mesh):
raise ValueError("Expected a Mesh or a list thereof.")
nnodes = [m.nnodes() for m in meshes]
nelems = [m.nelems() for m in meshes]
nplex = [m.nplex() for m in meshes]
self.meshes = meshes
self.cnodes = cumsum([0]+nnodes)
self.celems = cumsum([0]+nelems)
print("Finite Element Model")
print("Number of nodes: %s" % self.coords.shape[0])
print("Number of elements: %s" % self.celems[-1])
print("Number of element groups: %s" % len(nelems))
#print("Number of nodes per group: %s" % nnodes)
print("Number of elements per group: %s" % nelems)
print("Plexitude of each group: %s" % nplex)
# implement abstractmethods
[docs] def nelems(self):
"""Return the number of elements in the model."""
return self.celems[-1]
def _select(self, sel, compact=False):
return self
[docs]def mergedModel(meshes, **kargs):
"""Returns the fe Model obtained from merging individual meshes.
The input arguments are (coords,elems) tuples.
The return value is a merged fe Model.
"""
return Model(*mergeMeshes(meshes, **kargs))
# TODO: rename to 'collectRowsByColumnValue' and move to arraytools
[docs]def sortElemsByLoadedFace(ind):
"""Sort a set of face loaded elements by the loaded face local number
ind is a (nelems,2) array, where ind[:,0] are element numbers and
ind[:,1] are the local numbers of the loaded faces
Returns a dict with the loaded face number as key and a list of
element numbers as value.
For a typical use case, see the FePlast example.
"""
edgset = np.unique(ind[:, 1])
d = {}
for e in edgset:
d[e] = ind[np.where(ind[:, 1]==e)[0], 0]
return d
if __name__ == '__main__':
print(__doc__)
# End
