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truss_fe.py
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Thu, Nov 21, 12:26

truss_fe.py
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# ------------------------------------------------------------------------------
__author__ = "Nicolas Richart"
__copyright__ = "Copyright (C) 2016-2018, EPFL (Ecole Polytechnique Fédérale" \
" de Lausanne) Laboratory (LSMS - Laboratoire de Simulation" \
" en Mécanique des Solides)"
__credits__ = ["Nicolas Richart"]
__license__ = "L-GPLv3"
__maintainer__ = "Nicolas Richart"
__email__ = "nicolas.richart@epfl.ch"
# ------------------------------------------------------------------------------
import numpy as np
import copy
import scipy.sparse as sp
from . import export
from . import fe
@export
class TrussFE(fe.Model):
def __init__(self, **kwargs):
opt = copy.copy(kwargs)
self._A = opt.pop("A", 1.)
self._E = opt.pop("E", 1.)
self._L = opt.pop("L", 1.)
self._rho = opt.pop("rho", 1.)
self._F = opt.pop("F", {-10: [-1]})
self._blocked = opt.pop("blocked", ([0], [0]))
self._Ne = opt.pop("Ne", 1)
self._Le = self._L / self._Ne
self._F_ext = np.zeros((self._Ne + 1))
self._F_int = np.zeros((self._Ne + 1))
self._u = np.zeros((self._Ne + 1))
self._v = np.zeros((self._Ne + 1))
self._a = np.zeros((self._Ne + 1))
self.assembleMass()
def assembleMass(self):
Me = np.array([[2., 1.],
[1., 2.]])
Me *= self._rho * self._A * self._Le / 6
self._M = sp.lil_matrix((self._Ne + 1, self._Ne + 1))
for i in range(self._Ne):
self._M[i:i+2, i:i+2] += Me
self._M = self._M.tocsr()
def assembleStiffness(self):
Ke = np.array([[1., -1.],
[-1., 1.]])
Ke *= self._E * self._A / self._Le
self._K = sp.lil_matrix((self._Ne + 1, self._Ne + 1))
for i in range(self._Ne):
self._K[i:i+2, i:i+2] += Ke
self._K = self._K.tocsr()
def applyNeumannBC(self):
for force, nodes in self._F.items():
self._F_ext[nodes] = force
def applyDirichletBC(self):
for i, b in enumerate(self._blocked[0]):
self._u[b] = self._blocked[1][i]
def computeInternalForces(self):
self._F_int = self._K * self._u
@property
def K(self):
self.assembleStiffness()
return self._K
@property
def M(self):
return self._M
@property
def C(self):
return None
@property
def u(self):
self.applyDirichletBC()
return self._u
@u.setter
def u(self, x):
self._u = x
self.applyDirichletBC()
@property
def v(self):
return self._v
@v.setter
def v(self, v_):
self._v = v_
@property
def a(self):
return self._a
@a.setter
def a(self, a_):
self._a = a_
@property
def f_int(self):
self.computeInternalForces()
return self._F_int
@property
def f_ext(self):
self.applyNeumannBC()
return self._F_ext
@f_ext.setter
def f_ext(self, f):
self._F_ext = f
@property
def blocked(self):
return self._blocked[0]
@property
def Le(self):
return self._Le

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