def ComputeMass(self, node, element, dofMap=None):
etype = None
mtype = None
if (dofMap == None):
dofMap = dmap.FixedDofMap(self.dpn)
#mespace = len(element)*(element[0].NumNodes()*self.dpn)**2
mdata = basic.DelayedAssm(element, self.dpn)
for e in element:
ecoord = node[e.Connectivity(), :]
if (not etype == e.Type()):
etype = e.Type()
qr = e.QuadratureRule(2 * (e.Order()))
nne = e.NumNodes()
if (not e.Material() == mtype):
mtype = e.prop.material
rho = mtype.matprop['rho']
me = np.zeros((nne, nne))
for q in xrange(qr[1].size):
qpt = qr[0][q]
qwt = qr[1][q]
jac = e.Jacobian(ecoord, qpt)
N = e.N(qpt)
me = me + rho * np.outer(N, N) * jac * qwt
# scatter me into M
for s in self.SpacialDim():
sctr = dofMap.Sctr(e.Connectivity(), s)
mdata.AddLocalMatrix(me, sctr)
return mdata.GetCsrMatrix()
def ComputeStress(self, node, element, disp, dofMap=None):
if (dofMap == None):
dofMap = dmap.FixedDofMap(self.dpn)
ne = len(element)
strain = np.zeros((ne, self.vdim), dtype=basic.FLOAT_TYPE)
stress = np.zeros((ne, self.vdim), dtype=basic.FLOAT_TYPE)
svm = np.zeros(ne, dtype=basic.FLOAT_TYPE)
mtype = None
ei = 0
for e in element:
ecoord = node[e.Connectivity(), :]
#sctr = elem.sctr_array( e.Connectivity(), self.dpn )
sctr = dofMap.Sctr(e.Connectivity(), range(self.dpn))
if (not e.Material() == mtype):
mtype = e.prop.material
C = self.GetMaterialStiffness(e)
B, jac = e.BMat(ecoord)
strain[ei, :] = np.dot(B, disp[sctr])
stress[ei, :] = np.dot(C, strain[ei])
svm[ei] = self.ComputeMisesStress(stress[ei])
ei = ei + 1
return [stress, svm, strain]
def ComputeStiffness(self, node, element, dofMap=None):
etype = None
mtype = None
if (dofMap == None):
dofMap = dmap.FixedDofMap(self.dpn)
#kespace = len(element)*(element[0].NumNodes()*self.dpn)**2
kdata = basic.DelayedAssm(element, self.dpn)
for e in element:
ecoord = node[e.Connectivity(), :]
#pdb.set_trace()
sctr = dofMap.Sctr(e.Connectivity(), dofMap.LDOFs())
if (not etype == e.Type()):
etype = e.Type()
qr = e.QuadratureRule(2 * (e.Order()))
kdim = e.NumNodes() * self.dpn
if (not e.Material() == mtype):
mtype = e.prop.material
C = self.GetMaterialStiffness(e)
ke = np.zeros((kdim, kdim))
for q in xrange(qr[1].size):
qpt = qr[0][q]
qwt = qr[1][q]
ipm = e.BMat(ecoord, qpt)
jac = ipm[1]
B = ipm[0]
ke = ke + np.dot(np.dot(B.T, C), B) * jac * qwt
# scatter ke into K
kdata.AddLocalMatrix(ke, sctr)
return kdata.GetCsrMatrix()
print '********************* 3D FINITE ELEMENT PROGRAM *********************'
print 'Initializing grid'
# define the finite element mesh
pwidth = 20
plength = 20
pheight = 5
mat0 = matl.LinearElasticMat(10e6, .33,
2.45e-4) # linear elastic isotropic material
prop0 = prop.Solid3D(mat0) # 3D solid property
fegrid = mesh.MeshHexa8( np.array([ [0,0,0], [plength,0,0], [plength,pwidth,0], [0,pwidth,0], \
[0,0,pheight], [plength,0,pheight], [plength,pwidth,pheight], [0,pwidth,pheight] ]),\
21, 21, 6, prop0 )
# setup a simple dofmap with 3 dof per node
dofMap = dmap.FixedDofMap(3)
formulation = prob.Problem3D()
print 'Computing stiffness matrix'
# compute the stiffness matrix
Kmat = formulation.ComputeStiffness(fegrid.node, fegrid.element, dofMap)
# define symmetry boundary conditions
spcs = bcs.EssentialBCs()
spcs.AddSpcs(fegrid.FaceNIDs(1), [0], dofmap=dofMap) # fix -x face in x
spcs.AddSpcs(fegrid.FaceNIDs(3), [1], dofmap=dofMap) # fix -y face in y
spcs.AddSpcs(fegrid.FaceNIDs(5), [2], dofmap=dofMap) # fix -z face in z
# define rhs load
loads = bcs.NaturalBCs()
loads.AddTraction(fegrid.FaceElem(0), [100.0, 0.0, 0.0]) # load on the +x face
fext[sctr] = fext[sctr] + fe
return fext
#---------------------------------------------
import prop
import meshing as mesh
# define the finite element mesh
pwidth=20
pheight=5
mat0 = NewtonianFluid( )
prop0 = prop.PlaneStress( mat0, 1.0 )
fegrid = mesh.MeshQuad4( np.array([[0,0],[pwidth,0],[pwidth,pheight],[0,pheight]]), 5, 2, prop0 )
dofmap = dmap.FixedDofMap(2)
# define the velocity boundary conditions
inflow = bcs.NaturalBCs()
inflow.AddTraction( fegrid.EdgeElem(3), [10.0, 0.0] )
inflowspcs = bcs.EssentialBCs()
inflowspcs.AddSpcs( fegrid.EdgeNIDs(3), [0], [10.0], dofmap=dofmap ) # fix left edge in x
loads = bcs.NaturalBCs() # if there are external wall tractions on the flow
loads.AddTraction( fegrid.EdgeElem(0), [10.0, 0.0] )
# set the initial conditions
formulation = CBSMethod(sdim=2)
dt=.1
U=np.zeros(20,float)
U[::2]=fegrid.node[:,0]