def objf(xs):
"""
The objective function
generated in mk.yieldFunction.tuneH48.returnObjYS
Argument
--------
xs -- <f,g,h,n> the four Hill48 parameters
in the plane-stress space.
"""
nth = len(np.array(ref[0]))
th=np.linspace(-pi,+pi,nth)
x=cos(th); y=sin(th)
z=np.zeros(len(th))
s=np.array([x,y,z,z,z,z]).T
f,g,h,n = xs
X=[]; Y=[]
for i in xrange(len(s)):
rst=fYLD(s[i],f,g,h,n)
ys = rst[0]
X.append(ys[0])
Y.append(ys[1])
X=np.array(X)
Y=np.array(Y)
## rst to th-r coordinate
r,th = xy2rt(X,Y)
R,TH = xy2rt(ref[0],ref[1])
diff = ((r-R)**2).sum()/(len(th)-1)
return diff
def returnDiff(params):
"""
Tune using the given in-plane locus
Arguments
=========
params [0] : rb
params [1:4]: y45,y90,yb
"""
## Find 4 parameters...
paramR = np.ones(4)
paramY = np.ones(4)
paramR[0:4] = rv[0], rv[1], rv[2], params[0]
paramY[1:4] = params[1:4]
k = 2
m = 8 ## the exponent is fixed?
yldFunc = wrapYLD(r=paramR, y=paramY, m=m, k=k)
if type(yldFunc).__name__ == 'int':
if yldFunc == -1:
return 1
yldLocus = locus(yldFunc, 1000) ##
## convert yldLocus in to (th,r) coordinates
r, th = xy2rt(np.array(yldLocus[0]), np.array(yldLocus[1]))
th0, r0 = YS ## reference
radIntp = rad_xy2(r, th, th0)
radIntp = np.array(radIntp)
return np.sqrt(((radIntp - r0)**2).sum()) / (len(r) - 1)
def extractParamsFromYS(locus_planestress,psi_uni,rvs_uni,ys_uni):
"""
Given plane-stress yield locus, extract parameters.
"""
from vpscyld import lib_dat, calc_normal
## normalize the locus by stress along axis 1
ysx, ysy =lib_dat.nys_th(np.array(locus_planestress[0]),np.array(locus_planestress[1]),t=0)
ysr, yst = lib_dat.xy2rt(ysx,ysy)
yb = lib_dat.rad_xy(ysr,yst,45*np.pi/180.) ## balanced biaxial yield stress...
yb = yb / np.sqrt(2)
y0 = lib_dat.rad_xy(ysr,yst,0) ## balanced biaxial yield stress...
y90 = lib_dat.rad_xy(ysr,yst,90*np.pi/180.) ## balanced biaxial yield stress...
th = calc_normal.main_var(locus_xy=[ysr,yst],psi_ref=[45.])
rb = 1./np.tan(th[0])
y0_uni = ys_uni[0]
y90_uni = ys_uni[-1]
r0_uni = rvs_uni[0]
r90_uni = rvs_uni[-1]
r45_uni = np.interp(45*np.pi/180., psi_uni, rvs_uni)
y45_uni = np.interp(45*np.pi/180., psi_uni, ys_uni)
if abs(y0_uni-y0)>1e-3:
print 'y0 diff'
print y0_uni,y0
# raise IOError, 'Consider using finer step for yield locus'
if abs(y90_uni-y90)>1e-3:
print 'y90 diff'
print y90_uni, y90
# raise IOError, 'Consider using finer step for yield locus'
return y0,y90,yb,rb, y45_uni, r45_uni
def returnDiff(params):
"""
Tune using the given in-plane locus
Arguments
=========
params [0] : rb
params [1:4]: y45,y90,yb
"""
## Find 4 parameters...
paramR = np.ones(4)
paramY = np.ones(4)
paramR[0:4] = rv[0],rv[1],rv[2],params[0]
paramY[1:4] = params[1:4]
k=2; m=8 ## the exponent is fixed?
yldFunc = wrapYLD(r=paramR,y=paramY,m=m,k=k)
if type(yldFunc).__name__=='int':
if yldFunc==-1:
return 1
yldLocus = locus(yldFunc,1000) ##
## convert yldLocus in to (th,r) coordinates
r,th=xy2rt(np.array(yldLocus[0]),np.array(yldLocus[1]))
th0,r0 = YS## reference
radIntp = rad_xy2(r,th,th0)
radIntp = np.array(radIntp)
return np.sqrt(((radIntp-r0)**2).sum())/ (len(r)-1)
def ex1():
"""
Excercise - Tune H48 using three r-values and calculate YS.
Using the three given r-values used in H48
find rb, y0, y45, y90, and yb by fitting YS of H48 with
that of yld2000-2d
"""
import tuneH48
import mk.yieldFunction.yf2 as yf2
rv = [2.2, 2.0, 2.9]
f, g, h, n = tuneH48.tuneGenR(r=rv)
yfunc_H48 = yf2.wrapHill48Gen(f, g, h, n)
YS_H48X, YS_H48Y = locus(yfunc_H48, 1000)
r, th = xy2rt(np.array(YS_H48X), np.array(YS_H48Y))
## popt = [rv, y45, y90, yb]
popt = case2([r, th], rv=rv)
rv.append(popt[0])
ys = np.ones(4)
ys[1:] = popt[1:]
##
print 'rv:', rv
print 'ys:', ys
yfunc_yld2000 = wrapYLD(r=rv, y=ys, m=8)
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
YS_YLDX, YS_YLDY = locus(yfunc_yld2000, 1000)
ax.plot(YS_H48X, YS_H48Y, '-', label='Hill48')
ax.plot(YS_YLDX, YS_YLDY, '-', label='YLD2000')
ax.set_xlim(0., )
ax.set_ylim(0., )
ax.set_aspect('equal')
ax.legend(loc='best')
# print YS_YLDX
# print YS_YLDY
fig.savefig('Yld2000-Hill48.pdf')
def ex1():
"""
Excercise - Tune H48 using three r-values and calculate YS.
Using the three given r-values used in H48
find rb, y0, y45, y90, and yb by fitting YS of H48 with
that of yld2000-2d
"""
import tuneH48
import mk.yieldFunction.yf2 as yf2
rv=[2.2,2.0,2.9]
f,g,h,n = tuneH48.tuneGenR(r=rv)
yfunc_H48 = yf2.wrapHill48Gen(f,g,h,n)
YS_H48X, YS_H48Y = locus(yfunc_H48,1000)
r, th = xy2rt(np.array(YS_H48X), np.array(YS_H48Y))
## popt = [rv, y45, y90, yb]
popt = case2([r,th], rv=rv)
rv.append(popt[0])
ys = np.ones(4)
ys[1:] = popt[1:]
##
print 'rv:', rv
print 'ys:', ys
yfunc_yld2000 = wrapYLD(r=rv,y=ys,m=8)
import matplotlib.pyplot as plt
fig = plt.figure(); ax=fig.add_subplot(111)
YS_YLDX, YS_YLDY = locus(yfunc_yld2000,1000)
ax.plot(YS_H48X,YS_H48Y,'-',label='Hill48')
ax.plot(YS_YLDX,YS_YLDY,'-',label='YLD2000')
ax.set_xlim(0.,)
ax.set_ylim(0.,)
ax.set_aspect('equal')
ax.legend(loc='best')
# print YS_YLDX
# print YS_YLDY
fig.savefig('Yld2000-Hill48.pdf')
def extractParamsFromYS(locus_planestress, psi_uni, rvs_uni, ys_uni):
"""
Given plane-stress yield locus, extract parameters.
"""
from vpscyld import lib_dat, calc_normal
## normalize the locus by stress along axis 1
ysx, ysy = lib_dat.nys_th(np.array(locus_planestress[0]),
np.array(locus_planestress[1]),
t=0)
ysr, yst = lib_dat.xy2rt(ysx, ysy)
yb = lib_dat.rad_xy(ysr, yst,
45 * np.pi / 180.) ## balanced biaxial yield stress...
yb = yb / np.sqrt(2)
y0 = lib_dat.rad_xy(ysr, yst, 0) ## balanced biaxial yield stress...
y90 = lib_dat.rad_xy(ysr, yst, 90 * np.pi /
180.) ## balanced biaxial yield stress...
th = calc_normal.main_var(locus_xy=[ysr, yst], psi_ref=[45.])
rb = 1. / np.tan(th[0])
y0_uni = ys_uni[0]
y90_uni = ys_uni[-1]
r0_uni = rvs_uni[0]
r90_uni = rvs_uni[-1]
r45_uni = np.interp(45 * np.pi / 180., psi_uni, rvs_uni)
y45_uni = np.interp(45 * np.pi / 180., psi_uni, ys_uni)
if abs(y0_uni - y0) > 1e-3:
print 'y0 diff'
print y0_uni, y0
# raise IOError, 'Consider using finer step for yield locus'
if abs(y90_uni - y90) > 1e-3:
print 'y90 diff'
print y90_uni, y90
# raise IOError, 'Consider using finer step for yield locus'
return y0, y90, yb, rb, y45_uni, r45_uni
