def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs
def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs
def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out)
def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out)
def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action='store', dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action='store', dest='conf', default=None, help=helps['conf']) parser.add_argument('--mesh-size', type=float, metavar='float', action='store', dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action='store', dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action='store', dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action='store', dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action='store', dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--range', metavar='start,stop,count', action='store', dest='range', default='10,100,10', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action='store', dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action='store', dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action='store', dest='n_eigs', default=6, help=helps['n_eigs']) parser.add_argument('--eigs-only', action='store_true', dest='eigs_only', default=False, help=helps['eigs_only']) parser.add_argument('--solver-conf', metavar='dict-like', action='store', dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-materials', action='store_true', dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action='store_true', dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--silent', action='store_true', dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action='store_true', dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action='store', dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir, 'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod = import_file(options.conf) apply_units = mod.apply_units define = mod.define set_wave_dir = mod.set_wave_dir else: apply_units = apply_units_le define = define_le set_wave_dir = set_wave_dir_le options.pars = [float(ii) for ii in options.pars.split(',')] options.unit_multipliers = [ float(ii) for ii in options.unit_multipliers.split(',') ] options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')] aux = options.range.split(',') options.range = [float(aux[0]), float(aux[1]), int(aux[2])] options.solver_conf = dict_from_string(options.solver_conf) if options.clear: remove_files_patterns(output_dir, ['*.h5', '*.vtk', '*.txt'], ignores=['output_log.txt'], verbose=True) filename = os.path.join(output_dir, 'options.txt') ensure_path(filename) save_options(filename, [('options', vars(options))]) pars = apply_units(options.pars, options.unit_multipliers) output('material parameters with applied unit multipliers:') output(pars) if options.mode == 'omega': rng = copy(options.range) rng[:2] = apply_unit_multipliers(options.range[:2], ['wave_number', 'wave_number'], options.unit_multipliers) output('wave number range with applied unit multipliers:', rng) else: rng = copy(options.range) rng[:2] = apply_unit_multipliers(options.range[:2], ['frequency', 'frequency'], options.unit_multipliers) output('frequency range with applied unit multipliers:', rng) define_problem = functools.partial(define, filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane) conf = ProblemConf.from_dict(define_problem(), sys.modules[__name__]) pb = Problem.from_conf(conf) dim = pb.domain.shape.dim if dim != 2: options.plane = 'strain' wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() if options.save_materials or options.log_std_waves: stiffness = pb.evaluate('ev_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) if options.save_materials: out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) # Set the normalized wave vector direction to the material(s). set_wave_dir(pb.get_materials(), wdir) conf = pb.solver_confs['eig'] eig_solver = Solver.any_from_conf(conf) # Assemble the matrices. mtx_m = pb.mtx_a.copy() eq_m = pb.equations['M'] mtx_m = eq_m.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx_m) mtx_m.eliminate_zeros() mtx_k = pb.mtx_a.copy() eq_k = pb.equations['K'] mtx_k = eq_k.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx_k) mtx_k.eliminate_zeros() mtx_s = pb.mtx_a.copy() eq_s = pb.equations['S'] mtx_s = eq_s.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx_s) mtx_s.eliminate_zeros() mtx_r = pb.mtx_a.copy() eq_r = pb.equations['R'] mtx_r = eq_r.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx_r) mtx_r.eliminate_zeros() output('symmetry checks of real blocks:') output('M - M^T:', _max_diff_csr(mtx_m, mtx_m.T)) output('K - K^T:', _max_diff_csr(mtx_k, mtx_k.T)) output('S - S^T:', _max_diff_csr(mtx_s, mtx_s.T)) output('R + R^T:', _max_diff_csr(mtx_r, -mtx_r.T)) n_eigs = options.n_eigs if options.n_eigs > mtx_k.shape[0]: options.n_eigs = mtx_k.shape[0] n_eigs = None if options.mode == 'omega': eigenshapes_filename = os.path.join( output_dir, 'frequency-eigenshapes-%s.vtk' % stepper.suffix) extra = [] extra_plot_kwargs = [] if options.log_std_waves: lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) extra = [r'$\omega_p$', r'$\omega_s$'] extra_plot_kwargs = [{ 'ls': '--', 'color': 'k' }, { 'ls': '--', 'color': 'gray' }] log = Log( [[r'$\lambda_{%d}$' % ii for ii in range(options.n_eigs)], [r'$\omega_{%d}$' % ii for ii in range(options.n_eigs)] + extra], plot_kwargs=[{}, [{}] * options.n_eigs + extra_plot_kwargs], yscales=['linear', 'linear'], xlabels=[r'$\kappa$', r'$\kappa$'], ylabels=[r'eigenvalues $\lambda_i$', r'frequencies $\omega_i$'], log_filename=os.path.join(output_dir, 'frequencies.txt'), aggregate=1000, sleep=0.1) for iv, wmag in stepper: output('step %d: wave vector %s' % (iv, wmag * wdir)) mtx_a = mtx_k + wmag**2 * mtx_s + (1j * wmag) * mtx_r mtx_b = mtx_m output('A - A^H:', _max_diff_csr(mtx_a, mtx_a.H)) if options.eigs_only: eigs = eig_solver(mtx_a, mtx_b, n_eigs=n_eigs, eigenvectors=False) svecs = None else: eigs, svecs = eig_solver(mtx_a, mtx_b, n_eigs=options.n_eigs, eigenvectors=True) omegas = nm.sqrt(eigs) output('eigs, omegas:\n', nm.c_[eigs, omegas]) out = tuple(eigs) + tuple(omegas) if options.log_std_waves: out = out + (cp * wmag, cs * wmag) log(*out, x=[wmag, wmag]) save_eigenvectors(eigenshapes_filename % iv, svecs, pb) log(save_figure=os.path.join(output_dir, 'frequencies.png')) log(finished=True) else: import scipy.sparse as sps from sksparse.cholmod import cholesky eigenshapes_filename = os.path.join( output_dir, 'wave-number-eigenshapes-%s.vtk' % stepper.suffix) factor = cholesky(mtx_s) perm = factor.P() ir = nm.arange(len(perm)) mtx_p = sps.coo_matrix((nm.ones_like(perm), (ir, perm))) mtx_l = mtx_p.T * factor.L() mtx_eye = sps.eye(mtx_l.shape[0], dtype=nm.float64) output('S - LL^T:', _max_diff_csr(mtx_s, mtx_l * mtx_l.T)) log = Log([[r'$\kappa_{%d}$' % ii for ii in range(options.n_eigs)]], plot_kwargs=[{ 'ls': 'None', 'marker': 'o' }], yscales=['linear'], xlabels=[r'$\omega$'], ylabels=[r'wave numbers $\kappa_i$'], log_filename=os.path.join(output_dir, 'wave-numbers.txt'), aggregate=1000, sleep=0.1) for io, omega in stepper: output('step %d: frequency %s' % (io, omega)) mtx_a = sps.bmat([[mtx_k - omega**2 * mtx_m, None], [None, mtx_eye]]) mtx_b = sps.bmat([[1j * mtx_r, mtx_l], [mtx_l.T, None]]) output('A - A^T:', _max_diff_csr(mtx_a, mtx_a.T)) output('A - A^H:', _max_diff_csr(mtx_a, mtx_a.T)) output('B - B^H:', _max_diff_csr(mtx_b, mtx_b.H)) if options.eigs_only: eigs = eig_solver(mtx_a, mtx_b, n_eigs=n_eigs, eigenvectors=False) svecs = None else: eigs, svecs = eig_solver(mtx_a, mtx_b, n_eigs=options.n_eigs, eigenvectors=True) kappas = eigs output('kappas:\n', kappas[:, None]) out = tuple(kappas) log(*out, x=[omega]) save_eigenvectors(eigenshapes_filename % io, svecs, pb) log(save_figure=os.path.join(output_dir, 'wave-numbers.png')) log(finished=True)
def test_stiffness_tensors(self): import numpy as nm from sfepy.base.base import assert_ import sfepy.mechanics.matcoefs as mc ok = True lam = 1.0 mu = 4.0 lam = nm.array([lam] * 3) mu = nm.array([mu] * 3) d = nm.array([[ 9., 1., 1., 0., 0., 0.], [ 1., 9., 1., 0., 0., 0.], [ 1., 1., 9., 0., 0., 0.], [ 0., 0., 0., 4., 0., 0.], [ 0., 0., 0., 0., 4., 0.], [ 0., 0., 0., 0., 0., 4.]]) _ds = mc.stiffness_from_lame(3, lam, mu) assert_(_ds.shape == (3, 6, 6)) _ok = True for _d in _ds: __ok = nm.allclose(_d, d, rtol=0.0, atol=1e-14) _ok = _ok and __ok self.report('stiffness_from_lame():', _ok) ok = ok and _ok _lam, _mu = mc.lame_from_stiffness(d) _ok = (_lam == 1) and (_mu == 4) self.report('lame_from_stiffness():', _ok) ok = ok and _ok young = 1.0 poisson = 0.25 d = mc.stiffness_from_youngpoisson(3, young, poisson, plane='strain') _young, _poisson = mc.youngpoisson_from_stiffness(d, plane='strain') _ok = nm.allclose([young, poisson], [_young, _poisson], rtol=0.0, atol=1e-14) self.report('youngpoisson_from_stiffness(plane="strain"):', _ok) ok = ok and _ok d = mc.stiffness_from_youngpoisson(2, young, poisson, plane='stress') _young, _poisson = mc.youngpoisson_from_stiffness(d, plane='stress') _ok = nm.allclose([young, poisson], [_young, _poisson], rtol=0.0, atol=1e-14) self.report('youngpoisson_from_stiffness(plane="stress"):', _ok) ok = ok and _ok d = 4.0 / 3.0 * nm.array([[ 4., -2., -2., 0., 0., 0.], [-2., 4., -2., 0., 0., 0.], [-2., -2., 4., 0., 0., 0.], [ 0., 0., 0., 3., 0., 0.], [ 0., 0., 0., 0., 3., 0.], [ 0., 0., 0., 0., 0., 3.]]) _ds = mc.stiffness_from_lame_mixed(3, lam, mu) assert_(_ds.shape == (3, 6, 6)) _ok = True for _d in _ds: __ok = nm.allclose(_d, d, rtol=0.0, atol=1e-14) _ok = _ok and __ok self.report('stiffness_from_lame_mixed():', _ok) ok = ok and _ok blam = - mu * 2.0 / 3.0 _ds = mc.stiffness_from_lame(3, blam, mu) assert_(_ds.shape == (3, 6, 6)) _ok = True for _d in _ds: __ok = nm.allclose(_d, d, rtol=0.0, atol=1e-14) _ok = _ok and __ok self.report('stiffness_from_lame() with modified lambda:', _ok) ok = ok and _ok return ok