def test_equal_dof(): osi = o3.OpenSeesInstance(ndm=2, ndf=2) node1 = o3.node.Node(osi, 3, 4) node2 = o3.node.Node(osi, 3, 4) node3 = o3.node.Node(osi, 3, 4) o3.EqualDOF(osi, node1, node2, [o3.cc.DOF2D_X, o3.cc.DOF2D_Y]) # 1-to-1 sn = o3.node.build_regular_node_mesh(osi, [3, 4, 5], [1, 6]) o3.EqualDOFMulti(osi, node3, sn[0], [o3.cc.DOF2D_X, o3.cc.DOF2D_Y]) # 1-to-many o3.EqualDOFMulti(osi, sn[1], sn[2], [o3.cc.DOF2D_Y]) # many 1-to-1s
def load_element(nu_init, nu_setp): esig_v0 = 100.0 osi = o3.OpenSeesInstance(ndm=2, ndf=2) mat = o3.nd_material.ElasticIsotropic(osi, 1.0e6, nu=nu_init) h_ele = 1. nodes = [ o3.node.Node(osi, 0.0, 0.0), o3.node.Node(osi, h_ele, 0.0), o3.node.Node(osi, h_ele, h_ele), o3.node.Node(osi, 0.0, h_ele) ] # Fix bottom node o3.Fix2DOF(osi, nodes[0], o3.cc.FIXED, o3.cc.FIXED) o3.Fix2DOF(osi, nodes[1], o3.cc.FIXED, o3.cc.FIXED) o3.Fix2DOF(osi, nodes[2], o3.cc.FREE, o3.cc.FREE) o3.Fix2DOF(osi, nodes[3], o3.cc.FREE, o3.cc.FREE) # Set out-of-plane DOFs to be slaved o3.EqualDOF(osi, nodes[2], nodes[3], [o3.cc.X, o3.cc.Y]) ele = o3.element.SSPquad(osi, nodes, mat, 'PlaneStrain', 1, 0.0, 0.0) o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-3, max_iter=35, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.FullGeneral(osi) o3.integrator.DisplacementControl(osi, nodes[2], o3.cc.DOF2D_Y, 0.005) # o3.rayleigh.Rayleigh(osi, a0, a1, 0.0, 0.0) o3.analysis.Static(osi) o3.set_parameter(osi, value=nu_setp, eles=[ele], args=['nu', 1]) # Add static vertical pressure and stress bias # time_series = o3.time_series.Path(osi, time=[0, 100, 1e10], values=[0, 1, 1]) # o3.pattern.Plain(osi, time_series) ts0 = o3.time_series.Linear(osi, factor=1) o3.pattern.Plain(osi, ts0) o3.Load(osi, nodes[2], [0, -esig_v0 / 2]) o3.Load(osi, nodes[3], [0, -esig_v0 / 2]) o3.analyze(osi, num_inc=100) stresses = o3.get_ele_response(osi, ele, 'stress') print('init_stress0: ', stresses)
def run(show=0): # Load a ground motion record_filename = 'test_motion_dt0p01.txt' asig = eqsig.load_asig(ap.MODULE_DATA_PATH + 'gms/' + record_filename, m=0.5) # Define inelastic SDOF period = 1.0 xi = 0.05 mass = 1.0 f_yield = 1.5 # Reduce this to make it nonlinear r_post = 0.0 # Initialise OpenSees instance osi = o3.OpenSeesInstance(ndm=2, state=0) # Establish nodes bot_node = o3.node.Node(osi, 0, 0) top_node = o3.node.Node(osi, 0, 0) # Fix bottom node o3.Fix3DOF(osi, top_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED) o3.Fix3DOF(osi, bot_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED) # Set out-of-plane DOFs to be slaved o3.EqualDOF(osi, top_node, bot_node, [o3.cc.Y, o3.cc.ROTZ]) # nodal mass (weight / g): o3.Mass(osi, top_node, mass, 0., 0.) # Define material k_spring = 4 * np.pi**2 * mass / period**2 bilinear_mat = o3.uniaxial_material.Steel01(osi, fy=f_yield, e0=k_spring, b=r_post) # Assign zero length element, # Note: pass actual node and material objects into element o3.element.ZeroLength(osi, [bot_node, top_node], mats=[bilinear_mat], dirs=[o3.cc.DOF2D_X], r_flag=1) # Define the dynamic analysis # Define the dynamic analysis acc_series = o3.time_series.Path(osi, dt=asig.dt, values=-1 * asig.values) # should be negative o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series) # set damping based on first eigen mode angular_freq = o3.get_eigen(osi, solver='fullGenLapack', n=1)[0]**0.5 beta_k = 2 * xi / angular_freq o3.rayleigh.Rayleigh(osi, alpha_m=0.0, beta_k=beta_k, beta_k_init=0.0, beta_k_comm=0.0) # Run the dynamic analysis o3.wipe_analysis(osi) # Run the dynamic analysis o3.algorithm.Newton(osi) o3.system.SparseGeneral(osi) o3.numberer.RCM(osi) o3.constraints.Transformation(osi) o3.integrator.Newmark(osi, gamma=0.5, beta=0.25) o3.analysis.Transient(osi) o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10) analysis_time = asig.time[-1] analysis_dt = 0.001 outputs = { "time": [], "rel_disp": [], "rel_accel": [], "rel_vel": [], "force": [] } while o3.get_time(osi) < analysis_time: o3.analyze(osi, 1, analysis_dt) curr_time = o3.get_time(osi) outputs["time"].append(curr_time) outputs["rel_disp"].append(o3.get_node_disp(osi, top_node, o3.cc.X)) outputs["rel_vel"].append(o3.get_node_vel(osi, top_node, o3.cc.X)) outputs["rel_accel"].append(o3.get_node_accel(osi, top_node, o3.cc.X)) o3.gen_reactions(osi) outputs["force"].append(-o3.get_node_reaction( osi, bot_node, o3.cc.X)) # Negative since diff node o3.wipe(osi) for item in outputs: outputs[item] = np.array(outputs[item]) if show: import matplotlib.pyplot as plt plt.plot(outputs['time'], outputs['rel_disp'], label='o3seespy') periods = np.array([period]) # Compare closed form elastic solution from eqsig import sdof resp_u, resp_v, resp_a = sdof.response_series(motion=asig.values, dt=asig.dt, periods=periods, xi=xi) plt.plot(asig.time, resp_u[0], ls='--', label='Elastic') plt.legend() plt.show()
def site_response(sp, asig, freqs=(0.5, 10), xi=0.03, dy=0.5, analysis_time=None, outs=None, rec_dt=None, etype='implicit', forder=1.0): """ Run seismic analysis of a soil profile Parameters ---------- sp: sfsimodels.SoilProfile object A soil profile asig: eqsig.AccSignal object An acceleration signal Returns ------- """ if analysis_time is None: analysis_time = asig.time[-1] if outs is None: outs = {'ACCX': [0]} # Export the horizontal acceleration at the surface osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3) assert isinstance(sp, sm.SoilProfile) sp.gen_split(props=['shear_vel', 'unit_mass', 'g_mod', 'poissons_ratio'], target=dy) thicknesses = sp.split["thickness"] n_node_rows = len(thicknesses) + 1 node_depths = np.cumsum(sp.split["thickness"]) node_depths = np.insert(node_depths, 0, 0) ele_depths = (node_depths[1:] + node_depths[:-1]) / 2 rho = sp.split['unit_mass'] g_mod = sp.split['g_mod'] poi = sp.split['poissons_ratio'] lam = 2 * g_mod * poi / (1 - 2 * poi) mu = g_mod v_dil = np.sqrt((lam + 2 * mu) / rho) ele_h = sp.split['thickness'] dts = ele_h / v_dil min_dt = min(dts) print('min_dt: ', min_dt) grav = 9.81 ele_width = min(thicknesses) # Define nodes and set boundary conditions for simple shear deformation # Start at top and build down? sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]] for i in range(1, n_node_rows): # Establish left and right nodes sn.append([o3.node.Node(osi, 0, -node_depths[i]), o3.node.Node(osi, ele_width, -node_depths[i])]) # set x and y dofs equal for left and right nodes o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y]) # Fix base nodes o3.Fix2DOF(osi, sn[-1][0], o3.cc.FIXED, o3.cc.FIXED) o3.Fix2DOF(osi, sn[-1][1], o3.cc.FIXED, o3.cc.FIXED) # define materials ele_thick = 1.0 # m soil_mats = [] eles = [] prev_id = -1 for i in range(len(thicknesses)): y_depth = ele_depths[i] sl_id = sp.get_layer_index_by_depth(y_depth) sl = sp.layer(sl_id) mat = sl.o3_mat if sl_id != prev_id: mat.build(osi) soil_mats.append(mat) prev_id = sl_id # def element nodes = [sn[i+1][0], sn[i+1][1], sn[i][1], sn[i][0]] # anti-clockwise eles.append(o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick, 0.0, -grav)) for i, soil_mat in enumerate(soil_mats): if hasattr(soil_mat, 'update_to_linear'): print('Update model to linear') soil_mat.update_to_linear() # Gravity analysis o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=30, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.ProfileSPD(osi) o3.integrator.Newmark(osi, 5./6, 4./9) # include numerical damping o3.analysis.Transient(osi) o3.analyze(osi, 40, 1.) for i, soil_mat in enumerate(soil_mats): if hasattr(soil_mat, 'update_to_nonlinear'): print('Update model to nonlinear') soil_mat.update_to_nonlinear() if o3.analyze(osi, 50, 0.5): print('Model failed') return print('finished nonlinear gravity analysis') # reset time and analysis o3.set_time(osi, 0.0) o3.wipe_analysis(osi) n = 10 # omegas = np.array(o3.get_eigen(osi, solver='fullGenLapack', n=n)) ** 0.5 # DO NOT USE fullGenLapack omegas = np.array(o3.get_eigen(osi, n=n)) ** 0.5 periods = 2 * np.pi / omegas print('response_periods: ', periods) o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=10) o3.numberer.RCM(osi) if etype == 'implicit': o3.system.ProfileSPD(osi) o3.algorithm.NewtonLineSearch(osi, 0.75) o3.integrator.Newmark(osi, 0.5, 0.25) dt = 0.001 else: o3.algorithm.Linear(osi) if etype == 'newmark_explicit': o3.system.ProfileSPD(osi) o3.integrator.NewmarkExplicit(osi, gamma=0.5) explicit_dt = min_dt / 1 elif etype == 'central_difference': o3.system.ProfileSPD(osi) o3.integrator.CentralDifference(osi) explicit_dt = min_dt / 8 elif etype == 'explicit_difference': o3.system.Diagonal(osi) o3.integrator.ExplicitDifference(osi) explicit_dt = min_dt / 2 # need reduced time step due to Rayleigh damping else: raise ValueError(etype) ndp = np.ceil(np.log10(explicit_dt)) if 0.5 * 10 ** ndp < explicit_dt: dt = 0.5 * 10 ** ndp elif 0.2 * 10 ** ndp < explicit_dt: dt = 0.2 * 10 ** ndp elif 0.1 * 10 ** ndp < explicit_dt: dt = 0.1 * 10 ** ndp else: raise ValueError(explicit_dt, 0.1 * 10 ** ndp) print('explicit_dt: ', explicit_dt, dt) use_modal_damping = 0 if not use_modal_damping: omega_1 = 2 * np.pi * freqs[0] omega_2 = 2 * np.pi * freqs[1] a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2) a1 = 2 * xi / (omega_1 + omega_2) o3.rayleigh.Rayleigh(osi, a0, 0, a1, 0) else: o3.ModalDamping(osi, [xi]) o3.analysis.Transient(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-7, max_iter=10) rec_dt = 0.001 ods = {} for otype in outs: if otype == 'ACCX': ods['ACCX'] = [] if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all': ods['ACCX'] = o3.recorder.NodesToArrayCache(osi, nodes=sn[:][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt) else: for i in range(len(outs['ACCX'])): ind = np.argmin(abs(node_depths - outs['ACCX'][i])) ods['ACCX'].append(o3.recorder.NodeToArrayCache(osi, node=sn[ind][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt)) if otype == 'TAU': ods['TAU'] = [] if isinstance(outs['TAU'], str) and outs['TAU'] == 'all': ods['TAU'] = o3.recorder.ElementsToArrayCache(osi, eles=eles, arg_vals=['stress'], dt=rec_dt) else: for i in range(len(outs['TAU'])): ind = np.argmin(abs(ele_depths - outs['TAU'][i])) ods['TAU'].append(o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['stress'], dt=rec_dt)) if otype == 'STRS': ods['STRS'] = [] if isinstance(outs['STRS'], str) and outs['STRS'] == 'all': ods['STRS'] = o3.recorder.ElementsToArrayCache(osi, eles=eles, arg_vals=['strain'], dt=rec_dt) else: for i in range(len(outs['STRS'])): ind = np.argmin(abs(ele_depths - outs['STRS'][i])) ods['STRS'].append(o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['strain'], dt=rec_dt)) ods['time'] = o3.recorder.TimeToArrayCache(osi, dt=rec_dt) acc_series = o3.time_series.Path(osi, dt=asig.dt, values=asig.values) o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series) # Run the dynamic analysis inc = 1 if etype != 'implicit': inc = 10 o3.record(osi) while o3.get_time(osi) < analysis_time: print(o3.get_time(osi)) if o3.analyze(osi, inc, dt): print('failed') break o3.wipe(osi) out_dict = {} for otype in ods: if isinstance(ods[otype], list): out_dict[otype] = [] for i in range(len(ods[otype])): out_dict[otype].append(ods[otype][i].collect()) out_dict[otype] = np.array(out_dict[otype]) else: out_dict[otype] = ods[otype].collect().T return out_dict
def run(etype, xi): mass = 100.0 k = 100.0 omega = np.sqrt(k / mass) c = 2 * xi * k / omega osi = o3.OpenSeesInstance(ndm=1, ndf=1) mat = o3.uniaxial_material.Elastic(osi, k) dashpot_mat = o3.uniaxial_material.Viscous(osi, big_c=c, alpha=1.) n0 = o3.node.Node(osi, 0.0) n0a = o3.node.Node(osi, 0.0) n1 = o3.node.Node(osi, 0.0) n2 = o3.node.Node(osi, 0.0) o3.Mass2D(osi, n1, x_mass=mass) o3.Mass2D(osi, n2, x_mass=mass) o3.Fix1DOF(osi, n0, x=o3.cc.FIXED) o3.element.ZeroLength(osi, [n1, n2], mats=[mat], dirs=[o3.cc.X]) if xi > 0.0: o3.element.ZeroLength(osi, [n0, n0a], mats=[dashpot_mat], dirs=[o3.cc.X]) o3.EqualDOF(osi, n1, n0a, dofs=[o3.cc.X]) ts0 = o3.time_series.Linear(osi) o3.pattern.Plain(osi, ts0) o3.Load(osi, n1, [10]) min_dt = 2. / omega print('min_dt: ', min_dt) o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=10) o3.numberer.RCM(osi) if etype == 'implicit': o3.system.ProfileSPD(osi) o3.algorithm.NewtonLineSearch(osi, 0.75) o3.integrator.Newmark(osi, 0.5, 0.25) dt = min_dt else: o3.algorithm.Linear(osi, factor_once=True) if etype == 'newmark_explicit': o3.system.ProfileSPD(osi) o3.integrator.NewmarkExplicit(osi, gamma=0.5) explicit_dt = min_dt / 1 elif etype == 'central_difference': o3.system.FullGeneral(osi) o3.integrator.CentralDifference(osi) explicit_dt = min_dt / 1 elif etype == 'explicit_difference': o3.system.Diagonal(osi) o3.integrator.ExplicitDifference(osi) explicit_dt = min_dt / 1 else: raise ValueError(etype) ndp = np.ceil(np.log10(explicit_dt)) if 0.5 * 10**ndp < explicit_dt: dt = 0.5 * 10**ndp elif 0.2 * 10**ndp < explicit_dt: dt = 0.2 * 10**ndp elif 0.1 * 10**ndp < explicit_dt: dt = 0.1 * 10**ndp else: raise ValueError(explicit_dt, 0.1 * 10**ndp) print('explicit_dt: ', explicit_dt, dt) o3.analysis.Transient(osi) ttotal = 150 # s inc = 2 nn = int(ttotal / dt / inc) print(nn) time = [] disp1 = [] disp2 = [] for i in range(nn): time.append(o3.get_time(osi)) disp1.append(o3.get_node_disp(osi, n1, dof=o3.cc.X)) disp2.append(o3.get_node_disp(osi, n2, dof=o3.cc.X)) o3.analyze(osi, inc, dt) return time, disp1, disp2
def site_response(sp, asig, freqs=(0.5, 10), xi=0.03, dy=0.5, analysis_time=None, outs=None, rec_dt=None, etype='variable', forder=1.0): """ Run seismic analysis of a soil profile Parameters ---------- sp: sfsimodels.SoilProfile object A soil profile asig: eqsig.AccSignal object An acceleration signal Returns ------- """ if analysis_time is None: analysis_time = asig.time[-1] if outs is None: outs = { 'ACCX': [0] } # Export the horizontal acceleration at the surface osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3) assert isinstance(sp, sm.SoilProfile) sp.gen_split(props=['shear_vel', 'unit_mass'], target=dy) req_dt = min(sp.split["thickness"] / sp.split['shear_vel']) / 8 thicknesses = sp.split["thickness"] n_node_rows = len(thicknesses) + 1 node_depths = np.cumsum(sp.split["thickness"]) node_depths = np.insert(node_depths, 0, 0) ele_depths = (node_depths[1:] + node_depths[:-1]) / 2 unit_masses = sp.split["unit_mass"] / forder grav = 9.81 ele_width = min(thicknesses) total_soil_nodes = len(thicknesses) * 2 + 2 # Define nodes and set boundary conditions for simple shear deformation # Start at top and build down? sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]] for i in range(1, n_node_rows): # Establish left and right nodes sn.append([ o3.node.Node(osi, 0, -node_depths[i]), o3.node.Node(osi, ele_width, -node_depths[i]) ]) # set x and y dofs equal for left and right nodes o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y]) # Fix base nodes o3.Fix2DOF(osi, sn[-1][0], o3.cc.FIXED, o3.cc.FIXED) o3.Fix2DOF(osi, sn[-1][1], o3.cc.FIXED, o3.cc.FIXED) # define materials ele_thick = 1.0 # m soil_mats = [] eles = [] prev_id = -1 for i in range(len(thicknesses)): y_depth = ele_depths[i] sl_id = sp.get_layer_index_by_depth(y_depth) sl = sp.layer(sl_id) mat = sl.o3_mat if sl_id != prev_id: mat.build(osi) soil_mats.append(mat) prev_id = sl_id # def element nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1], sn[i][0]] # anti-clockwise eles.append( o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick, 0.0, -grav)) for i, soil_mat in enumerate(soil_mats): if hasattr(soil_mat, 'update_to_linear'): print('Update model to linear') soil_mat.update_to_linear() # Gravity analysis o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=30, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.ProfileSPD(osi) o3.integrator.Newmark(osi, 5. / 6, 4. / 9) # include numerical damping if etype == 'variable': o3.analysis.VariableTransient(osi) g_args = [0.5, 0.1, 2, 5] else: o3.analysis.Transient(osi) g_args = [0.5] fail = o3.analyze(osi, 40, *g_args) if fail: return for i, soil_mat in enumerate(soil_mats): if hasattr(soil_mat, 'update_to_nonlinear'): print('Update model to nonlinear') soil_mat.update_to_nonlinear() if o3.analyze(osi, 50, *g_args): print('Model failed') return print('finished nonlinear gravity analysis') # reset time and analysis o3.set_time(osi, 0.0) o3.wipe_analysis(osi) n = 10 # omegas = np.array(o3.get_eigen(osi, solver='fullGenLapack', n=n)) ** 0.5 # DO NOT USE fullGenLapack omegas = np.array(o3.get_eigen(osi, n=n))**0.5 periods = 2 * np.pi / omegas print('response_periods: ', periods) o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-8, max_iter=6, p_flag=0) o3.numberer.RCM(osi) o3.system.ProfileSPD(osi) # o3.algorithm.NewtonLineSearch(osi, 0.75) # o3.integrator.Newmark(osi, 0.5, 0.25) if etype == 'variable': # o3.analysis.VariableTransient(osi) o3.opy.analysis('VariableTransient') dyn_args = [20, 0.01, 0.0005, 0.01, 3] else: o3.analysis.Transient(osi) dyn_args = [20, 0.01] omega_1 = 2 * np.pi * freqs[0] omega_2 = 2 * np.pi * freqs[1] a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2) a1 = 2 * xi / (omega_1 + omega_2) o3.rayleigh.Rayleigh(osi, a0, 0, a1, 0) o3.extensions.to_py_file(osi, f'opy_var_integration_{etype}.py') # o3.test_check.NormDispIncr(osi, tol=1.0e-7, max_iter=10) rec_dt = 0.001 ods = {} for otype in outs: if otype == 'ACCX': ods['ACCX'] = [] if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all': ods['ACCX'] = o3.recorder.NodesToArrayCache(osi, nodes=sn[:][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt) else: for i in range(len(outs['ACCX'])): ind = np.argmin(abs(node_depths - outs['ACCX'][i])) ods['ACCX'].append( o3.recorder.NodeToArrayCache(osi, node=sn[ind][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt)) if otype == 'TAU': ods['TAU'] = [] if isinstance(outs['TAU'], str) and outs['TAU'] == 'all': ods['TAU'] = o3.recorder.ElementsToArrayCache( osi, eles=eles, arg_vals=['stress'], dt=rec_dt) else: for i in range(len(outs['TAU'])): ind = np.argmin(abs(ele_depths - outs['TAU'][i])) ods['TAU'].append( o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['stress'], dt=rec_dt)) if otype == 'STRS': ods['STRS'] = [] if isinstance(outs['STRS'], str) and outs['STRS'] == 'all': ods['STRS'] = o3.recorder.ElementsToArrayCache( osi, eles=eles, arg_vals=['strain'], dt=rec_dt) else: for i in range(len(outs['STRS'])): ind = np.argmin(abs(ele_depths - outs['STRS'][i])) ods['STRS'].append( o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['strain'], dt=rec_dt)) ods['time'] = o3.recorder.TimeToArrayCache(osi, dt=rec_dt) acc_series = o3.time_series.Path(osi, dt=asig.dt, values=asig.values) o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series) # Run the dynamic analysis inc = 1 o3.record(osi) while o3.get_time(osi) < analysis_time: print(o3.get_time(osi)) if o3.analyze(osi, *dyn_args): print('failed') break o3.wipe(osi) out_dict = {} for otype in ods: if isinstance(ods[otype], list): out_dict[otype] = [] for i in range(len(ods[otype])): out_dict[otype].append(ods[otype][i].collect()) out_dict[otype] = np.array(out_dict[otype]) else: out_dict[otype] = ods[otype].collect().T return out_dict
def site_response(sp, asig, freqs=(0.5, 10), xi=0.03, analysis_dt=0.001, dy=0.5, analysis_time=None, outs=None, rec_dt=None): """ Run seismic analysis of a soil profile - example based on: http://opensees.berkeley.edu/wiki/index.php/Site_Response_Analysis_of_a_Layered_Soil_Column_(Total_Stress_Analysis) Parameters ---------- sp: sfsimodels.SoilProfile object A soil profile asig: eqsig.AccSignal object An acceleration signal Returns ------- """ if analysis_time is None: analysis_time = asig.time[-1] if outs is None: outs = { 'ACCX': [0] } # Export the horizontal acceleration at the surface if rec_dt is None: rec_dt = analysis_dt osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3) assert isinstance(sp, sm.SoilProfile) sp.gen_split(props=['shear_vel', 'unit_mass'], target=dy) thicknesses = sp.split["thickness"] n_node_rows = len(thicknesses) + 1 node_depths = np.cumsum(sp.split["thickness"]) node_depths = np.insert(node_depths, 0, 0) ele_depths = (node_depths[1:] + node_depths[:-1]) / 2 unit_masses = sp.split["unit_mass"] / 1e3 grav = 9.81 omega_1 = 2 * np.pi * freqs[0] omega_2 = 2 * np.pi * freqs[1] a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2) a1 = 2 * xi / (omega_1 + omega_2) k0 = 0.5 pois = k0 / (1 + k0) newmark_gamma = 0.5 newmark_beta = 0.25 ele_width = min(thicknesses) total_soil_nodes = len(thicknesses) * 2 + 2 # Define nodes and set boundary conditions for simple shear deformation # Start at top and build down? sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]] for i in range(1, n_node_rows): # Establish left and right nodes sn.append([ o3.node.Node(osi, 0, -node_depths[i]), o3.node.Node(osi, ele_width, -node_depths[i]) ]) # set x and y dofs equal for left and right nodes o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y]) sn = np.array(sn) # Fix base nodes o3.Fix2DOF(osi, sn[-1][0], o3.cc.FREE, o3.cc.FIXED) o3.Fix2DOF(osi, sn[-1][1], o3.cc.FREE, o3.cc.FIXED) # Define dashpot nodes dashpot_node_l = o3.node.Node(osi, 0, -node_depths[-1]) dashpot_node_2 = o3.node.Node(osi, 0, -node_depths[-1]) o3.Fix2DOF(osi, dashpot_node_l, o3.cc.FIXED, o3.cc.FIXED) o3.Fix2DOF(osi, dashpot_node_2, o3.cc.FREE, o3.cc.FIXED) # define equal DOF for dashpot and soil base nodes o3.EqualDOF(osi, sn[-1][0], sn[-1][1], [o3.cc.X]) o3.EqualDOF(osi, sn[-1][0], dashpot_node_2, [o3.cc.X]) # define materials ele_thick = 1.0 # m soil_mats = [] strains = np.logspace(-6, -0.5, 16) ref_strain = 0.005 rats = 1. / (1 + (strains / ref_strain)**0.91) prev_args = [] prev_kwargs = {} prev_sl_type = None eles = [] tau_inds = [] total_stress_inds = 0 strs_inds = [] total_strain_inds = 0 for i in range(len(thicknesses)): y_depth = ele_depths[i] sl_id = sp.get_layer_index_by_depth(y_depth) sl = sp.layer(sl_id) app2mod = {} if y_depth > sp.gwl: umass = sl.unit_sat_mass / 1e3 else: umass = sl.unit_dry_mass / 1e3 # Define material if sl.type == 'pm4sand': sl_class = o3.nd_material.PM4Sand overrides = {'nu': pois, 'p_atm': 101, 'unit_moist_mass': umass} app2mod = sl.app2mod elif sl.type == 'sdmodel': sl_class = o3.nd_material.StressDensity overrides = {'nu': pois, 'p_atm': 101, 'unit_moist_mass': umass} app2mod = sl.app2mod elif sl.type == 'pimy': sl_class = o3.nd_material.PressureIndependMultiYield overrides = { 'nu': pois, 'p_atm': 101, 'rho': umass, 'nd': 2.0, 'g_mod_ref': sl.g_mod / 1e3, 'bulk_mod_ref': sl.bulk_mod / 1e3, 'cohesion': sl.cohesion / 1e3, 'd': 0.0, # 'no_yield_surf': 20 } tau_inds.append(total_stress_inds + 3) # 4th total_stress_inds += 5 strs_inds.append(total_strain_inds + 2) # 3rd total_strain_inds += 3 else: sl_class = o3.nd_material.ElasticIsotropic sl.e_mod = 2 * sl.g_mod * (1 - sl.poissons_ratio) / 1e3 app2mod['rho'] = 'unit_moist_mass' overrides = {'nu': sl.poissons_ratio, 'unit_moist_mass': umass} # opw.extensions.to_py_file(osi) args, kwargs = o3.extensions.get_o3_kwargs_from_obj( sl, sl_class, custom=app2mod, overrides=overrides) changed = 0 if sl.type != prev_sl_type or len(args) != len(prev_args) or len( kwargs) != len(prev_kwargs): changed = 1 else: for j, arg in enumerate(args): if not np.isclose(arg, prev_args[j]): changed = 1 for pm in kwargs: if pm not in prev_kwargs or not np.isclose( kwargs[pm], prev_kwargs[pm]): changed = 1 if changed: mat = sl_class(osi, *args, **kwargs) prev_sl_type = sl.type prev_args = copy.deepcopy(args) prev_kwargs = copy.deepcopy(kwargs) soil_mats.append(mat) # def element nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1], sn[i][0]] # anti-clockwise # ele = o3.element.Quad(osi, nodes, ele_thick, o3.cc.PLANE_STRAIN, mat, b2=grav * unit_masses[i]) ele = o3.element.SSPquad(osi, nodes, mat, 'PlaneStrain', ele_thick, 0.0, b2=grav * unit_masses[i]) eles.append(ele) # define material and element for viscous dampers base_sl = sp.layer(sp.n_layers) c_base = ele_width * base_sl.unit_dry_mass / 1e3 * sp.get_shear_vel_at_depth( sp.height) dashpot_mat = o3.uniaxial_material.Viscous(osi, c_base, alpha=1.) o3.element.ZeroLength(osi, [dashpot_node_l, dashpot_node_2], mats=[dashpot_mat], dirs=[o3.cc.DOF2D_X]) # Static analysis o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-4, max_iter=30, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.ProfileSPD(osi) o3.integrator.Newmark(osi, newmark_gamma, newmark_beta) o3.analysis.Transient(osi) o3.analyze(osi, 40, 1.) for i in range(len(soil_mats)): if isinstance(soil_mats[i], o3.nd_material.PM4Sand) or isinstance( soil_mats[i], o3.nd_material.PressureIndependMultiYield): o3.update_material_stage(osi, soil_mats[i], 1) o3.analyze(osi, 50, 0.5) # reset time and analysis o3.set_time(osi, 0.0) o3.wipe_analysis(osi) # o3.recorder.NodeToFile(osi, 'sample_out.txt', node=nd["R0L"], dofs=[o3.cc.X], res_type='accel') na = o3.recorder.NodeToArrayCache(osi, node=sn[0][0], dofs=[o3.cc.X], res_type='accel') otypes = ['ACCX', 'TAU', 'STRS'] ods = {} for otype in outs: if otype == 'ACCX': ods['ACCX'] = [] if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all': ods['ACCX'] = o3.recorder.NodesToArrayCache(osi, nodes=sn[:, 0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt) else: for i in range(len(outs['ACCX'])): ind = np.argmin(abs(node_depths - outs['ACCX'][i])) ods['ACCX'].append( o3.recorder.NodeToArrayCache(osi, node=sn[ind][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt)) if otype == 'TAU': ods['TAU'] = [] if isinstance(outs['TAU'], str) and outs['TAU'] == 'all': ods['TAU'] = o3.recorder.ElementsToArrayCache( osi, eles=eles, arg_vals=['stress'], dt=rec_dt) else: for i in range(len(outs['TAU'])): ind = np.argmin(abs(ele_depths - outs['TAU'][i])) ods['TAU'].append( o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['stress'], dt=rec_dt)) if otype == 'STRS': ods['STRS'] = [] if isinstance(outs['STRS'], str) and outs['STRS'] == 'all': ods['STRS'] = o3.recorder.ElementsToArrayCache( osi, eles=eles, arg_vals=['strain'], dt=rec_dt) else: for i in range(len(outs['STRS'])): ind = np.argmin(abs(ele_depths - outs['STRS'][i])) ods['STRS'].append( o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['strain'], dt=rec_dt)) # Define the dynamic analysis ts_obj = o3.time_series.Path(osi, dt=asig.dt, values=asig.velocity * -1, factor=c_base) o3.pattern.Plain(osi, ts_obj) o3.Load(osi, sn[-1][0], [1., 0.]) # Run the dynamic analysis o3.algorithm.Newton(osi) o3.system.SparseGeneral(osi) o3.numberer.RCM(osi) o3.constraints.Transformation(osi) o3.integrator.Newmark(osi, newmark_gamma, newmark_beta) o3.rayleigh.Rayleigh(osi, a0, a1, 0, 0) o3.analysis.Transient(osi) o3.test_check.EnergyIncr(osi, tol=1.0e-7, max_iter=10) o3.extensions.to_py_file(osi) while opy.getTime() < analysis_time: print(opy.getTime()) if o3.analyze(osi, 1, analysis_dt): print('failed') break opy.wipe() out_dict = {} for otype in ods: if isinstance(ods[otype], list): out_dict[otype] = [] for i in range(len(ods[otype])): a = ods[otype][i].collect() out_dict[otype].append( a[3::4]) # TODO: not working for generic case out_dict[otype] = np.array(out_dict[otype]) else: if otype == 'TAU': a = ods[otype].collect() out_dict[otype] = a[:, tau_inds].T * 1e3 elif otype == 'STRS': a = ods[otype].collect() out_dict[otype] = a[:, strs_inds].T else: out_dict[otype] = ods[otype].collect().T out_dict['time'] = np.arange(0, len(out_dict[otype][0])) * rec_dt return out_dict
def get_inelastic_response(mass, k_spring, f_yield, motion, dt, xi=0.05, r_post=0.0): """ Run seismic analysis of a nonlinear SDOF :param mass: SDOF mass :param k_spring: spring stiffness :param f_yield: yield strength :param motion: list, acceleration values :param dt: float, time step of acceleration values :param xi: damping ratio :param r_post: post-yield stiffness :return: """ osi = o3.OpenSeesInstance(ndm=2) # Establish nodes bot_node = o3.node.Node(osi, 0, 0) top_node = o3.node.Node(osi, 0, 0) # Fix bottom node o3.Fix3DOF(osi, top_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED) o3.Fix3DOF(osi, bot_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED) # Set out-of-plane DOFs to be slaved o3.EqualDOF(osi, top_node, bot_node, [o3.cc.Y, o3.cc.DOF2D_ROTZ]) # nodal mass (weight / g): o3.Mass(osi, top_node, mass, 0., 0.) # Define material bilinear_mat = o3.uniaxial_material.Steel01(osi, fy=f_yield, e0=k_spring, b=r_post) # Assign zero length element, # Note: pass actual node and material objects into element o3.element.ZeroLength(osi, [bot_node, top_node], mats=[bilinear_mat], dirs=[o3.cc.DOF2D_X], r_flag=1) # Define the dynamic analysis values = list(-1 * motion) # should be negative acc_series = o3.time_series.Path(osi, dt, values) o3.pattern.UniformExcitation(osi, o3.cc.X, accel_series=acc_series) # set damping based on first eigen mode angular_freq2 = o3.get_eigen(osi, solver='fullGenLapack', n=1) if hasattr(angular_freq2, '__len__'): angular_freq2 = angular_freq2[0] angular_freq = angular_freq2**0.5 beta_k = 2 * xi / angular_freq o3.rayleigh.Rayleigh(osi, alpha_m=0.0, beta_k=beta_k, beta_k_init=0.0, beta_k_comm=0.0) # Run the dynamic analysis o3.wipe_analysis(osi) newmark_gamma = 0.5 newmark_beta = 0.25 o3.algorithm.Newton(osi) o3.constraints.Transformation(osi) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.SparseGeneral(osi) o3.integrator.Newmark(osi, newmark_gamma, newmark_beta) o3.analysis.Transient(osi) o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10) analysis_time = (len(values) - 1) * dt analysis_dt = 0.001 outputs = {"time": [], "rel_disp": [], "rel_accel": [], "force": []} o3.record(osi) curr_time = o3.get_time(osi) while curr_time < analysis_time: outputs["time"].append(curr_time) outputs["rel_disp"].append(o3.get_node_disp(osi, top_node, o3.cc.X)) outputs["rel_accel"].append(o3.get_node_accel(osi, top_node, o3.cc.X)) o3.gen_reactions(osi) outputs["force"].append(-o3.get_node_reaction( osi, bot_node, o3.cc.X)) # Negative since diff node o3.analyze(osi, 1, analysis_dt) curr_time = o3.get_time(osi) o3.wipe(osi) for item in outputs: outputs[item] = np.array(outputs[item]) return outputs
def run_ts_custom_strain(mat, esig_v0, strains, osi=None, nu_dyn=None, target_d_inc=0.00001, k0=None, etype='newmark_explicit', handle='silent', verbose=0, opyfile=None, dss=False, plain_strain=True, min_n=10, nl=True): # if dss: # raise ValueError('dss option is not working') damp = 0.05 omega0 = 0.2 omega1 = 20.0 a1 = 2. * damp / (omega0 + omega1) a0 = a1 * omega0 * omega1 if osi is None: osi = o3.OpenSeesInstance(ndm=2, ndf=2) mat.build(osi) # Establish nodes h_ele = 1. nodes = [ o3.node.Node(osi, 0.0, 0.0), o3.node.Node(osi, h_ele, 0.0), o3.node.Node(osi, h_ele, h_ele), o3.node.Node(osi, 0.0, h_ele) ] # Fix bottom node o3.Fix2DOF(osi, nodes[0], o3.cc.FIXED, o3.cc.FIXED) if k0 is None: o3.Fix2DOF(osi, nodes[1], o3.cc.FIXED, o3.cc.FIXED) # Set out-of-plane DOFs to be slaved o3.EqualDOF(osi, nodes[2], nodes[3], [o3.cc.X, o3.cc.Y]) else: # control k0 with node forces o3.Fix2DOF(osi, nodes[1], o3.cc.FIXED, o3.cc.FREE) if plain_strain: oop = 'PlaneStrain' else: oop = 'PlaneStress' ele = o3.element.SSPquad(osi, nodes, mat, oop, 1, 0.0, 0.0) angular_freqs = np.array(o3.get_eigen(osi, solver='fullGenLapack', n=2)) ** 0.5 print('angular_freqs: ', angular_freqs) periods = 2 * np.pi / angular_freqs xi = 0.03 o3.ModalDamping(osi, [xi, xi]) print('periods: ', periods) o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=35, p_flag=0) o3.numberer.RCM(osi) if etype == 'implicit': o3.algorithm.Newton(osi) o3.system.FullGeneral(osi) o3.integrator.Newmark(osi, gamma=0.5, beta=0.25) dt = 0.01 else: o3.algorithm.Linear(osi, factor_once=True) o3.system.FullGeneral(osi) if etype == 'newmark_explicit': o3.integrator.NewmarkExplicit(osi, gamma=0.5) explicit_dt = periods[0] / np.pi / 8 elif etype == 'central_difference': o3.integrator.CentralDifference(osi) explicit_dt = periods[0] / np.pi / 16 # 0.5 is a factor of safety elif etype == 'hht_explicit': o3.integrator.HHTExplicit(osi, alpha=0.5) explicit_dt = periods[0] / np.pi / 8 elif etype == 'explicit_difference': o3.integrator.ExplicitDifference(osi) explicit_dt = periods[0] / np.pi / 4 else: raise ValueError(etype) print('explicit_dt: ', explicit_dt) dt = explicit_dt o3.analysis.Transient(osi) o3.update_material_stage(osi, mat, stage=0) # dt = 0.00001 tload = 60 n_steps = tload / dt # Add static vertical pressure and stress bias time_series = o3.time_series.Path(osi, time=[0, tload, 1e10], values=[0, 1, 1]) o3.pattern.Plain(osi, time_series) # ts0 = o3.time_series.Linear(osi, factor=1) # o3.pattern.Plain(osi, ts0) if k0: o3.Load(osi, nodes[2], [-esig_v0 / 2, -esig_v0 / 2]) o3.Load(osi, nodes[3], [esig_v0 / 2, -esig_v0 / 2]) o3.Load(osi, nodes[1], [-esig_v0 / 2, 0]) # node 0 is fixed else: o3.Load(osi, nodes[2], [0, -esig_v0 / 2]) o3.Load(osi, nodes[3], [0, -esig_v0 / 2]) print('Apply init stress to elastic element') o3.analyze(osi, num_inc=n_steps, dt=dt) stresses = o3.get_ele_response(osi, ele, 'stress') print('init_stress0: ', stresses) o3.load_constant(osi, tload) if hasattr(mat, 'update_to_nonlinear') and nl: print('set to nonlinear') mat.update_to_nonlinear() o3.analyze(osi, 10000, dt=dt) # if not nl: # mat.update_to_linear() if nu_dyn is not None: mat.set_nu(nu_dyn, eles=[ele]) o3.analyze(osi, 10000, dt=dt) # o3.extensions.to_py_file(osi) stresses = o3.get_ele_response(osi, ele, 'stress') print('init_stress1: ', stresses) # Prepare for reading results exit_code = None stresses = o3.get_ele_response(osi, ele, 'stress') if dss: o3.gen_reactions(osi) force0 = o3.get_node_reaction(osi, nodes[2], o3.cc.DOF2D_X) force1 = o3.get_node_reaction(osi, nodes[3], o3.cc.DOF2D_X) # force2 = o3.get_node_reaction(osi, nodes[0], o3.cc.DOF2D_X) stress = [force1 + force0] strain = [o3.get_node_disp(osi, nodes[2], dof=o3.cc.DOF2D_X)] sxy_ind = None gxy_ind = None # iforce0 = o3.get_node_reaction(osi, nodes[0], o3.cc.DOF2D_X) # iforce1 = o3.get_node_reaction(osi, nodes[1], o3.cc.DOF2D_X) # iforce2 = o3.get_node_reaction(osi, nodes[2], o3.cc.DOF2D_X) # iforce3 = o3.get_node_reaction(osi, nodes[3], o3.cc.DOF2D_X) # print(iforce0, iforce1, iforce2, iforce3, stresses[2]) else: ro = o3.recorder.load_recorder_options() import pandas as pd df = pd.read_csv(ro) mat_type = ele.mat.type dfe = df[(df['mat'] == mat_type) & (df['form'] == oop)] df_sxy = dfe[dfe['recorder'] == 'stress'] outs = df_sxy['outs'].iloc[0].split('-') sxy_ind = outs.index('sxy') df_gxy = dfe[dfe['recorder'] == 'strain'] outs = df_gxy['outs'].iloc[0].split('-') gxy_ind = outs.index('gxy') stress = [stresses[sxy_ind]] cur_strains = o3.get_ele_response(osi, ele, 'strain') strain = [cur_strains[gxy_ind]] time_series = o3.time_series.Path(osi, time=[0, tload, 1e10], values=[0, 1, 1]) o3.pattern.Plain(osi, time_series) disps = list(np.array(strains) * 1) d_per_dt = 0.01 diff_disps = np.diff(disps, prepend=0) time_incs = np.abs(diff_disps) / d_per_dt approx_n_steps = time_incs / dt time_incs = np.where(approx_n_steps < 800, 800 * dt, time_incs) approx_n_steps = time_incs / dt assert min(approx_n_steps) >= 8, approx_n_steps curr_time = o3.get_time(osi) times = list(np.cumsum(time_incs) + curr_time) disps.append(disps[-1]) times.append(1e10) disps = list(disps) n_steps_p2 = int((times[-2] - curr_time) / dt) + 10 print('n_steps: ', n_steps_p2) times.insert(0, curr_time) disps.insert(0, 0.0) init_disp = o3.get_node_disp(osi, nodes[2], dof=o3.cc.X) disps = list(np.array(disps) + init_disp) ts0 = o3.time_series.Path(osi, time=times, values=disps, factor=1) pat0 = o3.pattern.Plain(osi, ts0) o3.SP(osi, nodes[2], dof=o3.cc.X, dof_values=[1]) o3.SP(osi, nodes[3], dof=o3.cc.X, dof_values=[1]) print('init_disp: ', init_disp) print('path -times: ', times) print('path -values: ', disps) v_eff = [stresses[1]] h_eff = [stresses[0]] time = [o3.get_time(osi)] for i in range(int(n_steps_p2 / 200)): print(i / (n_steps_p2 / 200)) fail = o3.analyze(osi, 200, dt=dt) o3.gen_reactions(osi) stresses = o3.get_ele_response(osi, ele, 'stress') v_eff.append(stresses[1]) h_eff.append(stresses[0]) if dss: o3.gen_reactions(osi) force0 = o3.get_node_reaction(osi, nodes[2], o3.cc.DOF2D_X) force1 = o3.get_node_reaction(osi, nodes[3], o3.cc.DOF2D_X) stress.append(force1 + force0) strain.append(o3.get_node_disp(osi, nodes[2], dof=o3.cc.DOF2D_X)) else: stress.append(stresses[sxy_ind]) cur_strains = o3.get_ele_response(osi, ele, 'strain') strain.append(cur_strains[gxy_ind]) time.append(o3.get_time(osi)) if fail: break return np.array(stress), np.array(strain)-init_disp, np.array(v_eff), np.array(h_eff), np.array(time), exit_code
def _run_dyn_1d_site_response(region_based=None): osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3) # Establish nodes node_depths = np.arange(0, 5, 1) n_node_rows = len(node_depths) x_nodes = np.arange(0, 2, 1) nx = len(x_nodes) nd = {} for yy in range(0, len(node_depths)): for xx in range(nx): # Establish left and right nodes nd[f"X{xx}Y{yy}"] = o3.node.Node(osi, x_nodes[xx], -node_depths[yy]) # set x and y dofs equal for left and right nodes o3.EqualDOF(osi, nd[f"X0Y{yy}"], nd[f"X{nx - 1}Y{yy}"], [o3.cc.X]) # Fix base nodes for xx in range(nx): o3.Fix2DOF(osi, nd[f"X{xx}Y{n_node_rows -1}"], o3.cc.FIXED, o3.cc.FIXED) for yy in range(0, len(node_depths) - 1): for xx in range(nx): o3.Fix2DOF(osi, nd[f"X{xx}Y{yy}"], o3.cc.FREE, o3.cc.FIXED) vs = 150.0 rho = 1.8 g_mod = vs**2 * rho poissons_ratio = 0.3 e_mod = 2 * g_mod * (1 + poissons_ratio) ele_thick = 1.0 soil_mat = o3.nd_material.ElasticIsotropic(osi, e_mod=e_mod, nu=poissons_ratio, rho=rho) eles = [] for yy in range(0, len(node_depths) - 1): for xx in range(nx - 1): # def element nodes = [ nd[f"X{xx}Y{yy + 1}"], nd[f"X{xx + 1}Y{yy + 1}"], nd[f"X{xx + 1}Y{yy}"], nd[f"X{xx}Y{yy}"] ] eles.append( o3.element.SSPquad(osi, nodes, soil_mat, o3.cc.PLANE_STRAIN, ele_thick, 0.0, 0.0)) freqs = np.array([0.5, 15.0]) xi = 0.1 # high damping to see effects ang_f = np.pi / freqs alpha_m = xi * 2.0 * ang_f[0] * ang_f[1] / (ang_f[0] + ang_f[1] ) # mass proportional beta_k = xi * 2.0 / (ang_f[0] + ang_f[1]) # stiffness proportional if region_based == 'node': o3.region.NodeRegion(osi, nodes='all', rayleigh={ 'alpha_m': alpha_m, 'beta_k_init': beta_k }) if region_based == 'ele': o3.region.ElementRegion(osi, eles='all', rayleigh={ 'alpha_m': alpha_m, 'beta_k_init': beta_k }) else: o3.rayleigh.Rayleigh(osi, alpha_m=alpha_m, beta_k=0.0, beta_k_init=beta_k, beta_k_comm=0.0) # Define the dynamic analysis dt = 0.01 vals = np.sin(np.linspace(0, np.pi, 50)) acc_series = o3.time_series.Path(osi, dt=dt, values=-vals) # should be negative o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series) # Run the dynamic analysis o3.wipe_analysis(osi) o3.algorithm.Newton(osi) o3.system.SparseGeneral(osi) o3.numberer.RCM(osi) o3.constraints.Transformation(osi) o3.integrator.Newmark(osi, 0.5, 0.25) o3.analysis.Transient(osi) o3.test_check.EnergyIncr(osi, tol=1.0e-3, max_iter=10) analysis_time = 1.0 analysis_dt = 0.001 rec_dt = 0.01 tn = o3.recorder.NodeToArrayCache(osi, nd["X0Y0"], [o3.cc.DOF2D_X], 'accel', dt=rec_dt) if region_based: o3.extensions.to_py_file(osi, 'wr.py') else: o3.extensions.to_py_file(osi, 'wor.py') curr_time = o3.get_time(osi) while curr_time < analysis_time: status = o3.analyze(osi, 1, analysis_dt) curr_time = o3.get_time(osi) if status != 0: print('Not ok') print(status) o3.wipe(osi) x_acc = tn.collect() return x_acc
def test_2d_site_period(): osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3) # Establish nodes node_depths = np.arange(0, 10, 1) n_node_rows = len(node_depths) x_nodes = np.arange(0, 10, 1) nx = len(x_nodes) nd = {} for yy in range(0, len(node_depths)): for xx in range(nx): # Establish left and right nodes nd[f"X{xx}Y{yy}"] = o3.node.Node(osi, x_nodes[xx], -node_depths[yy]) # set x and y dofs equal for left and right nodes o3.EqualDOF(osi, nd[f"X0Y{yy}"], nd[f"X{nx - 1}Y{yy}"], [o3.cc.X]) # Fix base nodes for xx in range(nx): o3.Fix2DOF(osi, nd[f"X{xx}Y{n_node_rows -1}"], o3.cc.FIXED, o3.cc.FIXED) for yy in range(0, len(node_depths) - 1): for xx in range(nx): o3.Fix2DOF(osi, nd[f"X{xx}Y{yy}"], o3.cc.FREE, o3.cc.FIXED) vs = 150.0 rho = 1.8 g_mod = vs**2 * rho poissons_ratio = 0.3 e_mod = 2 * g_mod * (1 + poissons_ratio) ele_thick = 1.0 soil_mat = o3.nd_material.ElasticIsotropic(osi, e_mod=e_mod, nu=poissons_ratio, rho=rho) eles = [] for yy in range(0, len(node_depths) - 1): for xx in range(nx - 1): # def element nodes = [ nd[f"X{xx}Y{yy + 1}"], nd[f"X{xx + 1}Y{yy + 1}"], nd[f"X{xx + 1}Y{yy}"], nd[f"X{xx}Y{yy}"] ] eles.append( o3.element.SSPquad(osi, nodes, soil_mat, o3.cc.PLANE_STRAIN, ele_thick, 0.0, 0.0)) # set damping based on first eigen mode angular_freq_sqrd = o3.get_eigen(osi, solver='fullGenLapack', n=1) if hasattr(angular_freq_sqrd, '__len__'): angular_freq = angular_freq_sqrd[0]**0.5 else: angular_freq = angular_freq_sqrd**0.5 # o3.extensions.to_py_file(osi, 'many_eles_2d.py') response_period = 2 * np.pi / angular_freq expected_period = 4 * max(node_depths) / vs print('response_period: ', response_period, expected_period, response_period / expected_period) assert np.isclose(response_period, expected_period, rtol=0.01)
def site_response(sp, asig, freqs=(0.5, 10), xi=0.03, analysis_dt=0.001, dy=0.5, analysis_time=None, outs=None, rec_dt=None, forder=1.0e3): """ Run seismic analysis of a soil profile Parameters ---------- sp: sfsimodels.SoilProfile object A soil profile asig: eqsig.AccSignal object An acceleration signal Returns ------- """ if analysis_time is None: analysis_time = asig.time[-1] if outs is None: outs = { 'ACCX': [0] } # Export the horizontal acceleration at the surface if rec_dt is None: rec_dt = analysis_dt osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3) assert isinstance(sp, sm.SoilProfile) sp.gen_split(props=['shear_vel', 'unit_mass'], target=dy) thicknesses = sp.split["thickness"] n_node_rows = len(thicknesses) + 1 node_depths = np.cumsum(sp.split["thickness"]) node_depths = np.insert(node_depths, 0, 0) ele_depths = (node_depths[1:] + node_depths[:-1]) / 2 grav = 9.81 omega_1 = 2 * np.pi * freqs[0] omega_2 = 2 * np.pi * freqs[1] a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2) a1 = 2 * xi / (omega_1 + omega_2) k0 = 0.5 pois = k0 / (1 + k0) newmark_gamma = 0.5 newmark_beta = 0.25 ele_width = min(thicknesses) # Define nodes and set boundary conditions for simple shear deformation # Start at top and build down? sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]] for i in range(1, n_node_rows): # Establish left and right nodes sn.append([ o3.node.Node(osi, 0, -node_depths[i]), o3.node.Node(osi, ele_width, -node_depths[i]) ]) if i != n_node_rows - 1: # set x and y dofs equal for left and right nodes o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y]) # Fix base nodes o3.Fix2DOF(osi, sn[-1][0], o3.cc.FREE, o3.cc.FIXED) o3.Fix2DOF(osi, sn[-1][1], o3.cc.FREE, o3.cc.FIXED) o3.EqualDOF(osi, sn[-1][0], sn[-1][1], [o3.cc.X]) # Define dashpot nodes dashpot_node_1 = o3.node.Node(osi, 0, -node_depths[-1]) dashpot_node_2 = sn[-1][0] o3.Fix2DOF(osi, dashpot_node_1, o3.cc.FIXED, o3.cc.FIXED) # define materials ele_thick = 1.0 # m soil_mats = [] prev_args = [] prev_kwargs = {} prev_sl_type = None eles = [] for i in range(len(thicknesses)): y_depth = ele_depths[i] sl_id = sp.get_layer_index_by_depth(y_depth) sl = sp.layer(sl_id) app2mod = {} if y_depth > sp.gwl: umass = sl.unit_sat_mass / forder else: umass = sl.unit_dry_mass / forder p_atm = 101e3 / forder # Define material if sl.o3_type == 'pm4sand': sl_class = o3.nd_material.PM4Sand overrides = {'nu': pois, 'p_atm': p_atm, 'unit_moist_mass': umass} app2mod = sl.app2mod elif sl.o3_type == 'sdmodel': sl_class = o3.nd_material.StressDensity overrides = {'nu': pois, 'p_atm': p_atm, 'unit_moist_mass': umass} app2mod = sl.app2mod elif sl.o3_type == 'pimy': sl_class = o3.nd_material.PressureIndependMultiYield overrides = { 'nu': pois, 'p_atm': p_atm, 'rho': umass, 'nd': 2.0, 'g_mod_ref': sl.g_mod / forder, 'bulk_mod_ref': sl.bulk_mod / forder, 'peak_strain': 0.05, 'cohesion': sl.cohesion / forder, 'phi': sl.phi, 'p_ref': 101e3 / forder, 'd': 0.0, 'n_surf': 25 } else: sl_class = o3.nd_material.ElasticIsotropic sl.e_mod = 2 * sl.g_mod * (1 + sl.poissons_ratio) / forder app2mod['rho'] = 'unit_moist_mass' overrides = {'nu': sl.poissons_ratio, 'unit_moist_mass': umass} args, kwargs = o3.extensions.get_o3_kwargs_from_obj( sl, sl_class, custom=app2mod, overrides=overrides) changed = 0 if sl.type != prev_sl_type or len(args) != len(prev_args) or len( kwargs) != len(prev_kwargs): changed = 1 else: for j, arg in enumerate(args): if not np.isclose(arg, prev_args[j]): changed = 1 for pm in kwargs: if pm not in prev_kwargs or not np.isclose( kwargs[pm], prev_kwargs[pm]): changed = 1 if changed: mat = sl_class(osi, *args, **kwargs) prev_sl_type = sl.type prev_args = copy.deepcopy(args) prev_kwargs = copy.deepcopy(kwargs) soil_mats.append(mat) # def element nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1], sn[i][0]] # anti-clockwise eles.append( o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick, 0.0, -grav)) # Static analysis o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=30, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.ProfileSPD(osi) o3.integrator.Newmark(osi, 5. / 6, 4. / 9) # include numerical damping o3.analysis.Transient(osi) o3.analyze(osi, 40, 1.) for i, soil_mat in enumerate(soil_mats): if hasattr(soil_mat, 'update_to_nonlinear'): print('Update model to nonlinear') soil_mat.update_to_nonlinear() o3.analyze(osi, 50, 0.5) o3.extensions.to_py_file(osi, 'ofile_sra_pimy_og.py') # reset time and analysis o3.set_time(osi, 0.0) o3.wipe_analysis(osi) # define material and element for viscous dampers base_sl = sp.layer(sp.n_layers) c_base = ele_width * base_sl.unit_dry_mass / forder * sp.get_shear_vel_at_depth( sp.height) dashpot_mat = o3.uniaxial_material.Viscous(osi, c_base, alpha=1.) o3.element.ZeroLength(osi, [dashpot_node_1, dashpot_node_2], mats=[dashpot_mat], dirs=[o3.cc.DOF2D_X]) ods = {} for otype in outs: if otype == 'ACCX': ods['ACCX'] = [] if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all': ods['ACCX'] = o3.recorder.NodesToArrayCache(osi, nodes=sn[:][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt) else: for i in range(len(outs['ACCX'])): ind = np.argmin(abs(node_depths - outs['ACCX'][i])) ods['ACCX'].append( o3.recorder.NodeToArrayCache(osi, node=sn[ind][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt)) if otype == 'TAU': ods['TAU'] = [] if isinstance(outs['TAU'], str) and outs['TAU'] == 'all': ods['TAU'] = o3.recorder.ElementsToArrayCache( osi, eles=eles, arg_vals=['stress'], dt=rec_dt) else: for i in range(len(outs['TAU'])): ind = np.argmin(abs(ele_depths - outs['TAU'][i])) ods['TAU'].append( o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['stress'], dt=rec_dt)) if otype == 'STRS': ods['STRS'] = [] if isinstance(outs['STRS'], str) and outs['STRS'] == 'all': ods['STRS'] = o3.recorder.ElementsToArrayCache( osi, eles=eles, arg_vals=['strain'], dt=rec_dt) else: for i in range(len(outs['STRS'])): ind = np.argmin(abs(ele_depths - outs['STRS'][i])) ods['STRS'].append( o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['strain'], dt=rec_dt)) ods['time'] = o3.recorder.TimeToArrayCache(osi, dt=rec_dt) # Run the dynamic analysis o3.algorithm.Newton(osi) o3.system.SparseGeneral(osi) o3.numberer.RCM(osi) o3.constraints.Transformation(osi) o3.integrator.Newmark(osi, newmark_gamma, newmark_beta) o3.rayleigh.Rayleigh(osi, a0, a1, 0, 0) o3.analysis.Transient(osi) o3.test_check.EnergyIncr(osi, tol=1.0e-7, max_iter=10) # Define the dynamic analysis ts_obj = o3.time_series.Path(osi, dt=asig.dt, values=asig.velocity * 1, factor=c_base) o3.pattern.Plain(osi, ts_obj) o3.Load(osi, sn[-1][0], [1., 0.]) o3.analyze(osi, int(analysis_time / analysis_dt), analysis_dt) o3.wipe(osi) out_dict = {} for otype in ods: if isinstance(ods[otype], list): out_dict[otype] = [] for i in range(len(ods[otype])): out_dict[otype].append(ods[otype][i].collect()) out_dict[otype] = np.array(out_dict[otype]) else: out_dict[otype] = ods[otype].collect().T return out_dict
def gen_response(period, xi, asig, etype, fos_for_dt=None): # Define inelastic SDOF mass = 1.0 f_yield = 1.5 # Reduce this to make it nonlinear r_post = 0.0 # Initialise OpenSees instance osi = o3.OpenSeesInstance(ndm=2, state=0) # Establish nodes bot_node = o3.node.Node(osi, 0, 0) top_node = o3.node.Node(osi, 0, 0) # Fix bottom node o3.Fix3DOF(osi, top_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED) o3.Fix3DOF(osi, bot_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED) # Set out-of-plane DOFs to be slaved o3.EqualDOF(osi, top_node, bot_node, [o3.cc.Y, o3.cc.ROTZ]) # nodal mass (weight / g): o3.Mass(osi, top_node, mass, 0., 0.) # Define material k_spring = 4 * np.pi**2 * mass / period**2 # bilinear_mat = o3.uniaxial_material.Steel01(osi, fy=f_yield, e0=k_spring, b=r_post) mat = o3.uniaxial_material.Elastic(osi, e_mod=k_spring) # Assign zero length element, # Note: pass actual node and material objects into element o3.element.ZeroLength(osi, [bot_node, top_node], mats=[mat], dirs=[o3.cc.DOF2D_X], r_flag=1) # Define the dynamic analysis # Define the dynamic analysis acc_series = o3.time_series.Path(osi, dt=asig.dt, values=-1 * asig.values) # should be negative o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series) # set damping based on first eigen mode angular_freq = o3.get_eigen(osi, solver='fullGenLapack', n=1)[0]**0.5 period = 2 * np.pi / angular_freq beta_k = 2 * xi / angular_freq o3.rayleigh.Rayleigh(osi, alpha_m=0.0, beta_k=beta_k, beta_k_init=0.0, beta_k_comm=0.0) o3.set_time(osi, 0.0) # Run the dynamic analysis o3.wipe_analysis(osi) # Run the dynamic analysis o3.numberer.RCM(osi) o3.system.FullGeneral(osi) if etype == 'central_difference': o3.algorithm.Linear(osi, factor_once=True) o3.integrator.CentralDifference(osi) explicit_dt = 2 / angular_freq / fos_for_dt analysis_dt = explicit_dt elif etype == 'implicit': o3.algorithm.Newton(osi) o3.integrator.Newmark(osi, gamma=0.5, beta=0.25) analysis_dt = 0.001 else: raise ValueError() o3.constraints.Transformation(osi) o3.analysis.Transient(osi) o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10) analysis_time = asig.time[-1] outputs = { "time": [], "rel_disp": [], "rel_accel": [], "rel_vel": [], "force": [] } rec_dt = 0.002 n_incs = int(analysis_dt / rec_dt) n_incs = 1 while o3.get_time(osi) < analysis_time: o3.analyze(osi, n_incs, analysis_dt) curr_time = o3.get_time(osi) outputs["time"].append(curr_time) outputs["rel_disp"].append(o3.get_node_disp(osi, top_node, o3.cc.X)) outputs["rel_vel"].append(o3.get_node_vel(osi, top_node, o3.cc.X)) outputs["rel_accel"].append(o3.get_node_accel(osi, top_node, o3.cc.X)) o3.gen_reactions(osi) outputs["force"].append(-o3.get_node_reaction( osi, bot_node, o3.cc.X)) # Negative since diff node o3.wipe(osi) for item in outputs: outputs[item] = np.array(outputs[item]) return outputs
def run(out_folder): osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3) x_centre = 0.0 y_centre = 0.0 top_node = o3.node.Node(osi, x_centre, y_centre) fd_area = 1 fd_e_mod = 1e9 fd_iz = 1e6 top_nodes = [] bot_nodes = [] sf_eles = [] fd_eles = [] o3.Mass(osi, top_node, 10, 10) fy = 500 k = 1.0e4 b = 0.1 pro_params = [5, 0.925, 0.15] sf_mat = o3.uniaxial_material.SteelMPF(osi, fy, fy, k, b, b, params=pro_params) diff_pos = 0.5 depth = 1 bot_nodes.append(o3.node.Node(osi, x_centre - diff_pos, y_centre - depth)) o3.Fix2DOF(osi, bot_nodes[0], o3.cc.FIXED, o3.cc.FIXED) bot_nodes.append(o3.node.Node(osi, x_centre + diff_pos, y_centre - depth)) o3.Fix2DOF(osi, bot_nodes[1], o3.cc.FIXED, o3.cc.FIXED) top_nodes.append(o3.node.Node(osi, x_centre, y_centre)) sf_eles.append( o3.element.Truss(osi, [top_nodes[0], bot_nodes[0]], big_a=1.0, mat=sf_mat)) sf_eles.append( o3.element.Truss(osi, [top_nodes[0], bot_nodes[1]], big_a=1.0, mat=sf_mat)) o3.EqualDOF(osi, top_node, top_nodes[0], dofs=[o3.cc.DOF2D_X, o3.cc.DOF2D_Y]) ts0 = o3.time_series.Linear(osi, factor=1) o3.pattern.Plain(osi, ts0) o3.Load(osi, top_node, [100, -500]) o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=35, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.FullGeneral(osi) n_steps_gravity = 15 d_gravity = 1. / n_steps_gravity o3.integrator.LoadControl(osi, d_gravity, num_iter=10) # o3.rayleigh.Rayleigh(osi, a0, a1, 0.0, 0.0) o3.analysis.Static(osi) o3r = o3.results.Results2D(cache_path=out_folder, dynamic=True) o3r.pseudo_dt = 0.1 o3r.start_recorders(osi, dt=0.1) nr = o3.recorder.NodeToArrayCache(osi, top_node, [o3.cc.DOF2D_X, o3.cc.DOF2D_Y], 'disp') er = o3.recorder.ElementToArrayCache(osi, sf_eles[0], arg_vals=['force']) for i in range(n_steps_gravity): o3.analyze(osi, num_inc=1) o3.load_constant(osi, time=0.0) import o3seespy.extensions o3.extensions.to_py_file(osi, 'ofile.py') print('init_disp: ', o3.get_node_disp(osi, top_node, o3.cc.DOF2D_Y)) print('init_disp: ', o3.get_node_disp(osi, top_nodes[0], o3.cc.DOF2D_Y)) print('init_disp: ', o3.get_node_disp(osi, top_nodes[-1], o3.cc.DOF2D_Y)) o3.wipe(osi) o3r.save_to_cache() # o3r.coords = o3.get_all_node_coords(osi) # o3r.ele2node_tags = o3.get_all_ele_node_tags_as_dict(osi) data = nr.collect() edata = er.collect() # bf, sps = plt.subplots(nrows=2) # sps[0].plot(data[:, 0]) # sps[0].plot(data[:, 1]) # sps[1].plot(edata[:, 0]) # # sps[0].plot(data[1]) # plt.show() o3r.load_from_cache() o3plot.replot(o3r)
def run_2d_strain_driver(osi, mat, esig_v0, disps, target_d_inc=0.00001, handle='silent', verbose=0): k0 = 1.0 pois = k0 / (1 + k0) damp = 0.05 omega0 = 0.2 omega1 = 20.0 a1 = 2. * damp / (omega0 + omega1) a0 = a1 * omega0 * omega1 # Establish nodes h_ele = 1. nodes = [ o3.node.Node(osi, 0.0, 0.0), o3.node.Node(osi, h_ele, 0.0), o3.node.Node(osi, h_ele, h_ele), o3.node.Node(osi, 0.0, h_ele) ] # Fix bottom node o3.Fix2DOF(osi, nodes[0], o3.cc.FIXED, o3.cc.FIXED) o3.Fix2DOF(osi, nodes[1], o3.cc.FIXED, o3.cc.FIXED) o3.Fix2DOF(osi, nodes[2], o3.cc.FREE, o3.cc.FREE) o3.Fix2DOF(osi, nodes[3], o3.cc.FREE, o3.cc.FREE) # Set out-of-plane DOFs to be slaved o3.EqualDOF(osi, nodes[2], nodes[3], [o3.cc.X, o3.cc.Y]) ele = o3.element.SSPquad(osi, nodes, mat, 'PlaneStrain', 1, 0.0, 0.0) o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-3, max_iter=35, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.FullGeneral(osi) o3.integrator.DisplacementControl(osi, nodes[2], o3.cc.DOF2D_Y, 0.005) # o3.rayleigh.Rayleigh(osi, a0, a1, 0.0, 0.0) o3.analysis.Static(osi) o3.update_material_stage(osi, mat, stage=0) # Add static vertical pressure and stress bias # time_series = o3.time_series.Path(osi, time=[0, 100, 1e10], values=[0, 1, 1]) # o3.pattern.Plain(osi, time_series) ts0 = o3.time_series.Linear(osi, factor=1) o3.pattern.Plain(osi, ts0) o3.Load(osi, nodes[2], [0, -esig_v0 / 2]) o3.Load(osi, nodes[3], [0, -esig_v0 / 2]) o3.analyze(osi, num_inc=100) stresses = o3.get_ele_response(osi, ele, 'stress') print('init_stress0: ', stresses) # ts2 = o3.time_series.Path(osi, time=[110, 80000, 1e10], values=[1., 1., 1.], factor=1) # o3.pattern.Plain(osi, ts2, fact=1.) # y_vert = o3.get_node_disp(osi, nodes[2], o3.cc.Y) # o3.SP(osi, nodes[3], dof=o3.cc.Y, dof_values=[y_vert]) # o3.SP(osi, nodes[2], dof=o3.cc.Y, dof_values=[y_vert]) # # o3.analyze(osi, 25, dt=1) o3.wipe_analysis(osi) o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=35, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.FullGeneral(osi) o3.analysis.Static(osi) o3.update_material_stage(osi, mat, stage=1) o3.analyze(osi, 25, dt=1) # o3.set_parameter(osi, value=sl.poissons_ratio, eles=[ele], args=['poissonRatio', 1]) # o3.extensions.to_py_file(osi) stresses = o3.get_ele_response(osi, ele, 'stress') print('init_stress1: ', stresses) exit_code = None strain = [0] stresses = o3.get_ele_response(osi, ele, 'stress') force0 = o3.get_node_reaction(osi, nodes[0], o3.cc.DOF2D_X) force1 = o3.get_node_reaction(osi, nodes[1], o3.cc.DOF2D_X) stress = [-force0 - force1] v_eff = [stresses[1]] h_eff = [stresses[0]] d_incs = np.diff(disps, prepend=0) for i in range(len(disps)): d_inc_i = d_incs[i] if target_d_inc < abs(d_inc_i): n = int(abs(d_inc_i / target_d_inc)) d_step = d_inc_i / n else: n = 1 d_step = d_inc_i for j in range(n): o3.integrator.DisplacementControl(osi, nodes[2], o3.cc.DOF2D_X, -d_step) o3.Load(osi, nodes[2], [1.0, 0.0]) o3.Load(osi, nodes[3], [1.0, 0.0]) o3.analyze(osi, 1) o3.gen_reactions(osi) stresses = o3.get_ele_response(osi, ele, 'stress') print(stresses) v_eff.append(stresses[1]) h_eff.append(stresses[0]) force0 = o3.get_node_reaction(osi, nodes[0], o3.cc.DOF2D_X) force1 = o3.get_node_reaction(osi, nodes[1], o3.cc.DOF2D_X) stress.append(-force0 - force1) end_strain = o3.get_node_disp(osi, nodes[2], dof=o3.cc.DOF2D_X) strain.append(end_strain) return -np.array(stress), -np.array(strain), np.array(v_eff), np.array(h_eff), exit_code
def run_analysis(asig, period, xi, f_yield, etype): # Load a ground motion # Define inelastic SDOF mass = 1.0 r_post = 0.0 # Initialise OpenSees instance osi = o3.OpenSeesInstance(ndm=2, state=0) # Establish nodes bot_node = o3.node.Node(osi, 0, 0) top_node = o3.node.Node(osi, 0, 0) # Fix bottom node o3.Fix3DOF(osi, top_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED) o3.Fix3DOF(osi, bot_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED) # Set out-of-plane DOFs to be slaved o3.EqualDOF(osi, top_node, bot_node, [o3.cc.Y, o3.cc.ROTZ]) # nodal mass (weight / g): o3.Mass(osi, top_node, mass, 0., 0.) # Define material k_spring = 4 * np.pi**2 * mass / period**2 bilinear_mat = o3.uniaxial_material.Steel01(osi, fy=f_yield, e0=k_spring, b=r_post) # Assign zero length element, # Note: pass actual node and material objects into element o3.element.ZeroLength(osi, [bot_node, top_node], mats=[bilinear_mat], dirs=[o3.cc.DOF2D_X], r_flag=1) # Define the dynamic analysis # Define the dynamic analysis acc_series = o3.time_series.Path(osi, dt=asig.dt, values=-1 * asig.values) # should be negative o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series) # set damping based on first eigen mode angular_freqs = np.array(o3.get_eigen(osi, solver='fullGenLapack', n=1))**0.5 beta_k = 2 * xi / angular_freqs[0] print('angular_freqs: ', angular_freqs) periods = 2 * np.pi / angular_freqs o3.rayleigh.Rayleigh(osi, alpha_m=0.0, beta_k=beta_k, beta_k_init=0.0, beta_k_comm=0.0) # Run the dynamic analysis o3.wipe_analysis(osi) # Run the dynamic analysis o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=35, p_flag=0) o3.numberer.RCM(osi) if etype == 'implicit': o3.algorithm.Newton(osi) o3.system.SparseGeneral(osi) o3.integrator.Newmark(osi, gamma=0.5, beta=0.25) analysis_dt = 0.01 else: o3.algorithm.Linear(osi, factor_once=True) o3.system.FullGeneral(osi) if etype == 'newmark_explicit': o3.integrator.NewmarkExplicit(osi, gamma=0.6) explicit_dt = periods[0] / np.pi / 32 elif etype == 'central_difference': o3.integrator.CentralDifference(osi) o3.opy.integrator('HHTExplicit') explicit_dt = periods[0] / np.pi / 16 # 0.5 is a factor of safety elif etype == 'explicit_difference': o3.integrator.ExplicitDifference(osi) explicit_dt = periods[0] / np.pi / 32 else: raise ValueError(etype) print('explicit_dt: ', explicit_dt) analysis_dt = explicit_dt o3.analysis.Transient(osi) analysis_time = asig.time[-1] outputs = { "time": [], "rel_disp": [], "rel_accel": [], "rel_vel": [], "force": [] } while o3.get_time(osi) < analysis_time: o3.analyze(osi, 1, analysis_dt) curr_time = o3.get_time(osi) outputs["time"].append(curr_time) outputs["rel_disp"].append(o3.get_node_disp(osi, top_node, o3.cc.X)) outputs["rel_vel"].append(o3.get_node_vel(osi, top_node, o3.cc.X)) outputs["rel_accel"].append(o3.get_node_accel(osi, top_node, o3.cc.X)) o3.gen_reactions(osi) outputs["force"].append(-o3.get_node_reaction( osi, bot_node, o3.cc.X)) # Negative since diff node o3.wipe(osi) for item in outputs: outputs[item] = np.array(outputs[item]) return outputs
def site_response(sp, dy=0.5, forder=1.0e3, static=0): """ Run gravity analysis of a soil profile Parameters ---------- sp: sfsimodels.SoilProfile object A soil profile Returns ------- """ osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3) assert isinstance(sp, sm.SoilProfile) sp.gen_split(props=['shear_vel', 'unit_mass', 'g_mod', 'poissons_ratio'], target=dy) thicknesses = sp.split["thickness"] n_node_rows = len(thicknesses) + 1 node_depths = np.cumsum(sp.split["thickness"]) node_depths = np.insert(node_depths, 0, 0) ele_depths = (node_depths[1:] + node_depths[:-1]) / 2 rho = sp.split['unit_mass'] g_mod = sp.split['g_mod'] poi = sp.split['poissons_ratio'] lam = 2 * g_mod * poi / (1 - 2 * poi) mu = g_mod v_dil = np.sqrt((lam + 2 * mu) / rho) ele_h = sp.split['thickness'] dts = ele_h / v_dil min_dt = min(dts) print('min_dt: ', min_dt) grav = 9.81 ele_width = min(thicknesses) # Define nodes and set boundary conditions for simple shear deformation # Start at top and build down? sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]] for i in range(1, n_node_rows): # Establish left and right nodes sn.append([ o3.node.Node(osi, 0, -node_depths[i]), o3.node.Node(osi, ele_width, -node_depths[i]) ]) # set x and y dofs equal for left and right nodes o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y]) # Fix base nodes o3.Fix2DOF(osi, sn[-1][0], o3.cc.FIXED, o3.cc.FIXED) o3.Fix2DOF(osi, sn[-1][1], o3.cc.FIXED, o3.cc.FIXED) # define materials ele_thick = 1.0 # m soil_mats = [] prev_args = [] prev_kwargs = {} prev_sl_type = None eles = [] for i in range(len(thicknesses)): y_depth = ele_depths[i] sl_id = sp.get_layer_index_by_depth(y_depth) sl = sp.layer(sl_id) app2mod = {} if y_depth > sp.gwl: umass = sl.unit_sat_mass / forder else: umass = sl.unit_dry_mass / forder # Define material sl_class = o3.nd_material.ElasticIsotropic sl.e_mod = 2 * sl.g_mod * (1 + sl.poissons_ratio) / forder app2mod['rho'] = 'unit_moist_mass' overrides = {'nu': sl.poissons_ratio, 'unit_moist_mass': umass} args, kwargs = o3.extensions.get_o3_kwargs_from_obj( sl, sl_class, custom=app2mod, overrides=overrides) changed = 0 if sl.type != prev_sl_type or len(args) != len(prev_args) or len( kwargs) != len(prev_kwargs): changed = 1 else: for j, arg in enumerate(args): if not np.isclose(arg, prev_args[j]): changed = 1 for pm in kwargs: if pm not in prev_kwargs or not np.isclose( kwargs[pm], prev_kwargs[pm]): changed = 1 if changed: mat = sl_class(osi, *args, **kwargs) prev_sl_type = sl.type prev_args = copy.deepcopy(args) prev_kwargs = copy.deepcopy(kwargs) soil_mats.append(mat) # def element nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1], sn[i][0]] # anti-clockwise eles.append( o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick, 0.0, -grav)) # Gravity analysis if not static: o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=30, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.ProfileSPD(osi) o3.integrator.Newmark(osi, 5. / 6, 4. / 9) # include numerical damping o3.analysis.Transient(osi) o3.analyze(osi, 40, 1.) # reset time and analysis o3.set_time(osi, 0.0) o3.wipe_analysis(osi) else: o3.domain_change(osi) o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=10, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.apply_rcm(osi) o3.system.Mumps(osi) o3.integrator.LoadControl(osi, 0.1) o3.analysis.Static(osi) o3.analyze(osi, 10) ys = [] for nn in range(len(sn)): nd = sn[nn][0] ys.append(o3.get_node_disp(osi, nd, dof=o3.cc.Y)) return np.array(ys)
def site_response(sp, asig, linear=0): """ Run seismic analysis of a soil profile - example based on: http://opensees.berkeley.edu/wiki/index.php/Site_Response_Analysis_of_a_Layered_Soil_Column_(Total_Stress_Analysis) :param sp: sfsimodels.SoilProfile object A soil profile :param asig: eqsig.AccSignal object An acceleration signal :return: """ osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3) assert isinstance(sp, sm.SoilProfile) sp.gen_split(props=['shear_vel', 'unit_mass', 'cohesion', 'phi', 'bulk_mod', 'poissons_ratio', 'strain_peak']) thicknesses = sp.split["thickness"] n_node_rows = len(thicknesses) + 1 node_depths = np.cumsum(sp.split["thickness"]) node_depths = np.insert(node_depths, 0, 0) ele_depths = (node_depths[1:] + node_depths[:-1]) / 2 shear_vels = sp.split["shear_vel"] unit_masses = sp.split["unit_mass"] / 1e3 g_mods = unit_masses * shear_vels ** 2 poissons_ratio = sp.split['poissons_ratio'] youngs_mods = 2 * g_mods * (1 - poissons_ratio) bulk_mods = youngs_mods / (3 * (1 - 2 * poissons_ratio)) bulk_mods = sp.split['bulk_mod'] / 1e3 ref_pressure = 80.0 cohesions = sp.split['cohesion'] / 1e3 phis = sp.split['phi'] strain_peaks = sp.split['strain_peak'] grav = 9.81 damping = 0.03 omega_1 = 2 * np.pi * 0.5 omega_2 = 2 * np.pi * 10 a0 = 2 * damping * omega_1 * omega_2 / (omega_1 + omega_2) a1 = 2 * damping / (omega_1 + omega_2) newmark_gamma = 0.5 newmark_beta = 0.25 ele_width = min(thicknesses) total_soil_nodes = len(thicknesses) * 2 + 2 # Define nodes and set boundary conditions for simple shear deformation # Start at top and build down? nd = OrderedDict() nd["R0L"] = o3.node.Node(osi, 0, 0) # row 0 left nd["R0R"] = o3.node.Node(osi, ele_width, 0) for i in range(1, n_node_rows): # Establish left and right nodes nd[f"R{i}L"] = o3.node.Node(osi, 0, -node_depths[i]) nd[f"R{i}R"] = o3.node.Node(osi, ele_width, -node_depths[i]) # set x and y dofs equal for left and right nodes o3.EqualDOF(osi, nd[f"R{i}L"], nd[f"R{i}R"], [o3.cc.X, o3.cc.Y]) # Fix base nodes o3.Fix2DOF(osi, nd[f"R{n_node_rows - 1}L"], o3.cc.FREE, o3.cc.FIXED) o3.Fix2DOF(osi, nd[f"R{n_node_rows - 1}R"], o3.cc.FREE, o3.cc.FIXED) # Define dashpot nodes dashpot_node_l = o3.node.Node(osi, 0, -node_depths[-1]) dashpot_node_2 = o3.node.Node(osi, 0, -node_depths[-1]) o3.Fix2DOF(osi, dashpot_node_l, o3.cc.FIXED, o3.cc.FIXED) o3.Fix2DOF(osi, dashpot_node_2, o3.cc.FREE, o3.cc.FIXED) # define equal DOF for dashpot and soil base nodes o3.EqualDOF(osi, nd[f"R{n_node_rows - 1}L"], nd[f"R{n_node_rows - 1}R"], [o3.cc.X]) o3.EqualDOF(osi, nd[f"R{n_node_rows - 1}L"], dashpot_node_2, [o3.cc.X]) # define materials ele_thick = 1.0 # m soil_mats = [] strains = np.logspace(-6, -0.5, 16) ref_strain = 0.005 rats = 1. / (1 + (strains / ref_strain) ** 0.91) eles = [] for i in range(len(thicknesses)): if not linear: mat = o3.nd_material.PressureIndependMultiYield(osi, 2, unit_masses[i], g_mods[i], bulk_mods[i], cohesions[i], strain_peaks[i], phis[i], d=0.0, n_surf=16, strains=strains, ratios=rats) else: mat = o3.nd_material.ElasticIsotropic(osi, youngs_mods[i], poissons_ratio[i], rho=unit_masses[i]) soil_mats.append(mat) # def element nodes = [nd[f"R{i + 1}L"], nd[f"R{i + 1}R"], nd[f"R{i}R"], nd[f"R{i}L"]] ele = o3.element.Quad(osi, nodes, ele_thick, o3.cc.PLANE_STRAIN, mat, b2=grav * unit_masses[i]) eles.append(ele) # define material and element for viscous dampers c_base = ele_width * unit_masses[-1] * shear_vels[-1] dashpot_mat = o3.uniaxial_material.Viscous(osi, c_base, alpha=1.) o3.element.ZeroLength(osi, [dashpot_node_l, dashpot_node_2], mats=[dashpot_mat], dirs=[o3.cc.DOF2D_X]) # Static analysis o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-4, max_iter=30, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.ProfileSPD(osi) o3.integrator.Newmark(osi, newmark_gamma, newmark_beta) o3.analysis.Transient(osi) o3.analyze(osi, 40, 1.) # for i in range(len(soil_mats)): # o3.update_material_stage(osi, soil_mats[i], 1) o3.analyze(osi, 50, 0.5) # reset time and analysis o3.set_time(osi, 0.0) o3.wipe_analysis(osi) na = o3.recorder.NodeToArrayCache(osi, node=nd["R0L"], dofs=[o3.cc.X], res_type='accel') es = o3.recorder.ElementsToArrayCache(osi, eles=eles, arg_vals=['stress']) # Define the dynamic analysis ts_obj = o3.time_series.Path(osi, dt=asig.dt, values=asig.velocity * -1, factor=c_base) o3.pattern.Plain(osi, ts_obj) o3.Load(osi, nd["R{0}L".format(n_node_rows - 1)], [1., 0.]) # Run the dynamic analysis o3.algorithm.Newton(osi) o3.system.SparseGeneral(osi) o3.numberer.RCM(osi) o3.constraints.Transformation(osi) o3.integrator.Newmark(osi, newmark_gamma, newmark_beta) o3.rayleigh.Rayleigh(osi, a0, a1, 0, 0) o3.analysis.Transient(osi) o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10) analysis_time = asig.time[-1] analysis_dt = 0.01 # o3.extensions.to_py_file(osi) while o3.get_time(osi) < analysis_time: o3.analyze(osi, 1, analysis_dt) o3.wipe(osi) outputs = { "time": np.arange(0, analysis_time, analysis_dt), "rel_disp": [], "rel_accel": na.collect(), 'ele_stresses': es.collect() } return outputs
def site_response(sp, asig, freqs=(0.5, 10), xi=0.03, dtype='rayleigh', analysis_dt=0.001, dy=0.5, analysis_time=None, outs=None, rec_dt=None): """ Run seismic analysis of a soil profile Parameters ---------- sp: sfsimodels.SoilProfile object A soil profile asig: eqsig.AccSignal object An acceleration signal Returns ------- """ if analysis_time is None: analysis_time = asig.time[-1] if outs is None: outs = { 'ACCX': [0] } # Export the horizontal acceleration at the surface if rec_dt is None: rec_dt = analysis_dt osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3) assert isinstance(sp, sm.SoilProfile) sp.gen_split(props=['shear_vel', 'unit_mass'], target=dy) thicknesses = sp.split["thickness"] n_node_rows = len(thicknesses) + 1 node_depths = np.cumsum(sp.split["thickness"]) node_depths = np.insert(node_depths, 0, 0) ele_depths = (node_depths[1:] + node_depths[:-1]) / 2 grav = 9.81 k0 = 0.5 pois = k0 / (1 + k0) newmark_gamma = 0.5 newmark_beta = 0.25 ele_width = min(thicknesses) # Define nodes and set boundary conditions for simple shear deformation # Start at top and build down? sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]] for i in range(1, n_node_rows): # Establish left and right nodes sn.append([ o3.node.Node(osi, 0, -node_depths[i]), o3.node.Node(osi, ele_width, -node_depths[i]) ]) # set x and y dofs equal for left and right nodes o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y]) # Fix base nodes o3.Fix2DOF(osi, sn[-1][0], o3.cc.FIXED, o3.cc.FIXED) o3.Fix2DOF(osi, sn[-1][1], o3.cc.FIXED, o3.cc.FIXED) # define materials ele_thick = 1.0 # m soil_mats = [] prev_pms = [0, 0, 0] eles = [] for i in range(len(thicknesses)): y_depth = ele_depths[i] sl_id = sp.get_layer_index_by_depth(y_depth) sl = sp.layer(sl_id) # Define material e_mod = 2 * sl.g_mod * (1 + sl.poissons_ratio) umass = sl.unit_dry_mass nu = sl.poissons_ratio pms = [e_mod, nu, umass] changed = 0 for pp in range(len(pms)): if not np.isclose(pms[pp], prev_pms[pp]): changed = 1 if changed: mat = o3.nd_material.ElasticIsotropic(osi, e_mod=e_mod, nu=nu, rho=umass) soil_mats.append(mat) # def element nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1], sn[i][0]] # anti-clockwise eles.append( o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick, 0.0, grav * umass)) # Static analysis o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=30, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.ProfileSPD(osi) o3.integrator.Newmark(osi, 5. / 6, 4. / 9) # include numerical damping o3.analysis.Transient(osi) o3.analyze(osi, 40, 1.) # reset time and analysis o3.set_time(osi, 0.0) o3.wipe_analysis(osi) ods = {} for otype in outs: if otype == 'ACCX': ods['ACCX'] = [] if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all': ods['ACCX'] = o3.recorder.NodesToArrayCache(osi, nodes=sn[:][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt) else: for i in range(len(outs['ACCX'])): ind = np.argmin(abs(node_depths - outs['ACCX'][i])) ods['ACCX'].append( o3.recorder.NodeToArrayCache(osi, node=sn[ind][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt)) # Run the dynamic analysis o3.algorithm.Newton(osi) o3.system.SparseGeneral(osi) o3.numberer.RCM(osi) o3.constraints.Transformation(osi) o3.integrator.Newmark(osi, newmark_gamma, newmark_beta) if dtype == 'rayleigh': omega_1 = 2 * np.pi * freqs[0] omega_2 = 2 * np.pi * freqs[1] a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2) a1 = 2 * xi / (omega_1 + omega_2) o3.rayleigh.Rayleigh(osi, a0, a1, 0, 0) else: n = 20 omegas = np.array(o3.get_eigen(osi, n=n))**0.5 o3.ModalDamping(osi, [xi]) o3.analysis.Transient(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-7, max_iter=10) # Define the dynamic analysis acc_series = o3.time_series.Path(osi, dt=asig.dt, values=asig.values) o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series) while o3.get_time(osi) < analysis_time: print(o3.get_time(osi)) if o3.analyze(osi, 1, analysis_dt): print('failed') break o3.wipe(osi) out_dict = {} for otype in ods: if isinstance(ods[otype], list): out_dict[otype] = [] for i in range(len(ods[otype])): out_dict[otype].append(ods[otype][i].collect()) out_dict[otype] = np.array(out_dict[otype]) else: out_dict[otype] = ods[otype].collect().T out_dict['time'] = np.arange(0, analysis_time, rec_dt) return out_dict
def site_response(sp, asig, freqs=(0.5, 10), xi=0.03, analysis_dt=0.001, dy=0.5, analysis_time=None, outs=None, rec_dt=None, use_explicit=0): """ Run seismic analysis of a soil profile that has a compliant base Parameters ---------- sp: sfsimodels.SoilProfile object A soil profile asig: eqsig.AccSignal object An acceleration signal Returns ------- """ if analysis_time is None: analysis_time = asig.time[-1] if outs is None: outs = { 'ACCX': [0] } # Export the horizontal acceleration at the surface if rec_dt is None: rec_dt = analysis_dt osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3) assert isinstance(sp, sm.SoilProfile) sp.gen_split(props=['shear_vel', 'unit_mass'], target=dy) thicknesses = sp.split["thickness"] n_node_rows = len(thicknesses) + 1 node_depths = np.cumsum(sp.split["thickness"]) node_depths = np.insert(node_depths, 0, 0) ele_depths = (node_depths[1:] + node_depths[:-1]) / 2 unit_masses = sp.split["unit_mass"] / 1e3 grav = 9.81 omega_1 = 2 * np.pi * freqs[0] omega_2 = 2 * np.pi * freqs[1] a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2) a1 = 2 * xi / (omega_1 + omega_2) k0 = 0.5 pois = k0 / (1 + k0) newmark_gamma = 0.5 newmark_beta = 0.25 ele_width = min(thicknesses) # Define nodes and set boundary conditions for simple shear deformation # Start at top and build down? sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]] for i in range(1, n_node_rows): # Establish left and right nodes sn.append([ o3.node.Node(osi, 0, -node_depths[i]), o3.node.Node(osi, ele_width, -node_depths[i]) ]) # set x and y dofs equal for left and right nodes o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y]) # Fix base nodes o3.Fix2DOF(osi, sn[-1][0], o3.cc.FREE, o3.cc.FIXED) o3.Fix2DOF(osi, sn[-1][1], o3.cc.FREE, o3.cc.FIXED) # Define dashpot nodes dashpot_node_l = o3.node.Node(osi, 0, -node_depths[-1]) dashpot_node_2 = o3.node.Node(osi, 0, -node_depths[-1]) o3.Fix2DOF(osi, dashpot_node_l, o3.cc.FIXED, o3.cc.FIXED) o3.Fix2DOF(osi, dashpot_node_2, o3.cc.FREE, o3.cc.FIXED) # define equal DOF for dashpot and soil base nodes o3.EqualDOF(osi, sn[-1][0], sn[-1][1], [o3.cc.X]) o3.EqualDOF(osi, sn[-1][0], dashpot_node_2, [o3.cc.X]) # define materials ele_thick = 1.0 # m soil_mats = [] prev_args = [] prev_kwargs = {} prev_sl_type = None eles = [] for i in range(len(thicknesses)): y_depth = ele_depths[i] sl_id = sp.get_layer_index_by_depth(y_depth) sl = sp.layer(sl_id) app2mod = {} if y_depth > sp.gwl: umass = sl.unit_sat_mass / 1e3 else: umass = sl.unit_dry_mass / 1e3 # Define material sl_class = o3.nd_material.ElasticIsotropic sl.e_mod = 2 * sl.g_mod * (1 + sl.poissons_ratio) / 1e3 app2mod['rho'] = 'unit_moist_mass' overrides = {'nu': sl.poissons_ratio, 'unit_moist_mass': umass} args, kwargs = o3.extensions.get_o3_kwargs_from_obj( sl, sl_class, custom=app2mod, overrides=overrides) changed = 0 if sl.type != prev_sl_type or len(args) != len(prev_args) or len( kwargs) != len(prev_kwargs): changed = 1 else: for j, arg in enumerate(args): if not np.isclose(arg, prev_args[j]): changed = 1 for pm in kwargs: if pm not in prev_kwargs or not np.isclose( kwargs[pm], prev_kwargs[pm]): changed = 1 if changed: mat = sl_class(osi, *args, **kwargs) prev_sl_type = sl.type prev_args = copy.deepcopy(args) prev_kwargs = copy.deepcopy(kwargs) soil_mats.append(mat) # def element nodes = [sn[i + 1][0], sn[i + 1][1], sn[i][1], sn[i][0]] # anti-clockwise eles.append( o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick, 0.0, -grav)) # eles.append(o3.element.Quad(osi, nodes, mat=mat, otype=o3.cc.PLANE_STRAIN, thick=ele_thick, pressure=0.0, rho=unit_masses[i], b2=grav)) # define material and element for viscous dampers base_sl = sp.layer(sp.n_layers) c_base = ele_width * base_sl.unit_dry_mass / 1e3 * sp.get_shear_vel_at_depth( sp.height) dashpot_mat = o3.uniaxial_material.Viscous(osi, c_base, alpha=1.) o3.element.ZeroLength(osi, [dashpot_node_l, dashpot_node_2], mats=[dashpot_mat], dirs=[o3.cc.DOF2D_X]) # Static analysis o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-4, max_iter=30, p_flag=0) o3.algorithm.Newton(osi) o3.numberer.RCM(osi) o3.system.ProfileSPD(osi) o3.integrator.Newmark(osi, newmark_gamma, newmark_beta) o3.analysis.Transient(osi) o3.analyze(osi, 40, 1.) for i in range(len(soil_mats)): if isinstance(soil_mats[i], o3.nd_material.PM4Sand) or isinstance( soil_mats[i], o3.nd_material.PressureIndependMultiYield): o3.update_material_stage(osi, soil_mats[i], 1) o3.analyze(osi, 50, 0.5) # reset time and analysis o3.set_time(osi, 0.0) o3.wipe_analysis(osi) ods = {} for otype in outs: if otype == 'ACCX': ods['ACCX'] = [] if isinstance(outs['ACCX'], str) and outs['ACCX'] == 'all': ods['ACCX'] = o3.recorder.NodesToArrayCache(osi, nodes=sn[:][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt) else: for i in range(len(outs['ACCX'])): ind = np.argmin(abs(node_depths - outs['ACCX'][i])) ods['ACCX'].append( o3.recorder.NodeToArrayCache(osi, node=sn[ind][0], dofs=[o3.cc.X], res_type='accel', dt=rec_dt)) if otype == 'TAU': ods['TAU'] = [] if isinstance(outs['TAU'], str) and outs['TAU'] == 'all': ods['TAU'] = o3.recorder.ElementsToArrayCache( osi, eles=eles, arg_vals=['stress'], dt=rec_dt) else: for i in range(len(outs['TAU'])): ind = np.argmin(abs(ele_depths - outs['TAU'][i])) ods['TAU'].append( o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['stress'], dt=rec_dt)) if otype == 'STRS': ods['STRS'] = [] if isinstance(outs['STRS'], str) and outs['STRS'] == 'all': ods['STRS'] = o3.recorder.ElementsToArrayCache( osi, eles=eles, arg_vals=['strain'], dt=rec_dt) else: for i in range(len(outs['STRS'])): ind = np.argmin(abs(ele_depths - outs['STRS'][i])) ods['STRS'].append( o3.recorder.ElementToArrayCache(osi, ele=eles[ind], arg_vals=['strain'], dt=rec_dt)) # Define the dynamic analysis ts_obj = o3.time_series.Path(osi, dt=asig.dt, values=asig.velocity * 1, factor=c_base) o3.pattern.Plain(osi, ts_obj) o3.Load(osi, sn[-1][0], [1., 0.]) # Run the dynamic analysis if use_explicit: o3.system.FullGeneral(osi) # o3.algorithm.Newton(osi) o3.algorithm.Linear(osi) # o3.integrator.ExplicitDifference(osi) # o3.integrator.CentralDifference(osi) o3.integrator.NewmarkExplicit(osi, newmark_gamma) # also works else: o3.system.SparseGeneral(osi) o3.algorithm.Newton(osi) o3.integrator.Newmark(osi, newmark_gamma, newmark_beta) o3.numberer.RCM(osi) o3.constraints.Transformation(osi) n = 2 modal_damp = 0 omegas = np.array(o3.get_eigen(osi, n=n))**0.5 response_periods = 2 * np.pi / omegas print('response_periods: ', response_periods) if not modal_damp: o3.rayleigh.Rayleigh(osi, a0, a1, 0, 0) else: o3.ModalDamping(osi, [xi, xi]) o3.analysis.Transient(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=10) while o3.get_time(osi) < analysis_time: print(o3.get_time(osi)) if o3.analyze(osi, 1, analysis_dt): print('failed') break o3.wipe(osi) out_dict = {} for otype in ods: if isinstance(ods[otype], list): out_dict[otype] = [] for i in range(len(ods[otype])): out_dict[otype].append(ods[otype][i].collect()) out_dict[otype] = np.array(out_dict[otype]) else: out_dict[otype] = ods[otype].collect().T out_dict['time'] = np.arange(0, analysis_time, rec_dt) return out_dict
def get_elastic_response(mass, k_spring, motion, dt, xi=0.05, r_post=0.0): """ Run seismic analysis of a nonlinear SDOF :param mass: SDOF mass :param k_spring: spring stiffness :param motion: array_like, acceleration values :param dt: float, time step of acceleration values :param xi: damping ratio :param r_post: post-yield stiffness :return: """ osi = o3.OpenSeesInstance(ndm=2, state=3) height = 5. # Establish nodes bot_node = o3.node.Node(osi, 0, 0) top_node = o3.node.Node(osi, 0, height) # Fix bottom node o3.Fix3DOF(osi, top_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FREE) o3.Fix3DOF(osi, bot_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED) # Set out-of-plane DOFs to be slaved o3.EqualDOF(osi, top_node, bot_node, [o3.cc.Y]) # nodal mass (weight / g): o3.Mass(osi, top_node, mass, 0., 0.) # Define material transf = o3.geom_transf.Linear2D(osi, []) area = 1.0 e_mod = 1.0e6 iz = k_spring * height ** 3 / (3 * e_mod) ele_nodes = [bot_node, top_node] ele = o3.element.ElasticBeamColumn2D(osi, ele_nodes, area=area, e_mod=e_mod, iz=iz, transf=transf) # Define the dynamic analysis acc_series = o3.time_series.Path(osi, dt=dt, values=-motion) # should be negative o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series) # set damping based on first eigen mode angular_freq = o3.get_eigen(osi, solver='fullGenLapack', n=1)[0] ** 0.5 response_period = 2 * np.pi / angular_freq print('response_period: ', response_period) beta_k = 2 * xi / angular_freq o3.rayleigh.Rayleigh(osi, alpha_m=0.0, beta_k=beta_k, beta_k_init=0.0, beta_k_comm=0.0) # Run the dynamic analysis o3.wipe_analysis(osi) o3.algorithm.Newton(osi) o3.system.SparseGeneral(osi) o3.numberer.RCM(osi) o3.constraints.Transformation(osi) o3.integrator.Newmark(osi, 0.5, 0.25) o3.analysis.Transient(osi) o3.extensions.to_py_file(osi, 'simple.py') o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10) analysis_time = (len(motion) - 1) * dt analysis_dt = 0.001 outputs = { "time": [], "rel_disp": [], "rel_accel": [], "rel_vel": [], "force": [] } while o3.get_time(osi) < analysis_time: o3.analyze(osi, 1, analysis_dt) curr_time = o3.get_time(osi) outputs["time"].append(curr_time) outputs["rel_disp"].append(o3.get_node_disp(osi, top_node, o3.cc.X)) outputs["rel_vel"].append(o3.get_node_vel(osi, top_node, o3.cc.X)) outputs["rel_accel"].append(o3.get_node_accel(osi, top_node, o3.cc.X)) o3.gen_reactions(osi) outputs["force"].append(o3.get_ele_response(osi, ele, 'force')) o3.wipe(osi) for item in outputs: outputs[item] = np.array(outputs[item]) return outputs
def run_pm4sand_et(sl, csr, esig_v0=101.0e3, static_bias=0.0, n_lim=100, k0=0.5, strain_limit=0.03, strain_inc=5.0e-6, etype='implicit'): nu_init = k0 / (1 + k0) damp = 0.02 omega0 = 0.2 omega1 = 20.0 a1 = 2. * damp / (omega0 + omega1) a0 = a1 * omega0 * omega1 # Initialise OpenSees instance osi = o3.OpenSeesInstance(ndm=2, ndf=3, state=3) # Establish nodes h_ele = 1. bl_node = o3.node.Node(osi, 0, 0) br_node = o3.node.Node(osi, h_ele, 0) tr_node = o3.node.Node(osi, h_ele, h_ele) tl_node = o3.node.Node(osi, 0, h_ele) all_nodes = [bl_node, br_node, tr_node, tl_node] # Fix bottom node o3.Fix3DOF(osi, bl_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED) o3.Fix3DOF(osi, br_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED) o3.Fix3DOF(osi, tr_node, o3.cc.FREE, o3.cc.FREE, o3.cc.FIXED) o3.Fix3DOF(osi, tl_node, o3.cc.FREE, o3.cc.FREE, o3.cc.FIXED) # Set out-of-plane DOFs to be slaved o3.EqualDOF(osi, tr_node, tl_node, [o3.cc.X, o3.cc.Y]) # Define material pm4sand = o3.nd_material.PM4Sand(osi, sl.relative_density, sl.g0_mod, sl.h_po, sl.unit_sat_mass, 101.3, nu=nu_init) # Note water bulk modulus is irrelevant since constant volume test - so as soil skeleton contracts # the bulk modulus of the soil skeleton controls the change in effective stress water_bulk_mod = 2.2e6 ele = o3.element.SSPquadUP(osi, all_nodes, pm4sand, 1.0, water_bulk_mod, 1., sl.permeability, sl.permeability, sl.e_curr, alpha=1.0e-5, b1=0.0, b2=0.0) o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=35, p_flag=0) o3.numberer.RCM(osi) omegas = np.array(o3.get_eigen(osi, n=1))**0.5 periods = 2 * np.pi / omegas periods = [0.001] if etype == 'implicit': o3.algorithm.Newton(osi) o3.system.FullGeneral(osi) o3.integrator.Newmark(osi, gamma=5. / 6, beta=4. / 9) dt = 0.01 else: o3.algorithm.Linear(osi, factor_once=True) o3.system.FullGeneral(osi) if etype == 'newmark_explicit': o3.integrator.NewmarkExplicit(osi, gamma=0.5) explicit_dt = periods[0] / np.pi / 8 elif etype == 'central_difference': o3.integrator.CentralDifference(osi) explicit_dt = periods[0] / np.pi / 16 # 0.5 is a factor of safety elif etype == 'hht_explicit': o3.integrator.HHTExplicit(osi, alpha=0.5) explicit_dt = periods[0] / np.pi / 8 elif etype == 'explicit_difference': o3.integrator.ExplicitDifference(osi) explicit_dt = periods[0] / np.pi / 4 else: raise ValueError(etype) print('explicit_dt: ', explicit_dt) dt = explicit_dt o3.analysis.Transient(osi) freqs = [0.5, 10] xi = 0.1 use_modal_damping = 0 if use_modal_damping: omega_1 = 2 * np.pi * freqs[0] omega_2 = 2 * np.pi * freqs[1] a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2) a1 = 2 * xi / (omega_1 + omega_2) o3.rayleigh.Rayleigh(osi, a0, 0, a1, 0) else: o3.ModalDamping(osi, [xi]) o3.update_material_stage(osi, pm4sand, stage=0) # print('here1: ', o3.get_ele_response(osi, ele, 'stress'), esig_v0, csr) all_stresses_cache = o3.recorder.ElementToArrayCache(osi, ele, arg_vals=['stress']) all_strains_cache = o3.recorder.ElementToArrayCache(osi, ele, arg_vals=['strain']) nodes_cache = o3.recorder.NodesToArrayCache(osi, all_nodes, dofs=[1, 2, 3], res_type='disp') o3.recorder.NodesToFile(osi, 'node_disp.txt', all_nodes, dofs=[1, 2, 3], res_type='disp') # Add static vertical pressure and stress bias ttime = 30 time_series = o3.time_series.Path(osi, time=[0, ttime, 1e10], values=[0, 1, 1]) o3.pattern.Plain(osi, time_series) o3.Load(osi, tl_node, [0, -esig_v0 / 2, 0]) o3.Load(osi, tr_node, [0, -esig_v0 / 2, 0]) o3.analyze(osi, num_inc=int(ttime / dt) + 10, dt=dt) ts2 = o3.time_series.Path(osi, time=[ttime, 80000, 1e10], values=[1., 1., 1.], factor=1) o3.pattern.Plain(osi, ts2, fact=1.) y_vert = o3.get_node_disp(osi, tr_node, o3.cc.Y) o3.SP(osi, tl_node, dof=o3.cc.Y, dof_values=[y_vert]) o3.SP(osi, tr_node, dof=o3.cc.Y, dof_values=[y_vert]) # Close the drainage valves for node in all_nodes: o3.remove_sp(osi, node, dof=3) o3.analyze(osi, int(5 / dt), dt=dt) print('here3: ', o3.get_ele_response(osi, ele, 'stress'), esig_v0, csr) o3.update_material_stage(osi, pm4sand, stage=1) o3.set_parameter(osi, value=0, eles=[ele], args=['FirstCall', pm4sand.tag]) o3.analyze(osi, int(5 / dt), dt=dt) o3.set_parameter(osi, value=sl.poissons_ratio, eles=[ele], args=['poissonRatio', pm4sand.tag]) o3.extensions.to_py_file(osi) n_cyc = 0.0 target_strain = 1.1 * strain_limit target_disp = target_strain * h_ele limit_reached = 0 export = 1 while n_cyc < n_lim: print('n_cyc: ', n_cyc) h_disp = o3.get_node_disp(osi, tr_node, o3.cc.X) curr_time = o3.get_time(osi) steps = target_strain / strain_inc ts0 = o3.time_series.Path(osi, time=[curr_time, curr_time + steps, 1e10], values=[h_disp, target_disp, target_disp], factor=1) pat0 = o3.pattern.Plain(osi, ts0) o3.SP(osi, tr_node, dof=o3.cc.X, dof_values=[1.0]) curr_stress = o3.get_ele_response(osi, ele, 'stress')[2] if math.isnan(curr_stress): raise ValueError if export: o3.extensions.to_py_file(osi) export = 0 while curr_stress < (csr - static_bias) * esig_v0: o3.analyze(osi, int(0.1 / dt), dt=dt) curr_stress = o3.get_ele_response(osi, ele, 'stress')[2] h_disp = o3.get_node_disp(osi, tr_node, o3.cc.X) print(h_disp, target_disp) if h_disp >= target_disp: print('STRAIN LIMIT REACHED - on load') limit_reached = 1 break if limit_reached: break n_cyc += 0.25 print('load reversal, n_cyc: ', n_cyc) curr_time = o3.get_time(osi) o3.remove_load_pattern(osi, pat0) o3.remove(osi, ts0) o3.remove_sp(osi, tr_node, dof=o3.cc.X) # Reverse cycle steps = (h_disp + target_disp) / (strain_inc * h_ele) ts0 = o3.time_series.Path(osi, time=[curr_time, curr_time + steps, 1e10], values=[h_disp, -target_disp, -target_disp], factor=1) pat0 = o3.pattern.Plain(osi, ts0) o3.SP(osi, tr_node, dof=o3.cc.X, dof_values=[1.0]) i = 0 while curr_stress > -(csr + static_bias) * esig_v0: o3.analyze(osi, int(0.1 / dt), dt=dt) curr_stress = o3.get_ele_response(osi, ele, 'stress')[2] h_disp = o3.get_node_disp(osi, tr_node, o3.cc.X) if -h_disp >= target_disp: print('STRAIN LIMIT REACHED - on reverse') limit_reached = 1 break i += 1 if i > steps: break if limit_reached: break n_cyc += 0.5 print('reload, n_cyc: ', n_cyc) curr_time = o3.get_time(osi) o3.remove_load_pattern(osi, pat0) o3.remove(osi, ts0) o3.remove_sp(osi, tr_node, dof=o3.cc.X) # reload cycle steps = (-h_disp + target_disp) / (strain_inc * h_ele) ts0 = o3.time_series.Path(osi, time=[curr_time, curr_time + steps, 1e10], values=[h_disp, target_disp, target_disp], factor=1) pat0 = o3.pattern.Plain(osi, ts0) o3.SP(osi, tr_node, dof=o3.cc.X, dof_values=[1.0]) while curr_stress < static_bias * esig_v0: o3.analyze(osi, int(0.1 / dt), dt=dt) curr_stress = o3.get_ele_response(osi, ele, 'stress')[2] h_disp = o3.get_node_disp(osi, tr_node, o3.cc.X) if h_disp >= target_disp: print('STRAIN LIMIT REACHED - on reload') limit_reached = 1 break if limit_reached: break o3.remove_load_pattern(osi, pat0) o3.remove(osi, ts0) o3.remove_sp(osi, tr_node, dof=o3.cc.X) n_cyc += 0.25 o3.wipe(osi) all_stresses = all_stresses_cache.collect() all_strains = all_strains_cache.collect() disps = nodes_cache.collect() stress = all_stresses[:, 2] strain = all_strains[:, 2] ppt = all_stresses[:, 1] return stress, strain, ppt, disps pass
def run(etype, xi): rho = 10.0 e_mod = 100.0e3 nu = 0.3 osi = o3.OpenSeesInstance(ndm=2, ndf=2) n_node_rows = 2 ele_width = 1.0 ele_thick = 1.0 ele_h = 1.0 node_depths = np.arange(n_node_rows) * ele_h grav = 0.0 eles = [] sn = [[o3.node.Node(osi, 0, 0), o3.node.Node(osi, ele_width, 0)]] for i in range(1, n_node_rows): # Establish left and right nodes sn.append([ o3.node.Node(osi, 0, -node_depths[i]), o3.node.Node(osi, ele_width, -node_depths[i]) ]) # set x and y dofs equal for left and right nodes if i != n_node_rows - 1: # Note this is crucial otherwise explicit solver does not compute correctly!!! o3.EqualDOF(osi, sn[i][0], sn[i][1], [o3.cc.X, o3.cc.Y]) mat = o3.nd_material.ElasticIsotropic(osi, e_mod, nu, rho) nodes = [sn[i][0], sn[i][1], sn[i - 1][1], sn[i - 1][0]] # anti-clockwise eles.append( o3.element.SSPquad(osi, nodes, mat, o3.cc.PLANE_STRAIN, ele_thick, 0.0, -grav)) # Fix base nodes o3.Fix2DOF(osi, sn[-1][0], o3.cc.FREE, o3.cc.FIXED) o3.Fix2DOF(osi, sn[-1][1], o3.cc.FREE, o3.cc.FIXED) o3.EqualDOF(osi, sn[-1][0], sn[-1][1], [o3.cc.X]) # Define dashpot nodes dashpot_node_1 = o3.node.Node(osi, 0, -node_depths[-1]) o3.Fix2DOF(osi, dashpot_node_1, o3.cc.FIXED, o3.cc.FIXED) dashpot_node_2 = sn[-1][0] g_mod = e_mod / (2 * (1 + nu)) v_s = np.sqrt(g_mod / rho) c_base = ele_width * rho * v_s dashpot_mat = o3.uniaxial_material.Viscous(osi, c_base, alpha=1.) o3.element.ZeroLength(osi, [dashpot_node_1, dashpot_node_2], mats=[dashpot_mat], dirs=[o3.cc.DOF2D_X]) # spring_mat = o3.uniaxial_material.Elastic(osi, e_mod * 0.1) # o3.element.ZeroLength(osi, [dashpot_node_l, dashpot_node_2], mats=[spring_mat], dirs=[o3.cc.DOF2D_X]) lam = 2 * g_mod * nu / (1 - 2 * nu) mu = g_mod v_dil = np.sqrt((lam + 2 * mu) / rho) min_dt = ele_h / v_dil ts0 = o3.time_series.Linear(osi) o3.pattern.Plain(osi, ts0) o3.Load(osi, sn[-1][0], [1., 0.]) print('min_dt: ', min_dt) o3.constraints.Transformation(osi) o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=10) o3.numberer.RCM(osi) if etype == 'implicit': o3.system.ProfileSPD(osi) o3.algorithm.NewtonLineSearch(osi, 0.75) o3.integrator.Newmark(osi, 0.5, 0.25) else: o3.algorithm.Linear(osi, factor_once=True) if etype == 'newmark_explicit': o3.system.ProfileSPD(osi) o3.integrator.NewmarkExplicit(osi, gamma=0.5) elif etype == 'central_difference': o3.system.FullGeneral(osi) o3.integrator.CentralDifference(osi) elif etype == 'explicit_difference': o3.system.Diagonal(osi) o3.integrator.ExplicitDifference(osi) else: raise ValueError(etype) ndp = np.ceil(np.log10(min_dt)) if 0.5 * 10**ndp < min_dt: dt = 0.5 * 10**ndp elif 0.2 * 10**ndp < min_dt: dt = 0.2 * 10**ndp elif 0.1 * 10**ndp < min_dt: dt = 0.1 * 10**ndp else: raise ValueError(min_dt, 0.1 * 10**ndp) print('dt: ', min_dt, dt) o3.analysis.Transient(osi) ttotal = 15 # s inc = 2 nn = int(ttotal / dt / inc) print(nn) time = [] disp1 = [] disp2 = [] for i in range(nn): time.append(o3.get_time(osi)) disp1.append(o3.get_node_disp(osi, sn[0][0], dof=o3.cc.X)) disp2.append(o3.get_node_disp(osi, sn[-1][0], dof=o3.cc.X)) o3.analyze(osi, inc, dt) return time, disp1, disp2