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allow for outboard loads on wing as signomial model #163

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merged 9 commits into from
Apr 21, 2018
Merged

allow for outboard loads on wing as signomial model #163

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0b9702b
move beam to sparloading
Apr 9, 2018
fbcbcd1
insert beam into sparloading
Apr 16, 2018
016a561
move beam function into sparloading
Apr 17, 2018
bbbd56b
allow for outboard weights on wing
Apr 17, 2018
46955f1
delete unnecessary lines
Apr 20, 2018
6bafbd3
Merge branch 'master' into outboardloads
Apr 20, 2018
08b419f
fix cvxopt runs
Apr 20, 2018
07c738b
update tip values to allow for feasible solution with cvxopt
Apr 20, 2018
6c6cc70
add drag margin and number of plys to elliptical fuselage
Apr 20, 2018
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6 changes: 4 additions & 2 deletions gpkitmodels/GP/aircraft/fuselage/elliptical_fuselage.py
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Original file line number Diff line number Diff line change
Expand Up @@ -12,6 +12,7 @@ class FuselageAero(Model):
Cf [-] fuselage skin friction coefficient
Re [-] fuselage reynolds number
Cd [-] fuselage drag coefficient
mfac 1.0 [-] fuselage drag margin

"""
def setup(self, static, state):
Expand All @@ -26,7 +27,7 @@ def setup(self, static, state):
constraints = [
Re == V*rho*l/mu,
Cf >= 0.455/Re**0.3,
Cd >= Cf*k
Cd/mfac >= Cf*k
]

return constraints
Expand All @@ -47,6 +48,7 @@ class Fuselage(Model):
rhofuel 6.01 [lbf/gallon] density of 100LL
rhocfrp 1.6 [g/cm^3] density of CFRP
t [in] fuselage skin thickness
nply 2 [-] number of plys

"""
material = cfrpfabric
Expand All @@ -64,7 +66,7 @@ def setup(self):
3*(S/np.pi)**1.6075 >= 2*(l*R*2)**1.6075 + (2*R)**(2*1.6075),
Vol <= 4*np.pi/3*(l/2)*R**2,
W/mfac >= S*rhocfrp*t*g,
t >= 2*tmin,
t >= nply*tmin,
]

return constraints
Expand Down
21 changes: 6 additions & 15 deletions gpkitmodels/GP/aircraft/wing/gustloading.py
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Original file line number Diff line number Diff line change
Expand Up @@ -26,18 +26,6 @@ class GustL(SparLoading):
agust [-] gust angle of attack
cosminus1 self.return_cosm1 [-] 1 minus cosine factor

Upper Unbounded
---------------
v, cl, wing.spar.I, wing.spar.tshear, wing.spar.Sy
J (if wingSparJ)
theta (if not wingSparJ), M (if not wingSparJ)

Lower Unbounded
---------------
Ww, wing.planform.b, wing.planform.cave
wing.planform.CM (if wingSparJ), qne (if wingSparJ)
theta (if not wingSparJ), M (if not wingSparJ)

LaTex Strings
-------------
vgust V_{\\mathrm{gust}}
Expand All @@ -53,12 +41,15 @@ class GustL(SparLoading):
return_cosm1 = lambda self, c: hstack(
[adnumber(1e-10), 1-array(cos(c[self.wing.planform.eta][1:]*pi/2))])

def setup(self, wing, state):
def setup(self, wing, state, sp=False):
exec parse_variables(GustL.__doc__)
self.load = SparLoading.setup(self, wing, state)
self.load = SparLoading.setup(self, wing, state, sp=sp)

cbar = self.wing.planform.cbar
W = self.W # from SparLoading
q = self.q
N = self.N
b = self.b

path = os.path.dirname(os.path.abspath(__file__))
df = pd.read_csv(path + os.sep + "arctan_fit.csv").to_dict(
Expand All @@ -67,7 +58,7 @@ def setup(self, wing, state):
constraints = [
# fit for arctan from 0 to 1, RMS = 0.044
FitCS(df, agust, [cosminus1*vgust/v]),
self.beam["\\bar{q}"] >= cbar*(1 + 2*pi*agust/cl*(1+Ww/W)),
q >= W*N/b*cbar*(1 + 2*pi*agust/cl*(1+Ww/W)),
]

return self.load, constraints
66 changes: 37 additions & 29 deletions gpkitmodels/GP/aircraft/wing/sparloading.py
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
" spar loading "
from gpkit import Model, parse_variables
from gpkit import Model, parse_variables, SignomialsEnabled
from gpkitmodels.GP.beam.beam import Beam
from gpkitmodels.GP.aircraft.tail.tail_boom import TailBoomState
from numpy import pi
Expand All @@ -16,24 +16,27 @@ class SparLoading(Model):
Nsafety 1.0 [-] safety load factor
kappa 0.2 [-] max tip deflection ratio
W [lbf] loading weight
N [-] loading factor
twmax 30.*pi/180 [-] max tip twist
Stip 1e-10 [N] tip loading
Mtip 1e-10 [N*m] tip moment
throot 1e-10 [-] root deflection angle
wroot 1e-10 [m] root deflection

Variables of length wing.N
--------------------------
q [N/m] distributed wing loading
S [N] shear along wing
M [N*m] wing section root moment
th [-] deflection angle
w [m] wing deflection

Variables of length wing.N-1
----------------------------
Mr [N*m] wing section root moment
M [N*m] local moment
Mtw [N*m] local moment due to twisting
theta [-] twist deflection

Upper Unbounded
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why'd you remove all the bounds? :p

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I removed the bounds because it got really annoying as I was debugging

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Do you think they're a useful feature overall? (during dev you can add SKIP VERIFICATION to disable checking)

---------------
I, Sy, J (if wingSparJ)
theta (if not wingSparJ), M (if not wingSparJ)

Lower Unbounded
---------------
b, W, cave
wing.planform.CM (if wingSparJ), qne (if wingSparJ)
theta (if not wingSparJ), M (if not wingSparJ)
EIbar [-] EIbar
Sout [N] outboard weights

LaTex Strings
-------------
Expand All @@ -49,29 +52,34 @@ def new_qbarFun(self, c):

new_SbarFun = None

def setup(self, wing, state):
def setup(self, wing, state, sp=False):
self.wing = wing
exec parse_variables(SparLoading.__doc__)

Beam.qbarFun = self.new_qbarFun
Beam.SbarFun = self.new_SbarFun
self.beam = Beam(self.wing.N)

b = self.b = self.wing.planform.b
I = self.I = self.wing.spar.I
Sy = self.Sy = self.wing.spar.Sy
cave = self.cave = self.wing.planform.cave
cbar = self.cbar = self.wing.planform.cbar
E = self.wing.spar.material.E
sigma = self.wing.spar.material.sigma
deta = self.wing.planform.deta

if sp:
with SignomialsEnabled():
shear = S[:-1] >= (S[1:] + 0.5*deta*(b/2.)*(q[:-1] + q[1:])
- Sout)
else:
shear = S[:-1] >= S[1:] + 0.5*deta*(b/2.)*(q[:-1] + q[1:])

constraints = [
# dimensionalize moment of inertia and young's modulus
self.beam["dx"] == deta,
self.beam["\\bar{EI}"] <= 8*E*I/Nmax/Nsafety/W/b**2,
Mr >= self.beam["\\bar{M}"][:-1]*W*Nmax*Nsafety*b/4,
sigma >= Mr/Sy,
self.beam["\\bar{\\delta}"][-1] <= kappa,
N == Nsafety*Nmax, q >= N*W/b*cbar,
shear, S[-1] >= Stip,
M[:-1] >= M[1:] + 0.5*deta*(b/2)*(S[:-1] + S[1:]), M[-1] >= Mtip,
th[0] >= throot,
th[1:] >= th[:-1] + 0.5*deta*(b/2)*(M[1:] + M[:-1])/E/I,
w[0] >= wroot, w[1:] >= w[:-1] + 0.5*deta*(b/2)*(th[1:] + th[:-1]),
sigma >= M[:-1]/Sy, w[-1]/(b/2) <= kappa,
]

self.wingSparJ = hasattr(self.wing.spar, "J")
Expand All @@ -82,9 +90,9 @@ def setup(self, wing, state):
G = self.wing.spar.shearMaterial.G
cm = self.wing.planform.CM
constraints.extend([
M >= cm*cave**2*qne*deta*b/2*Nsafety,
theta[0] >= M[0]/G/J[0]*deta[0]*b/2,
theta[1:] >= theta[:-1] + M[1:]/G/J[1:]*deta[1:]*b/2,
Mtw >= cm*cave**2*qne*deta*b/2*Nsafety,
theta[0] >= Mtw[0]/G/J[0]*deta[0]*b/2,
theta[1:] >= theta[:-1] + Mtw[1:]/G/J[1:]*deta[1:]*b/2,
twmax >= theta[-1]
])
return self.beam, constraints
return constraints
10 changes: 4 additions & 6 deletions gpkitmodels/GP/aircraft/wing/wing_test.py
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Original file line number Diff line number Diff line change
Expand Up @@ -39,9 +39,8 @@ def wing_test():
from gpkit import settings
if settings["default_solver"] == "cvxopt":
for l in loading:
for v in ["\\bar{M}_{tip}", "\\bar{S}_{tip}",
"\\bar{\\delta}_{root}", "\\theta_{root}"]:
l.substitutions[v] = 1e-3
for v in ["Mtip", "Stip", "wroot", "throot"]:
l.substitutions[v] = 1e-1
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huh why so much larger?

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I'm not sure. But it gave me unknown at 1e-2 so...


m = Model(perf.Cd, [
loading[1].v == fs.V,
Expand All @@ -68,9 +67,8 @@ def box_spar():
from gpkit import settings
if settings["default_solver"] == "cvxopt":
for l in loading:
for v in ["\\bar{M}_{tip}", "\\bar{S}_{tip}",
"\\bar{\\delta}_{root}", "\\theta_{root}"]:
l.substitutions[v] = 1e-3
for v in ["Mtip", "Stip", "wroot", "throot"]:
l.substitutions[v] = 1e-2

m = Model(perf.Cd, [
loading[1].v == fs.V,
Expand Down