def getULInternalForce(self, elemdat):
n = self.dofCount()
state0 = elemdat.state - elemdat.Dstate
curCrds = elemdat.coords + reshape(state0, elemdat.coords.shape)
sData0 = getElemShapeData(elemdat.coords)
sDataC = getElemShapeData(curCrds)
for iOrig, iCurr in zip(sData0, sDataC):
r = dot(curCrds[:, 0], iOrig.h)
r0 = dot(elemdat.coords[:, 0], iOrig.h)
weight = 2.0 * pi * r * iCurr.weight
kin = self.getKinematics(iOrig.dhdx, iOrig.h, elemdat, r0)
B = self.getULBmatrix(iCurr.dhdx, iCurr.h, r)
sigma, tang = self.mat.getStress(kin)
s4 = self.stress6to4(sigma)
elemdat.fint += dot(B.transpose(), s4) * weight
self.appendNodalOutput(self.mat.outLabels(), self.mat.outData())
def getTangentStiffness(self, elemdat):
sData = getElemShapeData(elemdat.coords)
kin = Kinematics(3, 6)
elemdat.outlabel.append(["s11", "s22", "s33", "s23", "s13", "s12"])
elemdat.outdata = zeros(shape=(len(elemdat.nodes), 6))
for iData in sData:
b = self.getBmatrix(iData.dhdx)
kin.strain = dot(b, elemdat.state)
kin.dstrain = dot(b, elemdat.Dstate)
sigma, tang = self.mat.getStress(kin)
elemdat.stiff += dot(b.transpose(), dot(tang, b)) * iData.weight
elemdat.fint += dot(b.transpose(), sigma) * iData.weight
elemdat.outdata += outer(ones(len(elemdat.nodes)), sigma)
elemdat.outdata *= 1.0 / len(sData)
def getInternalForce(self, elemdat):
sData = getElemShapeData(elemdat.coords, -1)
elemdat.outlabel.append(self.outputLabels)
elemdat.outdata = zeros(shape=(len(elemdat.nodes), 6))
eps0 = zeros(3)
kappa = zeros(3)
for iData in sData:
eps0[0] = dot(iData.dhdx[:, 0], elemdat.state[0:20:5])
eps0[1] = dot(iData.dhdx[:, 1], elemdat.state[1:20:5])
eps0[2] = dot(iData.dhdx[:,1],elemdat.state[0:20:5])+\
dot(iData.dhdx[:,0],elemdat.state[1:20:5])
kappa[0] = dot(iData.dhdx[:, 0], elemdat.state[3:20:5])
kappa[1] = dot(iData.dhdx[:, 1], elemdat.state[4:20:5])
kappa[2]= dot(iData.dhdx[:,1],elemdat.state[3:20:5])+\
dot(iData.dhdx[:,0],elemdat.state[4:20:5])
for i, pp in enumerate(self.postProcess):
eps = eps0 + pp.z * kappa
sigma = stressTransformation(dot(pp.Qbar, eps), pp.theta)
self.appendNodalOutput(pp.labels, sigma)
def getTangentStiffness ( self, elemdat ):
n = self.dofCount()
sData = getElemShapeData( elemdat.coords )
elemdat.outlabel.append("stresses")
elemdat.outdata = zeros( shape=(len(elemdat.nodes),3) )
for iData in sData:
kin = self.getKinematics( iData.dhdx , elemdat.state )
B = self.getBmatrix ( iData.dhdx , kin.F )
sigma,tang = self.mat.getStress( kin )
elemdat.stiff += dot ( B.transpose() , dot ( tang , B ) ) * iData.weight
T = self.stress2matrix( sigma )
Bnl = self.getBNLmatrix ( iData.dhdx )
elemdat.stiff += dot ( Bnl.transpose() , dot( T , Bnl ) ) * iData.weight
elemdat.fint += dot ( B.transpose() , sigma ) * iData.weight
elemdat.outdata += outer( ones(len(elemdat.nodes)), sigma )
elemdat.outdata *= 1.0 / len(sData)
def getInternalForce(self, elemdat):
sData = getElemShapeData(elemdat.coords)
for iData in sData:
r = dot(elemdat.coords[:, 0], iData.h)
weight = 2.0 * pi * r * iData.weight
b = self.getBmatrix(iData.dhdx, iData.h, r)
strain = dot(b, elemdat.state)
#self.kin.dstrain = dot ( b , elemdat.Dstate )
self.kin.strain[0] = strain[0]
self.kin.strain[1] = strain[1]
self.kin.strain[2] = strain[2]
self.kin.strain[3] = 0.
self.kin.strain[4] = 0.
self.kin.strain[5] = strain[3]
#self.kin.dstrain = dot ( b , elemdat.Dstate )
sigma, tang = self.mat.getStress(self.kin)
s4 = self.stress6to4(sigma)
elemdat.fint += dot(b.transpose(), s4) * weight
self.appendNodalOutput(self.mat.outLabels(), self.mat.outData())
def getTangentStiffness(self, elemdat):
n = self.dofCount()
sData = getElemShapeData(elemdat.coords)
elemdat.outlabel.append("stresses")
elemdat.outdata = zeros(shape=(len(elemdat.nodes), 3))
for iData in sData:
kin = self.getKinematics(iData.dhdx, elemdat.state)
B = self.getBmatrix(iData.dhdx, kin.F)
sigma, tang = self.mat.getStress(kin)
elemdat.stiff += dot(B.transpose(), dot(tang, B)) * iData.weight
T = self.stress2matrix(sigma)
Bnl = self.getBNLmatrix(iData.dhdx)
elemdat.stiff += dot(Bnl.transpose(), dot(T, Bnl)) * iData.weight
elemdat.fint += dot(B.transpose(), sigma) * iData.weight
elemdat.outdata += outer(ones(len(elemdat.nodes)), sigma)
elemdat.outdata *= 1.0 / len(sData)
def getTangentStiffness(self, elemdat):
sData = getElemShapeData(elemdat.coords)
nDof = len(elemdat.coords)
temp0 = elemdat.state - elemdat.Dstate
if self.transient:
ctt = zeros(shape=(nDof, nDof))
invdtime = 1.0 / self.solverStat.dtime
for iInt, iData in enumerate(sData):
gradTemp = dot(iData.dhdx.transpose(), elemdat.state)
elemdat.stiff += \
dot ( iData.dhdx , dot( self.D , iData.dhdx.transpose() ) ) * iData.weight
if self.transient:
ctt += self.capac * outer(iData.h, iData.h) * iData.weight
self.appendNodalOutput(self.labels, dot(self.D, gradTemp))
if self.transient:
ktt0 = invdtime * ctt - elemdat.stiff * (1.0 - self.theta)
elemdat.stiff *= self.theta
elemdat.stiff += invdtime * ctt
elemdat.fint += dot(elemdat.stiff, elemdat.state)
if self.transient:
elemdat.fint += -dot(ktt0, temp0)
def getTangentStiffness(self, elemdat):
n = self.dofCount()
sData = getElemShapeData(elemdat.coords)
elemdat.outlabel.append("stresses")
elemdat.outdata = zeros(shape=(len(elemdat.nodes), 3))
for iData in sData:
kin = self.getKinematics(iData.dhdx, elemdat.state)
firstPiola, K4tang = self.mat.getStress(kin)
K4 = ut.transform_4thTensor_to_2ndTensor_inlargestrain(K4tang)
firstPiola_vector = ut.transform_matrix_to_vector(firstPiola)
Bnl = self.getBNLmatrix(iData.dhdx)
elemdat.stiff += dot(Bnl.transpose(), dot(K4, Bnl)) * iData.weight
elemdat.fint += dot(Bnl.transpose(),
firstPiola_vector) * iData.weight
secondPiola = dot(np.linalg.inv(kin.F), firstPiola)
secondPiola_vector = np.array(
[secondPiola[0, 0], secondPiola[1, 1], secondPiola[0, 1]])
elemdat.outdata += outer(ones(len(elemdat.nodes)),
secondPiola_vector)
# elemdat.stiff += dot(B.transpose(), dot(tang, B)) * iData.weight # nonlinear material: dF : (F . DS) -> (dF.F) : C DE -> (dF.F) : C : (DF.F)
# T = self.stress2matrix(sigma)
# Bnl = self.getBNLmatrix(iData.dhdx)
# elemdat.stiff += dot(Bnl.transpose(), dot(T, Bnl)) * iData.weight # nonlinear geometry: dF : (DF . S)
# elemdat.fint += dot(B.transpose(), sigma) * iData.weight # power conjugate: chuyen tu F:P sang E:S -> 1/2(FT.F + F.FT):S -> FT.F : S (vi S symmetry)
# elemdat.outdata += outer(ones(len(elemdat.nodes)), sigma)
elemdat.outdata *= 1.0 / len(sData)
def getInternalForce ( self, elemdat ):
sData = getElemShapeData( elemdat.coords , -1 )
elemdat.outlabel.append(self.outputLabels)
elemdat.outdata = zeros( shape=(len(elemdat.nodes),6) )
eps0 = zeros(3)
epss = zeros(2)
kappa = zeros(3)
for iData in sData:
eps0[0] = dot(iData.dhdx[:,0],elemdat.state[0:20:5])
eps0[1] = dot(iData.dhdx[:,1],elemdat.state[1:20:5])
eps0[2] = dot(iData.dhdx[:,1],elemdat.state[0:20:5])+\
dot(iData.dhdx[:,0],elemdat.state[1:20:5])
epss[0] = dot(iData.dhdx[:,1],elemdat.state[2:20:5])+\
dot(iData.h ,elemdat.state[4:20:5])
epss[1] = dot(iData.dhdx[:,0],elemdat.state[2:20:5])+\
dot(iData.h ,elemdat.state[3:20:5])
kappa[0]= dot(iData.dhdx[:,0],elemdat.state[3:20:5])
kappa[1]= dot(iData.dhdx[:,1],elemdat.state[4:20:5])
kappa[2]= dot(iData.dhdx[:,1],elemdat.state[3:20:5])+\
dot(iData.dhdx[:,0],elemdat.state[4:20:5])
# for pp in postProcess:
# eps = eps0 + pp.z*kappa
# sigma = com
elemdat.outdata += 0.0#eps0 #outer( ones(len(self)), sigma )
elemdat.outdata *= 1.0 / len(sData)
def getTangentStiffness(self, elemdat):
n = self.dofCount()
sData = getElemShapeData(elemdat.coords)
elemdat.outlabel.append("stresses")
elemdat.outdata = zeros(shape=(len(elemdat.nodes), 3))
for iData in sData:
kin = self.getKinematics(iData.dhdx, elemdat.state)
B = self.getBmatrix(iData.dhdx, kin.F)
sigma, tang = self.mat.getStress(kin)
elemdat.stiff += dot(
B.transpose(), dot(tang, B)
) * iData.weight # nonlinear material: dF : (F . DS) -> (dF.F) : C DE -> (dF.F) : C : (DF.F)
T = self.stress2matrix(sigma)
Bnl = self.getBNLmatrix(iData.dhdx)
elemdat.stiff += dot(Bnl.transpose(), dot(
T, Bnl)) * iData.weight # nonlinear geometry: dF : (DF . S)
elemdat.fint += dot(
B.transpose(), sigma
) * iData.weight # power conjugate: chuyen tu F:P sang E:S -> 1/2(FT.F + F.FT):S -> FT.F : S (vi S symmetry)
elemdat.outdata += outer(ones(len(elemdat.nodes)), sigma)
elemdat.outdata *= 1.0 / len(sData)
def getTangentStiffness ( self, elemdat ):
n = self.dofCount()
sData = getElemShapeData( elemdat.coords )
elemdat.outlabel.append(self.outputLabels)
elemdat.outdata = zeros( shape=(len(elemdat.nodes),self.nstr) )
for iData in sData:
self.kin = self.getKinematics( iData.dhdx , elemdat.state )
B = self.getBmatrix ( iData.dhdx , self.kin.F )
sigma,tang = self.mat.getStress( self.kin )
elemdat.stiff += dot ( B.transpose() , dot ( tang , B ) ) * iData.weight
T = self.stress2matrix( sigma )
Bnl = self.getBNLmatrix ( iData.dhdx )
elemdat.stiff += dot ( Bnl.transpose() , dot( T , Bnl ) ) * iData.weight
elemdat.fint += dot ( B.transpose() , sigma ) * iData.weight
self.appendNodalOutput( self.mat.outLabels() , self.mat.outData() )
def getTangentStiffness ( self, elemdat ):
print(self.rank)
sData = getElemShapeData( elemdat.coords )
uDofs,pDofs = self.splitDofIDs( len(elemdat.coords) )
for iInt,iData in enumerate(sData):
B = self.getBmatrix( iData.dhdx )
self.kin.strain = dot ( B , elemdat.state [uDofs] )
self.kin.dstrain = dot ( B , elemdat.Dstate[uDofs] )
phase = dot( iData.h , elemdat.state[pDofs] )
gradPhase = dot( iData.dhdx.transpose() , elemdat.state[pDofs] )
sigma,tang = self.mat.getStress( self.kin )
energy = 0.5*sum(self.kin.strain*sigma)
if energy > self.hisOld[iInt]:
self.hisNew[iInt] = energy
else:
self.hisNew[iInt] = self.hisOld[iInt]
factor = 1.0-phase*phase+self.k
# -- Displacement contributions
uStiff = dot ( B.transpose() , dot ( factor*tang , B ) )
elemdat.stiff[ix_(uDofs,uDofs)] += uStiff * iData.weight
dispForce = dot ( B.transpose() , factor*sigma )
elemdat.fint[uDofs] += dispForce * iData.weight
pStiff = (self.Gc/self.l0+2.0*self.hisNew[iInt])*outer(iData.h , iData.h )
pStiff += self.Gc*self.l0*dot( iData.dhdx,iData.dhdx.transpose() )
pStiff = iData.weight * pStiff
elemdat.stiff[ix_(pDofs,pDofs)] += pStiff
# -- Phase field contributions
pfint = self.Gc*self.l0*dot( iData.dhdx , gradPhase );
pfint += self.Gc/self.l0*iData.h*phase;
pfint += 2.0*( phase-1.0 ) * iData.h * self.hisNew[iInt]
elemdat.fint[pDofs] += pfint * iData.weight
# -- Coupling terms
vecu = -2.0 * ( 1.0 - phase ) * dot( B.transpose() , sigma ) * iData.weight
elemdat.stiff[ix_(uDofs,pDofs)] += outer( vecu , iData.h )
elemdat.stiff[ix_(pDofs,uDofs)] += outer( iData.h , vecu )
# Coupling terms need TOBEIMPLEMENTED
self.appendNodalOutput( self.mat.outLabels() , self.mat.outData() )
def getTangentStiffness ( self, elemdat ):
sData = getElemShapeData( elemdat.coords )
dDofs,tDofs = self.splitDofIDs( len(elemdat.coords) )
temp0 = elemdat.state [tDofs] - elemdat.Dstate[tDofs]
if self.transient:
ctt = zeros(shape=(len(tDofs),len(tDofs)))
invdtime = 1.0/self.solverStat.dtime
for iInt,iData in enumerate(sData):
B = self.getBmatrix( iData.dhdx )
self.kin.strain = dot ( B , elemdat.state [dDofs] )
self.kin.dstrain = dot ( B , elemdat.Dstate[dDofs] )
temp = sum( iData.h * elemdat.state [tDofs] )
dtemp = sum( iData.h * elemdat.Dstate[tDofs] )
gradTemp = dot( iData.dhdx.transpose() , elemdat.state [tDofs] )
self.kin.strain[:self.nstr] += -self.alpha * temp
self.kin.dstrain[:self.nstr] += -self.alpha * dtemp
sigma,tang = self.mat.getStress( self.kin )
elemdat.stiff[ix_(dDofs,dDofs)] += \
dot ( B.transpose() , dot ( tang , B ) ) * iData.weight
dsdt = -1.0 * dot( tang , self.alpha )
elemdat.stiff[ix_(dDofs,tDofs)] += \
dot ( B.transpose() , outer ( dsdt , iData.h ) ) * iData.weight
elemdat.stiff[ix_(tDofs,tDofs)] += \
dot ( iData.dhdx , dot( self.D , iData.dhdx.transpose() ) ) * iData.weight
elemdat.fint[dDofs] += dot ( B.transpose() , sigma ) * iData.weight
if self.transient:
ctt += self.capac * outer( iData.h , iData.h ) * iData.weight
self.appendNodalOutput( self.mat.outLabels() , self.mat.outData() )
self.appendNodalOutput( self.labels , dot(self.D,gradTemp) )
if self.transient:
ktt0 = invdtime * ctt - elemdat.stiff[ix_(tDofs,tDofs)] * \
( 1.0-self.theta )
elemdat.stiff *= self.theta
elemdat.stiff[ix_(tDofs,tDofs)] += invdtime * ctt
elemdat.fint[tDofs] += \
dot ( elemdat.stiff[ix_(tDofs,tDofs)] , elemdat.state[tDofs] )
if self.transient:
elemdat.fint[tDofs] += -dot ( ktt0 , temp0 )
def getULTangentStiffness(self, elemdat):
state0 = elemdat.state - elemdat.Dstate
curCrds = elemdat.coords + reshape(state0, elemdat.coords.shape)
sData0 = getElemShapeData(elemdat.coords)
sDataC = getElemShapeData(curCrds)
for iOrig, iCurr in zip(sData0, sDataC):
r = dot(curCrds[:, 0], iOrig.h)
r0 = dot(elemdat.coords[:, 0], iOrig.h)
weight = 2.0 * pi * r * iCurr.weight
kin = self.getKinematics(iOrig.dhdx, iOrig.h, elemdat, r0)
B = self.getULBmatrix(iCurr.dhdx, iCurr.h, r)
sigma, tang = self.mat.getStress(kin)
t4 = self.tang6to4(tang)
s4 = self.stress6to4(sigma)
stiff = dot(B.transpose(), dot(t4, B))
for i, dpi in enumerate(iCurr.dhdx):
for j, dpj in enumerate(iCurr.dhdx):
stiff[
2 * i, 2 *
j] += s4[0] * dpi[0] * dpj[0] + s4[1] * dpi[1] * dpj[1]
stiff[2 * i,
2 * j] += s4[2] * iCurr.h[i] * iCurr.h[j] / (r * r)
stiff[2 * i,
2 * j] += s4[3] * (dpi[0] * dpj[1] + dpi[1] * dpj[0])
stiff[
2 * i + 1, 2 * j +
1] += s4[0] * dpi[0] * dpj[0] + s4[1] * dpi[1] * dpj[1]
stiff[2 * i + 1, 2 * j +
1] += s4[3] * (dpi[0] * dpj[1] + dpi[1] * dpj[0])
elemdat.stiff += stiff * weight
elemdat.fint += dot(B.transpose(), s4) * weight
self.appendNodalOutput(self.mat.outLabels(), self.mat.outData())
def getULInternalForce(self, elemdat):
state0 = elemdat.state - elemdat.Dstate
curCrds = elemdat.coords + reshape(state0, elemdat.coords.shape)
sData0 = getElemShapeData(elemdat.coords)
sDataC = getElemShapeData(curCrds)
for iOrig, iCurr in zip(sData0, sDataC):
self.kin = self.getKinematics(iOrig.dhdx, elemdat)
B = self.getULBmatrix(iCurr.dhdx)
sigma, tang = self.mat.getStress(self.kin)
elemdat.fint += dot(B.transpose(), sigma) * iCurr.weight
self.appendNodalOutput(self.mat.outLabels(), self.mat.outData())
def getInternalForce(self, elemdat):
sData = getElemShapeData(elemdat.coords, elemType="Line2")
for iData in sData:
temp = sum(iData.h * elemdat.state)
elemdat.fint += iData.h * ( self.convection * ( temp - self.extTemp ) + \
self.Boltzman * self.emissivity * ( temp**4 - self.extTemp4 ) ) * iData.weight
def getShapeData( self , elemdat ):
crd = elemdat.coords
nNod = crd.shape[0]
if self.rank == 2:
b = zeros(3)
b[2] = 1.0
if nNod == 2:
sData = getElemShapeData( elemdat.coords , elemType = "Line2" )
a = self.getDirection(crd,1,0)
elif nNod == 3:
sData = getElemShapeData( elemdat.coords , elemType = "Line3" )
a = self.getDirection(crd,2,0)
else:
raise RuntimeError("The rank is 2, the number of nodes must be 2 or 3.")
elif self.rank == 3:
if nNod == 3:
a = self.getDirection(crd,1,0)
b = self.getDirection(crd,2,0)
elif nNod == 4:
sData = getElemShapeData( elemdat.coords , elemType = "Quad4" )
a = self.getDirection(crd,1,0)
b = self.getDirection(crd,2,0)
elif nNod == 6:
sData = getElemShapeData( elemdat.coords , elemType = "Tria6" )
a = self.getDirection(crd,1,0)
b = self.getDirection(crd,2,0)
elif nNod == 8:
sData = getElemShapeData( elemdat.coords , elemType = "Quad8" )
a = self.getDirection(crd,1,0)
b = self.getDirection(crd,2,0)
else:
raise RuntimeError("The rank is 3, the number of nodes must be 3, 4, 6 or 8.")
else:
raise RuntimeError("The element must be rank 3.")
for iData in sData:
iData.normal = cross(a,b)
iData.normal *= 1.0/sqrt(dot(iData.normal,iData.normal))
return sData
def getMassMatrix(self, elemdat):
sData = getElemShapeData(elemdat.coords)
rho = elemdat.matprops.rho
for iData in sData:
N = self.getNmatrix(iData.h)
elemdat.mass += dot(N.transpose(), N) * rho * iData.weight
elemdat.lumped = sum(elemdat.mass)
def getMassMatrix ( self, elemdat ):
sData = getElemShapeData( elemdat.coords )
rho = elemdat.matprops.rho
for iData in sData:
N = self.getNmatrix( iData.h )
elemdat.mass += dot ( N.transpose() , N ) * rho * iData.weight
elemdat.lumped = sum(elemdat.mass)
def getTangentStiffness(self, elemdat):
sData = getElemShapeData(elemdat.coords, elemType="Line2")
for iData in sData:
temp = sum(iData.h * elemdat.state)
elemdat.stiff += outer ( iData.h , iData.h ) * \
( self.convection + 4.0 * self.Boltzman * self.emissivity * temp**3 ) * iData.weight
elemdat.fint += iData.h * ( self.convection * ( temp - self.extTemp ) + \
self.Boltzman * self.emissivity * ( temp**4 - self.extTemp4 ) ) * iData.weight
def getShapeData(self, elemdat):
nNod = elemdat.coords.shape[0]
if self.rank == 2:
if nNod == 2:
return getElemShapeData(elemdat.coords, elemType="Line2")
elif nNod == 3:
return getElemShapeData(elemdat.coords, elemType="Line3")
else:
raise RuntimeError(
"The rank is 2, the number of nodes must be 2 or 3.")
elif self.rank == 3:
if nNod == 3:
return getElemShapeData(elemdat.coords, elemType="Tria3")
elif nNod == 4:
return getElemShapeData(elemdat.coords, elemType="Quad4")
elif nNod == 6:
return getElemShapeData(elemdat.coords, elemType="Tria6")
elif nNod == 8:
return getElemShapeData(elemdat.coords, elemType="Quad8")
else:
raise RuntimeError(
"The rank is 3, the number of nodes must be 3, 4, 6 or 8.")
else:
raise RuntimeError("The element must be rank 3.")
return None
def getMassMatrix ( self, elemdat ):
sData = getElemShapeData( elemdat.coords )
rho = self.rho * eye(2)
for iData in sData:
N = self.getNmatrix( iData.h )
Nt = N.transpose()
elemdat.mass += dot ( Nt , dot( rho , N ) ) * iData.weight
elemdat.lumped = sum(elemdat.mass)
def getMassMatrix(self, elemdat):
sData = getElemShapeData(elemdat.coords)
rho = self.rho * eye(2)
for iData in sData:
N = self.getNmatrix(iData.h)
Nt = N.transpose()
elemdat.mass += dot(Nt, dot(rho, N)) * iData.weight
elemdat.lumped = sum(elemdat.mass)
def getTLInternalForce(self, elemdat):
sData = getElemShapeData(elemdat.coords)
for iData in sData:
self.kin = self.getKinematics(iData.dhdx, elemdat)
B = self.getBmatrix(iData.dhdx, self.kin.F)
sigma, tang = self.mat.getStress(self.kin)
elemdat.fint += dot(B.transpose(), sigma) * iData.weight
self.appendNodalOutput(self.mat.outLabels(), self.mat.outData())
def getULTangentStiffness(self, elemdat):
state0 = elemdat.state - elemdat.Dstate
curCrds = elemdat.coords + reshape(state0, elemdat.coords.shape)
sData0 = getElemShapeData(elemdat.coords)
sDataC = getElemShapeData(curCrds)
for iOrig, iCurr in zip(sData0, sDataC):
self.kin = self.getKinematics(iOrig.dhdx, elemdat)
B = self.getULBmatrix(iCurr.dhdx)
sigma, tang = self.mat.getStress(self.kin)
elemdat.stiff += dot(B.transpose(), dot(tang, B)) * iCurr.weight
T = self.stress2matrix(sigma)
Bnl = self.getBNLmatrix(iCurr.dhdx)
elemdat.stiff += dot(Bnl.transpose(), dot(T, Bnl)) * iCurr.weight
elemdat.fint += dot(B.transpose(), sigma) * iCurr.weight
self.appendNodalOutput(self.mat.outLabels(), self.mat.outData())
def getDissipation(self, elemdat):
sData = getElemShapeData(elemdat.coords)
for iData in sData:
self.kin = self.getKinematics(iData.dhdx, elemdat)
B = self.getBmatrix(iData.dhdx, self.kin.F)
self.mat.getStress(self.kin)
self.kin.dgdstrain = zeros(3)
self.kin.g = 0.0
elemdat.fint += dot(B.transpose(),
self.kin.dgdstrain) * iData.weight
elemdat.diss += self.kin.g * iData.weight
def getTangentStiffness(self, element_data):
sData = getElemShapeData(element_data.coords)
kinematic = Kinematics(2, 3)
element_data.outlabel.append("stresses")
element_data.outdata = zeros(shape=(len(element_data.nodes), 3))
for iData in sData:
B_matrix = self.getBmatrix(iData.dhdx)
kinematic.strain = dot(B_matrix, element_data.state)
kinematic.dstrain = dot(B_matrix, element_data.Dstate)
sigma, tangent_moduli = self.mat.getStress(kinematic)
element_data.stiff += dot(B_matrix.transpose(),
dot(tangent_moduli,
B_matrix)) * iData.weight
element_data.fint += dot(B_matrix.transpose(),
sigma) * iData.weight
element_data.outdata += outer(ones(len(element_data.nodes)), sigma)
element_data.outdata *= 1.0 / len(sData)
def initIntShapeFuncs(self):
isoCoords = zeros(shape=(4, 2))
isoCoords[0, 0] = -1.0
isoCoords[0, 1] = -1.0
isoCoords[1, 0] = 1.0
isoCoords[1, 1] = -1.0
isoCoords[2, 0] = 1.0
isoCoords[2, 1] = 1.0
isoCoords[3, 0] = -1.0
isoCoords[3, 1] = 1.0
intshape = getElemShapeData(isoCoords)
for sdat, idat in zip(self.shape, intshape):
sdat.psi = idat.h
def getInternalForce ( self, elemdat ):
sData = getElemShapeData( elemdat.coords )
uDofs,pDofs = self.splitDofIDs( len(elemdat.coords) )
for iInt,iData in enumerate(sData):
B = self.getBmatrix( iData.dhdx )
self.kin.strain = dot ( B , elemdat.state [uDofs] )
self.kin.dstrain = dot ( B , elemdat.Dstate[uDofs] )
phase = dot( iData.h , elemdat.state[pDofs] )
gradPhase = dot( iData.dhdx.transpose() , elemdat.state[pDofs] )
sigma,tang = self.mat.getStress( self.kin )
energy = 0.5*sum(self.kin.strain*sigma)
if energy > self.hisOld[iInt]:
self.hisNew[iInt] = energy
else:
self.hisNew[iInt] = self.hisOld[iInt]
factor = 1.0-phase*phase+self.k
# -- Displacement contributions
dispForce = dot ( B.transpose() , factor*sigma )
elemdat.fint[uDofs] += dispForce * iData.weight
# -- Phase field contributions
pfint = self.Gc*self.l0*dot( iData.dhdx , gradPhase );
pfint += self.Gc/self.l0*iData.h*phase;
pfint += 2.0*( phase-1.0 ) * iData.h * self.hisNew[iInt]
elemdat.fint[pDofs] += pfint * iData.weight
# -- Coupling terms
# Coupling terms need TOBEIMPLEMENTED
self.appendNodalOutput( self.mat.outLabels() , self.mat.outData() )
def initExtShapeFuncs(self):
isoCoords = zeros(shape=(4, 2))
isoCoords[0, 0] = -1.0
isoCoords[0, 1] = -1.0
isoCoords[1, 0] = 1.0
isoCoords[1, 1] = -1.0
isoCoords[2, 0] = 1.0
isoCoords[2, 1] = 1.0
isoCoords[3, 0] = -1.0
isoCoords[3, 1] = 1.0
self.shape = getElemShapeData(isoCoords)
for sdat in self.shape:
sdat.h *= 0.5
sdat.dhdx *= 0.5
def getDissipation(self, elemdat):
rot = self.getRotation(elemdat.coords, elemdat.state)
sData = getElemShapeData(elemdat.coords[:2, :],
method=self.intMethod,
elemType="Line2")
kin = Kinematics(2, 2)
for iData in sData:
B = self.getBmatrix(iData.h, rot)
kin.strain = dot(B, elemdat.state)
sigma, tang = self.mat.getStress(kin)
elemdat.fint += dot(B.transpose(), kin.dgdstrain) * iData.weight
elemdat.diss += kin.g * iData.weight
def getInternalForce(self, elemdat):
sData = getElemShapeData(elemdat.coords)
elemdat.outlabel.append(self.outputLabels)
elemdat.outdata = zeros(shape=(len(elemdat.nodes), self.nstr))
for iData in sData:
b = self.getBmatrix(iData.dhdx)
self.kin.strain = dot(b, elemdat.state)
self.kin.dstrain = dot(b, elemdat.Dstate)
sigma, tang = self.mat.getStress(self.kin)
elemdat.fint += dot(b.transpose(), sigma) * iData.weight
self.appendNodalOutput(self.mat.outLabels(), self.mat.outData())
def getDissipation(self, elemdat):
sData = getElemShapeData(elemdat.coords)
for iData in sData:
b = self.getBmatrix(iData.dhdx)
self.kin.strain = dot(b, elemdat.state)
self.kin.dstrain = dot(b, elemdat.Dstate)
self.mat.getStress(self.kin)
self.kin.dgdstrain = zeros(3)
self.kin.g = 0.0
elemdat.fint += dot(b.transpose(),
self.kin.dgdstrain) * iData.weight
elemdat.diss += self.kin.g * iData.weight
def getInternalForce ( self, elemdat ):
rot = self.getRotation( elemdat.coords , elemdat.state )
sData = getElemShapeData( elemdat.coords[:2,:] , method = self.intMethod , elemType = "Line2" )
elemdat.outlabel.append("tractions")
elemdat.outdata = zeros( shape=(len(elemdat.nodes),2) )
kin = Kinematics(2,2)
for iData in sData:
B = self.getBmatrix( iData.h , rot )
kin.strain = dot( B , elemdat.state )
sigma,tang = self.mat.getStress( kin )
elemdat.fint += dot ( B.transpose() , sigma ) * iData.weight
elemdat.outdata += outer( ones(len(elemdat.nodes)), sigma )
def getInternalForce ( self, elemdat ):
n = self.dofCount()
sData = getElemShapeData( elemdat.coords )
elemdat.outlabel.append("stresses")
elemdat.outdata = zeros( shape=(len(elemdat.nodes),3) )
for iData in sData:
kin = self.getKinematics( iData.dhdx , elemdat.state )
B = self.getBmatrix ( iData.dhdx , kin.F )
sigma,tang = self.mat.getStress( kin )
elemdat.fint += dot ( B.transpose() , sigma ) * iData.weight
elemdat.outdata += outer( ones(len(elemdat.nodes)), sigma )
elemdat.outdata *= 1.0 / len(sData)
def getInternalForce ( self, elemdat ):
sData = getElemShapeData( elemdat.coords )
elemdat.outlabel.append("stresses")
elemdat.outdata = zeros( shape=(len(elemdat.nodes),3) )
kin = Kinematics(2,3)
for iData in sData:
b = self.getBmatrix( iData.dhdx )
kin.strain = dot ( b , elemdat.state )
kin.dstrain = dot ( b , elemdat.Dstate )
sigma,tang = self.mat.getStress( kin )
elemdat.fint += dot ( b.transpose() , sigma ) * iData.weight
elemdat.outdata += outer( ones(len(self)), sigma )
elemdat.outdata *= 1.0 / len(sData)
presVals[2 * presNodes] = [upres(crd) for crd in coords[presNodes, :]]
presVals[2 * presNodes + 1] = [vpres(crd) for crd in coords[presNodes, :]]
# ----------------------------------------------------------------------
# Calculate K
# ----------------------------------------------------------------------
totDof = 2 * len(coords)
K = zeros(shape=(totDof, totDof))
for elem in elems:
elemDofs = getDofs(elem)
sData = getElemShapeData(coords[elem, :])
for iData in sData:
b = getBmatrix(iData.dhdx)
K[ix_(elemDofs, elemDofs)] += dot(b.transpose(), dot(D, b)) * iData.weight
# ----------------------------------------------------------------------
# Solve Ka=f
# ----------------------------------------------------------------------
consDof = len(presInds)
C = zeros(shape=(totDof, totDof - consDof))
j = 0
