def post_process(out, pb, state, extend=False): """ Compute derived quantities: strain, stresses. Store also the loading temperature. """ ev = pb.evaluate strain = ev("ev_cauchy_strain.2.Omega( u )", mode="el_avg") out["cauchy_strain"] = Struct(name="output_data", mode="cell", data=strain, dofs=None) e_stress = ev("ev_cauchy_stress.2.Omega( solid.D, u )", mode="el_avg") out["elastic_stress"] = Struct(name="output_data", mode="cell", data=e_stress, dofs=None) t_stress = ev("ev_biot_stress.2.Omega( solid.alpha, T )", mode="el_avg") out["thermal_stress"] = Struct(name="output_data", mode="cell", data=t_stress, dofs=None) out["total_stress"] = Struct(name="output_data", mode="cell", data=e_stress + t_stress, dofs=None) out["von_mises_stress"] = aux = out["total_stress"].copy() vms = get_von_mises_stress(aux.data.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out["von_mises_stress"].data = vms val = pb.get_variables()["T"]() val.shape = (val.shape[0], 1) out["T"] = Struct(name="output_data", mode="vertex", data=val + T0, dofs=None) return out
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out
def post_process(out, pb, state, extend=False): """ Calculate and output strain and stress for given displacements. """ from sfepy.base.base import Struct ev = pb.evaluate stress = ev('ev_cauchy_stress.2.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms, dofs=None) dim = pb.domain.shape.dim us = state().reshape((-1, dim)) field = pb.fields['displacement'] if dim == 2: ii = field.get_dofs_in_region(pb.domain.regions['Top']) output('top LCBC (u.0 - u.1 = 0):') output('\n', nm.c_[us[ii], nm.diff(us[ii], 1)]) ii = field.get_dofs_in_region(pb.domain.regions['Bottom']) output('bottom LCBC (u.0 + u.1 = -0.1):') output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)]) ii = field.get_dofs_in_region(pb.domain.regions['Right']) output('right LCBC (u.0 + u.1 = linspace(0, 0.1)):') output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)]) else: ii = field.get_dofs_in_region(pb.domain.regions['Top']) output('top LCBC (u.0 - u.1 + u.2 = 0):') output('\n', nm.c_[us[ii], us[ii, 0] - us[ii, 1] + us[ii, 2]]) output('top LCBC (u.0 + 0.5 u.1 + 0.1 u.2 = 0.05):') output('\n', nm.c_[us[ii], us[ii, 0] + 0.5 * us[ii, 1] + 0.1 * us[ii, 2]]) ii = field.get_dofs_in_region(pb.domain.regions['Bottom']) output('bottom LCBC (u.2 - 0.1 u.1 = 0.2):') output('\n', nm.c_[us[ii], us[ii, 2] - 0.1 * us[ii, 1]]) ii = field.get_dofs_in_region(pb.domain.regions['Right']) output('right LCBC (u.0 + u.1 + u.2 = linspace(0, 0.1)):') output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)]) return out
def post_process(out, pb, state, extend=False): """ Calculate and output strain and stress for given displacements. """ from sfepy.base.base import Struct ev = pb.evaluate stress = ev('ev_cauchy_stress.2.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms, dofs=None) dim = pb.domain.shape.dim us = state().reshape((-1, dim)) field = pb.fields['displacement'] if dim == 2: ii = field.get_dofs_in_region(pb.domain.regions['Top']) output('top LCBC (u.0 - u.1 = 0):') output('\n', nm.c_[us[ii], nm.diff(us[ii], 1)]) ii = field.get_dofs_in_region(pb.domain.regions['Bottom']) output('bottom LCBC (u.0 + u.1 = -0.1):') output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)]) ii = field.get_dofs_in_region(pb.domain.regions['Right']) output('right LCBC (u.0 + u.1 = linspace(0, 0.1)):') output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)]) else: ii = field.get_dofs_in_region(pb.domain.regions['Top']) output('top LCBC (u.0 - u.1 + u.2 = 0):') output('\n', nm.c_[us[ii], us[ii, 0] - us[ii, 1] + us[ii, 2]]) output('top LCBC (u.0 + 0.5 u.1 + 0.1 u.2 = 0.05):') output('\n', nm.c_[us[ii], us[ii, 0] + 0.5 * us[ii, 1] + 0.1 * us[ii, 2]]) ii = field.get_dofs_in_region(pb.domain.regions['Bottom']) output('bottom LCBC (u.2 - 0.1 u.1 = 0.2):') output('\n', nm.c_[us[ii], us[ii, 2] - 0.1 * us[ii, 1]]) ii = field.get_dofs_in_region(pb.domain.regions['Right']) output('right LCBC (u.0 + u.1 + u.2 = linspace(0, 0.1)):') output('\n', nm.c_[us[ii], nm.sum(us[ii], 1)]) return out
def post_process(out, pb, state, extend=False): """ Calculate and output strain and stress for given displacements. """ from sfepy.base.base import Struct ev = pb.evaluate stress = ev('ev_cauchy_stress.2.Omega(solid.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms, dofs=None) return out
def post_process(out, pb, state, extend=False): """ Calculate and output strain and stress for given displacements. """ from sfepy.base.base import Struct ev = pb.evaluate stress = ev('ev_cauchy_stress.2.Omega(solid.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms, dofs=None) return out
def post_process(out, pb, state, extend=False): """ Compute derived quantities: strain, stresses. Store also the loading temperature. """ ev = pb.evaluate strain = ev('ev_cauchy_strain.2.Omega( u )', mode='el_avg') out['cauchy_strain'] = Struct(name='output_data', mode='cell', data=strain, dofs=None) e_stress = ev('ev_cauchy_stress.2.Omega( solid.D, u )', mode='el_avg') out['elastic_stress'] = Struct(name='output_data', mode='cell', data=e_stress, dofs=None) t_stress = ev('ev_biot_stress.2.Omega( solid.alpha, T )', mode='el_avg') out['thermal_stress'] = Struct(name='output_data', mode='cell', data=t_stress, dofs=None) out['total_stress'] = Struct(name='output_data', mode='cell', data=e_stress + t_stress, dofs=None) out['von_mises_stress'] = aux = out['total_stress'].copy() vms = get_von_mises_stress(aux.data.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'].data = vms val = pb.get_variables()['T']() val.shape = (val.shape[0], 1) out['T'] = Struct(name='output_data', mode='vertex', data=val + T0, dofs=None) return out
def test_tensors(self): import numpy as nm import sfepy.mechanics.tensors as tn ok = True a_full = 2.0 * nm.ones((5,3,3), dtype=nm.float64) a_sym = 2.0 * nm.ones((5,6), dtype=nm.float64) _tr = nm.array([6.0] * 5, dtype=nm.float64) _vt_full = 2.0 * nm.tile(nm.eye(3, dtype=nm.float64), (5,1,1)) _vt_sym = nm.tile(nm.array([2, 2, 2, 0, 0, 0], dtype=nm.float64), (5,1,1)) _dev_full = a_full - _vt_full _dev_sym = a_sym - _vt_sym _vms = 6.0 * nm.ones((5,1), dtype=nm.float64) tr = tn.get_trace(a_full, sym_storage=False) _ok = nm.allclose(tr, _tr, rtol=0.0, atol=1e-14) self.report('trace full: %s' % _ok) ok = ok and _ok tr = tn.get_trace(a_sym, sym_storage=True) ok = ok and nm.allclose(tr, _tr, rtol=0.0, atol=1e-14) self.report('trace sym: %s' % _ok) ok = ok and _ok vt = tn.get_volumetric_tensor(a_full, sym_storage=False) _ok = nm.allclose(vt, _vt_full, rtol=0.0, atol=1e-14) self.report('volumetric tensor full: %s' % _ok) ok = ok and _ok vt = tn.get_volumetric_tensor(a_sym, sym_storage=True) _ok = nm.allclose(vt, _vt_sym, rtol=0.0, atol=1e-14) self.report('volumetric tensor sym: %s' % _ok) ok = ok and _ok dev = tn.get_deviator(a_full, sym_storage=False) _ok = nm.allclose(dev, _dev_full, rtol=0.0, atol=1e-14) self.report('deviator full: %s' % _ok) ok = ok and _ok aux = (dev * nm.transpose(dev, (0, 2, 1))).sum(axis=1).sum(axis=1) vms2 = nm.sqrt((3.0/2.0) * aux)[:,None] dev = tn.get_deviator(a_sym, sym_storage=True) _ok = nm.allclose(dev, _dev_sym, rtol=0.0, atol=1e-14) self.report('deviator sym: %s' % _ok) ok = ok and _ok vms = tn.get_von_mises_stress(a_full, sym_storage=False) _ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress full: %s' % _ok) ok = ok and _ok vms = tn.get_von_mises_stress(a_sym, sym_storage=True) _ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress sym: %s' % _ok) ok = ok and _ok _ok = nm.allclose(vms2, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress via deviator: %s' % _ok) ok = ok and _ok return ok
def test_tensors(self): import numpy as nm import sfepy.mechanics.tensors as tn ok = True a_full = 2.0 * nm.ones((5,3,3), dtype=nm.float64) a_sym = 2.0 * nm.ones((5,6), dtype=nm.float64) _tr = nm.array([6.0] * 5, dtype=nm.float64) _vt_full = 2.0 * nm.tile(nm.eye(3, dtype=nm.float64), (5,1,1)) _vt_sym = nm.tile(nm.array([2, 2, 2, 0, 0, 0], dtype=nm.float64), (5,1,1)) _dev_full = a_full - _vt_full _dev_sym = a_sym - _vt_sym _vms = 6.0 * nm.ones((5,1), dtype=nm.float64) tr = tn.get_trace(a_full, sym_storage=False) _ok = nm.allclose(tr, _tr, rtol=0.0, atol=1e-14) self.report('trace full: %s' % _ok) ok = ok and _ok tr = tn.get_trace(a_sym, sym_storage=True) ok = ok and nm.allclose(tr, _tr, rtol=0.0, atol=1e-14) self.report('trace sym: %s' % _ok) ok = ok and _ok vt = tn.get_volumetric_tensor(a_full, sym_storage=False) _ok = nm.allclose(vt, _vt_full, rtol=0.0, atol=1e-14) self.report('volumetric tensor full: %s' % _ok) ok = ok and _ok vt = tn.get_volumetric_tensor(a_sym, sym_storage=True) _ok = nm.allclose(vt, _vt_sym, rtol=0.0, atol=1e-14) self.report('volumetric tensor sym: %s' % _ok) ok = ok and _ok dev = tn.get_deviator(a_full, sym_storage=False) _ok = nm.allclose(dev, _dev_full, rtol=0.0, atol=1e-14) self.report('deviator full: %s' % _ok) ok = ok and _ok aux = (dev * nm.transpose(dev, (0, 2, 1))).sum(axis=1).sum(axis=1) vms2 = nm.sqrt((3.0/2.0) * aux)[:,None] dev = tn.get_deviator(a_sym, sym_storage=True) _ok = nm.allclose(dev, _dev_sym, rtol=0.0, atol=1e-14) self.report('deviator sym: %s' % _ok) ok = ok and _ok vms = tn.get_von_mises_stress(a_full, sym_storage=False) _ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress full: %s' % _ok) ok = ok and _ok vms = tn.get_von_mises_stress(a_sym, sym_storage=True) _ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress sym: %s' % _ok) ok = ok and _ok _ok = nm.allclose(vms2, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress via deviator: %s' % _ok) ok = ok and _ok t2s = nm.arange(9).reshape(3, 3) t2s = (t2s + t2s.T) / 2 t4 = tn.get_t4_from_t2s(t2s) expected = nm.array([[[[0, 4], [4, 2]], [[4, 8], [8, 6]]], [[[4, 8], [8, 6]], [[2, 6], [6, 4]]]]) _ok = nm.allclose(t4, expected, rtol=0.0, atol=1e-14) self.report('full 4D tensor from 2D matrix, 2D space: %s' % _ok) ok = ok and _ok return ok
def test_tensors(self): import numpy as nm import sfepy.mechanics.tensors as tn ok = True a_full = 2.0 * nm.ones((5,3,3), dtype=nm.float64) a_sym = 2.0 * nm.ones((5,6), dtype=nm.float64) _tr = nm.array([6.0] * 5, dtype=nm.float64) _vt_full = 2.0 * nm.tile(nm.eye(3, dtype=nm.float64), (5,1,1)) _vt_sym = nm.tile(nm.array([2, 2, 2, 0, 0, 0], dtype=nm.float64), (5,1,1)) _dev_full = a_full - _vt_full _dev_sym = a_sym - _vt_sym _vms = 6.0 * nm.ones((5,1), dtype=nm.float64) tr = tn.get_trace(a_full, sym_storage=False) _ok = nm.allclose(tr, _tr, rtol=0.0, atol=1e-14) self.report('trace full: %s' % _ok) ok = ok and _ok tr = tn.get_trace(a_sym, sym_storage=True) ok = ok and nm.allclose(tr, _tr, rtol=0.0, atol=1e-14) self.report('trace sym: %s' % _ok) ok = ok and _ok vt = tn.get_volumetric_tensor(a_full, sym_storage=False) _ok = nm.allclose(vt, _vt_full, rtol=0.0, atol=1e-14) self.report('volumetric tensor full: %s' % _ok) ok = ok and _ok vt = tn.get_volumetric_tensor(a_sym, sym_storage=True) _ok = nm.allclose(vt, _vt_sym, rtol=0.0, atol=1e-14) self.report('volumetric tensor sym: %s' % _ok) ok = ok and _ok dev = tn.get_deviator(a_full, sym_storage=False) _ok = nm.allclose(dev, _dev_full, rtol=0.0, atol=1e-14) self.report('deviator full: %s' % _ok) ok = ok and _ok aux = (dev * nm.transpose(dev, (0, 2, 1))).sum(axis=1).sum(axis=1) vms2 = nm.sqrt((3.0/2.0) * aux)[:,None] dev = tn.get_deviator(a_sym, sym_storage=True) _ok = nm.allclose(dev, _dev_sym, rtol=0.0, atol=1e-14) self.report('deviator sym: %s' % _ok) ok = ok and _ok vms = tn.get_von_mises_stress(a_full, sym_storage=False) _ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress full: %s' % _ok) ok = ok and _ok vms = tn.get_von_mises_stress(a_sym, sym_storage=True) _ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress sym: %s' % _ok) ok = ok and _ok _ok = nm.allclose(vms2, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress via deviator: %s' % _ok) ok = ok and _ok t2s = nm.arange(9).reshape(3, 3) t2s = (t2s + t2s.T) / 2 t4 = tn.get_t4_from_t2s(t2s) expected = nm.array([[[[0, 4], [4, 2]], [[4, 8], [8, 6]]], [[[4, 8], [8, 6]], [[2, 6], [6, 4]]]]) _ok = nm.allclose(t4, expected, rtol=0.0, atol=1e-14) self.report('full 4D tensor from 2D matrix, 2D space: %s' % _ok) ok = ok and _ok return ok
pb = Problem('elasticity', equations=eqs) pb.save_regions_as_groups('regions') 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')
def test_tensors(self): import numpy as nm import sfepy.mechanics.tensors as tn ok = True a_full = 2.0 * nm.ones((5, 3, 3), dtype=nm.float64) a_sym = 2.0 * nm.ones((5, 6), dtype=nm.float64) _tr = nm.array([6.0] * 5, dtype=nm.float64) _vt_full = 2.0 * nm.tile(nm.eye(3, dtype=nm.float64), (5, 1, 1)) _vt_sym = nm.tile(nm.array([2, 2, 2, 0, 0, 0], dtype=nm.float64), (5, 1, 1)) _dev_full = a_full - _vt_full _dev_sym = a_sym - _vt_sym _vms = 6.0 * nm.ones((5, 1), dtype=nm.float64) tr = tn.get_trace(a_full, sym_storage=False) _ok = nm.allclose(tr, _tr, rtol=0.0, atol=1e-14) self.report('trace full: %s' % _ok) ok = ok and _ok tr = tn.get_trace(a_sym, sym_storage=True) ok = ok and nm.allclose(tr, _tr, rtol=0.0, atol=1e-14) self.report('trace sym: %s' % _ok) ok = ok and _ok vt = tn.get_volumetric_tensor(a_full, sym_storage=False) _ok = nm.allclose(vt, _vt_full, rtol=0.0, atol=1e-14) self.report('volumetric tensor full: %s' % _ok) ok = ok and _ok vt = tn.get_volumetric_tensor(a_sym, sym_storage=True) _ok = nm.allclose(vt, _vt_sym, rtol=0.0, atol=1e-14) self.report('volumetric tensor sym: %s' % _ok) ok = ok and _ok dev = tn.get_deviator(a_full, sym_storage=False) _ok = nm.allclose(dev, _dev_full, rtol=0.0, atol=1e-14) self.report('deviator full: %s' % _ok) ok = ok and _ok aux = (dev * nm.transpose(dev, (0, 2, 1))).sum(axis=1).sum(axis=1) vms2 = nm.sqrt((3.0 / 2.0) * aux)[:, None] dev = tn.get_deviator(a_sym, sym_storage=True) _ok = nm.allclose(dev, _dev_sym, rtol=0.0, atol=1e-14) self.report('deviator sym: %s' % _ok) ok = ok and _ok vms = tn.get_von_mises_stress(a_full, sym_storage=False) _ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress full: %s' % _ok) ok = ok and _ok vms = tn.get_von_mises_stress(a_sym, sym_storage=True) _ok = nm.allclose(vms, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress sym: %s' % _ok) ok = ok and _ok _ok = nm.allclose(vms2, _vms, rtol=0.0, atol=1e-14) self.report('von Mises stress via deviator: %s' % _ok) ok = ok and _ok return ok