NEUMANN_BOUNDARY = 1
DIRICHLET_BOUNDARY = 2
m.set_region(NEUMANN_BOUNDARY, ftop)
m.set_region(DIRICHLET_BOUNDARY, fbot)
# assembly
nbd = mfd.nbdof()
print "nbd: ", nbd
F = gf.asm_boundary_source(NEUMANN_BOUNDARY, mim, mfu, mfd,
np.repeat([[0], [-100], [0]], nbd, 1))
print "F.shape: ", F.shape
print "mfu.nbdof(): ", mfu.nbdof()
print "np.repeat([[0],[-100],[0]],nbd,1).shape:", np.repeat([[0], [-100], [0]],
nbd, 1).shape
K = gf.asm_linear_elasticity(mim, mfu, mfd, np.repeat([Lambda], nbd),
np.repeat([Mu], nbd))
print "K.info: ", K.info # Spmat instance
print "np.repeat([Lambda], nbd).shape:", np.repeat([Lambda], nbd).shape
print "np.repeat([Mu], nbd).shape:", np.repeat([Mu], nbd).shape
# handle Dirichlet condition
(H, R) = gf.asm_dirichlet(DIRICHLET_BOUNDARY, mim, mfu, mfd,
mfd.eval('numpy.identity(3)'), mfd.eval('[0,0,0]'))
print "H.info: ", H.info # Spmat instance
print "R.shape: ", R.shape
print "mfd.eval('numpy.identity(3)').shape: ", mfd.eval(
'numpy.identity(3)').shape
print "mfd.eval('[0,0,0]').shape: ", mfd.eval('[0,0,0]').shape
(N, U0) = H.dirichlet_nullspace(R)
print "N.info: ", N.info # Spmat instance
ftop = m.faces_from_pid(pidtop)
fbot = m.faces_from_pid(pidbot)
print "create boundary region"
NEUMANN_BOUNDARY = 1
DIRICHLET_BOUNDARY = 2
m.set_region(NEUMANN_BOUNDARY,ftop)
m.set_region(DIRICHLET_BOUNDARY,fbot)
print "create a MeshFem object"
mfd = gf.MeshFem(m, 1) # data
print "assign the FEM"
mfd.set_fem(gf.Fem('FEM_QK(3,3)'))
print "assembly"
nbd = mfd.nbdof()
K = gf.asm_linear_elasticity(mim, mfu, mfd, np.repeat([Lambda], nbd), np.repeat([Mu], nbd))
M = gf.asm_mass_matrix(mim, mfu)*rho
K.save('hb', 'K.hb')
M.save('hb', 'M.hb')
print "solve"
A = io.hb_read('M.hb')
B = io.hb_read('K.hb')
K = B.todense()
np.savetxt("K.txt", K, fmt=' (%+.18e) ')
###############################################################################
# We get the mass and stiffness matrices using asm function.
#
mass_matrixs = []
linear_elasticitys = []
for i, (mfu, mfd, mim) in enumerate(zip(mfus, mfds, mims)):
mass_matrix = gf.asm_mass_matrix(mim, mfu, mfu)
mass_matrix.scale(rho)
mass_matrixs.append(mass_matrix)
lambda_d = np.repeat(clambda, mfd.nbdof())
mu_d = np.repeat(cmu, mfd.nbdof())
linear_elasticity = gf.asm_linear_elasticity(mim, mfu, mfd, lambda_d, mu_d)
linear_elasticitys.append(linear_elasticity)
mass_matrix.save("hb", "M" + "{:02}".format(i) + ".hb")
linear_elasticity.save("hb", "K" + "{:02}".format(i) + ".hb")
print("Time for assemble matrix", time.process_time() - t)
t = time.process_time()
###############################################################################
# Solve the eigenproblem.
#
# Compute the residual error for SciPy.
#
# :math:`Err=\frac{||(K-\lambda.M).\phi||_2}{||K.\phi||_2}`
#
def import_fem2(sico):
""" Build a mesh object using getfem.
We use getfem++ to build the finite element model and
to fill in the operators required by siconos:
- the mass matrix (Mass)
- the stiffness matrix (Stiff)
- the matrix that links global coordinates and local coord. at contact points (H)
"""
############################
# The geometry and the mesh
############################
dimX = 10.01 ; dimY = 10.01 ; dimZ = 10.01
stepX = 1.0 ; stepY = 1.0 ; stepZ = 1.0
x=np.arange(0,dimX,stepX)
y=np.arange(0,dimY,stepY)
z=np.arange(0,dimZ,stepZ)
m = gf.Mesh('regular simplices', x,y,z)
m.set('optimize_structure')
# Export the mesh to vtk
m.export_to_vtk("BlockMesh.vtk")
# Create MeshFem objects
# (i.e. assign elements onto the mesh for each variable)
mfu = gf.MeshFem(m,3) # displacement
mfd = gf.MeshFem(m,1) # data
mff = gf.MeshFem(m,1) # for plot von-mises
# assign the FEM
mfu.set_fem(gf.Fem('FEM_PK(3,1)'))
mfd.set_fem(gf.Fem('FEM_PK(3,0)'))
mff.set_fem(gf.Fem('FEM_PK_DISCONTINUOUS(3,1,0.01)'))
# mfu.export_to_vtk("BlockMeshDispl.vtk")
# Set the integration method
mim = gf.MeshIm(m,gf.Integ('IM_TETRAHEDRON(5)'))
# Summary
print(' ==================================== \n Mesh details: ')
print(' Problem dimension:', mfu.qdim(), '\n Number of elements: ', m.nbcvs(), '\n Number of nodes: ', m.nbpts())
print(' Number of dof: ', mfu.nbdof(), '\n Element type: ', mfu.fem()[0].char())
print(' ====================================')
###########################
# Set the parameters
# for the constitutive law
###########################
E = 1e3 # Young modulus
Nu = 0.3 # Poisson coef.
# Lame coeff.
Lambda = E*Nu/((1+Nu)*(1-2*Nu))
Mu = E/(2*(1+Nu))
# Density
Rho=7800
############################
# Boundaries detection
############################
allPoints = m.pts()
# Bottom points and faces
cbot = (abs(allPoints[2,:]) < 1e-6)
pidbot = np.compress(cbot,list(range(0,m.nbpts())))
fbot = m.faces_from_pid(pidbot)
BOTTOM = 1
m.set_region(BOTTOM,fbot)
# Top points and faces
ctop = (abs(allPoints[2,:]) > dimZ-stepZ)
pidtop = np.compress(ctop,list(range(0,m.nbpts())))
ftop = m.faces_from_pid(pidtop)
TOP = 2
m.set_region(TOP,ftop)
# Top-Left points and faces
cleft = (abs(allPoints[1,:]) < 1e-6)
clefttop=cleft*ctop
pidlefttop = np.compress(clefttop,list(range(0,m.nbpts())))
flefttop = m.faces_from_pid(pidlefttop)
pidleft = np.compress(cleft,list(range(0,m.nbpts())))
fleft= m.faces_from_pid(pidleft)
LEFTTOP = 3
m.set_region(LEFTTOP,flefttop)
LEFT = 4
m.set_region(LEFT,fleft)
############################
# Assembly
############################
nbd = mfd.nbdof()
# Stiffness matrix
sico.Stiff=gf.asm_linear_elasticity(mim, mfu, mfd,np.repeat([Lambda], nbd), np.repeat([Mu], nbd))
# Mass matrix
sico.Mass=Rho*gf.asm_mass_matrix(mim, mfu)
# Right-hand side
Ftop = gf.asm_boundary_source(TOP, mim, mfu, mfd, np.repeat([[0],[0],[-1]],nbd,1))
Fleft= gf.asm_boundary_source(LEFT, mim, mfu, mfd, np.repeat([[0],[10],[0]],nbd,1))
sico.RHS = Ftop + Fleft
sico.nbdof = mfu.nbdof()
sico.q0 = mfu.basic_dof_from_cvid()
sico.bot = pidbot
# H-Matrix
fillH(pidbot,sico,mfu.nbdof())
return m
def import_fem2(sico):
""" Build a mesh object using getfem.
We use getfem++ to build the finite element model and
to fill in the operators required by siconos:
- the mass matrix (Mass)
- the stiffness matrix (Stiff)
- the matrix that links global coordinates and local coord. at contact points (H)
"""
############################
# The geometry and the mesh
############################
dimX = 10.01
dimY = 10.01
dimZ = 10.01
stepX = 1.0
stepY = 1.0
stepZ = 1.0
x = np.arange(0, dimX, stepX)
y = np.arange(0, dimY, stepY)
z = np.arange(0, dimZ, stepZ)
m = gf.Mesh('regular simplices', x, y, z)
m.set('optimize_structure')
# Export the mesh to vtk
m.export_to_vtk("BlockMesh.vtk")
# Create MeshFem objects
# (i.e. assign elements onto the mesh for each variable)
mfu = gf.MeshFem(m, 3) # displacement
mfd = gf.MeshFem(m, 1) # data
mff = gf.MeshFem(m, 1) # for plot von-mises
# assign the FEM
mfu.set_fem(gf.Fem('FEM_PK(3,1)'))
mfd.set_fem(gf.Fem('FEM_PK(3,0)'))
mff.set_fem(gf.Fem('FEM_PK_DISCONTINUOUS(3,1,0.01)'))
# mfu.export_to_vtk("BlockMeshDispl.vtk")
# Set the integration method
mim = gf.MeshIm(m, gf.Integ('IM_TETRAHEDRON(5)'))
# Summary
print(' ==================================== \n Mesh details: ')
print(' Problem dimension:', mfu.qdim(), '\n Number of elements: ',
m.nbcvs(), '\n Number of nodes: ', m.nbpts())
print(' Number of dof: ', mfu.nbdof(), '\n Element type: ',
mfu.fem()[0].char())
print(' ====================================')
###########################
# Set the parameters
# for the constitutive law
###########################
E = 1e3 # Young modulus
Nu = 0.3 # Poisson coef.
# Lame coeff.
Lambda = E * Nu / ((1 + Nu) * (1 - 2 * Nu))
Mu = E / (2 * (1 + Nu))
# Density
Rho = 7800
############################
# Boundaries detection
############################
allPoints = m.pts()
# Bottom points and faces
cbot = (abs(allPoints[2, :]) < 1e-6)
pidbot = np.compress(cbot, list(range(0, m.nbpts())))
fbot = m.faces_from_pid(pidbot)
BOTTOM = 1
m.set_region(BOTTOM, fbot)
# Top points and faces
ctop = (abs(allPoints[2, :]) > dimZ - stepZ)
pidtop = np.compress(ctop, list(range(0, m.nbpts())))
ftop = m.faces_from_pid(pidtop)
TOP = 2
m.set_region(TOP, ftop)
# Top-Left points and faces
cleft = (abs(allPoints[1, :]) < 1e-6)
clefttop = cleft * ctop
pidlefttop = np.compress(clefttop, list(range(0, m.nbpts())))
flefttop = m.faces_from_pid(pidlefttop)
pidleft = np.compress(cleft, list(range(0, m.nbpts())))
fleft = m.faces_from_pid(pidleft)
LEFTTOP = 3
m.set_region(LEFTTOP, flefttop)
LEFT = 4
m.set_region(LEFT, fleft)
############################
# Assembly
############################
nbd = mfd.nbdof()
# Stiffness matrix
sico.Stiff = gf.asm_linear_elasticity(mim, mfu, mfd,
np.repeat([Lambda], nbd),
np.repeat([Mu], nbd))
# Mass matrix
sico.Mass = Rho * gf.asm_mass_matrix(mim, mfu)
# Right-hand side
Ftop = gf.asm_boundary_source(TOP, mim, mfu, mfd,
np.repeat([[0], [0], [-1]], nbd, 1))
Fleft = gf.asm_boundary_source(LEFT, mim, mfu, mfd,
np.repeat([[0], [10], [0]], nbd, 1))
sico.RHS = Ftop + Fleft
sico.nbdof = mfu.nbdof()
sico.q0 = mfu.basic_dof_from_cvid()
sico.bot = pidbot
# H-Matrix
fillH(pidbot, sico, mfu.nbdof())
return m