def from_conf(conf, options): import sfepy from sfepy.discrete.fem import Mesh, FEDomain, Field mesh = Mesh.from_file('meshes/2d/rectangle_tri.mesh', prefix_dir=sfepy.data_dir) domain = FEDomain('domain', mesh) dim = domain.shape.dim 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) test = Test(conf=conf, options=options, dim=dim, omega=omega, gamma1=gamma1, gamma2=gamma2, field=field) return test
def test_evaluate_at(self): from sfepy import data_dir from sfepy.discrete.fem import Mesh from sfepy.discrete import Variables from sfepy.discrete.fem import FEDomain, Field meshes = { 'tp': Mesh.from_file(data_dir + '/meshes/3d/block.mesh'), } datas = gen_datas(meshes) fields = { 'scalar_tp': ((1, 1), 'Omega', 1), 'vector_tp': ((3, 1), 'Omega', 1), } ok = True for field_name in ['scalar_tp', 'vector_tp']: d = FEDomain('d', meshes['tp']) d.create_region('Omega', 'all') f = fields[field_name] field = Field.from_args('f', nm.complex128, f[0], d.regions[f[1]], approx_order=f[2]) ff = {field.name: field} vv = Variables.from_conf(transform_variables(variables), ff) u = vv['u'] bbox = d.get_mesh_bounding_box() t = nm.expand_dims(nm.linspace(0, 1, 100), 1) coors = nm.expand_dims(bbox[1] - bbox[0], 0) * t + bbox[0] data_r = datas[field_name] data_i = 2. / (1 + datas[field_name]) u.set_from_mesh_vertices(data_r) vals_r = u.evaluate_at(coors) u.set_from_mesh_vertices(data_i) vals_i = u.evaluate_at(coors) u.set_from_mesh_vertices(data_r + data_i * 1j) vals = u.evaluate_at(coors) _ok = nm.allclose(vals_r + vals_i * 1j, vals, rtol=0.0, atol=1e-12) _ok = _ok and nm.abs(vals).sum() > 1 self.report('evaluating complex field %s: %s' % (field_name, _ok)) ok = ok and _ok return ok
def test_evaluate_at(self): from sfepy import data_dir from sfepy.discrete.fem import Mesh from sfepy.discrete import Variables from sfepy.discrete.fem import FEDomain, Field meshes = { 'tp' : Mesh.from_file(data_dir + '/meshes/3d/block.mesh'), } datas = gen_datas(meshes) fields = { 'scalar_tp' : ((1,1), 'Omega', 1), 'vector_tp' : ((3,1), 'Omega', 1), } ok = True for field_name in ['scalar_tp', 'vector_tp']: d = FEDomain('d', meshes['tp']) d.create_region('Omega', 'all') f = fields[field_name] field = Field.from_args('f', nm.complex128, f[0], d.regions[f[1]], approx_order=f[2]) ff = {field.name : field} vv = Variables.from_conf(transform_variables(variables), ff) u = vv['u'] bbox = d.get_mesh_bounding_box() t = nm.expand_dims(nm.linspace(0, 1, 100), 1) coors = nm.expand_dims(bbox[1] - bbox[0], 0) * t + bbox[0] data_r = datas[field_name] data_i = 2. / (1 + datas[field_name]) u.set_from_mesh_vertices(data_r) vals_r = u.evaluate_at(coors) u.set_from_mesh_vertices(data_i) vals_i = u.evaluate_at(coors) u.set_from_mesh_vertices(data_r + data_i * 1j) vals = u.evaluate_at(coors) _ok = nm.allclose(vals_r + vals_i * 1j, vals, rtol=0.0, atol=1e-12) _ok = _ok and nm.abs(vals).sum() > 1 self.report('evaluating complex field %s: %s' % (field_name, _ok)) ok = ok and _ok return ok
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(cli_args): dims = parse_argument_list(cli_args.dims, float) shape = parse_argument_list(cli_args.shape, int) centre = parse_argument_list(cli_args.centre, float) material_parameters = parse_argument_list(cli_args.material_parameters, float) order = cli_args.order ts_vals = cli_args.ts.split(',') ts = { 't0' : float(ts_vals[0]), 't1' : float(ts_vals[1]), 'n_step' : int(ts_vals[2])} do_plot = cli_args.plot ### Mesh and regions ### mesh = gen_block_mesh( dims, shape, centre, name='block', verbose=False) domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') lbn, rtf = domain.get_mesh_bounding_box() box_regions = define_box_regions(3, lbn, rtf) regions = dict([ [r, domain.create_region(r, box_regions[r][0], box_regions[r][1])] for r in box_regions]) ### Fields ### scalar_field = Field.from_args( 'fu', np.float64, 'scalar', omega, approx_order=order-1) vector_field = Field.from_args( 'fv', np.float64, 'vector', omega, approx_order=order) u = FieldVariable('u', 'unknown', vector_field, history=1) v = FieldVariable('v', 'test', vector_field, primary_var_name='u') p = FieldVariable('p', 'unknown', scalar_field, history=1) q = FieldVariable('q', 'test', scalar_field, primary_var_name='p') ### Material ### c10, c01 = material_parameters m = Material( 'm', mu=2*c10, kappa=2*c01, ) ### Boundary conditions ### x_sym = EssentialBC('x_sym', regions['Left'], {'u.0' : 0.0}) y_sym = EssentialBC('y_sym', regions['Near'], {'u.1' : 0.0}) z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2' : 0.0}) disp_fun = Function('disp_fun', get_displacement) displacement = EssentialBC( 'displacement', regions['Right'], {'u.0' : disp_fun}) ebcs = Conditions([x_sym, y_sym, z_sym, displacement]) ### Terms and equations ### integral = Integral('i', order=2*order) term_neohook = Term.new( 'dw_tl_he_neohook(m.mu, v, u)', integral, omega, m=m, v=v, u=u) term_mooney = Term.new( 'dw_tl_he_mooney_rivlin(m.kappa, v, u)', integral, omega, m=m, v=v, u=u) term_pressure = Term.new( 'dw_tl_bulk_pressure(v, u, p)', integral, omega, v=v, u=u, p=p) term_volume_change = Term.new( 'dw_tl_volume(q, u)', integral, omega, q=q, u=u, term_mode='volume') term_volume = Term.new( 'dw_volume_integrate(q)', integral, omega, q=q) eq_balance = Equation('balance', term_neohook+term_mooney+term_pressure) eq_volume = Equation('volume', term_volume_change-term_volume) equations = Equations([eq_balance, eq_volume]) ### Solvers ### ls = ScipyDirect({}) nls_status = IndexedStruct() nls = Newton( {'i_max' : 5}, lin_solver=ls, status=nls_status ) ### Problem ### pb = Problem('hyper', equations=equations) pb.set_bcs(ebcs=ebcs) pb.set_ics(ics=Conditions([])) tss = SimpleTimeSteppingSolver(ts, nls=nls, context=pb) pb.set_solver(tss) ### Solution ### axial_stress = [] axial_displacement = [] def stress_strain_fun(*args, **kwargs): return stress_strain( *args, order=order, global_stress=axial_stress, global_displacement=axial_displacement, **kwargs) pb.solve(save_results=True, post_process_hook=stress_strain_fun) if do_plot: plot_graphs( material_parameters, axial_stress, axial_displacement, undeformed_length=dims[0])
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()
eig_conf = Struct(name='evp', kind=aux[0], **kwargs) dims = nm.array([1.0, 1.5], dtype=nm.float64) dim = len(dims) centre = nm.array([0.0, 0.0], dtype=nm.float64)[:dim] shape = nm.array([11, 16], dtype=nm.int32)[:dim] mesh = gen_block_mesh(dims, shape, centre, name='mesh') 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[:, -1] eps = 1e-8 * (max_coor - min_coor) ax = 'xyz'[:dim][-1] 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=1) u = FieldVariable('u', 'unknown', field) v = FieldVariable('v', 'test', field, primary_var_name = 'u') mtx_d = stiffness_from_youngpoisson(dim, 6.80, 0.36) young = 6.8
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(cli_args): dims = parse_argument_list(cli_args.dims, float) shape = parse_argument_list(cli_args.shape, int) centre = parse_argument_list(cli_args.centre, float) material_parameters = parse_argument_list(cli_args.material_parameters, float) order = cli_args.order ts_vals = cli_args.ts.split(',') ts = { 't0': float(ts_vals[0]), 't1': float(ts_vals[1]), 'n_step': int(ts_vals[2]) } do_plot = cli_args.plot ### Mesh and regions ### mesh = gen_block_mesh(dims, shape, centre, name='block', verbose=False) domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') lbn, rtf = domain.get_mesh_bounding_box() box_regions = define_box_regions(3, lbn, rtf) regions = dict( [[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])] for r in box_regions]) ### Fields ### scalar_field = Field.from_args('fu', np.float64, 'scalar', omega, approx_order=order - 1) vector_field = Field.from_args('fv', np.float64, 'vector', omega, approx_order=order) u = FieldVariable('u', 'unknown', vector_field, history=1) v = FieldVariable('v', 'test', vector_field, primary_var_name='u') p = FieldVariable('p', 'unknown', scalar_field, history=1) q = FieldVariable('q', 'test', scalar_field, primary_var_name='p') ### Material ### c10, c01 = material_parameters m = Material( 'm', mu=2 * c10, kappa=2 * c01, ) ### Boundary conditions ### x_sym = EssentialBC('x_sym', regions['Left'], {'u.0': 0.0}) y_sym = EssentialBC('y_sym', regions['Near'], {'u.1': 0.0}) z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2': 0.0}) disp_fun = Function('disp_fun', get_displacement) displacement = EssentialBC('displacement', regions['Right'], {'u.0': disp_fun}) ebcs = Conditions([x_sym, y_sym, z_sym, displacement]) ### Terms and equations ### integral = Integral('i', order=2 * order) term_neohook = Term.new('dw_tl_he_neohook(m.mu, v, u)', integral, omega, m=m, v=v, u=u) term_mooney = Term.new('dw_tl_he_mooney_rivlin(m.kappa, v, u)', integral, omega, m=m, v=v, u=u) term_pressure = Term.new('dw_tl_bulk_pressure(v, u, p)', integral, omega, v=v, u=u, p=p) term_volume_change = Term.new('dw_tl_volume(q, u)', integral, omega, q=q, u=u, term_mode='volume') term_volume = Term.new('dw_volume_integrate(q)', integral, omega, q=q) eq_balance = Equation('balance', term_neohook + term_mooney + term_pressure) eq_volume = Equation('volume', term_volume_change - term_volume) equations = Equations([eq_balance, eq_volume]) ### Solvers ### ls = ScipyDirect({}) nls_status = IndexedStruct() nls = Newton({'i_max': 5}, lin_solver=ls, status=nls_status) ### Problem ### pb = Problem('hyper', equations=equations) pb.set_bcs(ebcs=ebcs) pb.set_ics(ics=Conditions([])) tss = SimpleTimeSteppingSolver(ts, nls=nls, context=pb) pb.set_solver(tss) ### Solution ### axial_stress = [] axial_displacement = [] def stress_strain_fun(*args, **kwargs): return stress_strain(*args, order=order, global_stress=axial_stress, global_displacement=axial_displacement, **kwargs) pb.solve(save_results=True, post_process_hook=stress_strain_fun) if do_plot: plot_graphs(material_parameters, axial_stress, axial_displacement, undeformed_length=dims[0])
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(): 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)
from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer import matplotlib.pyplot as plt print "inside main" from sfepy import data_dir #mesh = Mesh.from_file(data_dir + '/meshes/2d/rectangle_tri.mesh') mesh = gen_block_mesh([2], [100, 100], [0, 0], coors=[-2, 2]) 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') gammaL = domain.create_region('Gamma_Left', 'vertices in x < %.9f' % (min_x + eps), 'facet') gammaR = domain.create_region('Gamma_Right', 'vertices in x > %.9f' % (max_x - eps), 'facet') min_y, max_y = domain.get_mesh_bounding_box()[:, 1] eps = 1e-8 * (max_y - min_y) gammaT = domain.create_region('Gamma_Top', 'vertices in y < %.9f' % (min_y + eps), 'facet') gammaB = domain.create_region('Gamma_Bottom', 'vertices in y > %.9f' % (max_y - eps), 'facet') # def get_forcing_term(coors, domain=None):
from sfepy.base.base import IndexedStruct from sfepy.discrete import (FieldVariable, Material, Integral, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson from sfepy.mechanics.tensors import get_von_mises_stress mesh = Mesh.from_file('meshes/strut_test.vtk') domain = FEDomain('domain', mesh) min_z, max_z = domain.get_mesh_bounding_box()[:, 2] eps = 1e-4 * (max_z - min_z) omega = domain.create_region('Omega', 'all') bot = domain.create_region('Bot', 'vertices in z < %.10f' % (min_z + eps), 'vertex') top = domain.create_region('Top', 'vertices in z > %.10f' % (max_z - eps), 'vertex') field = Field.from_args('fu', np.float64, 'vector', omega, approx_order=1) u = FieldVariable('u', 'unknown', field) v = FieldVariable('v', 'test', field, primary_var_name='u') m = Material('m', D=stiffness_from_youngpoisson(dim=3, young=6.8e10, poisson=0.36), rho=2700.0)
def _solve(self, property_array): """ Solve the Sfepy problem for one sample. Args: property_array: array of shape (n_x, n_y, 2) where the last index is for Lame's parameter and shear modulus, respectively. Returns: the strain field of shape (n_x, n_y, 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, # pylint: disable=no-member 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.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) try: pb.set_solvers_instances(ls, nls) except AttributeError: pb.set_solver(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', copy_materials=False)) 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', copy_materials=False)) stress_reshape = np.reshape(stress, (shape + stress.shape[-1:])) return strain_reshape, u_reshape, stress_reshape
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(): 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 = 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)