def ex2():
''' DKT esimerkki 1, pyörähdyssymmetrinen laatta jakautuneella kuormalla '''
t = 25e-3
E = 100e9
nu = 0.3
q = 100e3
a = 1
D = E * t**3 / (12 * (1 - nu**2))
w = lambda r: -a**4 * q * (1 - r**2 / a**2)**2 / (64 * D)
vmis = lambda r: (36 * D**2 * (a**2 * q * (1 - r**2 / a**2) /
(8 * D) - q * r**2 /
(8 * D))**2 / t**4 - 36 * D**2 *
(a**2 * q * (1 - r**2 / a**2) / (8 * D) - q * r**2 /
(8 * D)) *
(a**2 * nu * q * (1 - r**2 / a**2) /
(16 * D) + a**2 * q * (1 - r**2 / a**2) /
(16 * D) - q * r**2 / (8 * D)) / t**4 + 36 * D**2 *
(a**2 * nu * q * (1 - r**2 / a**2) /
(16 * D) + a**2 * q * (1 - r**2 / a**2) /
(16 * D) - q * r**2 / (8 * D))**2 / t**4)**(1 / 2)
mesh = teefem.mesh.unitcircle(R=1)
mat = teefem.materials.elastic(E=E, nu=nu)
mdl = DKT(mesh=mesh)
OM_el = mdl.elset['OM1']
GA1_no = mdl.nset['GA1']
teefem.assign_material(elements=OM_el, material=mat)
bc1 = teefem.pressure_bc(pressure=lambda k, e: -q)
bc2 = teefem.dirichlet_bc(encastre=True)
teefem.assign_bc(elements=OM_el, bc=bc1)
teefem.assign_bc(nodes=GA1_no, bc=bc2)
carel = teefem.plate_functions.PlateCharacteristic(
thickness=lambda k, e: t)
teefem.assign_char(elements=OM_el, char=carel)
mdl.static_solve()
dymin = min([node.fields['DEPL']['DZ'] for node in mdl.nodes])
print("DZ (acc) : %0.14E" % (-w(0)))
print("DZ : %0.14E" % (dymin))
# print("DZ (CA) : %0.14E"%(-1.74644966293971E-01))
import matplotlib.pylab as plt
# mdl.plot()
plotmdl(mdl, vmis)
plt.show()
def ex1():
''' Mindlin esimerkki 1, pyörähdyssymmetrinen laatta jakautuneella kuormalla '''
t = 25e-3
q = 100e3
nu = 0.3
E = 100.0e9
a = 1
D = E*t**3/(12*(1-nu**2))
phi = 16/5*(t/a)**2/(1-nu)
print phi
w0 = q*a**4/(64*D)*(1+phi)
mesh = teefem.mesh.unitcircle(R=1)
mat = teefem.materials.elastic(E = E, nu = nu)
mdl = MINR(mesh = mesh)
# mdl = MIN(mesh = mesh)
OM_el = mdl.elset['OM1']
GA1_no = mdl.nset['GA1']
teefem.assign_material(elements = OM_el, material = mat)
bc1 = teefem.pressure_bc(pressure = lambda k,e: -q)
bc2 = teefem.dirichlet_bc(encastre = True)
teefem.assign_bc(elements = OM_el, bc = bc1)
teefem.assign_bc(nodes = GA1_no, bc = bc2)
carel = teefem.plate_functions.PlateCharacteristic(thickness = lambda k,e: t)
teefem.assign_char(elements = OM_el, char = carel)
mdl.static_solve()
dz = [node.fields['DEPL']['DZ'] for node in mdl.nodes]
print np.average(dz)
dzmin = min(dz)
print("DZ (acc) : %0.14E"%(w0))
print("DZ : %0.14E"%(dzmin))
import matplotlib.pylab as plt
mdl.plot()
plt.show()
def test1():
''' Kalvo-ongelma testi, yksikkökalvo jota venytetään toisen akselin suuntaisesti '''
q = 100
# w = lambda r: -a**4*q*(1 - r**2/a**2)**2/(64*D) ???
mesh = teefem.mesh.unitsquare()
mdl = membrane(mesh = mesh)
# Painekuorma
teefem.assign_bc(
elements = mdl.elset['OM1'],
bc = teefem.pressure_bc(pressure = lambda k,e: -q),
)
# Vasen ja oikea reuna kiinni
nset1 = set().union(mdl.nset['GA1'], mdl.nset['GA3'])
# nset1 = set().union(mdl.nset['GA1'], mdl.nset['GA2'], mdl.nset['GA3'], mdl.nset['GA4'])
teefem.assign_bc(
nodes = nset1,
bc = teefem.dirichlet_bc(encastre = True)
)
# Esijännitys
car = memchar(Tx = lambda k,e: 100)
# car = memchar(Tx = lambda k,e: 100, Ty = lambda k,e: 100)
teefem.assign_char(elements = mdl.elements, char = car)
mdl.static_solve(export_matrices = False)
dz = [node.fields['DEPL']['DZ'] for node in mdl.nodes]
dymin = min(dz)
# print("DZ (acc) : %0.14E"%(-w(0)))
print("DZ : %0.14E"%(dymin))
# print("DZ (CA) : %0.14E"%(-1.74644966293971E-01))
import matplotlib.pylab as plt
mdl.plot()
plt.show()
def ex2():
''' DKT esimerkki 1, pyörähdyssymmetrinen laatta jakautuneella kuormalla '''
t = 25e-3
E = 100e9
nu = 0.3
q = 100e3
a = 1
D = E*t**3/(12*(1-nu**2))
w = lambda r: -a**4*q*(1 - r**2/a**2)**2/(64*D)
vmis = lambda r: (36*D**2*(a**2*q*(1 - r**2/a**2)/(8*D) - q*r**2/(8*D))**2/t**4 - 36*D**2*(a**2*q*(1 - r**2/a**2)/(8*D) - q*r**2/(8*D))*(a**2*nu*q*(1 - r**2/a**2)/(16*D) + a**2*q*(1 - r**2/a**2)/(16*D) - q*r**2/(8*D))/t**4 + 36*D**2*(a**2*nu*q*(1 - r**2/a**2)/(16*D) + a**2*q*(1 - r**2/a**2)/(16*D) - q*r**2/(8*D))**2/t**4)**(1/2)
mesh = teefem.mesh.unitcircle(R=1)
mat = teefem.materials.elastic(E = E, nu = nu)
mdl = DKT(mesh = mesh)
OM_el = mdl.elset['OM1']
GA1_no = mdl.nset['GA1']
teefem.assign_material(elements = OM_el, material = mat)
bc1 = teefem.pressure_bc(pressure = lambda k,e: -q)
bc2 = teefem.dirichlet_bc(encastre = True)
teefem.assign_bc(elements = OM_el, bc = bc1)
teefem.assign_bc(nodes = GA1_no, bc = bc2)
carel = teefem.plate_functions.PlateCharacteristic(thickness = lambda k,e: t)
teefem.assign_char(elements = OM_el, char = carel)
mdl.static_solve()
dymin = min([node.fields['DEPL']['DZ'] for node in mdl.nodes])
print("DZ (acc) : %0.14E"%(-w(0)))
print("DZ : %0.14E"%(dymin))
# print("DZ (CA) : %0.14E"%(-1.74644966293971E-01))
import matplotlib.pylab as plt
# mdl.plot()
plotmdl(mdl, vmis)
plt.show()
def ex1():
''' Suorakaidelaatta, tasan jakautunut kuorma '''
mesh = teefem.mesh.unitsquare()
print mesh.status(fulloutput = True)
mdl = DKT(mesh = mesh)
mat = teefem.materials.elastic(E = 100.0e9, nu = 0.3)
teefem.assign_material(elements = mdl.elset['OM1'], material = mat)
load = teefem.pressure_bc(pressure = lambda k,e: -100.0e3)
encastre = teefem.dirichlet_bc(encastre = True)
teefem.assign_bc(elements = mdl.elset['OM1'], bc = load)
teefem.assign_bc(nodes = mdl.nset['GA1'], bc = encastre)
teefem.assign_bc(nodes = mdl.nset['GA2'], bc = encastre)
teefem.assign_bc(nodes = mdl.nset['GA3'], bc = encastre)
teefem.assign_bc(nodes = mdl.nset['GA4'], bc = encastre)
carel = teefem.plate_functions.PlateCharacteristic(thickness = lambda k,e: 20e-3)
teefem.assign_char(elements = mdl.elset['OM1'], char = carel)
mdl.static_solve()
dymin = min([node.fields['DEPL']['DZ'] for node in mdl.nodes])
print("DZ: %0.14E"%(dymin*1000))
plotmdl(mdl)
def ex1():
''' Suorakaidelaatta, tasan jakautunut kuorma '''
mesh = teefem.mesh.unitsquare()
print mesh.status(fulloutput=True)
mdl = DKT(mesh=mesh)
mat = teefem.materials.elastic(E=100.0e9, nu=0.3)
teefem.assign_material(elements=mdl.elset['OM1'], material=mat)
load = teefem.pressure_bc(pressure=lambda k, e: -100.0e3)
encastre = teefem.dirichlet_bc(encastre=True)
teefem.assign_bc(elements=mdl.elset['OM1'], bc=load)
teefem.assign_bc(nodes=mdl.nset['GA1'], bc=encastre)
teefem.assign_bc(nodes=mdl.nset['GA2'], bc=encastre)
teefem.assign_bc(nodes=mdl.nset['GA3'], bc=encastre)
teefem.assign_bc(nodes=mdl.nset['GA4'], bc=encastre)
carel = teefem.plate_functions.PlateCharacteristic(
thickness=lambda k, e: 20e-3)
teefem.assign_char(elements=mdl.elset['OM1'], char=carel)
mdl.static_solve()
dymin = min([node.fields['DEPL']['DZ'] for node in mdl.nodes])
print("DZ: %0.14E" % (dymin * 1000))
plotmdl(mdl)
def test1():
''' Kalvo-ongelma testi, yksikkökalvo jota venytetään toisen akselin suuntaisesti '''
q = 100
# w = lambda r: -a**4*q*(1 - r**2/a**2)**2/(64*D) ???
mesh = teefem.mesh.unitsquare()
mdl = membrane(mesh=mesh)
# Painekuorma
teefem.assign_bc(
elements=mdl.elset['OM1'],
bc=teefem.pressure_bc(pressure=lambda k, e: -q),
)
# Vasen ja oikea reuna kiinni
nset1 = set().union(mdl.nset['GA1'], mdl.nset['GA3'])
# nset1 = set().union(mdl.nset['GA1'], mdl.nset['GA2'], mdl.nset['GA3'], mdl.nset['GA4'])
teefem.assign_bc(nodes=nset1, bc=teefem.dirichlet_bc(encastre=True))
# Esijännitys
car = memchar(Tx=lambda k, e: 100)
# car = memchar(Tx = lambda k,e: 100, Ty = lambda k,e: 100)
teefem.assign_char(elements=mdl.elements, char=car)
mdl.static_solve(export_matrices=False)
dz = [node.fields['DEPL']['DZ'] for node in mdl.nodes]
dymin = min(dz)
# print("DZ (acc) : %0.14E"%(-w(0)))
print("DZ : %0.14E" % (dymin))
# print("DZ (CA) : %0.14E"%(-1.74644966293971E-01))
import matplotlib.pylab as plt
mdl.plot()
plt.show()
mesh = teefem.geom.mesh(filename=meshfile) mdl = teefem.models.cplan(mesh=mesh) # Ryhmät OM1_el = mdl.elset['OM1'] # Koko domain GA1_no = mdl.nset['GA1'] # Vasen reuna GA2_el = mdl.elset['GA2'] # Yläreuna P1_no = mdl.nset['P1'] # Pistevoima # Materiaali mat = teefem.materials.elastic(E=210.0e9, nu=0.3) teefem.assign_material(elements=OM1_el, material=mat) # Reunaehdot, huom. TeeFEMissä tasojännitystila-elementin paksuus on oletuksena 1 bc1 = teefem.pressure_bc(pressure=lambda k: -q / t) bc2 = teefem.dirichlet_bc(encastre=True) bc3 = teefem.nodal_force(fy=-F / t) # Kytketään reunaehdot malliin # 1. Jakautunut kuormitus elementtiryhmään GA2 teefem.assign_bc(elements=GA2_el, bc=bc1) # 2. Vasen reuna jäykästi kiinni teefem.assign_bc(nodes=GA1_no, bc=bc2) # 3. Pistevoima alareunaan teefem.assign_bc(nodes=P1_no, bc=bc3) # Ratkaisu import time t0 = time.clock() mdl.static_solve()
mesh = tf.geom.mesh(filename = 'tria3_50.msh')
#mesh = tf.geom.mesh(filename = 'tria3_5000.msh')
mesh.create_node_groups()
mdl = model(mesh = mesh)
tf.assign_material(
elements = mdl.elset['OM1'],
material = tf.materials.elastic(E = E, nu = nu),
)
# Jakautunut kuormitus
tf.assign_bc(
elements = mdl.elset['OM1'],
bc = tf.pressure_bc(pressure = lambda k,e: -p0),
)
# Jäykkä tuenta vasemmalle reunalle (GA4)
tf.assign_bc(
nodes = mdl.nset['GA4'],
bc = tf.dirichlet_bc(encastre = True),
)
# Niveltuenta ylös ja alas
bcnod = set().union(mdl.nset['GA1'],mdl.nset['GA3'])
tf.assign_bc(nodes = bcnod, bc = tf.dirichlet_bc(dz = 0))
carel = tf.plate_functions.PlateCharacteristic(thickness = t)
tf.assign_char(elements = mdl.elset['OM1'], char = carel)
(a**2 * nu * q * (1 - r**2 / a**2) / (16 * D) + a**2 * q *
(1 - r**2 / a**2) / (16 * D) - q * r**2 /
(8 * D)) / t**4 + 36 * D**2 *
(a**2 * nu * q * (1 - r**2 / a**2) / (16 * D) + a**2 * q *
(1 - r**2 / a**2) / (16 * D) - q * r**2 /
(8 * D))**2 / t**4)**(1 / 2)
mesh = teefem.mesh.unitcircle(R=1)
mat = teefem.materials.elastic(E=E, nu=nu)
mdl = model(mesh=mesh)
OM_el = mdl.elset['OM1']
GA1_no = mdl.nset['GA1']
teefem.assign_material(elements=OM_el, material=mat)
bc1 = teefem.pressure_bc(pressure=lambda k, e: -q)
bc2 = teefem.dirichlet_bc(encastre=True)
teefem.assign_bc(elements=OM_el, bc=bc1)
teefem.assign_bc(nodes=GA1_no, bc=bc2)
carel = teefem.plate_functions.PlateCharacteristic(thickness=lambda k, e: t)
teefem.assign_char(elements=OM_el, char=carel)
mdl.static_solve()
dymin = min([node.fields['DEPL']['DZ'] for node in mdl.nodes])
print("DZ (acc) : %0.14E" % (w(0)))
print("DZ : %0.14E" % (dymin))
+ a ** 2 * q * (1 - r ** 2 / a ** 2) / (16 * D)
- q * r ** 2 / (8 * D)
)
** 2
/ t ** 4
) ** (1 / 2)
mesh = teefem.mesh.unitcircle(R=1)
mat = teefem.materials.elastic(E=E, nu=nu)
mdl = model(mesh=mesh)
OM_el = mdl.elset["OM1"]
GA1_no = mdl.nset["GA1"]
teefem.assign_material(elements=OM_el, material=mat)
bc1 = teefem.pressure_bc(pressure=lambda k, e: -q)
bc2 = teefem.dirichlet_bc(encastre=True)
teefem.assign_bc(elements=OM_el, bc=bc1)
teefem.assign_bc(nodes=GA1_no, bc=bc2)
carel = teefem.plate_functions.PlateCharacteristic(thickness=lambda k, e: t)
teefem.assign_char(elements=OM_el, char=carel)
mdl.static_solve()
dymin = min([node.fields["DEPL"]["DZ"] for node in mdl.nodes])
print("DZ (acc) : %0.14E" % (w(0)))
print("DZ : %0.14E" % (dymin))
def malli0():
''' Tasojännitystilan ratkaisu. '''
mesh = teefem.geom.mesh(filename='cplangeo.msh')
mdl = cplan.cplan(mesh=mesh)
OM1_el = mdl.elset['OM1']
mat = teefem.materials.elastic(E=210.0e9, nu=0.3)
teefem.assign_material(elements=OM1_el, material=mat)
# nset1 = set().union(mdl.nset['GA1'], mdl.nset['GA2'], mdl.nset['GA3'], mdl.nset['GA4'])
# nset1 = set().union(mdl.nset['GA2'], mdl.nset['GA4'])
teefem.assign_bc(
nodes=mdl.nset['GA5'],
bc=teefem.dirichlet_bc(dx=0, dy=0),
)
teefem.assign_bc(
elements=mdl.elset['GA1'],
bc=teefem.pressure_bc(pressure=lambda k: +q), # TJT oletuspaksuus t=1
)
teefem.assign_bc(
elements=mdl.elset['GA3'],
bc=teefem.pressure_bc(pressure=lambda k: -q), # TJT oletuspaksuus t=1
)
mdl.static_solve()
### Jälkikäsittelyä ###
from scipy.interpolate import griddata
# Primäärikenttä solmupisteissä
x = []
y = []
dx = []
dy = []
for n in mdl.nodes:
x.append(n.x)
y.append(n.y)
dx.append(n.fields['DEPL']['DX'])
dy.append(n.fields['DEPL']['DY'])
xx = []
yy = []
Nx = []
Ny = []
Nxy = []
vmis = []
for e in mdl.elset['OM1']:
for ke in e.ipoints:
xx.append(e.geom.x(*ke))
yy.append(e.geom.y(*ke))
S = e.S(*ke)
Nx.append(S[0, 0])
Ny.append(S[1, 0])
Nxy.append(S[2, 0])
vmis.append(e.vmis(*ke))
def plot(x, y, data, filename):
plt.figure()
# define grid.
xi = np.linspace(min(x), max(x), 100)
yi = np.linspace(min(y), max(y), 100)
# grid the data.
si = griddata((x, y),
data, (xi[None, :], yi[:, None]),
method='linear')
# contour the gridded data, plotting dots at the randomly spaced data points.
CS = plt.contour(xi, yi, si, 30, linewidths=0.5, colors='k')
CS = plt.contourf(xi, yi, si, 30, cmap=plt.cm.jet)
plt.colorbar() # draw colorbar
# plot data points.
# plt.scatter(x,y,marker='o',c='b',s=5)
plt.xlim(min(x), max(x))
plt.ylim(min(y), max(y))
plt.savefig(filename)
#plt.tight_layout()
plot(x, y, dx, 'dx.pdf')
plot(x, y, dy, 'dy.pdf')
plot(xx, yy, Nx, 'Nx.pdf')
plot(xx, yy, Ny, 'Ny.pdf')
plot(xx, yy, Nxy, 'Nxy.pdf')
plt.show()
def malli0():
''' Tasojännitystilan ratkaisu. '''
mesh = teefem.geom.mesh(filename = 'cplangeo.msh')
mdl = cplan.cplan(mesh = mesh)
OM1_el = mdl.elset['OM1']
mat = teefem.materials.elastic(E = 210.0e9, nu = 0.3)
teefem.assign_material(elements = OM1_el, material = mat)
# nset1 = set().union(mdl.nset['GA1'], mdl.nset['GA2'], mdl.nset['GA3'], mdl.nset['GA4'])
# nset1 = set().union(mdl.nset['GA2'], mdl.nset['GA4'])
teefem.assign_bc(
nodes = mdl.nset['GA5'],
bc = teefem.dirichlet_bc(dx=0,dy=0),
)
teefem.assign_bc(
elements = mdl.elset['GA1'],
bc = teefem.pressure_bc(pressure = lambda k: +q), # TJT oletuspaksuus t=1
)
teefem.assign_bc(
elements = mdl.elset['GA3'],
bc = teefem.pressure_bc(pressure = lambda k: -q), # TJT oletuspaksuus t=1
)
mdl.static_solve()
### Jälkikäsittelyä ###
from scipy.interpolate import griddata
# Primäärikenttä solmupisteissä
x = []
y = []
dx = []
dy = []
for n in mdl.nodes:
x.append(n.x)
y.append(n.y)
dx.append(n.fields['DEPL']['DX'])
dy.append(n.fields['DEPL']['DY'])
xx = []
yy = []
Nx = []
Ny = []
Nxy = []
vmis = []
for e in mdl.elset['OM1']:
for ke in e.ipoints:
xx.append(e.geom.x(*ke))
yy.append(e.geom.y(*ke))
S = e.S(*ke)
Nx.append(S[0,0])
Ny.append(S[1,0])
Nxy.append(S[2,0])
vmis.append(e.vmis(*ke))
def plot(x,y,data,filename):
plt.figure()
# define grid.
xi = np.linspace(min(x),max(x),100)
yi = np.linspace(min(y),max(y),100)
# grid the data.
si = griddata((x, y), data, (xi[None,:], yi[:,None]), method='linear')
# contour the gridded data, plotting dots at the randomly spaced data points.
CS = plt.contour(xi,yi,si,30,linewidths=0.5,colors='k')
CS = plt.contourf(xi,yi,si,30,cmap=plt.cm.jet)
plt.colorbar() # draw colorbar
# plot data points.
# plt.scatter(x,y,marker='o',c='b',s=5)
plt.xlim(min(x),max(x))
plt.ylim(min(y),max(y))
plt.savefig(filename)
#plt.tight_layout()
plot(x,y,dx,'dx.pdf')
plot(x,y,dy,'dy.pdf')
plot(xx,yy,Nx,'Nx.pdf')
plot(xx,yy,Ny,'Ny.pdf')
plot(xx,yy,Nxy,'Nxy.pdf')
plt.show()
mesh = teefem.geom.mesh(filename = meshfile) mdl = teefem.models.cplan(mesh = mesh) # Ryhmät OM1_el = mdl.elset['OM1'] # Koko domain GA1_no = mdl.nset['GA1'] # Vasen reuna GA2_el = mdl.elset['GA2'] # Yläreuna P1_no = mdl.nset['P1'] # Pistevoima # Materiaali mat = teefem.materials.elastic(E = 210.0e9, nu = 0.3) teefem.assign_material(elements = OM1_el, material = mat) # Reunaehdot, huom. TeeFEMissä tasojännitystila-elementin paksuus on oletuksena 1 bc1 = teefem.pressure_bc(pressure = lambda k: -q/t) bc2 = teefem.dirichlet_bc(encastre = True) bc3 = teefem.nodal_force(fy = -F/t) # Kytketään reunaehdot malliin # 1. Jakautunut kuormitus elementtiryhmään GA2 teefem.assign_bc(elements = GA2_el, bc = bc1) # 2. Vasen reuna jäykästi kiinni teefem.assign_bc(nodes = GA1_no, bc = bc2) # 3. Pistevoima alareunaan teefem.assign_bc(nodes = P1_no, bc = bc3) # Ratkaisu import time t0 = time.clock() mdl.static_solve()
