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Copy pathprototipo_NR_para_malla.py
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prototipo_NR_para_malla.py
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import numpy as np
import matplotlib.pyplot as plt
class Mallita(object):
def __init__(self):
# long de lado
self.L = 1.
# posiciones iniciales
self.nnodos = 6
self.r0 = np.array(
[
[0., 0.],
[1., 0.],
[1., 1.],
[0., 1.],
[.2, .5],
[.8, .5]
],
dtype=float
)
# tipos (1=frontera, 2=interseccion)
self.tipos = np.transpose(np.array(
[
[1, 1, 1, 1, 2, 2]
],
dtype=int
))
# fibras: conectividad de nodos
self.nfibras = 5
self.fibras = np.array(
[
[0,4],
[1,5],
[2,5],
[3,4],
[4,5]
],
dtype=int
)
# parametros constitutivos
self.param = np.array(
[
[1.0, 10., .1],
[1.0, 10., .1],
[1.0, 10., .1],
[1.0, 10., .1],
[1.5, 10., .1]
],
dtype=float
)
# ------------------------------
# posiciones actuales
self.r = self.r0.copy()
# longitudes iniciales
self.longs0 = self.calcular_longitudes_iniciales()
# fuerzas (escalares)
self.fuerzas = np.zeros( (self.nfibras,1), dtype=float)
@staticmethod
def fuerza_fibra(lam, lam_r=1.1, k1=10., k2=.1):
""" fuerza de una fibra """
if lam<=lam_r:
return k2*(lam-1.)
else:
return k2*(lam_r-1.) + k1*(lam/lam_r - 1.)
def calcular_longitudes_iniciales(self):
fibras_dr0 = self.r0[ self.fibras[:,1] ] - self.r0[ self.fibras[:,0] ]
fibras_dl0 = np.sqrt( np.sum( fibras_dr0*fibras_dr0, axis=1, keepdims=True ) )
return fibras_dl0
def setear_r(self, r):
self.r = r
def calcular_vectores_fibras(self):
fibras_dr = self.r[ self.fibras[:,1] ] - self.r[ self.fibras[:,0] ]
return fibras_dr
def calcular_fuerzas(self):
drs = self.calcular_vectores_fibras()
longs = np.sqrt(np.sum(drs*drs, axis=1, keepdims=True))
lams = longs / self.longs0
mr = np.greater(lams, self.param[:,0,None]) # mask rectas
me = np.logical_not(mr) # mask enruladas
lamsr = self.param[:,0,None] # el None es para tener un vector columna
ks1 = self.param[:,1,None]
ks2 = self.param[:,2,None]
fuerzas_de_reclut = ks2*(lamsr-1.)
self.fuerzas[mr] = fuerzas_de_reclut[mr] + ks1[mr]*(lams[mr]/lamsr[mr] - 1.)
self.fuerzas[me] = ks2[me]*(lams[me] - 1.)
a = self.fuerzas/longs * drs
return a
def calcular_fuerza_de_una_fibra(self, f, r_n0, r_n1):
dr = r_n1 - r_n0
long = np.sqrt(np.sum(dr*dr))
lam = long / self.longs0[f]
lamr, k1, k2 = self.param[f]
k1 = self.param[f,1]
fuerza_de_reclut = k2*(lamr-1.)
if lam > lamr:
fuerza = fuerza_de_reclut + k1*(lam/lamr - 1.)
else:
fuerza = k2*(lam-1.)
return fuerza/long * dr[:,None]
def calcular_matriz_tangente(self):
nG = self.nnodos*2
matG = np.zeros( (nG,nG), dtype=float )
vecG = np.zeros( (nG,1), dtype=float )
nL = 2 # tengo que armar la matriz tangente respecto de un solo nodo (hay doble simetria)
matL = np.zeros( (nL,nL), dtype=float )
vecL = np.zeros( (nL,1), dtype=float )
#
delta = 1.e-4
delta21 = 1. / (2.*delta)
delta_x = delta * np.array( [1., 0.], dtype=float )
delta_y = delta * np.array( [0., 1.], dtype=float )
for f, (n0,n1) in enumerate(self.fibras):
if f==2:
pass
r_n0 = self.r[n0]
r_n1 = self.r[n1]
r_n0_px = self.r[n0] + delta_x
r_n0_mx = self.r[n0] - delta_x
r_n0_py = self.r[n0] + delta_y
r_n0_my = self.r[n0] - delta_y
F_c = self.calcular_fuerza_de_una_fibra(f, r_n0, r_n1)
F_mx = self.calcular_fuerza_de_una_fibra(f, r_n0_mx, r_n1)
F_px = self.calcular_fuerza_de_una_fibra(f, r_n0_px, r_n1)
F_my = self.calcular_fuerza_de_una_fibra(f, r_n0_my, r_n1)
F_py = self.calcular_fuerza_de_una_fibra(f, r_n0_py, r_n1)
dFdx = (F_px - F_mx) * delta21
dFdy = (F_py - F_my) * delta21
matL[:,0] = dFdx[:,0]
matL[:,1] = dFdy[:,0]
vecL = - F_c
# ahora a ensamblar
# primero el vector de cargas
row = n0*2
col = n1*2
vecG[row:row+2] += vecL
vecG[col:col+2] += -vecL
# luego matriz local va a 4 submatrices de la global
# primero en el nodo 0
row = n0*2
col = n0*2
matG[row:row+2,col:col+2] += matL
# luego lo mismo en el nodo 1
row = n1*2
col = n1*2
matG[row:row+2,col:col+2] += matL
# luego las cruzadas
row = n0*2
col = n1*2
matG[row:row+2,col:col+2] += - matL
row = n1*2
col = n0*2
matG[row:row+2,col:col+2] += - matL
# ahora las condiciones de dirichlet
for n, (x0,y0) in enumerate(self.r0):
if self.tipos[n] == 1:
ix = 2*n
iy = 2*n+1
matG[ix,:] = 0.
matG[ix,ix] = 1.
vecG[ix] = 0.
matG[iy,:] = 0.
matG[iy,iy] = 1.
vecG[iy] = 0.
# fin
return matG, vecG
m = Mallita()
m.r[2,:] = [1.1, 1.1]
F = m.calcular_fuerzas()
print "F"
print F
print "---"
A, b = m.calcular_matriz_tangente()
print "A // b"
msg = ""
for n in range(m.nnodos):
for i in range(2):
for o in range(m.nnodos):
msg += "{:12.2e}{:12.2e}".format(A[2*n+i,2*o+0],A[2*n+i,2*o+1])
msg += " // "
msg += "{:12.2e}".format(b[2*n+i,0])
msg += "\n"
print msg
print "---"
dr = np.linalg.solve(A,b)
print "dr"
print dr
print "---"
# bb = np.matmul(A,dr)
# print "bb"
# print bb
# print "---"
print "ITER 2"
m.r = m.r + dr.reshape(-1,2)
F = m.calcular_fuerzas()
print "F"
print F
print "---"
A, b = m.calcular_matriz_tangente()
print "A // b"
msg = ""
for n in range(m.nnodos):
for i in range(2):
for o in range(m.nnodos):
msg += "{:12.2e}{:12.2e}".format(A[2*n+i,2*o+0],A[2*n+i,2*o+1])
msg += " // "
msg += "{:12.2e}".format(b[2*n+i,0])
msg += "\n"
print msg
print "---"
dr = np.linalg.solve(A,b)
print "dr"
print dr
print "---"
print "ITER 3"
m.r = m.r + dr.reshape(-1,2)
F = m.calcular_fuerzas()
print "F"
print F
print "---"
A, b = m.calcular_matriz_tangente()
print "A // b"
msg = ""
for n in range(m.nnodos):
for i in range(2):
for o in range(m.nnodos):
msg += "{:12.2e}{:12.2e}".format(A[2*n+i,2*o+0],A[2*n+i,2*o+1])
msg += " // "
msg += "{:12.2e}".format(b[2*n+i,0])
msg += "\n"
print msg
print "---"
dr = np.linalg.solve(A,b)
print "dr"
print dr
print "---"
print "r"
print m.r
print "---"
print m.longs0
drs = m.calcular_vectores_fibras()
print np.sqrt(np.sum(drs*drs,axis=1,keepdims=True))
m.r = m.r + dr.reshape(-1,2)
fig,ax = plt.subplots()
for f, (n0,n1) in enumerate(m.fibras):
x0, y0 = m.r0[n0]
dx, dy = m.r0[n1] - m.r0[n0]
ax.arrow(x0,y0,dx,dy, linestyle=":")
for f, (n0,n1) in enumerate(m.fibras):
x0, y0 = m.r[n0]
dx, dy = m.r[n1] - m.r[n0]
ax.arrow(x0,y0,dx,dy)
plt.show()