def calc_matrices(c, g,
prefix='print_derivations', NL_kinematics='donnell',
analytical=True):
NL_kinematics = NL_kinematics.lower()
if (NL_kinematics=='donnell'):
from kinematics_donnell import d, A, Gaux
elif NL_kinematics=='donnellmb_rev_00':
from kinematics_donnellmb_rev_00 import d, A, Gaux
elif NL_kinematics=='sanders_rev_00':
from kinematics_sanders_rev_00 import d, A, Gaux
else:
print NL_kinematics
raise ValueError(
'Non-linear kinematics option "{}" not defined!'.format(
NL_kinematics))
print('Non-linear kinematics: {}'.format(NL_kinematics))
matrices = {}
#
B0 = evaluateExpr(d*g)
e0 = B0*c
G = evaluateExpr(Gaux*g)
BL = A*G
#
sufix = 'ALL'
#
not_assigned = []
# creating a nan that will be useful to track if sth goes wrong
wx = wt = sympy.nan
for matrix in [c, g, d, A, Gaux]:
for expr in matrix:
for s in expr.free_symbols:
s.__class__.is_commutative = False
if str(s)=='x':
x = s
elif str(s)=='t':
t = s
elif str(s)=='r':
r = s
elif str(s)=='ux':
ux = s
elif str(s)=='ut':
ut = s
elif str(s)=='v':
v = s
elif str(s)=='vx':
vx = s
elif str(s)=='wx':
wx = s
elif str(s)=='wt':
wt = s
elif str(s)=='sina':
sina = s
elif str(s)=='cosa':
cosa = s
else:
not_assigned.append(s)
print('Not assigned variables:')
print('\t{}'.format(set(not_assigned)))
#
print 'here1'
if analytical:
# NON-LINEAR substitutions
dummy, dummy, wxb = g.diff(x)*c
dummy, dummy, wtb = g.diff(t)*c
subs_b = {
wx: wxb,
wt: wtb,
}
BL = BL.subs(subs_b)
print 'here2'
#
eL = (BL/2)*c
#
print 'here3'
# kG linear
Nxx, Ntt, Nxt, Mxx, Mtt, Mxt = sympy.var(
'Nxx, Ntt, Nxt, Mxx, Mtt, Mxt')
N = Matrix([[Nxx, Nxt],
[Nxt, Ntt]])
if NL_kinematics=='donnellmb_rev_00':
N = Matrix(
[[Ntt*cosa**2, -1/(2*r)*Mtt*sina*cosa, 0, -1/r*Mxt*cosa, -1/(2*r)*Mtt*cosa],
[-1/(2*r)*Mtt*sina*cosa, Nxx, Nxt + Mxt*cosa/r, 0, 0],
[0, Nxt + Mxt*cosa/r, Ntt + Mtt*cosa/r, 0, 0],
[-1/r*Mxt*cosa, 0, 0, 0, 0],
[-1/(2*r)*Mtt*cosa, 0, 0, 0, 0]])
elif NL_kinematics=='sanders_rev_00':
N = Matrix(
[[0, 0, -Nxt*sina, 0, 0, 0],
[0, 0, -Ntt*sina, 0, 0, 0],
[-Nxt*sina, -Ntt*sina, Ntt, 0, -Nxt*cosa, -Ntt*cosa],
[0, 0, 0, Nxx, 0, 0 ],
[0, 0, -Nxt*cosa, 0, Nxx, Nxt],
[0, 0, -Ntt*cosa, 0, Nxt, Ntt]])
# kG NL
N_vec = LC*(e0 + eL)
Nxx = N_vec[0]
Ntt = N_vec[1]
Nxt = N_vec[2]
Mxx = N_vec[3]
Mtt = N_vec[4]
Mxt = N_vec[5]
N_NL = Matrix([[Nxx, Nxt],
[Nxt, Ntt]])
print 'here4'
if NL_kinematics=='donnellmb_rev_00':
N_NL = Matrix(
[[Ntt*cosa**2, -1/(2*r)*Mtt*sina*cosa, 0, -1/r*Mxt*cosa, -1/(2*r)*Mtt*cosa],
[-1/(2*r)*Mtt*sina*cosa, Nxx, Nxt + Mxt*cosa/r, 0, 0],
[0, Nxt + Mxt*cosa/r, Ntt + Mtt*cosa/r, 0, 0],
[-1/r*Mxt*cosa, 0, 0, 0, 0],
[-1/(2*r)*Mtt*cosa, 0, 0, 0, 0]])
elif NL_kinematics=='sanders_rev_00':
N_NL = Matrix(
[[0, 0, -Nxt*sina, 0, 0, 0],
[0, 0, -Ntt*sina, 0, 0, 0],
[-Nxt*sina, -Ntt*sina, Ntt, 0, -Nxt*cosa, -Ntt*cosa],
[0, 0, 0, Nxx, 0, 0 ],
[0, 0, -Nxt*cosa, 0, Nxx, Nxt],
[0, 0, -Ntt*cosa, 0, Nxt, Ntt]])
#
kLL = r*B0.T*LC*B0
kLNL = r*B0.T*LC*BL
kNLL = r*BL.T*LC*B0
kNLNL = r*BL.T*LC*BL
#
print 'here5'
# kG
kG = r*G.T*N*G
kG_NL = r*G.T*N_NL*G
#
print 'here6'
#
ks = [['k00'+sufix, kLL],
['k0L'+sufix, kLNL],
['kLL'+sufix, kNLNL],
['kG'+sufix, kG],
['kG_NL'+sufix, kG_NL],
['e0', e0],
['eL', eL],
]
#
print 'here7'
#
with open('{prefix}_k{sufix}.txt'.format(prefix=prefix,
sufix=sufix), 'w') as outf:
def myprint(sth):
outf.write(str(sth).strip() + '\n')
for kname, kab in ks:
myprint('#')
myprint('# {0}'.format(kname))
myprint('#')
myprint(kab)
myprint('#')
for (i, j), v in np.ndenumerate(kab):
if v:
myprint(kname+'[{0},{1}] = {2}'.format(i, j, str(v)))
#
print 'here8'
#
matrices['kALL'] = ks
return matrices
def calc_matrices(cs_left, gs_left, cs_right, gs_right,
prefix='print_derivations', NL_kinematics='donnell_rev_03'):
sanders = False
NL_kinematics = NL_kinematics.lower()
if NL_kinematics==('donnell_rev_03' or 'donnell_rev_04' or
'donnell_rev_05'):
from kinematics_donnell import d, A_w, Gaux_w
elif NL_kinematics=='donnellmb_rev_00':
from kinematics_donnellmb_rev_00 import d, A_w, Gaux_w
elif NL_kinematics=='sanders_rev_00':
sanders = True
from kinematics_sanders_rev_00 import d, A_v, A_w, Gaux_v, Gaux_w
elif NL_kinematics=='full':
from kinematics_full import d, dNL
else:
raise ValueError(
'Non-linear kinematics option "{}" not defined!'.format(
NL_kinematics))
print('Non-linear kinematics: {}'.format(NL_kinematics))
matrices = {}
csa = cs_left
gsa = gs_left
csb = cs_right
gsb = gs_right
na = len(csa)
nb = len(csb)
#
g = Matrix(np.hstack(gsb))
c = Matrix(np.vstack(csb))
e0 = evaluateExpr(d*g)*c
G_w = evaluateExpr(Gaux_w*g)
BL = A_w*G_w
if sanders:
G_v = evaluateExpr(Gaux_v*g)
BL += A_v*G_v
else:
A_v = None
G_v = None
eL = BL*c/2
#
for mi, mj in product(range(na), range(nb)):
sufix = '{0}{1}'.format(str(mi), str(mj))
ca = csa[mi]
ga = gsa[mi]
cb = csb[mj]
gb = gsb[mj]
#
not_assigned = []
# creating a nan that will be useful to track if sth goes wrong
w = wx = w0x = wt = w0t = wxt = wtt = sympy.nan
for matrix in [ca, ga, cb, gb, d, A_v, A_w, Gaux_v, Gaux_w]:
if matrix==None:
continue
for expr in matrix:
for s in expr.free_symbols:
s.__class__.is_commutative = False
if str(s)=='x':
x = s
elif str(s)=='t':
t = s
elif str(s)=='r':
r = s
elif str(s)=='v':
v = s
elif str(s)=='vx':
vx = s
elif str(s)=='vt':
vt = s
elif str(s)=='w':
w = s
elif str(s)=='wx':
wx = s
elif str(s)=='wt':
wt = s
elif str(s)=='wxt':
wxt = s
elif str(s)=='wtt':
wtt = s
elif str(s)=='w0x':
w0x = s
elif str(s)=='w0t':
w0t = s
elif str(s)=='sina':
sina = s
elif str(s)=='cosa':
cosa = s
else:
not_assigned.append(s)
print('Not assigned variables:')
print('\t{}'.format(set(not_assigned)))
#
B0a = evaluateExpr(d*ga)
B0b = evaluateExpr(d*gb)
Ga_w = evaluateExpr(Gaux_w*ga)
Gb_w = evaluateExpr(Gaux_w*gb)
BLa = A_w*Ga_w
BLb = A_w*Gb_w
if sanders:
Ga_v = evaluateExpr(Gaux_v*ga)
Gb_v = evaluateExpr(Gaux_v*gb)
BLa += A_v*Ga_v
BLb += A_v*Gb_v
#
k00 = r*B0a.T*LC*B0b
k0L = r*B0a.T*LC*BLb
kNLL = r*BLa.T*LC*B0b
kLL = r*BLa.T*LC*BLb
#
# kG
Nxx, Ntt, Nxt = sympy.var('Nxx, Ntt, Nxt')
N = Matrix([[Nxx, Nxt],
[Nxt, Ntt]])
# kG
if NL_kinematics=='donnellmb':
Nxx, Ntt, Nxt, Mxx, Mtt, Mxt = sympy.var(
'Nxx, Ntt, Nxt, Mxx, Mtt, Mxt')
N = Matrix(
[[Ntt*cosa**2, -1/(2*r)*Mtt*sina*cosa, 0, -1/r*Mxt*cosa, -1/(2*r)*Mtt*cosa],
[-1/(2*r)*Mtt*sina*cosa, Nxx, Nxt + Mxt*cosa/r, 0, 0],
[0, Nxt + Mxt*cosa/r, Ntt + Mtt*cosa/r, 0, 0],
[-1/r*Mxt*cosa, 0, 0, 0, 0],
[-1/(2*r)*Mtt*cosa, 0, 0, 0, 0]])
#
kG = r*Ga_w.T*N*Gb_w
if sanders:
kG += r*Ga_v.T*N*Gb_v
#
ks = [['k00'+sufix, k00],
['k0L'+sufix, k0L],
['kLL'+sufix, kLL],
['kG'+sufix, kG],
['e0', e0],
['eL', eL],
['BL', BL],
]
#
with open('{prefix}_k{sufix}.txt'.format(prefix=prefix,
sufix=sufix), 'w') as outf:
def myprint(sth):
outf.write(str(sth).strip() + '\n')
for kname, kab in ks:
myprint('#')
num = len([kabi for kabi in kab if kabi])
myprint('# {0} with {1} non-null temrs'.format(kname, num))
myprint('#')
myprint(kab)
myprint('#')
for (i, j), v in np.ndenumerate(kab):
if v:
myprint(kname+'[{0},{1}] = {2}'.format(i, j, str(v)))
matrices['k{0}{1}'.format(mi, mj)] = ks
with open('all_matrices.txt', 'w') as outf:
def myprint(sth):
outf.write(str(sth).strip() + '\n')
all = []
m = matrices
for a,dummy in enumerate(ks):
full = Matrix(
np.vstack((np.hstack((m['k00'][a][1], m['k01'][a][1], m['k02'][a][1])),
np.hstack((m['k10'][a][1], m['k11'][a][1], m['k12'][a][1])),
np.hstack((m['k20'][a][1], m['k21'][a][1], m['k22'][a][1]))))
)
kname = m['k00'][a][0]
for (i, j), v in np.ndenumerate(full):
if v:
myprint(kname+'[{0},{1}] = {2}'.format(i, j, str(v)))
return matrices
def calc_matrices(cs_left,
gs_left,
cs_right,
gs_right,
prefix='print_derivations',
NL_kinematics='donnell_rev_03'):
sanders = False
NL_kinematics = NL_kinematics.lower()
if NL_kinematics == ('donnell_rev_03' or 'donnell_rev_04'
or 'donnell_rev_05'):
from kinematics_donnell import d, A_w, Gaux_w
elif NL_kinematics == 'donnellmb_rev_00':
from kinematics_donnellmb_rev_00 import d, A_w, Gaux_w
elif NL_kinematics == 'sanders_rev_00':
sanders = True
from kinematics_sanders_rev_00 import d, A_v, A_w, Gaux_v, Gaux_w
elif NL_kinematics == 'full':
from kinematics_full import d, dNL
else:
raise ValueError(
'Non-linear kinematics option "{}" not defined!'.format(
NL_kinematics))
print('Non-linear kinematics: {}'.format(NL_kinematics))
matrices = {}
csa = cs_left
gsa = gs_left
csb = cs_right
gsb = gs_right
na = len(csa)
nb = len(csb)
#
g = Matrix(np.hstack(gsb))
c = Matrix(np.vstack(csb))
e0 = evaluateExpr(d * g) * c
G_w = evaluateExpr(Gaux_w * g)
BL = A_w * G_w
if sanders:
G_v = evaluateExpr(Gaux_v * g)
BL += A_v * G_v
else:
A_v = None
G_v = None
eL = BL * c / 2
#
for mi, mj in product(range(na), range(nb)):
sufix = '{0}{1}'.format(str(mi), str(mj))
ca = csa[mi]
ga = gsa[mi]
cb = csb[mj]
gb = gsb[mj]
#
not_assigned = []
# creating a nan that will be useful to track if sth goes wrong
w = wx = w0x = wt = w0t = wxt = wtt = sympy.nan
for matrix in [ca, ga, cb, gb, d, A_v, A_w, Gaux_v, Gaux_w]:
if matrix == None:
continue
for expr in matrix:
for s in expr.free_symbols:
s.__class__.is_commutative = False
if str(s) == 'x':
x = s
elif str(s) == 't':
t = s
elif str(s) == 'r':
r = s
elif str(s) == 'v':
v = s
elif str(s) == 'vx':
vx = s
elif str(s) == 'vt':
vt = s
elif str(s) == 'w':
w = s
elif str(s) == 'wx':
wx = s
elif str(s) == 'wt':
wt = s
elif str(s) == 'wxt':
wxt = s
elif str(s) == 'wtt':
wtt = s
elif str(s) == 'w0x':
w0x = s
elif str(s) == 'w0t':
w0t = s
elif str(s) == 'sina':
sina = s
elif str(s) == 'cosa':
cosa = s
else:
not_assigned.append(s)
print('Not assigned variables:')
print('\t{}'.format(set(not_assigned)))
#
B0a = evaluateExpr(d * ga)
B0b = evaluateExpr(d * gb)
Ga_w = evaluateExpr(Gaux_w * ga)
Gb_w = evaluateExpr(Gaux_w * gb)
BLa = A_w * Ga_w
BLb = A_w * Gb_w
if sanders:
Ga_v = evaluateExpr(Gaux_v * ga)
Gb_v = evaluateExpr(Gaux_v * gb)
BLa += A_v * Ga_v
BLb += A_v * Gb_v
#
k00 = r * B0a.T * LC * B0b
k0L = r * B0a.T * LC * BLb
kNLL = r * BLa.T * LC * B0b
kLL = r * BLa.T * LC * BLb
#
# kG
Nxx, Ntt, Nxt = sympy.var('Nxx, Ntt, Nxt')
N = Matrix([[Nxx, Nxt], [Nxt, Ntt]])
# kG
if NL_kinematics == 'donnellmb':
Nxx, Ntt, Nxt, Mxx, Mtt, Mxt = sympy.var(
'Nxx, Ntt, Nxt, Mxx, Mtt, Mxt')
N = Matrix([[
Ntt * cosa**2, -1 / (2 * r) * Mtt * sina * cosa, 0,
-1 / r * Mxt * cosa, -1 / (2 * r) * Mtt * cosa
],
[
-1 / (2 * r) * Mtt * sina * cosa, Nxx,
Nxt + Mxt * cosa / r, 0, 0
],
[0, Nxt + Mxt * cosa / r, Ntt + Mtt * cosa / r, 0, 0],
[-1 / r * Mxt * cosa, 0, 0, 0, 0],
[-1 / (2 * r) * Mtt * cosa, 0, 0, 0, 0]])
#
kG = r * Ga_w.T * N * Gb_w
if sanders:
kG += r * Ga_v.T * N * Gb_v
#
ks = [
['k00' + sufix, k00],
['k0L' + sufix, k0L],
['kLL' + sufix, kLL],
['kG' + sufix, kG],
['e0', e0],
['eL', eL],
['BL', BL],
]
#
with open('{prefix}_k{sufix}.txt'.format(prefix=prefix, sufix=sufix),
'w') as outf:
def myprint(sth):
outf.write(str(sth).strip() + '\n')
for kname, kab in ks:
myprint('#')
num = len([kabi for kabi in kab if kabi])
myprint('# {0} with {1} non-null temrs'.format(kname, num))
myprint('#')
myprint(kab)
myprint('#')
for (i, j), v in np.ndenumerate(kab):
if v:
myprint(kname + '[{0},{1}] = {2}'.format(i, j, str(v)))
matrices['k{0}{1}'.format(mi, mj)] = ks
with open('all_matrices.txt', 'w') as outf:
def myprint(sth):
outf.write(str(sth).strip() + '\n')
all = []
m = matrices
for a, dummy in enumerate(ks):
full = Matrix(
np.vstack(
(np.hstack(
(m['k00'][a][1], m['k01'][a][1], m['k02'][a][1])),
np.hstack(
(m['k10'][a][1], m['k11'][a][1], m['k12'][a][1])),
np.hstack(
(m['k20'][a][1], m['k21'][a][1], m['k22'][a][1])))))
kname = m['k00'][a][0]
for (i, j), v in np.ndenumerate(full):
if v:
myprint(kname + '[{0},{1}] = {2}'.format(i, j, str(v)))
return matrices