def _calculateStiffnessMat(self):
"""
Calculate stiffness matrix.
"""
import feutils
K = numpy.zeros( (self.spaceDim*self.numVertices,
self.spaceDim*self.numVertices),
dtype=numpy.float64)
# Matrix of elasticity values
D = self._calculateElasticityMat()
for cell in self.cells:
cellK = numpy.zeros( (self.spaceDim*self.numBasis,
self.spaceDim*self.numBasis),
dtype=numpy.float64)
vertices = self.vertices[cell, :]
(jacobian, jacobianInv, jacobianDet, basisDeriv) = \
feutils.calculateJacobian(self.quadrature, vertices)
fieldTpdt = self.fieldT + self.fieldTIncr
for iQuad in xrange(self.numQuadPts):
wt = self.quadWts[iQuad] * jacobianDet[iQuad]
BL0 = self._calculateBasisDerivMatLinear0(basisDeriv, iQuad)
BL1 = self._calculateBasisDerivMatLinear1(basisDeriv, iQuad, fieldTpdt)
BL = BL0 + BL1
cellK[:] += wt * numpy.dot(numpy.dot(BL.transpose(), D), BL)
BNL = self._calculateBasisDerivMatNonlinear(basisDeriv, iQuad)
strain = self._calculateStrain(basisDeriv, iQuad, fieldTpdt)
S = self._calculateStress(strain, D)
cellK[:] += wt * numpy.dot(numpy.dot(BNL.transpose(), S), BNL)
feutils.assembleMat(K, cellK, cell, self.spaceDim)
return K
def _calculateStiffnessMat(self):
"""
Calculate stiffness matrix.
"""
import feutils
K = numpy.zeros( (self.spaceDim*self.numVertices,
self.spaceDim*self.numVertices),
dtype=numpy.float64)
# Matrix of elasticity values
D = self._calculateElasticityMat()
for cell in self.cells:
cellK = numpy.zeros( (self.spaceDim*self.numBasis,
self.spaceDim*self.numBasis),
dtype=numpy.float64)
vertices = self.vertices[cell, :]
(jacobian, jacobianInv, jacobianDet, basisDeriv) = \
feutils.calculateJacobian(self.quadrature, vertices)
for iQuad in xrange(self.numQuadPts):
wt = self.quadWts[iQuad] * jacobianDet[iQuad]
B = self._calculateBasisDerivMat(basisDeriv, iQuad)
cellK[:] += wt * numpy.dot(numpy.dot(B.transpose(), D), B)
feutils.assembleMat(K, cellK, cell, self.spaceDim)
return K
def _calculateStiffnessMat(self):
"""
Calculate stiffness matrix.
"""
import feutils
K = numpy.zeros( (self.spaceDim*self.numVertices,
self.spaceDim*self.numVertices),
dtype=numpy.float64)
# Matrix of elasticity values
D = self._calculateElasticityMat()
for cell in self.cells:
cellK = numpy.zeros( (self.spaceDim*self.numBasis,
self.spaceDim*self.numBasis),
dtype=numpy.float64)
vertices = self.vertices[cell, :]
(jacobian, jacobianInv, jacobianDet, basisDeriv) = \
feutils.calculateJacobian(self.quadrature, vertices)
for iQuad in xrange(self.numQuadPts):
wt = self.quadWts[iQuad] * jacobianDet[iQuad]
B = self._calculateBasisDerivMat(basisDeriv, iQuad)
cellK[:] += wt * numpy.dot(numpy.dot(B.transpose(), D), B)
feutils.assembleMat(K, cellK, cell, self.spaceDim)
return K
def _calculateStiffnessMat(self):
"""
Calculate stiffness matrix.
"""
import feutils
K = numpy.zeros((self.spaceDim * self.numVertices,
self.spaceDim * self.numVertices),
dtype=numpy.float64)
# Matrix of elasticity values
D = self._calculateElasticityMat()
for cell in self.cells:
cellK = numpy.zeros(
(self.spaceDim * self.numBasis, self.spaceDim * self.numBasis),
dtype=numpy.float64)
vertices = self.vertices[cell, :]
(jacobian, jacobianInv, jacobianDet, basisDeriv) = \
feutils.calculateJacobian(self.quadrature, vertices)
fieldTpdt = self.fieldT + self.fieldTIncr
for iQuad in xrange(self.numQuadPts):
wt = self.quadWts[iQuad] * jacobianDet[iQuad]
BL0 = self._calculateBasisDerivMatLinear0(basisDeriv, iQuad)
BL1 = self._calculateBasisDerivMatLinear1(
basisDeriv, iQuad, fieldTpdt)
BL = BL0 + BL1
cellK[:] += wt * numpy.dot(numpy.dot(BL.transpose(), D), BL)
BNL = self._calculateBasisDerivMatNonlinear(basisDeriv, iQuad)
strain = self._calculateStrain(basisDeriv, iQuad, fieldTpdt)
S = self._calculateStress(strain, D)
cellK[:] += wt * numpy.dot(numpy.dot(BNL.transpose(), S), BNL)
feutils.assembleMat(K, cellK, cell, self.spaceDim)
return K
def _calculateMassMat(self):
"""
Calculate mass matrix.
"""
M = numpy.zeros((self.spaceDim * self.numVertices, self.spaceDim * self.numVertices), dtype=numpy.float64)
for cell in self.cells:
cellM = numpy.zeros((self.spaceDim * self.numBasis, self.spaceDim * self.numBasis), dtype=numpy.float64)
vertices = self.vertices[cell, :]
(jacobian, jacobianInv, jacobianDet, basisDeriv) = feutils.calculateJacobian(self.quadrature, vertices)
for iQuad in xrange(self.numQuadPts):
wt = self.quadWts[iQuad] * jacobianDet[iQuad]
N = self._calculateBasisMat(iQuad)
cellM[:] += self.density * wt * numpy.dot(N.transpose(), N)
feutils.assembleMat(M, cellM, cell, self.spaceDim)
return M
def _calculateMassMat(self):
"""
Calculate mass matrix.
"""
M = numpy.zeros( (self.spaceDim*self.numVertices,
self.spaceDim*self.numVertices),
dtype=numpy.float64)
for cell in self.cells:
cellM = numpy.zeros( (self.spaceDim*self.numBasis,
self.spaceDim*self.numBasis),
dtype=numpy.float64)
vertices = self.vertices[cell, :]
(jacobian, jacobianInv, jacobianDet, basisDeriv) = \
feutils.calculateJacobian(self.quadrature, vertices)
for iQuad in xrange(self.numQuadPts):
wt = self.quadWts[iQuad] * jacobianDet[iQuad]
N = self._calculateBasisMat(iQuad)
cellM[:] += self.density * wt * numpy.dot(N.transpose(), N)
feutils.assembleMat(M, cellM, cell, self.spaceDim)
return M
