def test_solving(self): from sfepy.base.base import IndexedStruct from sfepy.discrete import (FieldVariable, Material, Problem, Function, Equation, Equations, Integral) from sfepy.discrete.conditions import Conditions, EssentialBC from sfepy.terms import Term from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.mechanics.matcoefs import stiffness_from_lame u = FieldVariable('u', 'unknown', self.field) v = FieldVariable('v', 'test', self.field, primary_var_name='u') m = Material('m', D=stiffness_from_lame(self.dim, 1.0, 1.0)) f = Material('f', val=[[0.02], [0.01]]) bc_fun = Function('fix_u_fun', fix_u_fun, extra_args={'extra_arg' : 'hello'}) fix_u = EssentialBC('fix_u', self.gamma1, {'u.all' : bc_fun}) shift_u = EssentialBC('shift_u', self.gamma2, {'u.0' : 0.1}) integral = Integral('i', order=3) t1 = Term.new('dw_lin_elastic(m.D, v, u)', integral, self.omega, m=m, v=v, u=u) t2 = Term.new('dw_volume_lvf(f.val, v)', integral, self.omega, f=f, v=v) eq = Equation('balance', t1 + t2) eqs = Equations([eq]) ls = ScipyDirect({}) nls_status = IndexedStruct() nls = Newton({}, lin_solver=ls, status=nls_status) pb = Problem('elasticity', equations=eqs) ## pb.save_regions_as_groups('regions') pb.set_bcs(ebcs=Conditions([fix_u, shift_u])) pb.set_solver(nls) state = pb.solve() name = op.join(self.options.out_dir, 'test_high_level_solving.vtk') pb.save_state(name, state) ok = nls_status.condition == 0 if not ok: self.report('solver did not converge!') _ok = state.has_ebc() if not _ok: self.report('EBCs violated!') ok = ok and _ok return ok
def test_solving(self): from sfepy.base.base import IndexedStruct from sfepy.discrete import (FieldVariable, Material, Problem, Function, Equation, Equations, Integral) from sfepy.discrete.conditions import Conditions, EssentialBC from sfepy.terms import Term from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.mechanics.matcoefs import stiffness_from_lame u = FieldVariable('u', 'unknown', self.field) v = FieldVariable('v', 'test', self.field, primary_var_name='u') m = Material('m', D=stiffness_from_lame(self.dim, 1.0, 1.0)) f = Material('f', val=[[0.02], [0.01]]) bc_fun = Function('fix_u_fun', fix_u_fun, extra_args={'extra_arg' : 'hello'}) fix_u = EssentialBC('fix_u', self.gamma1, {'u.all' : bc_fun}) shift_u = EssentialBC('shift_u', self.gamma2, {'u.0' : 0.1}) integral = Integral('i', order=3) t1 = Term.new('dw_lin_elastic(m.D, v, u)', integral, self.omega, m=m, v=v, u=u) t2 = Term.new('dw_volume_lvf(f.val, v)', integral, self.omega, f=f, v=v) eq = Equation('balance', t1 + t2) eqs = Equations([eq]) 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])) state = pb.solve() name = op.join(self.options.out_dir, 'test_high_level_solving.vtk') pb.save_state(name, state) ok = nls_status.condition == 0 if not ok: self.report('solver did not converge!') _ok = state.has_ebc() if not _ok: self.report('EBCs violated!') ok = ok and _ok return ok
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__.rstrip(), formatter_class=RawDescriptionHelpFormatter) parser.add_argument('output_dir', help=helps['output_dir']) parser.add_argument('--dims', metavar='dims', action='store', dest='dims', default='1.0,1.0,1.0', help=helps['dims']) parser.add_argument('--shape', metavar='shape', action='store', dest='shape', default='7,7,7', help=helps['shape']) parser.add_argument('--centre', metavar='centre', action='store', dest='centre', default='0.0,0.0,0.0', help=helps['centre']) parser.add_argument('-3', '--3d', action='store_true', dest='is_3d', default=False, help=helps['3d']) parser.add_argument('--order', metavar='int', type=int, action='store', dest='order', default=1, help=helps['order']) options = parser.parse_args() dim = 3 if options.is_3d else 2 dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim] shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim] centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim] output('dimensions:', dims) output('shape: ', shape) output('centre: ', centre) mesh0 = gen_block_mesh(dims, shape, centre, name='block-fem', verbose=True) domain0 = FEDomain('d', mesh0) bbox = domain0.get_mesh_bounding_box() min_x, max_x = bbox[:, 0] eps = 1e-8 * (max_x - min_x) cnt = (shape[0] - 1) // 2 g0 = 0.5 * dims[0] grading = nm.array([g0 / 2**ii for ii in range(cnt)]) + eps + centre[0] - g0 domain, subs = refine_towards_facet(domain0, grading, '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, 1, omega, approx_order=options.order) if subs is not None: field.substitute_dofs(subs) u = FieldVariable('u', 'unknown', field) v = FieldVariable('v', 'test', field, primary_var_name='u') integral = Integral('i', order=2*options.order) t1 = Term.new('dw_laplace(v, u)', integral, omega, v=v, u=u) eq = Equation('eq', t1) eqs = Equations([eq]) def u_fun(ts, coors, bc=None, problem=None): """ Define a displacement depending on the y coordinate. """ if coors.shape[1] == 2: min_y, max_y = bbox[:, 1] y = (coors[:, 1] - min_y) / (max_y - min_y) val = (max_y - min_y) * nm.cos(3 * nm.pi * y) else: min_y, max_y = bbox[:, 1] min_z, max_z = bbox[:, 2] y = (coors[:, 1] - min_y) / (max_y - min_y) z = (coors[:, 2] - min_z) / (max_z - min_z) val = ((max_y - min_y) * (max_z - min_z) * nm.cos(3 * nm.pi * y) * (1.0 + 3.0 * (z - 0.5)**2)) return val bc_fun = Function('u_fun', u_fun) fix1 = EssentialBC('shift_u', gamma1, {'u.0' : bc_fun}) fix2 = EssentialBC('fix2', gamma2, {'u.all' : 0.0}) ls = ScipyDirect({}) nls = Newton({}, lin_solver=ls) pb = Problem('heat', equations=eqs, nls=nls, ls=ls) pb.time_update(ebcs=Conditions([fix1, fix2])) state = pb.solve() if subs is not None: field.restore_dofs() filename = os.path.join(options.output_dir, 'hanging.vtk') ensure_path(filename) pb.save_state(filename, state) if options.order > 1: pb.save_state(filename, state, linearization=Struct(kind='adaptive', min_level=0, max_level=8, eps=1e-3))
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('--young', metavar='float', type=float, action='store', dest='young', default=2000.0, help=helps['young']) parser.add_option('--poisson', metavar='float', type=float, action='store', dest='poisson', default=0.4, help=helps['poisson']) parser.add_option('--load', metavar='float', type=float, action='store', dest='load', default=-1000.0, help=helps['load']) parser.add_option('--order', metavar='int', type=int, action='store', dest='order', default=1, help=helps['order']) parser.add_option('-r', '--refine', metavar='int', type=int, action='store', dest='refine', default=0, help=helps['refine']) parser.add_option('-s', '--show', action="store_true", dest='show', default=False, help=helps['show']) parser.add_option('-p', '--probe', action="store_true", dest='probe', default=False, help=helps['probe']) 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!') output('using values:') output(" Young's modulus:", options.young) output(" Poisson's ratio:", options.poisson) output(' vertical load:', options.load) output('uniform mesh refinement level:', options.refine) # Build the problem definition. mesh = Mesh.from_file(data_dir + '/meshes/2d/its2D.mesh') domain = FEDomain('domain', mesh) if options.refine > 0: for ii in range(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) omega = domain.create_region('Omega', 'all') left = domain.create_region('Left', 'vertices in x < 0.001', 'facet') bottom = domain.create_region('Bottom', 'vertices in y < 0.001', 'facet') top = domain.create_region('Top', 'vertex 2', 'vertex') 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') D = stiffness_from_youngpoisson(2, options.young, options.poisson) asphalt = Material('Asphalt', D=D) load = Material('Load', values={'.val' : [0.0, options.load]}) integral = Integral('i', order=2*options.order) integral0 = Integral('i', order=0) t1 = Term.new('dw_lin_elastic(Asphalt.D, v, u)', integral, omega, Asphalt=asphalt, v=v, u=u) t2 = Term.new('dw_point_load(Load.val, v)', integral0, top, Load=load, v=v) eq = Equation('balance', t1 - t2) eqs = Equations([eq]) xsym = EssentialBC('XSym', bottom, {'u.1' : 0.0}) ysym = EssentialBC('YSym', left, {'u.0' : 0.0}) ls = ScipyDirect({}) nls_status = IndexedStruct() nls = Newton({}, lin_solver=ls, status=nls_status) pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls) pb.time_update(ebcs=Conditions([xsym, ysym])) # Solve the problem. state = pb.solve() output(nls_status) # Postprocess the solution. out = state.create_output_dict() out = stress_strain(out, pb, state, extend=True) pb.save_state('its2D_interactive.vtk', out=out) gdata = geometry_data['2_3'] nc = len(gdata.coors) integral_vn = Integral('ivn', coors=gdata.coors, weights=[gdata.volume / nc] * nc) nodal_stress(out, pb, state, integrals=Integrals([integral_vn])) if options.probe: # Probe the solution. probes, labels = gen_lines(pb) sfield = Field.from_args('sym_tensor', nm.float64, 3, omega, approx_order=options.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=options.order - 1) component = FieldVariable('component', 'parameter', cfield, primary_var_name='(set-to-None)') ev = pb.evaluate order = 2 * (options.order - 1) strain_qp = ev('ev_cauchy_strain.%d.Omega(u)' % order, mode='qp') stress_qp = ev('ev_cauchy_stress.%d.Omega(Asphalt.D, u)' % order, mode='qp', copy_materials=False) project_by_component(strain, strain_qp, component, order) project_by_component(stress, stress_qp, component, order) all_results = [] for ii, probe in enumerate(probes): fig, results = probe_results(u, strain, stress, probe, labels[ii]) fig.savefig('its2D_interactive_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 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 view = Viewer('its2D_interactive.vtk') view(vector_mode='warp_norm', rel_scaling=1, 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() 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(): 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)
def main(): from sfepy import data_dir parser = OptionParser(usage=usage, version='%prog') parser.add_option('--young', metavar='float', type=float, action='store', dest='young', default=2000.0, help=helps['young']) parser.add_option('--poisson', metavar='float', type=float, action='store', dest='poisson', default=0.4, help=helps['poisson']) parser.add_option('--load', metavar='float', type=float, action='store', dest='load', default=-1000.0, help=helps['load']) parser.add_option('--order', metavar='int', type=int, action='store', dest='order', default=1, help=helps['order']) parser.add_option('-r', '--refine', metavar='int', type=int, action='store', dest='refine', default=0, help=helps['refine']) parser.add_option('-s', '--show', action="store_true", dest='show', default=False, help=helps['show']) parser.add_option('-p', '--probe', action="store_true", dest='probe', default=False, help=helps['probe']) 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!') output('using values:') output(" Young's modulus:", options.young) output(" Poisson's ratio:", options.poisson) output(' vertical load:', options.load) output('uniform mesh refinement level:', options.refine) # Build the problem definition. mesh = Mesh.from_file(data_dir + '/meshes/2d/its2D.mesh') domain = FEDomain('domain', mesh) if options.refine > 0: for ii in xrange(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) omega = domain.create_region('Omega', 'all') left = domain.create_region('Left', 'vertices in x < 0.001', 'facet') bottom = domain.create_region('Bottom', 'vertices in y < 0.001', 'facet') top = domain.create_region('Top', 'vertex 2', 'vertex') 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') D = stiffness_from_youngpoisson(2, options.young, options.poisson) asphalt = Material('Asphalt', D=D) load = Material('Load', values={'.val': [0.0, options.load]}) integral = Integral('i', order=2 * options.order) integral0 = Integral('i', order=0) t1 = Term.new('dw_lin_elastic(Asphalt.D, v, u)', integral, omega, Asphalt=asphalt, v=v, u=u) t2 = Term.new('dw_point_load(Load.val, v)', integral0, top, Load=load, v=v) eq = Equation('balance', t1 - t2) eqs = Equations([eq]) xsym = EssentialBC('XSym', bottom, {'u.1': 0.0}) ysym = EssentialBC('YSym', left, {'u.0': 0.0}) ls = ScipyDirect({}) nls_status = IndexedStruct() nls = Newton({}, lin_solver=ls, status=nls_status) pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls) pb.time_update(ebcs=Conditions([xsym, ysym])) # Solve the problem. state = pb.solve() output(nls_status) # Postprocess the solution. out = state.create_output_dict() out = stress_strain(out, pb, state, extend=True) pb.save_state('its2D_interactive.vtk', out=out) gdata = geometry_data['2_3'] nc = len(gdata.coors) integral_vn = Integral('ivn', coors=gdata.coors, weights=[gdata.volume / nc] * nc) nodal_stress(out, pb, state, integrals=Integrals([integral_vn])) if options.probe: # Probe the solution. probes, labels = gen_lines(pb) sfield = Field.from_args('sym_tensor', nm.float64, 3, omega, approx_order=options.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=options.order - 1) component = FieldVariable('component', 'parameter', cfield, primary_var_name='(set-to-None)') ev = pb.evaluate order = 2 * (options.order - 1) strain_qp = ev('ev_cauchy_strain.%d.Omega(u)' % order, mode='qp') stress_qp = ev('ev_cauchy_stress.%d.Omega(Asphalt.D, u)' % order, mode='qp', copy_materials=False) project_by_component(strain, strain_qp, component, order) project_by_component(stress, stress_qp, component, order) all_results = [] for ii, probe in enumerate(probes): fig, results = probe_results(u, strain, stress, probe, labels[ii]) fig.savefig('its2D_interactive_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 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 view = Viewer('its2D_interactive.vtk') view(vector_mode='warp_norm', rel_scaling=1, is_scalar_bar=True, is_wireframe=True)
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)
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) xGrid = mesh.coors[:, 0].reshape(100, 100) yGrid = mesh.coors[:, 1].reshape(100, 100) analyticSolution = np.sin(xGrid / np.pi) * np.sin(yGrid / np.pi) errorData = 100 * (solutionData - analyticSolution) / analyticSolution plt.subplot(221) plt.title('numerics')
pb.set_bcs(ebcs=Conditions([fix_bot, fix_top])) pb.set_solver(nls) status = IndexedStruct() state = pb.solve(status=status) strain = pb.evaluate('ev_cauchy_strain.2.Omega(u)', u=u, mode='el_avg') stress = pb.evaluate('ev_cauchy_stress.2.Omega(m.D, u)', m=m, u=u, mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) np.savetxt('tmp_vms.dat', vms) vms = np.loadtxt('tmp_vms.dat') vol = mesh.cmesh.get_volumes(3) np.savetxt('tmp_vol.dat', vol) vol = np.loadtxt('tmp_vol.dat') vm_stresses[i, 0] = np.sum(vms * vol) / np.sum(vol) vm_stresses[i, 1] = np.max(vms) pb.save_state('linear_elasticity_%f.vtk' % z_displacement, state) # show = False # if 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__.rstrip(), formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-o', '--output-dir', default='.', help=helps['output_dir']) parser.add_argument('--R1', metavar='R1', action='store', dest='R1', default='0.5', help=helps['R1']) parser.add_argument('--R2', metavar='R2', action='store', dest='R2', default='1.0', help=helps['R2']) parser.add_argument('--C1', metavar='C1', action='store', dest='C1', default='0.0,0.0', help=helps['C1']) parser.add_argument('--C2', metavar='C2', action='store', dest='C2', default='0.0,0.0', help=helps['C2']) parser.add_argument('--order', metavar='int', type=int, action='store', dest='order', default=2, help=helps['order']) parser.add_argument('-v', '--viewpatch', action='store_true', dest='viewpatch', default=False, help=helps['viewpatch']) options = parser.parse_args() # Creation of the NURBS-patch with igakit R1 = eval(options.R1) R2 = eval(options.R2) C1 = list(eval(options.C1)) C2 = list(eval(options.C2)) order = options.order viewpatch = options.viewpatch create_patch(R1, R2, C1, C2, order=order, viewpatch=viewpatch) # Setting a Domain instance filename_domain = data_dir + '/meshes/iga/concentric_circles.iga' domain = IGDomain.from_file(filename_domain) # Sub-domains omega = domain.create_region('Omega', 'all') Gamma_out = domain.create_region('Gamma_out', 'vertices of set xi01', kind='facet') Gamma_in = domain.create_region('Gamma_in', 'vertices of set xi00', kind='facet') # Field (featuring order elevation) order_increase = order - domain.nurbs.degrees[0] order_increase *= int(order_increase > 0) field = Field.from_args('fu', nm.float64, 'scalar', omega, approx_order='iga', space='H1', poly_space_base='iga') # Variables u = FieldVariable('u', 'unknown', field) # unknown function v = FieldVariable('v', 'test', field, primary_var_name='u') # test function # Integral integral = Integral('i', order=2 * field.approx_order) # Term t = Term.new('dw_laplace( v, u )', integral, omega, v=v, u=u) # Equation eq = Equation('laplace', t) eqs = Equations([eq]) # Boundary Conditions u_in = EssentialBC('u_in', Gamma_in, {'u.all': 7.0}) u_out = EssentialBC('u_out', Gamma_out, {'u.all': 3.0}) # solvers ls = ScipyDirect({}) nls_status = IndexedStruct() nls = Newton({}, lin_solver=ls, status=nls_status) # problem instance pb = Problem('potential', equations=eqs, active_only=True) # Set boundary conditions pb.set_bcs(ebcs=Conditions([u_in, u_out])) # solving pb.set_solver(nls) status = IndexedStruct() state = pb.solve(status=status, save_results=True, verbose=True) # Saving the results to a classic VTK file filename = os.path.join(options.output_dir, 'concentric_circles.vtk') ensure_path(filename) pb.save_state(filename, state)
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)