def __init__ ( self, elnodes , props ):
Element.__init__( self, elnodes , props )
self.material = Laminate( props )
self.A = self.material.getA()
self.B = self.material.getB()
self.D = self.material.getD()
Ashear = self.material.getAshear()
self.A44 = Ashear[0,0]
self.A45 = Ashear[0,1]
self.A55 = Ashear[1,1]
self.inertia = self.material.getMassInertia()
print(self.inertia)
self.outputLabels = ["epsx","epsy","gamxy","s23","s13","s12"]
def __init__(self, elnodes, props):
Element.__init__(self, elnodes, props)
self.material = Laminate(props)
self.A = self.material.getA()
self.B = self.material.getB()
self.D = self.material.getD()
Ashear = self.material.getAshear()
self.A44 = Ashear[0, 0]
self.A45 = Ashear[0, 1]
self.A55 = Ashear[1, 1]
self.inertia = self.material.getMassInertia()
self.initPostProcessing()
self.outputLabels = self.postProcess[0].labels + self.postProcess[
1].labels
class Plate(Element):
dofTypes = ['u', 'v', 'w', 'rx', 'ry']
#-------------------------------------------------------------------------------
#
#-------------------------------------------------------------------------------
def __init__(self, elnodes, props):
Element.__init__(self, elnodes, props)
self.material = Laminate(props)
self.A = self.material.getA()
self.B = self.material.getB()
self.D = self.material.getD()
self.Ashear = self.material.getAshear()
self.A44 = self.Ashear[0, 0]
self.A45 = self.Ashear[0, 1]
self.A55 = self.Ashear[1, 1]
self.inertia = self.material.getMassInertia()
self.initPostProcessing()
self.outputLabels = self.postProcess[0].labels + self.postProcess[
1].labels
self.family = "SHELL"
#-------------------------------------------------------------------------------
#
#-------------------------------------------------------------------------------
def __type__(self):
return name
#-------------------------------------------------------------------------------
#
#-------------------------------------------------------------------------------
def getTangentStiffness(self, elemdat):
sData = getElemShapeData(elemdat.coords)
nNel = elemdat.coords.shape[0]
nDof = 5 * nNel
eps0 = zeros(3)
kappa = zeros(3)
gamma = zeros(2)
for d in sData:
stiff = zeros(shape=(nDof, nDof))
fint = zeros(nDof)
N11 = self.A[0, 0] * d.dhdx[:, 0] + self.A[0, 2] * d.dhdx[:, 1]
N21 = self.A[0, 1] * d.dhdx[:, 1] + self.A[0, 2] * d.dhdx[:, 0]
N41 = self.B[0, 0] * d.dhdx[:, 0] + self.B[0, 2] * d.dhdx[:, 1]
N51 = self.B[0, 1] * d.dhdx[:, 1] + self.B[0, 2] * d.dhdx[:, 0]
N12 = self.A[0, 1] * d.dhdx[:, 0] + self.A[1, 2] * d.dhdx[:, 1]
N22 = self.A[1, 1] * d.dhdx[:, 1] + self.A[1, 2] * d.dhdx[:, 0]
N42 = self.B[0, 1] * d.dhdx[:, 0] + self.B[1, 2] * d.dhdx[:, 1]
N52 = self.B[1, 1] * d.dhdx[:, 1] + self.B[1, 2] * d.dhdx[:, 0]
N16 = self.A[0, 2] * d.dhdx[:, 0] + self.A[2, 2] * d.dhdx[:, 1]
N26 = self.A[1, 2] * d.dhdx[:, 1] + self.A[2, 2] * d.dhdx[:, 0]
N46 = self.B[0, 2] * d.dhdx[:, 0] + self.B[2, 2] * d.dhdx[:, 1]
N56 = self.B[1, 2] * d.dhdx[:, 1] + self.B[2, 2] * d.dhdx[:, 0]
M11 = self.B[0, 0] * d.dhdx[:, 0] + self.B[0, 2] * d.dhdx[:, 1]
M21 = self.B[0, 1] * d.dhdx[:, 1] + self.B[0, 2] * d.dhdx[:, 0]
M41 = self.D[0, 0] * d.dhdx[:, 0] + self.D[0, 2] * d.dhdx[:, 1]
M51 = self.D[0, 1] * d.dhdx[:, 1] + self.D[0, 2] * d.dhdx[:, 0]
M12 = self.B[0, 1] * d.dhdx[:, 0] + self.B[1, 2] * d.dhdx[:, 1]
M22 = self.B[1, 1] * d.dhdx[:, 1] + self.B[1, 2] * d.dhdx[:, 0]
M42 = self.D[0, 1] * d.dhdx[:, 0] + self.D[1, 2] * d.dhdx[:, 1]
M52 = self.D[1, 1] * d.dhdx[:, 1] + self.D[1, 2] * d.dhdx[:, 0]
M16 = self.B[0, 2] * d.dhdx[:, 0] + self.B[2, 2] * d.dhdx[:, 1]
M26 = self.B[1, 2] * d.dhdx[:, 1] + self.B[2, 2] * d.dhdx[:, 0]
M46 = self.D[0, 2] * d.dhdx[:, 0] + self.D[2, 2] * d.dhdx[:, 1]
M56 = self.D[1, 2] * d.dhdx[:, 1] + self.D[2, 2] * d.dhdx[:, 0]
eps0[0] = dot(d.dhdx[:, 0], elemdat.state[0:nDof:5])
eps0[1] = dot(d.dhdx[:, 1], elemdat.state[1:nDof:5])
eps0[2] = dot(d.dhdx[:,1],elemdat.state[0:nDof:5])+\
dot(d.dhdx[:,0],elemdat.state[1:nDof:5])
kappa[0] = dot(d.dhdx[:, 0], elemdat.state[3:nDof:5])
kappa[1] = dot(d.dhdx[:, 1], elemdat.state[4:nDof:5])
kappa[2]= dot(d.dhdx[:,1],elemdat.state[3:nDof:5])+\
dot(d.dhdx[:,0],elemdat.state[4:nDof:5])
N = dot(self.A, eps0) + dot(self.B, kappa)
M = dot(self.B, eps0) + dot(self.D, kappa)
for ppdat in self.postProcess:
eps = eps0 + ppdat.z * kappa
sigma = stressTransformation(dot(ppdat.Qbar, eps), ppdat.theta)
self.appendNodalOutput(ppdat.labels, sigma)
for i in range(nNel):
fint[5 * i + 0] += d.dhdx[i, 0] * N[0] + d.dhdx[i, 1] * N[2]
fint[5 * i + 1] += d.dhdx[i, 1] * N[1] + d.dhdx[i, 0] * N[2]
fint[5 * i + 3] += d.dhdx[i, 0] * M[0] + d.dhdx[i, 1] * M[2]
fint[5 * i + 4] += d.dhdx[i, 0] * M[2] + d.dhdx[i, 1] * M[1]
for j in range(nNel):
#K1
stiff[5 * i + 0, 5 * j +
0] += d.dhdx[i, 0] * N11[j] + d.dhdx[i, 1] * N16[j]
stiff[5 * i + 1, 5 * j +
0] += d.dhdx[i, 0] * N16[j] + d.dhdx[i, 1] * N12[j]
stiff[5 * i + 3, 5 * j +
0] += d.dhdx[i, 0] * M11[j] + d.dhdx[i, 1] * M16[j]
stiff[5 * i + 4, 5 * j +
0] += d.dhdx[i, 0] * M16[j] + d.dhdx[i, 1] * M12[j]
#K2
stiff[5 * i + 0, 5 * j +
1] += d.dhdx[i, 0] * N21[j] + d.dhdx[i, 1] * N26[j]
stiff[5 * i + 1, 5 * j +
1] += d.dhdx[i, 0] * N26[j] + d.dhdx[i, 1] * N22[j]
stiff[5 * i + 3, 5 * j +
1] += d.dhdx[i, 0] * M21[j] + d.dhdx[i, 1] * M26[j]
stiff[5 * i + 4, 5 * j +
1] += d.dhdx[i, 0] * M26[j] + d.dhdx[i, 1] * M22[j]
#K4
stiff[5 * i + 0, 5 * j +
3] += d.dhdx[i, 0] * N41[j] + d.dhdx[i, 1] * N46[j]
stiff[5 * i + 1, 5 * j +
3] += d.dhdx[i, 0] * N46[j] + d.dhdx[i, 1] * N42[j]
stiff[5 * i + 3, 5 * j +
3] += d.dhdx[i, 0] * M41[j] + d.dhdx[i, 1] * M46[j]
stiff[5 * i + 4, 5 * j +
3] += d.dhdx[i, 0] * M46[j] + d.dhdx[i, 1] * M42[j]
#K5
stiff[5 * i + 0, 5 * j +
4] += d.dhdx[i, 0] * N51[j] + d.dhdx[i, 1] * N56[j]
stiff[5 * i + 1, 5 * j +
4] += d.dhdx[i, 0] * N56[j] + d.dhdx[i, 1] * N52[j]
stiff[5 * i + 3, 5 * j +
4] += d.dhdx[i, 0] * M51[j] + d.dhdx[i, 1] * M56[j]
stiff[5 * i + 4, 5 * j +
4] += d.dhdx[i, 0] * M56[j] + d.dhdx[i, 1] * M52[j]
elemdat.fint += fint * d.weight
elemdat.stiff += stiff * d.weight
sData = getElemShapeData(elemdat.coords, -1)
for d in sData:
stiff = zeros(shape=(nDof, nDof))
fint = zeros(nDof)
Q41 = self.A55 * d.h
Q42 = self.A45 * d.h
Q51 = self.A45 * d.h
Q52 = self.A44 * d.h
Q31 = self.A55 * d.dhdx[:, 0] + self.A45 * d.dhdx[:, 1]
Q32 = self.A45 * d.dhdx[:, 0] + self.A44 * d.dhdx[:, 1]
gamma[0] = dot(d.dhdx[:,0],elemdat.state[2:nDof:5])+\
dot(d.h,elemdat.state[3:nDof:5])
gamma[1] = dot(d.dhdx[:,1],elemdat.state[2:nDof:5])+\
dot(d.h,elemdat.state[4:nDof:5])
Q = dot(self.Ashear, gamma)
for i in range(nNel):
fint[5 * i + 2] += d.dhdx[i, 0] * Q[0] + d.dhdx[i, 1] * Q[1]
fint[5 * i + 3] += d.h[i] * Q[0]
fint[5 * i + 4] += d.h[i] * Q[1]
for j in range(nNel):
#K3
stiff[5 * i + 2, 5 * j +
2] += d.dhdx[i, 0] * Q31[j] + d.dhdx[i, 1] * Q32[j]
stiff[5 * i + 3, 5 * j + 2] += d.h[i] * Q31[j]
stiff[5 * i + 4, 5 * j + 2] += d.h[i] * Q32[j]
#K4
stiff[5 * i + 2, 5 * j +
3] += d.dhdx[i, 0] * Q41[j] + d.dhdx[i, 1] * Q42[j]
stiff[5 * i + 3, 5 * j + 3] += d.h[i] * Q41[j]
stiff[5 * i + 4, 5 * j + 3] += d.h[i] * Q42[j]
#K5
stiff[5 * i + 2, 5 * j +
4] += d.dhdx[i, 0] * Q51[j] + d.dhdx[i, 1] * Q52[j]
stiff[5 * i + 3, 5 * j + 4] += d.h[i] * Q51[j]
stiff[5 * i + 4, 5 * j + 4] += d.h[i] * Q52[j]
elemdat.fint += fint * d.weight
elemdat.stiff += stiff * d.weight
#-------------------------------------------------------------------------------
#
#-------------------------------------------------------------------------------
def getInternalForce(self, elemdat):
sData = getElemShapeData(elemdat.coords)
nNel = elemdat.coords.shape[0]
nDof = 5 * nNel
eps0 = zeros(3)
kappa = zeros(3)
gamma = zeros(2)
for d in sData:
fint = zeros(nDof)
eps0[0] = dot(d.dhdx[:, 0], elemdat.state[0:nDof:5])
eps0[1] = dot(d.dhdx[:, 1], elemdat.state[1:nDof:5])
eps0[2] = dot(d.dhdx[:,1],elemdat.state[0:nDof:5])+\
dot(d.dhdx[:,0],elemdat.state[1:nDof:5])
kappa[0] = dot(d.dhdx[:, 0], elemdat.state[3:nDof:5])
kappa[1] = dot(d.dhdx[:, 1], elemdat.state[4:nDof:5])
kappa[2]= dot(d.dhdx[:,1],elemdat.state[3:nDof:5])+\
dot(d.dhdx[:,0],elemdat.state[4:nDof:5])
N = dot(self.A, eps0) + dot(self.B, kappa)
M = dot(self.B, eps0) + dot(self.D, kappa)
for ppdat in self.postProcess:
eps = eps0 + ppdat.z * kappa
sigma = stressTransformation(dot(ppdat.Qbar, eps), ppdat.theta)
self.appendNodalOutput(ppdat.labels, sigma)
for i in range(nNel):
fint[5 * i + 0] += d.dhdx[i, 0] * N[0] + d.dhdx[i, 1] * N[2]
fint[5 * i + 1] += d.dhdx[i, 1] * N[1] + d.dhdx[i, 0] * N[2]
fint[5 * i + 3] += d.dhdx[i, 0] * M[0] + d.dhdx[i, 1] * M[2]
fint[5 * i + 4] += d.dhdx[i, 0] * M[2] + d.dhdx[i, 1] * M[1]
elemdat.fint += fint * d.weight
sData = getElemShapeData(elemdat.coords, -1)
for d in sData:
fint = zeros(nDof)
gamma[0] = dot(d.dhdx[:,0],elemdat.state[2:nDof:5])+\
dot(d.h,elemdat.state[3:nDof:5])
gamma[1] = dot(d.dhdx[:,1],elemdat.state[2:nDof:5])+\
dot(d.h,elemdat.state[4:nDof:5])
Q = dot(self.Ashear, gamma)
for i in range(nNel):
fint[5 * i + 2] += d.dhdx[i, 0] * Q[0] + d.dhdx[i, 1] * Q[1]
fint[5 * i + 3] += d.h[i] * Q[0]
fint[5 * i + 4] += d.h[i] * Q[1]
elemdat.fint += fint * d.weight
#-------------------------------------------------------------------------------
#
#-------------------------------------------------------------------------------
def getMassMatrix(self, elemdat):
sData = getElemShapeData(elemdat.coords)
mass = zeros(shape=(20, 20))
for d in sData:
for i in range(4):
for j in range(4):
shp = d.h[i] * d.h[j]
mass[5 * i + 0, 5 * j + 0] += self.inertia[0] * shp
mass[5 * i + 0, 5 * j + 3] += self.inertia[1] * shp
mass[5 * i + 1, 5 * j + 1] += self.inertia[0] * shp
mass[5 * i + 1, 5 * j + 4] += self.inertia[1] * shp
mass[5 * i + 2, 5 * j + 2] += self.inertia[0] * shp
mass[5 * i + 3, 5 * j + 0] += self.inertia[1] * shp
mass[5 * i + 3, 5 * j + 3] += self.inertia[0] * shp
mass[5 * i + 3, 5 * j + 4] += self.inertia[1] * shp
mass[5 * i + 4, 5 * j + 1] += self.inertia[1] * shp
mass[5 * i + 4, 5 * j + 3] += self.inertia[1] * shp
mass[5 * i + 4, 5 * j + 4] += self.inertia[0] * shp
elemdat.mass += mass * d.weight
#------------------------------------------------------------------------------
#
#------------------------------------------------------------------------------
def initPostProcessing(self):
layerCount = self.material.layerCount()
self.postProcess = []
pp = postProcessPoint()
pp.z = -0.5 * self.material.thick
pp.Qbar = self.material.getQbar(0)
pp.theta = self.material.layers[0].theta
pp.labels = ["s11bot", "s22bot", "s12bot"]
self.postProcess.append(pp)
pp = postProcessPoint()
pp.z = 0.5 * self.material.thick
pp.Qbar = self.material.getQbar(layerCount - 1)
pp.theta = self.material.layers[layerCount - 1].theta
pp.labels = ["s11top", "s22top", "s12top"]
self.postProcess.append(pp)
class Plate ( Element ):
#dofs per element
dofTypes = [ 'u' , 'v' , 'w' , 'rx' , 'ry' ]
#------------------------------------------------------------------------------
#
#------------------------------------------------------------------------------
def __init__ ( self, elnodes , props ):
Element.__init__( self, elnodes , props )
self.material = Laminate( props )
self.A = self.material.getA()
self.B = self.material.getB()
self.D = self.material.getD()
Ashear = self.material.getAshear()
self.A44 = Ashear[0,0]
self.A45 = Ashear[0,1]
self.A55 = Ashear[1,1]
self.inertia = self.material.getMassInertia()
print(self.inertia)
self.outputLabels = ["epsx","epsy","gamxy","s23","s13","s12"]
#------------------------------------------------------------------------------
#
#------------------------------------------------------------------------------
def __type__ ( self ):
return name
#------------------------------------------------------------------------------
#
#------------------------------------------------------------------------------
def getTangentStiffness ( self, elemdat ):
sData = getElemShapeData( elemdat.coords )
for d in sData:
stiff = zeros(shape=(20,20))
N11 = self.A[0,0]*d.dhdx[:,0] + self.A[0,2]*d.dhdx[:,1]
N21 = self.A[0,1]*d.dhdx[:,1] + self.A[0,2]*d.dhdx[:,0]
N41 = self.B[0,0]*d.dhdx[:,0] + self.B[0,2]*d.dhdx[:,1]
N51 = self.B[0,1]*d.dhdx[:,1] + self.B[0,2]*d.dhdx[:,0]
N12 = self.A[0,1]*d.dhdx[:,0] + self.A[1,2]*d.dhdx[:,1]
N22 = self.A[1,1]*d.dhdx[:,1] + self.A[1,2]*d.dhdx[:,0]
N42 = self.B[0,1]*d.dhdx[:,0] + self.B[1,2]*d.dhdx[:,1]
N52 = self.B[1,1]*d.dhdx[:,1] + self.B[1,2]*d.dhdx[:,0]
N16 = self.A[0,2]*d.dhdx[:,0] + self.A[2,2]*d.dhdx[:,1]
N26 = self.A[1,2]*d.dhdx[:,1] + self.A[2,2]*d.dhdx[:,0]
N46 = self.B[0,2]*d.dhdx[:,0] + self.B[2,2]*d.dhdx[:,1]
N56 = self.B[1,2]*d.dhdx[:,1] + self.B[2,2]*d.dhdx[:,0]
M11 = self.B[0,0]*d.dhdx[:,0] + self.B[0,2]*d.dhdx[:,1]
M21 = self.B[0,1]*d.dhdx[:,1] + self.B[0,2]*d.dhdx[:,0]
M41 = self.D[0,0]*d.dhdx[:,0] + self.D[0,2]*d.dhdx[:,1]
M51 = self.D[0,1]*d.dhdx[:,1] + self.D[0,2]*d.dhdx[:,0]
M12 = self.B[0,1]*d.dhdx[:,0] + self.B[1,2]*d.dhdx[:,1]
M22 = self.B[1,1]*d.dhdx[:,1] + self.B[1,2]*d.dhdx[:,0]
M42 = self.D[0,1]*d.dhdx[:,0] + self.D[1,2]*d.dhdx[:,1]
M52 = self.D[1,1]*d.dhdx[:,1] + self.D[1,2]*d.dhdx[:,0]
M16 = self.B[0,2]*d.dhdx[:,0] + self.B[2,2]*d.dhdx[:,1]
M26 = self.B[1,2]*d.dhdx[:,1] + self.B[2,2]*d.dhdx[:,0]
M46 = self.D[0,2]*d.dhdx[:,0] + self.D[2,2]*d.dhdx[:,1]
M56 = self.D[1,2]*d.dhdx[:,1] + self.D[2,2]*d.dhdx[:,0]
for i in range(4):
for j in range(4):
#K1
stiff[5*i+0,5*j+0] += d.dhdx[i,0]*N11[j]+d.dhdx[i,1]*N16[j]
stiff[5*i+1,5*j+0] += d.dhdx[i,0]*N16[j]+d.dhdx[i,1]*N12[j]
stiff[5*i+3,5*j+0] += d.dhdx[i,0]*M11[j]+d.dhdx[i,1]*M16[j]
stiff[5*i+4,5*j+0] += d.dhdx[i,0]*M16[j]+d.dhdx[i,1]*M12[j]
#K2
stiff[5*i+0,5*j+1] += d.dhdx[i,0]*N21[j]+d.dhdx[i,1]*N26[j]
stiff[5*i+1,5*j+1] += d.dhdx[i,0]*N26[j]+d.dhdx[i,1]*N22[j]
stiff[5*i+3,5*j+1] += d.dhdx[i,0]*M21[j]+d.dhdx[i,1]*M26[j]
stiff[5*i+4,5*j+1] += d.dhdx[i,0]*M26[j]+d.dhdx[i,1]*M22[j]
#K4
stiff[5*i+0,5*j+3] += d.dhdx[i,0]*N41[j]+d.dhdx[i,1]*N46[j]
stiff[5*i+1,5*j+3] += d.dhdx[i,0]*N46[j]+d.dhdx[i,1]*N42[j]
stiff[5*i+3,5*j+3] += d.dhdx[i,0]*M41[j]+d.dhdx[i,1]*M46[j]
stiff[5*i+4,5*j+3] += d.dhdx[i,0]*M46[j]+d.dhdx[i,1]*M42[j]
#K5
stiff[5*i+0,5*j+4] += d.dhdx[i,0]*N51[j]+d.dhdx[i,1]*N56[j]
stiff[5*i+1,5*j+4] += d.dhdx[i,0]*N56[j]+d.dhdx[i,1]*N52[j]
stiff[5*i+3,5*j+4] += d.dhdx[i,0]*M51[j]+d.dhdx[i,1]*M56[j]
stiff[5*i+4,5*j+4] += d.dhdx[i,0]*M56[j]+d.dhdx[i,1]*M52[j]
elemdat.stiff += stiff * d.weight
sData = getElemShapeData( elemdat.coords , -1 )
for d in sData:
stiff = zeros(shape=(20,20))
Q41 = self.A55*d.h
Q42 = self.A45*d.h
Q51 = self.A45*d.h
Q52 = self.A44*d.h
Q31 = self.A55*d.dhdx[:,0]+self.A45*d.dhdx[:,1]
Q32 = self.A45*d.dhdx[:,0]+self.A44*d.dhdx[:,1]
for i in range(4):
for j in range(4):
#K3
stiff[5*i+2,5*j+2] += d.dhdx[i,0]*Q31[j]+d.dhdx[i,1]*Q32[j]
stiff[5*i+3,5*j+2] += d.h[i]*Q31[j]
stiff[5*i+4,5*j+2] += d.h[i]*Q32[j]
#K4
stiff[5*i+2,5*j+3] += d.dhdx[i,0]*Q41[j]+d.dhdx[i,1]*Q42[j]
stiff[5*i+3,5*j+3] += d.h[i]*Q41[j]
stiff[5*i+4,5*j+3] += d.h[i]*Q42[j]
#K5
stiff[5*i+2,5*j+4] += d.dhdx[i,0]*Q51[j]+d.dhdx[i,1]*Q52[j]
stiff[5*i+3,5*j+4] += d.h[i]*Q51[j]
stiff[5*i+4,5*j+4] += d.h[i]*Q52[j]
elemdat.stiff += stiff * d.weight
#------------------------------------------------------------------------------
#
#------------------------------------------------------------------------------
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 getMassMatrix ( self, elemdat ):
sData = getElemShapeData( elemdat.coords )
mass = zeros( shape=(20,20) )
for d in sData:
for i in range(4):
for j in range(4):
shp = d.h[i]*d.h[j]
mass[5*i+0,5*j+0] += self.inertia[0]*shp
mass[5*i+0,5*j+3] += self.inertia[1]*shp
mass[5*i+1,5*j+1] += self.inertia[0]*shp
mass[5*i+1,5*j+4] += self.inertia[1]*shp
mass[5*i+2,5*j+2] += self.inertia[0]*shp
mass[5*i+3,5*j+0] += self.inertia[1]*shp
mass[5*i+3,5*j+3] += self.inertia[0]*shp
mass[5*i+3,5*j+4] += self.inertia[1]*shp
mass[5*i+4,5*j+1] += self.inertia[1]*shp
mass[5*i+4,5*j+3] += self.inertia[1]*shp
mass[5*i+4,5*j+4] += self.inertia[0]*shp
elemdat.mass += mass * d.weight
class Plate(Element):
#dofs per element
dofTypes = ['u', 'v', 'w', 'rx', 'ry']
#------------------------------------------------------------------------------
#
#------------------------------------------------------------------------------
def __init__(self, elnodes, props):
Element.__init__(self, elnodes, props)
self.material = Laminate(props)
self.A = self.material.getA()
self.B = self.material.getB()
self.D = self.material.getD()
Ashear = self.material.getAshear()
self.A44 = Ashear[0, 0]
self.A45 = Ashear[0, 1]
self.A55 = Ashear[1, 1]
self.inertia = self.material.getMassInertia()
self.initPostProcessing()
self.outputLabels = self.postProcess[0].labels + self.postProcess[
1].labels
#------------------------------------------------------------------------------
#
#------------------------------------------------------------------------------
def __type__(self):
return name
#------------------------------------------------------------------------------
#
#------------------------------------------------------------------------------
def getTangentStiffness(self, elemdat):
sData = getElemShapeData(elemdat.coords)
for d in sData:
stiff = zeros(shape=(20, 20))
N11 = self.A[0, 0] * d.dhdx[:, 0] + self.A[0, 2] * d.dhdx[:, 1]
N21 = self.A[0, 1] * d.dhdx[:, 1] + self.A[0, 2] * d.dhdx[:, 0]
N41 = self.B[0, 0] * d.dhdx[:, 0] + self.B[0, 2] * d.dhdx[:, 1]
N51 = self.B[0, 1] * d.dhdx[:, 1] + self.B[0, 2] * d.dhdx[:, 0]
N12 = self.A[0, 1] * d.dhdx[:, 0] + self.A[1, 2] * d.dhdx[:, 1]
N22 = self.A[1, 1] * d.dhdx[:, 1] + self.A[1, 2] * d.dhdx[:, 0]
N42 = self.B[0, 1] * d.dhdx[:, 0] + self.B[1, 2] * d.dhdx[:, 1]
N52 = self.B[1, 1] * d.dhdx[:, 1] + self.B[1, 2] * d.dhdx[:, 0]
N16 = self.A[0, 2] * d.dhdx[:, 0] + self.A[2, 2] * d.dhdx[:, 1]
N26 = self.A[1, 2] * d.dhdx[:, 1] + self.A[2, 2] * d.dhdx[:, 0]
N46 = self.B[0, 2] * d.dhdx[:, 0] + self.B[2, 2] * d.dhdx[:, 1]
N56 = self.B[1, 2] * d.dhdx[:, 1] + self.B[2, 2] * d.dhdx[:, 0]
M11 = self.B[0, 0] * d.dhdx[:, 0] + self.B[0, 2] * d.dhdx[:, 1]
M21 = self.B[0, 1] * d.dhdx[:, 1] + self.B[0, 2] * d.dhdx[:, 0]
M41 = self.D[0, 0] * d.dhdx[:, 0] + self.D[0, 2] * d.dhdx[:, 1]
M51 = self.D[0, 1] * d.dhdx[:, 1] + self.D[0, 2] * d.dhdx[:, 0]
M12 = self.B[0, 1] * d.dhdx[:, 0] + self.B[1, 2] * d.dhdx[:, 1]
M22 = self.B[1, 1] * d.dhdx[:, 1] + self.B[1, 2] * d.dhdx[:, 0]
M42 = self.D[0, 1] * d.dhdx[:, 0] + self.D[1, 2] * d.dhdx[:, 1]
M52 = self.D[1, 1] * d.dhdx[:, 1] + self.D[1, 2] * d.dhdx[:, 0]
M16 = self.B[0, 2] * d.dhdx[:, 0] + self.B[2, 2] * d.dhdx[:, 1]
M26 = self.B[1, 2] * d.dhdx[:, 1] + self.B[2, 2] * d.dhdx[:, 0]
M46 = self.D[0, 2] * d.dhdx[:, 0] + self.D[2, 2] * d.dhdx[:, 1]
M56 = self.D[1, 2] * d.dhdx[:, 1] + self.D[2, 2] * d.dhdx[:, 0]
for i in range(4):
for j in range(4):
#K1
stiff[5 * i + 0, 5 * j +
0] += d.dhdx[i, 0] * N11[j] + d.dhdx[i, 1] * N16[j]
stiff[5 * i + 1, 5 * j +
0] += d.dhdx[i, 0] * N16[j] + d.dhdx[i, 1] * N12[j]
stiff[5 * i + 3, 5 * j +
0] += d.dhdx[i, 0] * M11[j] + d.dhdx[i, 1] * M16[j]
stiff[5 * i + 4, 5 * j +
0] += d.dhdx[i, 0] * M16[j] + d.dhdx[i, 1] * M12[j]
#K2
stiff[5 * i + 0, 5 * j +
1] += d.dhdx[i, 0] * N21[j] + d.dhdx[i, 1] * N26[j]
stiff[5 * i + 1, 5 * j +
1] += d.dhdx[i, 0] * N26[j] + d.dhdx[i, 1] * N22[j]
stiff[5 * i + 3, 5 * j +
1] += d.dhdx[i, 0] * M21[j] + d.dhdx[i, 1] * M26[j]
stiff[5 * i + 4, 5 * j +
1] += d.dhdx[i, 0] * M26[j] + d.dhdx[i, 1] * M22[j]
#K4
stiff[5 * i + 0, 5 * j +
3] += d.dhdx[i, 0] * N41[j] + d.dhdx[i, 1] * N46[j]
stiff[5 * i + 1, 5 * j +
3] += d.dhdx[i, 0] * N46[j] + d.dhdx[i, 1] * N42[j]
stiff[5 * i + 3, 5 * j +
3] += d.dhdx[i, 0] * M41[j] + d.dhdx[i, 1] * M46[j]
stiff[5 * i + 4, 5 * j +
3] += d.dhdx[i, 0] * M46[j] + d.dhdx[i, 1] * M42[j]
#K5
stiff[5 * i + 0, 5 * j +
4] += d.dhdx[i, 0] * N51[j] + d.dhdx[i, 1] * N56[j]
stiff[5 * i + 1, 5 * j +
4] += d.dhdx[i, 0] * N56[j] + d.dhdx[i, 1] * N52[j]
stiff[5 * i + 3, 5 * j +
4] += d.dhdx[i, 0] * M51[j] + d.dhdx[i, 1] * M56[j]
stiff[5 * i + 4, 5 * j +
4] += d.dhdx[i, 0] * M56[j] + d.dhdx[i, 1] * M52[j]
elemdat.stiff += stiff * d.weight
sData = getElemShapeData(elemdat.coords, -1)
for d in sData:
stiff = zeros(shape=(20, 20))
Q41 = self.A55 * d.h
Q42 = self.A45 * d.h
Q51 = self.A45 * d.h
Q52 = self.A44 * d.h
Q31 = self.A55 * d.dhdx[:, 0] + self.A45 * d.dhdx[:, 1]
Q32 = self.A45 * d.dhdx[:, 0] + self.A44 * d.dhdx[:, 1]
for i in range(4):
for j in range(4):
#K3
stiff[5 * i + 2, 5 * j +
2] += d.dhdx[i, 0] * Q31[j] + d.dhdx[i, 1] * Q32[j]
stiff[5 * i + 3, 5 * j + 2] += d.h[i] * Q31[j]
stiff[5 * i + 4, 5 * j + 2] += d.h[i] * Q32[j]
#K4
stiff[5 * i + 2, 5 * j +
3] += d.dhdx[i, 0] * Q41[j] + d.dhdx[i, 1] * Q42[j]
stiff[5 * i + 3, 5 * j + 3] += d.h[i] * Q41[j]
stiff[5 * i + 4, 5 * j + 3] += d.h[i] * Q42[j]
#K5
stiff[5 * i + 2, 5 * j +
4] += d.dhdx[i, 0] * Q51[j] + d.dhdx[i, 1] * Q52[j]
stiff[5 * i + 3, 5 * j + 4] += d.h[i] * Q51[j]
stiff[5 * i + 4, 5 * j + 4] += d.h[i] * Q52[j]
elemdat.stiff += stiff * d.weight
#------------------------------------------------------------------------------
#
#------------------------------------------------------------------------------
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 getMassMatrix(self, elemdat):
sData = getElemShapeData(elemdat.coords)
mass = zeros(shape=(20, 20))
for d in sData:
for i in range(4):
for j in range(4):
shp = d.h[i] * d.h[j]
mass[5 * i + 0, 5 * j + 0] += self.inertia[0] * shp
mass[5 * i + 0, 5 * j + 3] += self.inertia[1] * shp
mass[5 * i + 1, 5 * j + 1] += self.inertia[0] * shp
mass[5 * i + 1, 5 * j + 4] += self.inertia[1] * shp
mass[5 * i + 2, 5 * j + 2] += self.inertia[0] * shp
mass[5 * i + 3, 5 * j + 0] += self.inertia[1] * shp
mass[5 * i + 3, 5 * j + 3] += self.inertia[0] * shp
mass[5 * i + 3, 5 * j + 4] += self.inertia[1] * shp
mass[5 * i + 4, 5 * j + 1] += self.inertia[1] * shp
mass[5 * i + 4, 5 * j + 3] += self.inertia[1] * shp
mass[5 * i + 4, 5 * j + 4] += self.inertia[0] * shp
elemdat.mass += mass * d.weight
#------------------------------------------------------------------------------
#
#------------------------------------------------------------------------------
def initPostProcessing(self):
layerCount = self.material.layerCount()
self.postProcess = []
pp = postProcessPoint()
pp.z = -0.5 * self.material.thick
pp.Qbar = self.material.getQbar(0)
pp.theta = self.material.layers[0].theta
pp.labels = ["s11bot", "s22bot", "s12bot"]
self.postProcess.append(pp)
pp = postProcessPoint()
pp.z = 0.5 * self.material.thick
pp.Qbar = self.material.getQbar(layerCount - 1)
pp.theta = self.material.layers[layerCount - 1].theta
pp.labels = ["s11top", "s22top", "s12top"]
self.postProcess.append(pp)