def main():
from sfepy import data_dir
parser = OptionParser(usage=usage, version="%prog")
parser.add_option("-s", "--show", action="store_true", dest="show", default=False, help=help["show"])
options, args = parser.parse_args()
mesh = Mesh.from_file(data_dir + "/meshes/2d/rectangle_tri.mesh")
domain = Domain("domain", mesh)
min_x, max_x = domain.get_mesh_bounding_box()[:, 0]
eps = 1e-8 * (max_x - min_x)
omega = domain.create_region("Omega", "all")
gamma1 = domain.create_region("Gamma1", "vertices in x < %.10f" % (min_x + eps), "facet")
gamma2 = domain.create_region("Gamma2", "vertices in x > %.10f" % (max_x - eps), "facet")
field = Field.from_args("fu", nm.float64, "vector", omega, approx_order=2)
u = FieldVariable("u", "unknown", field)
v = FieldVariable("v", "test", field, primary_var_name="u")
m = Material("m", lam=1.0, mu=1.0)
f = Material("f", val=[[0.02], [0.01]])
integral = Integral("i", order=3)
t1 = Term.new("dw_lin_elastic_iso(m.lam, m.mu, v, u)", integral, omega, m=m, v=v, u=u)
t2 = Term.new("dw_volume_lvf(f.val, v)", integral, omega, f=f, v=v)
eq = Equation("balance", t1 + t2)
eqs = Equations([eq])
fix_u = EssentialBC("fix_u", gamma1, {"u.all": 0.0})
bc_fun = Function("shift_u_fun", shift_u_fun, extra_args={"shift": 0.01})
shift_u = EssentialBC("shift_u", gamma2, {"u.0": bc_fun})
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem("elasticity", equations=eqs, nls=nls, ls=ls)
pb.save_regions_as_groups("regions")
pb.time_update(ebcs=Conditions([fix_u, shift_u]))
vec = pb.solve()
print nls_status
pb.save_state("linear_elasticity.vtk", vec)
if options.show:
view = Viewer("linear_elasticity.vtk")
view(vector_mode="warp_norm", rel_scaling=2, is_scalar_bar=True, is_wireframe=True)
def main():
from sfepy import data_dir
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-s',
'--show',
action="store_true",
dest='show',
default=False,
help=help['show'])
options, args = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/2d/rectangle_tri.mesh')
domain = FEDomain('domain', mesh)
min_x, max_x = domain.get_mesh_bounding_box()[:, 0]
eps = 1e-8 * (max_x - min_x)
omega = domain.create_region('Omega', 'all')
gamma1 = domain.create_region('Gamma1',
'vertices in x < %.10f' % (min_x + eps),
'facet')
gamma2 = domain.create_region('Gamma2',
'vertices in x > %.10f' % (max_x - eps),
'facet')
field = Field.from_args('fu', nm.float64, 'vector', omega, approx_order=2)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
m = Material('m', D=stiffness_from_lame(dim=2, lam=1.0, mu=1.0))
f = Material('f', val=[[0.02], [0.01]])
integral = Integral('i', order=3)
t1 = Term.new('dw_lin_elastic(m.D, v, u)', integral, omega, m=m, v=v, u=u)
t2 = Term.new('dw_volume_lvf(f.val, v)', integral, omega, f=f, v=v)
eq = Equation('balance', t1 + t2)
eqs = Equations([eq])
fix_u = EssentialBC('fix_u', gamma1, {'u.all': 0.0})
bc_fun = Function('shift_u_fun', shift_u_fun, extra_args={'shift': 0.01})
shift_u = EssentialBC('shift_u', gamma2, {'u.0': bc_fun})
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
pb.save_regions_as_groups('regions')
pb.time_update(ebcs=Conditions([fix_u, shift_u]))
vec = pb.solve()
print(nls_status)
pb.save_state('linear_elasticity.vtk', vec)
if options.show:
view = Viewer('linear_elasticity.vtk')
view(vector_mode='warp_norm',
rel_scaling=2,
is_scalar_bar=True,
is_wireframe=True)
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-d', '--dims', metavar='dims',
action='store', dest='dims',
default='[1.0, 1.0]', help=helps['dims'])
parser.add_argument('-c', '--centre', metavar='centre',
action='store', dest='centre',
default='[0.0, 0.0]', help=helps['centre'])
parser.add_argument('-s', '--shape', metavar='shape',
action='store', dest='shape',
default='[11, 11]', help=helps['shape'])
parser.add_argument('-b', '--bc-kind', metavar='kind',
action='store', dest='bc_kind',
choices=['free', 'cantilever', 'fixed'],
default='free', help=helps['bc_kind'])
parser.add_argument('-a', '--axis', metavar='0, ..., dim, or -1',
type=int, action='store', dest='axis',
default=-1, help=helps['axis'])
parser.add_argument('--young', metavar='float', type=float,
action='store', dest='young',
default=6.80e+10, help=helps['young'])
parser.add_argument('--poisson', metavar='float', type=float,
action='store', dest='poisson',
default=0.36, help=helps['poisson'])
parser.add_argument('--density', metavar='float', type=float,
action='store', dest='density',
default=2700.0, help=helps['density'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
parser.add_argument('-i', '--ignore', metavar='int', type=int,
action='store', dest='ignore',
default=None, help=helps['ignore'])
parser.add_argument('--solver', metavar='solver', action='store',
dest='solver',
default= \
"eig.scipy,method:'eigh',tol:1e-5,maxiter:1000",
help=helps['solver'])
parser.add_argument('--show',
action="store_true", dest='show',
default=False, help=helps['show'])
parser.add_argument('filename', nargs='?', default=None)
options = parser.parse_args()
aux = options.solver.split(',')
kwargs = {}
for option in aux[1:]:
key, val = option.split(':')
kwargs[key.strip()] = eval(val)
eig_conf = Struct(name='evp', kind=aux[0], **kwargs)
output('using values:')
output(" Young's modulus:", options.young)
output(" Poisson's ratio:", options.poisson)
output(' density:', options.density)
output('displacement field approximation order:', options.order)
output('requested %d eigenvalues' % options.n_eigs)
output('using eigenvalue problem solver:', eig_conf.kind)
output.level += 1
for key, val in six.iteritems(kwargs):
output('%s: %r' % (key, val))
output.level -= 1
assert_((0.0 < options.poisson < 0.5),
"Poisson's ratio must be in ]0, 0.5[!")
assert_((0 < options.order),
'displacement approximation order must be at least 1!')
filename = options.filename
if filename is not None:
mesh = Mesh.from_file(filename)
dim = mesh.dim
dims = nm.diff(mesh.get_bounding_box(), axis=0)
else:
dims = nm.array(eval(options.dims), dtype=nm.float64)
dim = len(dims)
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
output('dimensions:', dims)
output('centre: ', centre)
output('shape: ', shape)
mesh = gen_block_mesh(dims, shape, centre, name='mesh')
output('axis: ', options.axis)
assert_((-dim <= options.axis < dim), 'invalid axis value!')
eig_solver = Solver.any_from_conf(eig_conf)
# Build the problem definition.
domain = FEDomain('domain', mesh)
bbox = domain.get_mesh_bounding_box()
min_coor, max_coor = bbox[:, options.axis]
eps = 1e-8 * (max_coor - min_coor)
ax = 'xyz'[:dim][options.axis]
omega = domain.create_region('Omega', 'all')
bottom = domain.create_region('Bottom',
'vertices in (%s < %.10f)'
% (ax, min_coor + eps),
'facet')
bottom_top = domain.create_region('BottomTop',
'r.Bottom +v vertices in (%s > %.10f)'
% (ax, max_coor - eps),
'facet')
field = Field.from_args('fu', nm.float64, 'vector', omega,
approx_order=options.order)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
mtx_d = stiffness_from_youngpoisson(dim, options.young, options.poisson)
m = Material('m', D=mtx_d, rho=options.density)
integral = Integral('i', order=2*options.order)
t1 = Term.new('dw_lin_elastic(m.D, v, u)', integral, omega, m=m, v=v, u=u)
t2 = Term.new('dw_volume_dot(m.rho, v, u)', integral, omega, m=m, v=v, u=u)
eq1 = Equation('stiffness', t1)
eq2 = Equation('mass', t2)
lhs_eqs = Equations([eq1, eq2])
pb = Problem('modal', equations=lhs_eqs)
if options.bc_kind == 'free':
pb.time_update()
n_rbm = dim * (dim + 1) / 2
elif options.bc_kind == 'cantilever':
fixed = EssentialBC('Fixed', bottom, {'u.all' : 0.0})
pb.time_update(ebcs=Conditions([fixed]))
n_rbm = 0
elif options.bc_kind == 'fixed':
fixed = EssentialBC('Fixed', bottom_top, {'u.all' : 0.0})
pb.time_update(ebcs=Conditions([fixed]))
n_rbm = 0
else:
raise ValueError('unsupported BC kind! (%s)' % options.bc_kind)
if options.ignore is not None:
n_rbm = options.ignore
pb.update_materials()
# Assemble stiffness and mass matrices.
mtx_k = eq1.evaluate(mode='weak', dw_mode='matrix', asm_obj=pb.mtx_a)
mtx_m = mtx_k.copy()
mtx_m.data[:] = 0.0
mtx_m = eq2.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx_m)
try:
eigs, svecs = eig_solver(mtx_k, mtx_m, options.n_eigs + n_rbm,
eigenvectors=True)
except sla.ArpackNoConvergence as ee:
eigs = ee.eigenvalues
svecs = ee.eigenvectors
output('only %d eigenvalues converged!' % len(eigs))
output('%d eigenvalues converged (%d ignored as rigid body modes)' %
(len(eigs), n_rbm))
eigs = eigs[n_rbm:]
svecs = svecs[:, n_rbm:]
omegas = nm.sqrt(eigs)
freqs = omegas / (2 * nm.pi)
output('number | eigenvalue | angular frequency '
'| frequency')
for ii, eig in enumerate(eigs):
output('%6d | %17.12e | %17.12e | %17.12e'
% (ii + 1, eig, omegas[ii], freqs[ii]))
# Make full eigenvectors (add DOFs fixed by boundary conditions).
variables = pb.get_variables()
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=nm.float64)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
for ii in range(eigs.shape[0]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
strain = pb.evaluate('ev_cauchy_strain.i.Omega(u)',
integrals=Integrals([integral]),
mode='el_avg', verbose=False)
out['u%03d' % ii] = aux.popitem()[1]
out['strain%03d' % ii] = Struct(mode='cell', data=strain)
pb.save_state('eigenshapes.vtk', out=out)
pb.save_regions_as_groups('regions')
if len(eigs) and options.show:
# Show the solution. If the approximation order is greater than 1, the
# extra DOFs are simply thrown away.
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.domain_specific import DomainSpecificPlot
scaling = 0.05 * dims.max() / nm.abs(vecs).max()
ds = {}
for ii in range(eigs.shape[0]):
pd = DomainSpecificPlot('plot_displacements',
['rel_scaling=%s' % scaling,
'color_kind="tensors"',
'color_name="strain%03d"' % ii])
ds['u%03d' % ii] = pd
view = Viewer('eigenshapes.vtk')
view(domain_specific=ds, only_names=sorted(ds.keys()),
is_scalar_bar=False, is_wireframe=True)
def main():
from sfepy import data_dir
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-s', '--show',
action="store_true", dest='show',
default=False, help=help['show'])
options, args = parser.parse_args()
options_probe = True
folder = str(uuid.uuid4())
os.mkdir(folder)
os.chdir(folder)
file = open('README.txt', 'w')
file.write('DIMENSIONS\n')
file.write('Lx = '+str(dims[0])+' Ly = '+str(dims[1])+' Lz = '+str(dims[2])+'\n')
file.write('DISCRETIZATION (NX, NY, NZ)\n')
file.write(str(NX)+' '+str(NY)+' '+str(NZ)+'\n')
file.write('MATERIALS\n')
file.write(str(E_f)+' '+str(nu_f)+' '+str(E_m)+' '+str(nu_m)+'\n')
#mesh = Mesh.from_file(data_dir + '/meshes/2d/rectangle_tri.mesh')
mesh = mesh_generators.gen_block_mesh(dims,shape,centre,name='block')
domain = FEDomain('domain', mesh)
min_x, max_x = domain.get_mesh_bounding_box()[:,0]
min_y, max_y = domain.get_mesh_bounding_box()[:,1]
min_z, max_z = domain.get_mesh_bounding_box()[:,2]
eps = 1e-8 * (max_x - min_x)
print min_x, max_x
print min_y, max_y
print min_z, max_z
R1 = domain.create_region('Ym',
'vertices in z < %.10f' % (max_z/2))
R2 = domain.create_region('Yf',
'vertices in z >= %.10f' % (min_z/2))
omega = domain.create_region('Omega', 'all')
gamma1 = domain.create_region('Left',
'vertices in x < %.10f' % (min_x + eps),
'facet')
gamma2 = domain.create_region('Right',
'vertices in x > %.10f' % (max_x - eps),
'facet')
gamma3 = domain.create_region('Front',
'vertices in y < %.10f' % (min_y + eps),
'facet')
gamma4 = domain.create_region('Back',
'vertices in y > %.10f' % (max_y - eps),
'facet')
gamma5 = domain.create_region('Bottom',
'vertices in z < %.10f' % (min_z + eps),
'facet')
gamma6 = domain.create_region('Top',
'vertices in z > %.10f' % (max_z - eps),
'facet')
field = Field.from_args('fu', nm.float64, 'vector', omega, approx_order=2)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
mu=1.1
lam=1.0
m = Material('m', lam=lam, mu=mu)
f = Material('f', val=[[0.0], [0.0],[-1.0]])
load = Material('Load',val=[[0.0],[0.0],[-Load]])
D = stiffness_from_lame(3,lam, mu)
mat = Material('Mat', D=D)
get_mat = Function('get_mat1',get_mat1)
get_mat_f = Function('get_mat_f',get_mat1)
integral = Integral('i', order=3)
s_integral = Integral('is',order=2)
t1 = Term.new('dw_lin_elastic(Mat.D, v, u)',
integral, omega, Mat=mat, v=v, u=u)
t2 = Term.new('dw_volume_lvf(f.val, v)', integral, omega, f=f, v=v)
#t3 = Term.new('DotProductSurfaceTerm(Load.val, v)',s_integral,gamma5,Load=load,v=v)
t3 = Term.new('dw_surface_ltr( Load.val, v )',s_integral,gamma6,Load=load,v=v)
eq = Equation('balance', t1 + t2 + t3)
eqs = Equations([eq])
fix_u = EssentialBC('fix_u', gamma1, {'u.all' : 0.0})
left_bc = EssentialBC('Left', gamma1, {'u.0' : 0.0})
right_bc = EssentialBC('Right', gamma2, {'u.0' : 0.0})
back_bc = EssentialBC('Front', gamma3, {'u.1' : 0.0})
front_bc = EssentialBC('Back', gamma4, {'u.1' : 0.0})
bottom_bc = EssentialBC('Bottom', gamma5, {'u.all' : 0.0})
top_bc = EssentialBC('Top', gamma6, {'u.2' : 0.2})
bc=[left_bc,right_bc,back_bc,front_bc,bottom_bc]
#bc=[bottom_bc,top_bc]
##############################
# ##### SOLVER SECTION #####
##############################
conf = Struct(method='bcgsl', precond='jacobi', sub_precond=None,
i_max=10000, eps_a=1e-50, eps_r=1e-10, eps_d=1e4,
verbose=True)
ls = PETScKrylovSolver(conf)
file.write(str(ls.name)+' '+str(ls.conf.method)+' '+str(ls.conf.precond)+' '+str(ls.conf.eps_r)+' '+str(ls.conf.i_max)+'\n' )
nls_status = IndexedStruct()
nls = Newton({'i_max':1,'eps_a':1e-10}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
dd=pb.get_materials()['Mat']
dd.set_function(get_mat1)
#xload = pb.get_materials()['f']
#xload.set_function(get_mat_f)
pb.save_regions_as_groups('regions')
pb.time_update(ebcs=Conditions(bc))
vec = pb.solve()
print nls_status
file.write('TIME TO SOLVE\n')
file.write(str(nls.status.time_stats['solve'])+'\n')
file.write('TIME TO CREATE MATRIX\n')
file.write(str(nls.status.time_stats['matrix'])+'\n')
ev = pb.evaluate
out = vec.create_output_dict()
strain = ev('ev_cauchy_strain.3.Omega(u)', mode='el_avg')
stress = ev('ev_cauchy_stress.3.Omega(Mat.D, u)', mode='el_avg',
copy_materials=False)
out['cauchy_strain'] = Struct(name='output_data', mode='cell',
data=strain, dofs=None)
out['cauchy_stress'] = Struct(name='output_data', mode='cell',
data=stress, dofs=None)
pb.save_state('strain.vtk', out=out)
print nls_status
file.close()
def main():
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/2d/rectangle_tri.mesh')
domain = FEDomain('domain', mesh)
min_x, max_x = domain.get_mesh_bounding_box()[:,0]
eps = 1e-8 * (max_x - min_x)
omega = domain.create_region('Omega', 'all')
gamma1 = domain.create_region('Gamma1',
'vertices in x < %.10f' % (min_x + eps),
'facet')
gamma2 = domain.create_region('Gamma2',
'vertices in x > %.10f' % (max_x - eps),
'facet')
field = Field.from_args('fu', nm.float64, 'vector', omega,
approx_order=2)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
m = Material('m', D=stiffness_from_lame(dim=2, lam=1.0, mu=1.0))
f = Material('f', val=[[0.02], [0.01]])
integral = Integral('i', order=3)
t1 = Term.new('dw_lin_elastic(m.D, v, u)',
integral, omega, m=m, v=v, u=u)
t2 = Term.new('dw_volume_lvf(f.val, v)', integral, omega, f=f, v=v)
eq = Equation('balance', t1 + t2)
eqs = Equations([eq])
fix_u = EssentialBC('fix_u', gamma1, {'u.all' : 0.0})
bc_fun = Function('shift_u_fun', shift_u_fun,
extra_args={'shift' : 0.01})
shift_u = EssentialBC('shift_u', gamma2, {'u.0' : bc_fun})
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
pb.save_regions_as_groups('regions')
pb.time_update(ebcs=Conditions([fix_u, shift_u]))
vec = pb.solve()
print(nls_status)
pb.save_state('linear_elasticity.vtk', vec)
if options.show:
view = Viewer('linear_elasticity.vtk')
view(vector_mode='warp_norm', rel_scaling=2,
is_scalar_bar=True, is_wireframe=True)
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-d',
'--dims',
metavar='dims',
action='store',
dest='dims',
default='[1.0, 1.0]',
help=helps['dims'])
parser.add_argument('-c',
'--centre',
metavar='centre',
action='store',
dest='centre',
default='[0.0, 0.0]',
help=helps['centre'])
parser.add_argument('-s',
'--shape',
metavar='shape',
action='store',
dest='shape',
default='[11, 11]',
help=helps['shape'])
parser.add_argument('-b',
'--bc-kind',
metavar='kind',
action='store',
dest='bc_kind',
choices=['free', 'cantilever', 'fixed'],
default='free',
help=helps['bc_kind'])
parser.add_argument('-a',
'--axis',
metavar='0, ..., dim, or -1',
type=int,
action='store',
dest='axis',
default=-1,
help=helps['axis'])
parser.add_argument('--young',
metavar='float',
type=float,
action='store',
dest='young',
default=200e+9,
help=helps['young'])
parser.add_argument('--poisson',
metavar='float',
type=float,
action='store',
dest='poisson',
default=0.3,
help=helps['poisson'])
parser.add_argument('--density',
metavar='float',
type=float,
action='store',
dest='density',
default=7800.0,
help=helps['density'])
parser.add_argument('--order',
metavar='int',
type=int,
action='store',
dest='order',
default=1,
help=helps['order'])
parser.add_argument('-n',
'--n-eigs',
metavar='int',
type=int,
action='store',
dest='n_eigs',
default=6,
help=helps['n_eigs'])
parser.add_argument('-i',
'--ignore',
metavar='int',
type=int,
action='store',
dest='ignore',
default=None,
help=helps['ignore'])
parser.add_argument('--solver', metavar='solver', action='store',
dest='solver',
default= \
"eig.scipy,method:'eigh',tol:1e-5,maxiter:1000",
help=helps['solver'])
parser.add_argument('--show',
action="store_true",
dest='show',
default=False,
help=helps['show'])
#parser.add_argument('filename', nargs='?', default=None)
#read block.mesh
#parser.add_argument('filename', nargs='?', default="platehexat200mm.mesh")
parser.add_argument('filename', nargs='?', default="block_1m.mesh")
options = parser.parse_args()
aux = options.solver.split(',')
kwargs = {}
for option in aux[1:]:
key, val = option.split(':')
kwargs[key.strip()] = eval(val)
eig_conf = Struct(name='evp', kind=aux[0], **kwargs)
output('using values:')
output(" Young's modulus:", options.young)
output(" Poisson's ratio:", options.poisson)
output(' density:', options.density)
output('displacement field approximation order:', options.order)
output('requested %d eigenvalues' % options.n_eigs)
output('using eigenvalue problem solver:', eig_conf.kind)
output.level += 1
for key, val in six.iteritems(kwargs):
output('%s: %r' % (key, val))
output.level -= 1
assert_((0.0 < options.poisson < 0.5),
"Poisson's ratio must be in ]0, 0.5[!")
assert_((0 < options.order),
'displacement approximation order must be at least 1!')
filename = options.filename
if filename is not None:
mesh = Mesh.from_file(filename)
dim = mesh.dim
dims = nm.diff(mesh.get_bounding_box(), axis=0)
else:
dims = nm.array(eval(options.dims), dtype=nm.float64)
dim = len(dims)
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
output('dimensions:', dims)
output('centre: ', centre)
output('shape: ', shape)
mesh = gen_block_mesh(dims, shape, centre, name='mesh')
output('axis: ', options.axis)
assert_((-dim <= options.axis < dim), 'invalid axis value!')
eig_solver = Solver.any_from_conf(eig_conf)
# Build the problem definition.
domain = FEDomain('domain', mesh)
bbox = domain.get_mesh_bounding_box()
min_coor, max_coor = bbox[:, options.axis]
eps = 1e-8 * (max_coor - min_coor)
ax = 'xyz'[:dim][options.axis]
omega = domain.create_region('Omega', 'all')
"""
bottom = domain.create_region('Bottom',
'vertices in (%s < %.10f)'
% (ax, min_coor + eps),
'facet')
bottom_top = domain.create_region('BottomTop',
'r.Bottom +v vertices in (%s > %.10f)'
% (ax, max_coor - eps),
'facet')
"""
#import pdb; pdb.set_trace()
left = domain.create_region('left', 'vertices in (x < -0.49)', 'facet')
field = Field.from_args('fu',
nm.float64,
'vector',
omega,
approx_order=options.order)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
mtx_d = stiffness_from_youngpoisson(dim, options.young, options.poisson)
m = Material('m', D=mtx_d, rho=options.density)
integral = Integral('i', order=2 * options.order)
t1 = Term.new('dw_lin_elastic(m.D, v, u)', integral, omega, m=m, v=v, u=u)
t2 = Term.new('dw_volume_dot(m.rho, v, u)', integral, omega, m=m, v=v, u=u)
eq1 = Equation('stiffness', t1)
eq2 = Equation('mass', t2)
lhs_eqs = Equations([eq1, eq2])
pb = Problem('modal', equations=lhs_eqs)
"""
if options.bc_kind == 'free':
pb.time_update()
n_rbm = dim * (dim + 1) // 2
elif options.bc_kind == 'cantilever':
fixed = EssentialBC('Fixed', bottom, {'u.all' : 0.0})
pb.time_update(ebcs=Conditions([fixed]))
n_rbm = 0
elif options.bc_kind == 'fixed':
fixed = EssentialBC('Fixed', bottom_top, {'u.all' : 0.0})
pb.time_update(ebcs=Conditions([fixed]))
n_rbm = 0
else:
raise ValueError('unsupported BC kind! (%s)' % options.bc_kind)
if options.ignore is not None:
n_rbm = options.ignore
"""
fixed = EssentialBC('Fixed', left, {'u.all': 0.0})
pb.time_update(ebcs=Conditions([fixed]))
n_rbm = 0
pb.update_materials()
# Assemble stiffness and mass matrices.
mtx_k = eq1.evaluate(mode='weak', dw_mode='matrix', asm_obj=pb.mtx_a)
mtx_m = mtx_k.copy()
mtx_m.data[:] = 0.0
mtx_m = eq2.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx_m)
try:
eigs, svecs = eig_solver(mtx_k,
mtx_m,
options.n_eigs + n_rbm,
eigenvectors=True)
except sla.ArpackNoConvergence as ee:
eigs = ee.eigenvalues
svecs = ee.eigenvectors
output('only %d eigenvalues converged!' % len(eigs))
output('%d eigenvalues converged (%d ignored as rigid body modes)' %
(len(eigs), n_rbm))
eigs = eigs[n_rbm:]
svecs = svecs[:, n_rbm:]
omegas = nm.sqrt(eigs)
freqs = omegas / (2 * nm.pi)
output('number | eigenvalue | angular frequency '
'| frequency')
for ii, eig in enumerate(eigs):
output('%6d | %17.12e | %17.12e | %17.12e' %
(ii + 1, eig, omegas[ii], freqs[ii]))
# Make full eigenvectors (add DOFs fixed by boundary conditions).
variables = pb.get_variables()
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=nm.float64)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
for ii in range(eigs.shape[0]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
strain = pb.evaluate('ev_cauchy_strain.i.Omega(u)',
integrals=Integrals([integral]),
mode='el_avg',
verbose=False)
out['u%03d' % ii] = aux.popitem()[1]
out['strain%03d' % ii] = Struct(mode='cell', data=strain)
pb.save_state('eigenshapes.vtk', out=out)
pb.save_regions_as_groups('regions')
if len(eigs) and options.show:
# Show the solution. If the approximation order is greater than 1, the
# extra DOFs are simply thrown away.
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.domain_specific import DomainSpecificPlot
scaling = 0.05 * dims.max() / nm.abs(vecs).max()
ds = {}
for ii in range(eigs.shape[0]):
pd = DomainSpecificPlot('plot_displacements', [
'rel_scaling=%s' % scaling, 'color_kind="tensors"',
'color_name="strain%03d"' % ii
])
ds['u%03d' % ii] = pd
view = Viewer('eigenshapes.vtk')
view(domain_specific=ds,
only_names=sorted(ds.keys()),
is_scalar_bar=False,
is_wireframe=True)
set_bc_fun = Function('set_bc_impl', set_bc_impl)
bc1 = EssentialBC('Gamma_Left', gammaL, {'t.0': set_bc_fun})
bc2 = EssentialBC('Gamma_Right', gammaR, {'t.0': set_bc_fun})
bc3 = EssentialBC('Gamma_Top', gammaT, {'t.0': set_bc_fun})
bc4 = EssentialBC('Gamma_Bottom', gammaB, {'t.0': set_bc_fun})
ls = ScipyDirect({})
nls_status = IndexedStruct()
newtonConfig = {'i_max': 10, 'eps_a': 1e-10, 'eps_r': 1}
nls = Newton(newtonConfig, lin_solver=ls, status=nls_status)
pb = Problem('Poisson', equations=eqs, nls=nls, ls=ls)
pb.save_regions_as_groups('regions')
# pb.time_update(ebcs=Conditions([fix_u, t1, t2]))
pb.time_update(ebcs=Conditions([bc1, bc2, bc3, bc4]))
vec = pb.solve()
print nls_status
pb.save_state('customCylinder.vtk', vec)
# if options.show:
# view = Viewer('customCylinder.vtk')
# view(vector_mode='warp_norm', rel_scaling=2,
# is_scalar_bar=True, is_wireframe=True)
solutionData = vec.vec.reshape(100, 100)
def _solve(self, property_array):
"""
Solve the Sfepy problem for one sample.
Args:
property_array: array of shape (Nx, Ny, 2) where the last
index is for Lame's parameter and shear modulus,
respectively.
Returns:
the strain field of shape (Nx, Ny, 2) where the last
index represents the x and y displacements
"""
shape = property_array.shape[:-1]
mesh = self._get_mesh(shape)
domain = Domain('domain', mesh)
region_all = domain.create_region('region_all', 'all')
field = Field.from_args('fu',
np.float64,
'vector',
region_all,
approx_order=2)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
m = self._get_material(property_array, domain)
integral = Integral('i', order=4)
t1 = Term.new('dw_lin_elastic_iso(m.lam, m.mu, v, u)',
integral,
region_all,
m=m,
v=v,
u=u)
eq = Equation('balance_of_forces', t1)
eqs = Equations([eq])
epbcs, functions = self._get_periodicBCs(domain)
ebcs = self._get_displacementBCs(domain)
lcbcs = self._get_linear_combinationBCs(domain)
ls = ScipyDirect({})
pb = Problem('elasticity', equations=eqs, auto_solvers=None)
pb.save_regions_as_groups('regions')
pb.time_update(ebcs=ebcs,
epbcs=epbcs,
lcbcs=lcbcs,
functions=functions)
ev = pb.get_evaluator()
nls = Newton({},
lin_solver=ls,
fun=ev.eval_residual,
fun_grad=ev.eval_tangent_matrix)
pb.set_solvers_instances(ls, nls)
vec = pb.solve()
u = vec.create_output_dict()['u'].data
u_reshape = np.reshape(u, (tuple(x + 1 for x in shape) + u.shape[-1:]))
dims = domain.get_mesh_bounding_box().shape[1]
strain = np.squeeze(
pb.evaluate(
'ev_cauchy_strain.{dim}.region_all(u)'.format(dim=dims),
mode='el_avg'))
strain_reshape = np.reshape(strain, (shape + strain.shape[-1:]))
stress = np.squeeze(
pb.evaluate(
'ev_cauchy_stress.{dim}.region_all(m.D, u)'.format(dim=dims),
mode='el_avg'))
stress_reshape = np.reshape(stress, (shape + stress.shape[-1:]))
return strain_reshape, u_reshape, stress_reshape
def _solve(self, property_array):
"""
Solve the Sfepy problem for one sample.
Args:
property_array: array of shape (Nx, Ny, 2) where the last
index is for Lame's parameter and shear modulus,
respectively.
Returns:
the strain field of shape (Nx, Ny, 2) where the last
index represents the x and y displacements
"""
shape = property_array.shape[:-1]
mesh = self._get_mesh(shape)
domain = Domain('domain', mesh)
region_all = domain.create_region('region_all', 'all')
field = Field.from_args('fu', np.float64, 'vector', region_all,
approx_order=2)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
m = self._get_material(property_array, domain)
integral = Integral('i', order=4)
t1 = Term.new('dw_lin_elastic_iso(m.lam, m.mu, v, u)',
integral, region_all, m=m, v=v, u=u)
eq = Equation('balance_of_forces', t1)
eqs = Equations([eq])
epbcs, functions = self._get_periodicBCs(domain)
ebcs = self._get_displacementBCs(domain)
lcbcs = self._get_linear_combinationBCs(domain)
ls = ScipyDirect({})
pb = Problem('elasticity', equations=eqs, auto_solvers=None)
pb.save_regions_as_groups('regions')
pb.time_update(ebcs=ebcs, epbcs=epbcs, lcbcs=lcbcs, functions=functions)
ev = pb.get_evaluator()
nls = Newton({}, lin_solver=ls,
fun=ev.eval_residual, fun_grad=ev.eval_tangent_matrix)
pb.set_solvers_instances(ls, nls)
vec = pb.solve()
u = vec.create_output_dict()['u'].data
u_reshape = np.reshape(u, (tuple(x + 1 for x in shape) + u.shape[-1:]))
dims = domain.get_mesh_bounding_box().shape[1]
strain = np.squeeze(pb.evaluate('ev_cauchy_strain.{dim}.region_all(u)'.format(dim=dims),
mode='el_avg'))
strain_reshape = np.reshape(strain, (shape + strain.shape[-1:]))
stress = np.squeeze(pb.evaluate('ev_cauchy_stress.{dim}.region_all(m.D, u)'.format(dim=dims),
mode='el_avg'))
stress_reshape = np.reshape(stress, (shape + stress.shape[-1:]))
return strain_reshape, u_reshape, stress_reshape
def main():
from sfepy import data_dir
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-s', '--show',
action="store_true", dest='show',
default=False, help=help['show'])
options, args = parser.parse_args()
options_probe = True
folder = str(uuid.uuid4())
os.mkdir(folder)
os.chdir(folder)
file = open('README.txt', 'w')
file.write('DIMENSIONS\n')
file.write('Lx = '+str(dims[0])+' Ly = '+str(dims[1])+' Lz = '+str(dims[2])+'\n')
file.write('DISCRETIZATION (NX, NY, NZ)\n')
file.write(str(NX)+' '+str(NY)+' '+str(NZ)+'\n')
file.write('MATERIALS\n')
file.write(str(E_f)+' '+str(nu_f)+' '+str(E_m)+' '+str(nu_m)+'\n')
#mesh = Mesh.from_file(data_dir + '/meshes/2d/rectangle_tri.mesh')
mesh = mesh_generators.gen_block_mesh(dims,shape,centre,name='block')
domain = FEDomain('domain', mesh)
min_x, max_x = domain.get_mesh_bounding_box()[:,0]
min_y, max_y = domain.get_mesh_bounding_box()[:,1]
min_z, max_z = domain.get_mesh_bounding_box()[:,2]
eps = 1e-8 * (max_x - min_x)
print min_x, max_x
print min_y, max_y
print min_z, max_z
R1 = domain.create_region('Ym',
'vertices in z < %.10f' % (max_z/2))
R2 = domain.create_region('Yf',
'vertices in z >= %.10f' % (min_z/2))
omega = domain.create_region('Omega', 'all')
gamma1 = domain.create_region('Left',
'vertices in x < %.10f' % (min_x + eps),
'facet')
gamma2 = domain.create_region('Right',
'vertices in x > %.10f' % (max_x - eps),
'facet')
gamma3 = domain.create_region('Front',
'vertices in y < %.10f' % (min_y + eps),
'facet')
gamma4 = domain.create_region('Back',
'vertices in y > %.10f' % (max_y - eps),
'facet')
gamma5 = domain.create_region('Bottom',
'vertices in z < %.10f' % (min_z + eps),
'facet')
gamma6 = domain.create_region('Top',
'vertices in z > %.10f' % (max_z - eps),
'facet')
field = Field.from_args('fu', nm.float64, 'vector', omega, approx_order=2)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
mu=1.1
lam=1.0
m = Material('m', lam=lam, mu=mu)
f = Material('f', val=[[0.0], [0.0],[0.0]])
#mu,lam=m.get_constants_mu_lam()
#print mu.lam
D = stiffness_from_lame(3,lam, mu)
mat = Material('Mat', D=D)
#D = stiffness_from_youngpoisson(2, options.young, options.poisson)
get_mat = Function('get_mat1',get_mat1)
#get_mat1=Function('get_mat', (lambda ts, coors, mode=None, problem=None, **kwargs:
# get_mat(coors, mode, problem)))
#mat = Material('Mat', function=Function('get_mat1',get_mat1))
#mat = Material('Mat', 'get_mat')
integral = Integral('i', order=3)
t1 = Term.new('dw_lin_elastic(Mat.D, v, u)',
integral, omega, Mat=mat, v=v, u=u)
t2 = Term.new('dw_volume_lvf(f.val, v)', integral, omega, f=f, v=v)
eq = Equation('balance', t1 + t2)
eqs = Equations([eq])
fix_u = EssentialBC('fix_u', gamma1, {'u.all' : 0.0})
left_bc = EssentialBC('Left', gamma1, {'u.0' : 0.0})
right_bc = EssentialBC('Right', gamma2, {'u.0' : 0.0})
back_bc = EssentialBC('Front', gamma3, {'u.1' : 0.0})
front_bc = EssentialBC('Back', gamma4, {'u.1' : 0.0})
bottom_bc = EssentialBC('Bottom', gamma5, {'u.all' : 0.0})
top_bc = EssentialBC('Top', gamma6, {'u.2' : 0.2})
bc=[left_bc,right_bc,back_bc,front_bc,bottom_bc,top_bc]
#bc=[bottom_bc,top_bc]
bc_fun = Function('shift_u_fun', shift_u_fun, extra_args={'shift' : 0.01})
shift_u = EssentialBC('shift_u', gamma2, {'u.0' : bc_fun})
#get_mat = Function('get_mat1',get_mat1)
#mat = Material('Mat', function=Function('get_mat1',get_mat1))
#ls = ScipyDirect({'method':'umfpack'})
##############################
# ##### SOLVER SECTION #####
##############################
# GET MATRIX FOR PRECONTITIONER #
#ls = ScipyIterative({'method':'bicgstab','i_max':5000,'eps_r':1e-10})
#ls = ScipyIterative({})
#ls = PyAMGSolver({'i_max':5000,'eps_r':1e-10})
#conf = Struct(method='cg', precond='gamg', sub_precond=None,i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
#ls = PETScKrylovSolver({'method' : 'cg', 'precond' : 'icc', 'eps_r' : 1e-10, 'i_max' : 5000})
conf = Struct(method='bcgsl', precond='jacobi', sub_precond=None,
i_max=10000, eps_a=1e-50, eps_r=1e-10, eps_d=1e4,
verbose=True)
#conf = Struct(method = 'cg', precond = 'icc', eps_r = 1e-10, i_max = 5000)
ls = PETScKrylovSolver(conf)
#if hasattr(ls.name,'ls.scipy_iterative'):
file.write(str(ls.name)+' '+str(ls.conf.method)+' '+str(ls.conf.precond)+' '+str(ls.conf.eps_r)+' '+str(ls.conf.i_max)+'\n' )
# else:
#file.write(str(ls.name)+' '+str(ls.conf.method)+'\n')
# conf = Struct(method='bcgsl', precond='jacobi', sub_precond=None,
# i_max=10000, eps_a=1e-50, eps_r=1e-8, eps_d=1e4,
# verbose=True)
#ls = PETScKrylovSolver(conf)
#ls = ScipyIterative({'method':'bicgstab','i_max':100,'eps_r':1e-10})
nls_status = IndexedStruct()
nls = Newton({'i_max':1,'eps_a':1e-10}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
dd=pb.get_materials()['Mat']
dd.set_function(get_mat1)
pb.save_regions_as_groups('regions')
#pb.time_update(ebcs=Conditions([fix_u, shift_u]))
pb.time_update(ebcs=Conditions(bc))
pb.save_regions_as_groups('regions')
#ls = ScipyIterative({'method':'bicgstab','i_max':100,'eps_r':1e-10})
# A = pb.mtx_a
# M = spilu(A,fill_factor = 1)
#conf = Struct(solvers ='ScipyIterative',method='bcgsl', sub_precond=None,
# i_max=1000, eps_r=1e-8)
#pb.set_conf_solvers(conf)
vec = pb.solve()
print nls_status
file.write('TIME TO SOLVE\n')
file.write(str(nls.status.time_stats['solve'])+'\n')
file.write('TIME TO CREATE MATRIX\n')
file.write(str(nls.status.time_stats['matrix'])+'\n')
#out = post_process(out, pb, state, extend=False)
ev = pb.evaluate
out = vec.create_output_dict()
strain = ev('ev_cauchy_strain.3.Omega(u)', mode='el_avg')
stress = ev('ev_cauchy_stress.3.Omega(Mat.D, u)', mode='el_avg',
copy_materials=False)
out['cauchy_strain'] = Struct(name='output_data', mode='cell',
data=strain, dofs=None)
out['cauchy_stress'] = Struct(name='output_data', mode='cell',
data=stress, dofs=None)
# Postprocess the solution.
#out = vec.create_output_dict()
#out = stress_strain(out, pb, vec,lam,mu, extend=True)
#pb.save_state('its2D_interactive.vtk', out=out)
#print 'aqui estoy'
pb.save_state('strain.vtk', out=out)
#pb.save_state('disp.vtk', out=vec)
#print 'ahora estoy aqui'
#out = stress_strain(out, pb, vec, extend=True)
#pb.save_state('out.vtk', out=out)
print nls_status
order = 3
strain_qp = ev('ev_cauchy_strain.%d.Omega(u)' % order, mode='qp')
stress_qp = ev('ev_cauchy_stress.%d.Omega(Mat.D, u)' % order,
mode='qp', copy_materials=False)
file.close()
options_probe=False
if options_probe:
# Probe the solution.
probes, labels = gen_lines(pb)
nls_options = {'eps_a':1e-8,'i_max':1}
ls = ScipyDirect({})
ls2 = ScipyIterative({'method':'bicgstab','i_max':5000,'eps_r':1e-20})
order = 5
sfield = Field.from_args('sym_tensor', nm.float64, (3,), omega,
approx_order=order-1)
stress = FieldVariable('stress', 'parameter', sfield,
primary_var_name='(set-to-None)')
strain = FieldVariable('strain', 'parameter', sfield,
primary_var_name='(set-to-None)')
cfield = Field.from_args('component', nm.float64, 1, omega,
approx_order=order-1)
component = FieldVariable('component', 'parameter', cfield,
primary_var_name='(set-to-None)')
ev = pb.evaluate
order = 2*(order - 1) #2 * (2- 1)
print "before strain_qp"
strain_qp = ev('ev_cauchy_strain.%d.Omega(u)' % order, mode='qp')
stress_qp = ev('ev_cauchy_stress.%d.Omega(Mat.D, u)' % order,
mode='qp', copy_materials=False)
print "before projections"
print stress
project_by_component(strain, strain_qp, component, order,ls2,nls_options)
#print 'strain done'
project_by_component(stress, stress_qp, component, order,ls2,nls_options)
print "after projections"
all_results = []
for ii, probe in enumerate(probes):
fig, results = probe_results2(u, strain, stress, probe, labels[ii])
fig.savefig('test_probe_%d.png' % ii)
all_results.append(results)
for ii, results in enumerate(all_results):
output('probe %d:' % ii)
output.level += 2
for key, res in ordered_iteritems(results):
output(key + ':')
val = res[1]
output(' min: %+.2e, mean: %+.2e, max: %+.2e'
% (val.min(), val.mean(), val.max()))
output.level -= 2
def main():
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-d',
'--dims',
metavar='dims',
action='store',
dest='dims',
default='[1.0, 1.0]',
help=helps['dims'])
parser.add_option('-c',
'--centre',
metavar='centre',
action='store',
dest='centre',
default='[0.0, 0.0]',
help=helps['centre'])
parser.add_option('-s',
'--shape',
metavar='shape',
action='store',
dest='shape',
default='[11, 11]',
help=helps['shape'])
parser.add_option('-b',
'--bc-kind',
metavar='kind',
action='store',
dest='bc_kind',
choices=['free', 'clamped'],
default='free',
help=helps['bc_kind'])
parser.add_option('--young',
metavar='float',
type=float,
action='store',
dest='young',
default=6.80e+10,
help=helps['young'])
parser.add_option('--poisson',
metavar='float',
type=float,
action='store',
dest='poisson',
default=0.36,
help=helps['poisson'])
parser.add_option('--density',
metavar='float',
type=float,
action='store',
dest='density',
default=2700.0,
help=helps['density'])
parser.add_option('--order',
metavar='int',
type=int,
action='store',
dest='order',
default=1,
help=helps['order'])
parser.add_option('-n',
'--n-eigs',
metavar='int',
type=int,
action='store',
dest='n_eigs',
default=6,
help=helps['order'])
parser.add_option('',
'--show',
action="store_true",
dest='show',
default=False,
help=helps['show'])
options, args = parser.parse_args()
assert_((0.0 < options.poisson < 0.5),
"Poisson's ratio must be in ]0, 0.5[!")
assert_((0 < options.order),
'displacement approximation order must be at least 1!')
dims = nm.array(eval(options.dims), dtype=nm.float64)
dim = len(dims)
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
output('dimensions:', dims)
output('centre: ', centre)
output('shape: ', shape)
output('using values:')
output(" Young's modulus:", options.young)
output(" Poisson's ratio:", options.poisson)
output(' density:', options.density)
# Build the problem definition.
mesh = gen_block_mesh(dims, shape, centre, name='mesh')
domain = FEDomain('domain', mesh)
bbox = domain.get_mesh_bounding_box()
min_y, max_y = bbox[:, 1]
eps = 1e-8 * (max_y - min_y)
omega = domain.create_region('Omega', 'all')
bottom = domain.create_region('Bottom',
'vertices in (y < %.10f)' % (min_y + eps),
'facet')
field = Field.from_args('fu',
nm.float64,
'vector',
omega,
approx_order=options.order)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
mtx_d = stiffness_from_youngpoisson(dim, options.young, options.poisson)
m = Material('m', D=mtx_d, rho=options.density)
integral = Integral('i', order=2 * options.order)
t1 = Term.new('dw_lin_elastic(m.D, v, u)', integral, omega, m=m, v=v, u=u)
t2 = Term.new('dw_volume_dot(m.rho, v, u)', integral, omega, m=m, v=v, u=u)
eq1 = Equation('stiffness', t1)
eq2 = Equation('mass', t2)
lhs_eqs = Equations([eq1, eq2])
pb = Problem('modal', equations=lhs_eqs)
if options.bc_kind == 'free':
pb.time_update()
n_rbm = dim * (dim + 1) / 2
else:
fixed_b = EssentialBC('FixedB', bottom, {'u.all': 0.0})
pb.time_update(ebcs=Conditions([fixed_b]))
n_rbm = 0
pb.update_materials()
# Assemble stiffness and mass matrices.
mtx_k = eq1.evaluate(mode='weak', dw_mode='matrix', asm_obj=pb.mtx_a)
mtx_m = mtx_k.copy()
mtx_m.data[:] = 0.0
mtx_m = eq2.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx_m)
try:
eigs, svecs = sla.eigsh(mtx_k,
k=options.n_eigs + n_rbm,
M=mtx_m,
which='SM',
tol=1e-5,
maxiter=10000)
except sla.ArpackNoConvergence as ee:
eigs = ee.eigenvalues
svecs = ee.eigenvectors
output('only %d eigenvalues converged!' % len(eigs))
eigs = eigs[n_rbm:]
svecs = svecs[:, n_rbm:]
output('eigenvalues:', eigs)
output('eigen-frequencies:', nm.sqrt(eigs))
# Make full eigenvectors (add DOFs fixed by boundary conditions).
variables = pb.get_variables()
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=nm.float64)
for ii in xrange(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
for ii in xrange(eigs.shape[0]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
strain = pb.evaluate('ev_cauchy_strain.i.Omega(u)',
integrals=Integrals([integral]),
mode='el_avg',
verbose=False)
out['u%03d' % ii] = aux.popitem()[1]
out['strain%03d' % ii] = Struct(mode='cell', data=strain)
pb.save_state('eigenshapes.vtk', out=out)
pb.save_regions_as_groups('regions')
if options.show:
# Show the solution. If the approximation order is greater than 1, the
# extra DOFs are simply thrown away.
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.domain_specific import DomainSpecificPlot
scaling = 0.05 * dims.max() / nm.abs(vecs).max()
ds = {}
for ii in xrange(eigs.shape[0]):
pd = DomainSpecificPlot('plot_displacements', [
'rel_scaling=%s' % scaling, 'color_kind="tensors"',
'color_name="strain%03d"' % ii
])
ds['u%03d' % ii] = pd
view = Viewer('eigenshapes.vtk')
view(domain_specific=ds,
only_names=sorted(ds.keys()),
is_scalar_bar=False,
is_wireframe=True)