ctop = (abs(P[1, :] - 13) < 1e-6)
cbot = (abs(P[1, :] + 10) < 1e-6)
pidtop = np.compress(ctop, range(0, m.nbpts()))
pidbot = np.compress(cbot, range(0, m.nbpts()))
ftop = m.faces_from_pid(pidtop)
fbot = m.faces_from_pid(pidbot)
# create boundary region
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
(mim, "Simo_Miehe", "displacement_and_plastic_multiplier_and_pressure",
"u", "ksi", "p", "gamma0", "invCp0", _K_, _mu_, "hardening_law")
GAMMA = gf.asm_generic(mim, 1, "gamma*Test_t", -1, "gamma", False,
mimd1, md.variable("gamma0"), "t", True, mfout,
np.zeros(mfout.nbdof()))
GAMMA = np.transpose(gf.linsolve_mumps(mass_mat, GAMMA))
output += (mfout, GAMMA, "plastic strain")
mf1.export_to_vtk(
'%s/finite_strain_plasticity_%i.vtk' % (resultspath, step),
'ascii', *output)
DIRMULT = -md.variable(dirichlet_multname)
DIRMULT = np.reshape(DIRMULT, [1, DIRMULT.size])
if symmetric and not rigid_grip:
dfR = gf.asm_boundary_source(R_BOUNDARY, mim, mf1,
mf_dirichlet_mult, DIRMULT)
f.write(('step=%i fR=(%f,0) sR=(%f,0)\n') %
(step, dfR.sum(), dfR.sum() / H))
else:
dfR = gf.asm_boundary_source(R_BOUNDARY, mim, mfN,
mf_dirichlet_mult, DIRMULT)
f.write(('step=%i fR=(%f,%f) sR=(%f,%f)\n') %
(step, dfR[0::N].sum(), dfR[1::N].sum(),
dfR[0::N].sum() / H, dfR[1::N].sum() / H))
f.flush()
print('OVERALL SOLUTION TIME IS %f SEC' %
(time.process_time() - starttime_overall))
if MM < 1e-4:
MM = 0.
pseudodynamic = False
elif nit <= 6:
MM /= 2.
else:
TMP = md.interpolation("max(psi0_max,psi0)", mimd1, -1)
md.set_variable("psi0_max", TMP)
break
out = (mfu, md.variable("u"), "Displacements", mfphi,
md.variable("phi"), "phi")
for i, j in [[1, 1], [2, 2], [1, 2]]:
sigma = gf.asm_generic(mim, 1, "{sigma}({i},{j})*Test_t".format(sigma=_sigma_, i=i, j=j),
-1, md, "t", True, mfout, np.zeros(mfout.nbdof()))\
[md.nbdof():]
sigma = np.transpose(gf.linsolve_mumps(mass_mat, sigma))
out += (mfout, sigma, "Cauchy Stress {i}{j}".format(i=i, j=j))
mfout.export_to_vtk("%s/demo_phase_field_%i.vtk" % (resultspath, step),
*out)
DIRMULT = -md.variable(dirmultname)
DIRMULT = np.reshape(DIRMULT, [1, DIRMULT.size])
dfT = gf.asm_boundary_source(T_BOUNDARY, mim, mfu,
md.mesh_fem_of_variable(dirmultname),
DIRMULT)
f.write(("step=%i eps=%e fR=(%e,%e)\n") %
(step, eps, dfT[0::N].sum(), dfT[1::N].sum()))
f.flush()
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
# 以上で設定した、条件を使用して外力ベクトルと剛性行列を設定します。
# In[16]:
help(gf.asm_boundary_source)
# In[17]:
help(gf.asm_linear_elasticity)
# In[18]:
nbd = mfd.nbdof()
F = gf.asm_boundary_source(NEUMANN_BOUNDARY, mim, mfu, mfd, np.repeat([[0],[-100],[0]],nbd,1))
K = gf.asm_linear_elasticity(mim, mfu, mfd, np.repeat([Lambda], nbd), np.repeat([Mu], nbd))
# # 固定条件の設定
# DIRICHLET条件(固定端条件)の設定をします。
# In[19]:
(H,R) = gf.asm_dirichlet(DIRICHLET_BOUNDARY, mim, mfu, mfd, mfd.eval('[[1,0,0],[0,1,0],[0,0,1]]'), mfd.eval('[0,0,0]'))
(N,U0) = H.dirichlet_nullspace(R)
# In[20]:
Nt = gf.Spmat('copy',N)