def __init__(self,
gridpts,
dtdx,
ic,
scheme,
bc,
tmax=50,
spaceDomain=[0, 100]):
self.grid = mesh(gridpts, dtdx, tmax, spaceDomain)
self.grid.Q[:, :, 0] = ic(self.grid.x)
self.bc = bc
left_bc, right_bc = bc(0, self.grid.Q[:, :, 0])
self.grid.Q[:, 0, 0] = left_bc
self.grid.Q[:, -1, 0] = right_bc
self.grid.E[:, :, 0] = self.grid.compute_E(0)
self.scheme = scheme(self.grid.dtdx, bc)
def convergence_viscoelastic_study():
um1, nodes1, delta_t1, num_of_elements1, u_analytical, nr, uvalues = main(
E, v, Q, T, a, b, p_max, tL, tF, mesh_refinement_factor, 10, 2)
um2, nodes2, delta_t2, num_of_elements2, u_analytical, nr, uvalues = main(
E, v, Q, T, a, b, p_max, tL, tF, mesh_refinement_factor, 8, 4)
um3, nodes3, delta_t3, num_of_elements3, u_analytical, nr, uvalues = main(
E, v, Q, T, a, b, p_max, tL, tF, mesh_refinement_factor, 5, 5)
um4, nodes4, delta_t4, num_of_elements4, u_analytical, nr, uvalues = main(
E, v, Q, T, a, b, p_max, tL, tF, mesh_refinement_factor, 2, 15)
fig, ax = plt.subplots()
ax.scatter(mesh(a, b, 20, 2),
u_analytical,
c='black',
marker='*',
label="analytical")
ax.plot(nodes1,
um1,
'--',
label=f'time interval={delta_t1}, #elements={num_of_elements1}')
ax.plot(nodes2,
um2,
'--',
label=f'time interval={delta_t2}, #elements={num_of_elements2}')
ax.plot(nodes3,
um3,
'--',
label=f'time interval={delta_t3}, #elements={num_of_elements3}')
ax.plot(nodes4,
um4,
marker='+',
label=f'time interval={delta_t4}, #elements={num_of_elements4}')
ax.set_xlabel('Radius(r)')
ax.set_ylabel('Displacement(u)')
plt.legend()
plt.title('Viscoelastic')
plt.savefig('convergence_study_viscoelastic.png')
def convergence_elastic_study():
um1, nodes1, delta_t1, num_of_elements1, u_analytical, nr, uvalues = main(
E, v, 0, T, a, b, p_max, tL, tF, mesh_refinement_factor, 0.5, 1)
um2, nodes2, delta_t2, num_of_elements2, u_analytical, nr, uvalues = main(
E, v, 0, T, a, b, p_max, tL, tF, mesh_refinement_factor, 0.5, 2)
um3, nodes3, delta_t3, num_of_elements3, u_analytical, nr, uvalues = main(
E, v, 0, T, a, b, p_max, tL, tF, mesh_refinement_factor, 0.5, 5)
um4, nodes4, delta_t4, num_of_elements4, u_analytical, nr, uvalues = main(
E, v, 0, T, a, b, p_max, tL, tF, mesh_refinement_factor, 0.5, 10)
fig, ax = plt.subplots()
ax.scatter(mesh(a, b, 20, 2),
u_analytical,
marker='*',
c='black',
label="analytical")
ax.plot(nodes1,
um1,
'--',
label=f'time interval={delta_t1}, #elements={num_of_elements1}')
ax.plot(nodes2,
um2,
'--',
label=f'time interval={delta_t2}, #elements={num_of_elements2}')
ax.plot(nodes3,
um3,
'--',
label=f'time interval={delta_t3}, #elements={num_of_elements3}')
ax.plot(nodes4,
um4,
label=f'time interval={delta_t4}, #elements={num_of_elements4}')
plt.text(56, 0.0465, f'#NR runs for each time step={nr}')
ax.set_xlabel('Radius(r)')
ax.set_ylabel('Displacement(u)')
plt.legend()
plt.title('Elastic')
plt.savefig('convergence_study_elastic.png')
def main(E, v, Q, T, a, b, p_max, tL, tF, mesh_refinement_factor, delta_t,
num_of_elements):
"""
Global routine using a black box scheme.
"""
zeeta = 0
rnodes = mesh(a, b, num_of_elements, mesh_refinement_factor)
num_of_iterations = np.size(np.arange(0, tF + delta_t, delta_t))
def assignment_matrix(i, num_elements):
"""Transformation matrix calculation"""
A = np.zeros((2, num_elements + 1))
A[0, 0] = 1
A[1, 1] = 1
A[0] = np.roll(A[0], i - 1)
A[1] = np.roll(A[1], i - 1)
return A
##analytical solution
def analytical_elastic(E, v, p, a, b, element_nodes):
"""Analytical solution"""
r = element_nodes
return (1 + v) * (p / E) * (a**2 / (b**2 - a**2)) * ((1 - 2 * v) * r +
(b**2 / r))
def Infinity_norm(X):
"""returns Infinity Norm"""
return np.linalg.norm(X, np.inf)
##load scaling
delta_p = p_max / (tL / delta_t)
ps = 0
p = 0
#initialisation of variables.
ue = np.zeros((2, 1))
um = np.zeros((num_of_elements + 1, 1))
uk = np.zeros((num_of_elements + 1, 1))
uvalues = np.zeros((num_of_elements + 1, num_of_iterations))
strain_values = np.zeros((num_of_elements + 1, num_of_iterations),
dtype=object)
over_stress_values = np.zeros((num_of_elements + 1, num_of_iterations),
dtype=object)
stress_values = np.zeros((num_of_elements + 1, 2))
m = 1
delta_strain = np.zeros((2, 1))
count = 1
for time in np.arange(delta_t, tF + delta_t, delta_t):
"""Looping in time to find the displacements"""
##load scaling
if time < tL:
ps = ps + delta_p
p = ps
else:
p = p_max
uk = um
nr = 0 ##NR runs counter
delta_uk = np.zeros((num_of_elements + 1, 1))
um = um * 0
while True:
"""Newton Rapson for finding the displacement um at the given time"""
Kt = np.zeros((num_of_elements + 1, num_of_elements + 1))
Rk = np.zeros((num_of_elements + 1, 1))
F_ext = np.zeros((num_of_elements + 1, 1))
F_int = np.zeros((num_of_elements + 1, 1))
for e in range(
1, num_of_elements + 1
): ###assembling of internal and external forces and calculating displacements
##elemental structural data calculation
element_length = rnodes[e] - rnodes[e - 1]
element_nodes = np.reshape(
np.asanyarray((rnodes[e - 1], rnodes[e])), (2, 1))
A = assignment_matrix(e, num_of_elements)
ue = A @ uk
##elemental material data calculation
C_ = C(E, v)
N_ = N(0)
J_ = J(element_length)
B_ = B(N_, element_length, element_nodes)
Ct = material_tangent_stiffness(C_, delta_t, Q, T)
Kte = tangent_stiffness_matrix(J_, N_, B_, Ct, element_nodes)
strain_values[e, m] = strain(B_, ue)
delta_strain = strain_values[e, m] - strain_values[e, m - 1]
over_stress_values[e, m] = over_stress(
Q, over_stress_values[e, m - 1], delta_strain, tL, tF,
delta_t, T)
stress_ = stress(C_, strain_values[e, m],
over_stress_values[e, m])
stress_values[e, 0] = stress(
C_, strain_values[e, m], over_stress_values[e, m])[
0] ##saving sigma rr for result extraction
stress_values[e, 1] = stress(
C_, strain_values[e, m], over_stress_values[e, m])[
1] ##saving sigma phi for result extraction
##Elemental forces
f_internal_e = f_internal(B_, stress_, N_, J_, element_nodes)
f_external_e = f_external(p, a, e)
#Tangent stiffness matrix
Kt = Kt + ((A.T) @ (Kte) @ (A))
Rk = Rk + A.T @ (f_internal_e - f_external_e)
##Total Forces
F_ext = F_ext + A.T @ (f_external_e)
F_int = F_int + A.T.dot(f_internal_e)
###Data generation part - part of PPP###
f = open('data_linear_elastic.txt', 'a+')
G = E / (2 * (1 + v)) #to reduce dimensionality
if f_internal_e[0, 0] != 0 and f_internal_e[1, 0] != 0:
#print(G,e,p,np.format_float_scientific(f_internal_e[0,0]),np.format_float_scientific(f_internal_e[1,0]),f_external_e[0,0],Kte[0,0],Kte[1,0],Kte[1,1],sep=',', file=f)
print(G,
e,
p,
np.format_float_scientific(f_internal_e[0, 0]),
sep=',',
file=f)
f.close()
#########
count += 1
delta_uk = -1 * (np.linalg.inv(Kt) @ Rk)
um = uk + delta_uk
nr = nr + 1
if not Infinity_norm(
delta_uk) < 0.005 * Infinity_norm(um) or Infinity_norm(
F_int - F_ext) < 0.005 * Infinity_norm(
F_int): ##Exit statement as given in question
break
uvalues[:, m] = np.reshape(
um, num_of_elements +
1) ##array of displacement values in each time step
m = m + 1
if Q > 0: ##for plotting purposes
type_ = 'Viscoelastic'
else:
type_ = 'Elastic'
u_analytical = analytical_elastic(E, v, p, a, b,
mesh(a, b, num_of_elements,
2)) ##analytical solution
if (abs(u_analytical - um.T)).max() > 1e-10:
print('inaccurate solution', abs(u_analytical - um.T).max())
return um, rnodes, delta_t, num_of_elements, u_analytical, nr, uvalues
specie('13C' , specType = 0 , charge=0 , init=1),
specie('Na' , specType = 0 , charge=0 , init=1),
specie('Mg' , specType = 0 , charge=0 , init=1),
specie('Si' , specType = 0 , charge=0 , init=1),
specie('Cl' , specType = 0 , charge=0 , init=1),
specie('Fe' , specType = 0 , charge=0 , init=1),
specie('He' , specType = 0 , charge=0 , init=1),
specie('H' , specType = 0 , charge=0 , init=1),
specie('M' , specType = -1, charge=0 , init=1),
specie('C' , specType = 0 , charge=0 , init=1),
specie('N' , specType = 0 , charge=0 , init=1),
specie('O' , specType = 0 , charge=0 , init=1),
specie('P' , specType = 0 , charge=0 , init=1),
specie('S' , specType = 0 , charge=0 , init=1),
specie('e-' , specType = 0 , charge=-1, init=1) ]
#------------------------------------------------------------------
net = chemicalNetwork(rxnFile, baseSpec, UMISTVER = 'umist99')
# reading the species to be removed from a file
net.remove_species( underAbunFile = underAbunFile )
net.remove_species( species = removeManual )
# reading the species number and their corresponding indies and abundances from ascii files
net.assign_numbers_to_species(fileName = specNumFile)
m = mesh(meshFname, chemNet=net, metallicity=metallicity)
m.plot(plot_Av_range=[0,30])
pyl.show()
print 'done'
def buildBeamMod(modelName, x, z, y, seed, slabSeed): ''' Builds a beam model without step ''' col_height = 3000.0 beam_len = 7500.0 steel = 'DOMEX_S355' concrete = 'Concrete' rebarSteel = steel M=mdb.models[modelName] #=========== Parts ============# #Create Column createColumn(M, height=col_height, mat=steel, partName='COLUMN') #Create Beam createBeam(M, length=beam_len, mat=steel, partName='BEAM') #Create slab createSlab(M, t=200.0, mat=concrete, dim=beam_len, rebarMat=rebarSteel, partName='SLAB') #Add beam fluid inertia to beams and columns airDensity = 1.225e-12 #1.225 kg/m^3 M.sections['HEB300'].setValues(useFluidInertia=ON, fluidMassDensity=airDensity, crossSectionRadius=300.0, lateralMassCoef=1.0) M.sections['HUP300x300'].setValues(useFluidInertia=ON, fluidMassDensity=airDensity, crossSectionRadius=300.0, lateralMassCoef=1.0) #=========== Sets and surfaces ============# #A lot of surfaces are created with the joints createSets(M, col_height) createSurfs(M) #=========== Assembly ============# createAssembly(M, x, z, y, x_d = beam_len, z_d = beam_len, y_d = col_height) #=========== Mesh ============# mesh(M, seed, slabSeed) #=========== Joints ============# createJoints(M, x, z, y, x_d = beam_len, z_d = beam_len, y_d = col_height) #=========== Fix column base ============# mergeColBase(M,x,z) M.DisplacementBC( createStepName='Initial', name='fixColBases', region= M.rootAssembly.sets['col-bases'], u1=0.0, u2=0.0, u3=0.0, ur1=0.0, ur2=0.0, ur3=0.0)
# run with ./pyfem boxes_union_ng.py from mesh import * # define mesher parameters and outer box m = mesh(frequency=100, rod_length=0.7, bbox=[[-2.0, -2.0, -2.0], [2.0, 2.0, 2.0]]) # create a first box box1 = box(coords=[[0.0, 0.0, 0.0], [1.0, 1.0, 1.0]], shifting=[-0.5, -0.5, -0.5]) # create a secod box box2 = box(coords=[[0.0, 0.0, 0.0], [1.0, 1.0, 1.0]], shifting=[-0.0, -0.0, -0.0]) # unite them box3 = box1.unite(box2) # mesh the union m.mesh_it([box3], visual=True, save=["box_example_ng.ps", "/tmp/box_example_ng.vtk"])
def main(E, v, Q, T, a, b, p_max, tL, tF, mesh_refinement_factor, delta_t,
num_of_elements):
zeeta = 0
rnodes = mesh(a, b, num_of_elements, mesh_refinement_factor)
num_of_iterations = np.size(np.arange(0, tF + delta_t, delta_t))
def assignment_matrix(i, num_elements):
"""Transformation matrix calculation"""
A = np.zeros((2, num_elements + 1))
A[0, 0] = 1
A[1, 1] = 1
A[0] = np.roll(A[0], i - 1)
A[1] = np.roll(A[1], i - 1)
return A
##analytical solution
def analytical_elastic(E, v, p, a, b, element_nodes):
"""Analytical solution"""
r = element_nodes
return (1 + v) * (p / E) * (a**2 / (b**2 - a**2)) * ((1 - 2 * v) * r +
(b**2 / r))
def Infinity_norm(X):
"""returns Infinity Norm"""
return np.linalg.norm(X, np.inf)
##load scaling
delta_p = p_max / (tL / delta_t)
ps = 0
p = 0
ue = np.zeros((2, 1))
um = np.zeros((num_of_elements + 1, 1))
uk = np.zeros((num_of_elements + 1, 1))
uvalues = np.zeros((num_of_elements + 1, num_of_iterations))
strain_values = np.zeros((num_of_elements + 1, num_of_iterations),
dtype=object)
over_stress_values = np.zeros((num_of_elements + 1, num_of_iterations),
dtype=object)
stress_values = np.zeros((num_of_elements + 1, 2))
m = 1
delta_strain = np.zeros((2, 1))
for time in np.arange(delta_t, tF + delta_t, delta_t):
"""Looping in time to find the displacements"""
##load scaling
if time < tL:
ps = ps + delta_p
p = ps
else:
p = p_max
uk = um
nr = 0 ##NR runs counter
delta_uk = np.zeros((num_of_elements + 1, 1))
um = um * 0
while True:
"""Newton Rapson for finding the displacement um at the given time"""
Kt = np.zeros((num_of_elements + 1, num_of_elements + 1))
Rk = np.zeros((num_of_elements + 1, 1))
F_ext = np.zeros((num_of_elements + 1, 1))
F_int = np.zeros((num_of_elements + 1, 1))
for e in range(
1, num_of_elements + 1
): ###assembling of internal and external forces and calculating displacements
start_time = ti.time()
##elemental structural data calculation
element_length = rnodes[e] - rnodes[e - 1]
element_nodes = np.reshape(
np.asanyarray((rnodes[e - 1], rnodes[e])), (2, 1))
A = assignment_matrix(e, num_of_elements)
ue = A @ uk
##elemental material data calculation
element_start_time = ti.time()
C_ = C(E, v)
N_ = N(0)
J_ = J(element_length)
B_ = B(N_, element_length, element_nodes)
Ct = material_tangent_stiffness(C_, delta_t, Q, T)
Kte = tangent_stiffness_matrix(J_, N_, B_, Ct, element_nodes)
strain_values[e, m] = strain(B_, ue)
delta_strain = strain_values[e, m] - strain_values[e, m - 1]
over_stress_values[e, m] = over_stress(
Q, over_stress_values[e, m - 1], delta_strain, tL, tF,
delta_t, T)
stress_ = stress(C_, strain_values[e, m],
over_stress_values[e, m])
stress_values[e, 0] = stress(
C_, strain_values[e, m], over_stress_values[e, m])[
0] ##saving sigma rr for result extraction
stress_values[e, 1] = stress(
C_, strain_values[e, m], over_stress_values[e, m])[
1] ##saving sigma phi for result extraction
##Elemental forces
f_internal_e = f_internal(B_, stress_, N_, J_, element_nodes)
f_external_e = f_external(p, a, e)
element_end_time = ti.time()
print('element_duration',
(element_end_time - element_start_time), e)
Kt = Kt + ((A.T) @ (Kte) @ (A))
Rk = Rk + A.T @ (f_internal_e - f_external_e)
##Total Forces
F_ext = F_ext + A.T @ (f_external_e)
F_int = F_int + A.T.dot(f_internal_e)
elaspsed_time = start_time - ti.time()
print('total time =', elaspsed_time)
delta_uk = -1 * (np.linalg.inv(Kt) @ Rk)
um = uk + delta_uk
nr = nr + 1
if not Infinity_norm(delta_uk) < 0.005 * Infinity_norm(
um) or Infinity_norm(Rk) < 0.005 * Infinity_norm(
F_int): ##Exit statement as given in question
break
uvalues[:, m] = np.reshape(
um, num_of_elements +
1) ##array of displacement values in each time step
m = m + 1
f = open('results.txt', 'w') ##writing to output file
print("At final loading(tf):\n\n",
"Stresses\n\n\nRadial Stress(Sigma_rr):\n\n",
stress_values[1:, 0],
"\n\nCircumfrential Stress(Sigma_phi):\n\n",
stress_values[1:, 1],
file=f)
print("\n\nDisplacements\n\nU(r):\n ", um.T, file=f)
if Q > 0: ##for plotting purposes
type_ = 'Viscoelastic'
else:
type_ = 'Elastic'
u_analytical = analytical_elastic(E, v, p, a, b,
mesh(a, b, 20, 2)) ##analytical solution
fig, ax = plt.subplots()
ax.scatter(mesh(a, b, 20, mesh_refinement_factor),
u_analytical,
marker='*',
c='green',
label="analytical")
ax.plot(rnodes, um, marker='+', color='orange', label="fea")
ax.set_xlabel('Radius(r)')
ax.set_ylabel('Displacement(u)')
plt.text(60, 0.047, f'Time Interval(s)={delta_t}')
plt.text(60, 0.049, f'Number of elements={num_of_elements}')
plt.title(f'Convergence - {type_}')
plt.legend()
plt.savefig('convergence.png')
return um, rnodes, delta_t, num_of_elements, u_analytical, nr, uvalues
def buildBeamMod(modelName, x, z, y, seed, slabSeed):
'''
Builds a beam model without step
'''
col_height = 3000.0
beam_len = 7500.0
steel = 'DOMEX_S355'
concrete = 'Concrete'
rebarSteel = steel
M = mdb.models[modelName]
#=========== Parts ============#
#Create Column
createColumn(M, height=col_height, mat=steel, partName='COLUMN')
#Create Beam
createBeam(M, length=beam_len, mat=steel, partName='BEAM')
#Create slab
createSlab(M,
t=200.0,
mat=concrete,
dim=beam_len,
rebarMat=rebarSteel,
partName='SLAB')
#Add beam fluid inertia to beams and columns
airDensity = 1.225e-12 #1.225 kg/m^3
M.sections['HEB300'].setValues(useFluidInertia=ON,
fluidMassDensity=airDensity,
crossSectionRadius=300.0,
lateralMassCoef=1.0)
M.sections['HUP300x300'].setValues(useFluidInertia=ON,
fluidMassDensity=airDensity,
crossSectionRadius=300.0,
lateralMassCoef=1.0)
#=========== Sets and surfaces ============#
#A lot of surfaces are created with the joints
createSets(M, col_height)
createSurfs(M)
#=========== Assembly ============#
createAssembly(M, x, z, y, x_d=beam_len, z_d=beam_len, y_d=col_height)
#=========== Mesh ============#
mesh(M, seed, slabSeed)
#=========== Joints ============#
createJoints(M, x, z, y, x_d=beam_len, z_d=beam_len, y_d=col_height)
#=========== Fix column base ============#
mergeColBase(M, x, z)
M.DisplacementBC(createStepName='Initial',
name='fixColBases',
region=M.rootAssembly.sets['col-bases'],
u1=0.0,
u2=0.0,
u3=0.0,
ur1=0.0,
ur2=0.0,
ur3=0.0)
# run with ./pyfem fixed_points_2d.py from mesh import * # define mesher parameters and outer box m = mesh(frequency = 1000, rod_length = 0.5, bbox = [[-4.0,-4.0],[4.0,4.0]]) m.fixed_points = [[0.,0.],[-0.5,0.],[-0.5,0.5],[0.,0.5]] box1 = box(coords=[[0.0,0.0],[1.0,2.0]]) a = m.mesh_it([box1],visual=False, save=["fixed_points.ps"])
