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Shearflow.py
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Shearflow.py
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import numpy as np
import Properties
import math as m
from matplotlib import pyplot as plt
from matplotlib.collections import LineCollection
class ShearFlow:
def __init__(self, plane):
self.plane = plane
self.Ca = 0.484 # m
self.la = 1.691 # m
self.x1 = 0.149 # m
self.x2 = 0.554 # m
self.x3 = 1.541 # m
self.xa = 0.27 # m
self.ha = 0.173 # m
self.tsk = 1.1/1000 # m
self.tsp = 2.5/1000 # m
self.tst = 1.2/1000 # m
self.hst = 14./1000 # m
self.wst = 18./1000 # m
self.nst = 13 # -
self.d1 = 0.0681 # m
self.d3 = 0.0203 # m
self.theta = m.radians(26) # rad
self.P = 37.9*1000 # N
def summation(self,start,stop):
dist_stringers = Properties.Properties(1).St_plcmnt()
if start < 0:
return 0
B_i = 0
area_st = (self.hst + self.wst)*self.tst
for i in dist_stringers[:7]:
if abs(start) <= abs(i[0]) and abs(i[0]) <= abs(stop):
B_i += area_st*i[1]
return B_i
def summationyy(self,start,stop):
dist_stringers = Properties.Properties(1).St_plcmnt()
z_coord, y_coord = Properties.Properties(1).Centroid()
if start == stop:
return 0
B_i = 0
area_st = (self.hst + self.wst)*self.tst
for i in dist_stringers[:7]:
if abs(start) <= abs(i[0]) and abs(i[0]) <= abs(stop):
B_i += area_st*(i[0]-z_coord)
return B_i
def integrateSin(self, N, lowerbound, upperbound):
def f(x):
return m.sin(x)
number = 0
number1 = 0
for i in range(1, N + 1):
number += f(lowerbound + (i-(1/2))*((upperbound-lowerbound)/N))
number1 = ((upperbound-lowerbound)/N)*number
return number1
def integrate(self, N, lowerbound, upperbound):
def f(x):
return x
number = 0
number1 = 0
for i in range(1, N + 1):
number += f(lowerbound + (i-(1/2))*((upperbound-lowerbound)/N))
number1 = ((upperbound-lowerbound)/N)*number
return number1
def integrateCos(self, N, lowerbound, upperbound):
def f(x):
return m.cos(x)
number = 0
number1 = 0
for i in range(1, N + 1):
number += f(lowerbound + (i-(1/2))*((upperbound-lowerbound)/N))
number1 = ((upperbound-lowerbound)/N)*number
return number1
def shear(self, shearForce, Izz, thickness, y, integrate, lowerbound, upperbound, start, stop, qb_0):
return (-shearForce/Izz)*(thickness*y*integrate(10000, lowerbound, upperbound) + self.summation(start,stop)) + qb_0
def shearyy(self,shearForce, Izz, thickness, y, integrate, lowerbound, upperbound, start, stop, qb_0):
return (-shearForce/Izz)*(thickness*y*integrate(10000, lowerbound, upperbound) + self.summationyy(start,stop)) + qb_0
def Print_shear(self, Sy, Sx, T):
Izz, Iyy = Properties.Properties(1).MOI()
z_coord, y_coord = Properties.Properties(1).Centroid()
dist_stringers = Properties.Properties(1).St_plcmnt()
area_st = (self.hst + self.wst)*self.tst
length_schuin = np.sqrt((self.ha/2.)**2 + (self.Ca - self.ha/2.)**2.)
area1 = 0.5*np.pi*(self.ha/2)**2
area2 = (self.Ca-(self.ha/2))*(self.ha/2)
q1_shear = self.shear(Sy,Izz,self.tsk,(self.ha/2)**2,self.integrateSin,0,m.pi/2,0,self.ha/2,0)
q2_shear = self.shear(Sy,Izz,self.tsp,1,self.integrate,0,self.ha/2,-5,-5,0)
q3_shear = self.shear(Sy,Izz,self.tsk,self.ha/2 - (self.ha/2)/length_schuin,self.integrate,0,length_schuin,self.ha/2,self.Ca,q1_shear+q2_shear)
q4_shear = self.shear(Sy,Izz,self.tsk,(self.ha/2)/length_schuin,self.integrate,0,length_schuin,self.ha/2,self.Ca,q3_shear)
q5_shear = self.shear(Sy,Izz,self.tsp,1,self.integrate,0,-self.ha/2,-5,-5,0)
q6_shear = self.shear(Sy,Izz,self.tsk,(self.ha/2)**2,self.integrateSin,-m.pi/2,0,0,self.ha/2,q4_shear-q5_shear)
x1 = (self.ha)*((m.pi/2)*2)/self.tsk + self.ha/self.tsp
x2 = -1*(self.ha)/self.tsp
x3 = -1*(self.ha)/self.tsp
x4 = self.ha/self.tsp + 2*length_schuin/self.tsk
b1 = (self.ha/2)*(q1_shear*(m.pi/2) + q6_shear*(m.pi/2))/self.tsk + q2_shear*(self.ha/2)/self.tsp + q5_shear*(self.ha/2)/self.tsp
b2 = q2_shear*(self.ha/2)/self.tsp + q5_shear*(self.ha/2)/self.tsp + q3_shear*(length_schuin)/self.tsk + q4_shear*length_schuin/self.tsk
b = [-b1,-b2]
matrix = np.array([[x1,x2],[x3,x4]])
X2 = np.linalg.solve(matrix, b)
x1 = 1/(2*area1)*((1/self.tsk)*m.pi*(self.ha/2)+(1/self.tsp)*self.ha)
x2 = -1/(2*area1)*(self.ha/self.tsp)
x3 = -1/(2*area2)*(self.ha/self.tsp)
x4 = 1/(2*area2)*((1/self.tsk)*2*length_schuin + self.ha/self.tsp)
matrix = np.array([[2*area1, 2*area2, 0],[x1, x2, -1],[x3, x4,-1]])
b = [-T, 0, 0]
X = np.linalg.solve(matrix, b)
#region one
theta = np.linspace(0,m.pi/2,num = 100)
q1 =[]
for i in range(len(theta)):
a = (self.ha/2)-(self.ha/2)*m.cos(theta[i])
shear1 = 0
if a >= abs(dist_stringers[1][0]):
shear1 = (-Sy/Izz)*area_st*dist_stringers[1][1] + (-Sx/Iyy)*area_st*(dist_stringers[1][0]-z_coord)
shear1_zz = self.shear(Sy,Izz,self.tsk,(self.ha/2)**2, self.integrateSin, 0, theta[i], -5, -5,0)
shear1_yy = (-Sx/Iyy)*self.tsk*-1*(self.ha/2 + z_coord)*(self.ha/2)*theta[i]
shear1_yy += self.shearyy(Sx,Iyy,self.tsk,(self.ha/2)**2,self.integrateCos,0,theta[i],-5,-5,0)
q1.append((shear1_zz + shear1_yy + shear1 + X[0] + X2[0]))
#region two
y = np.linspace(0,self.ha/2.,num = 100)
q2 =[]
for i in range(len(y)):
q2_shear = self.shear(Sy,Izz,self.tsp,1,self.integrate,0,y[i],-5,-5,0)
q2_shear_yy = (-Sx/Iyy)*self.tsp*(-self.ha/2-z_coord)*y[i]
q2.append(q2_shear + q2_shear_yy + X[0] - X[1] + X2[1]-X2[0])
#region three
s = np.linspace(0,m.sqrt((self.Ca-self.ha/2.)**2+(self.ha/2.)**2),num = 100)
q3 =[]
for i in range(len(s)):
q3_shear = self.shear(Sy,Izz,self.tsk,-1*(self.ha/2)/length_schuin,self.integrate,0,s[i],self.ha/2,self.ha/2+s[i],0)
q3_shear += (-Sy/Izz)*self.tsk*(self.ha/2)*s[i]
q3_shear_yy = (-Sx/Iyy)*(self.tsk*(-self.ha/2-z_coord))*s[i]
q3_shear_yy += self.shearyy(Sx,Iyy,self.tsk,-(self.Ca - self.ha/2)/length_schuin,self.integrate,0,s[i],self.ha/2,self.ha/2+s[i],0)
q3.append(q3_shear + q3_shear_yy + q1[-1] + q2[-1] + X[1])
#region four
s = np.linspace(m.sqrt((self.Ca-self.ha/2.)**2+(self.ha/2.)**2),0,num = 100)
q4 = []
theta = m.acos((self.Ca-self.ha/2)/length_schuin)
counter = 7
for j in range(len(s)):
q4_shear = self.shear(Sy,Izz,self.tsk,(-self.ha/2)/length_schuin,self.integrate,0,s[j],-5,-5,0)
q4_shear_yy = (-Sx/Iyy)*(self.tsk*(-self.Ca-z_coord))*s[j]
q4_shear_yy += self.shearyy(Sx,Iyy,self.tsk,(self.Ca - self.ha/2)/length_schuin,self.integrate,0,s[j],-5,-5,0)
for i in dist_stringers[6:counter]:
if abs(i[0]) >= self.ha/2+s[j]*m.cos(theta):
q4_shear += (-Sy/Izz)*area_st*i[1] + (-Sx/Iyy)*area_st*(i[0]-z_coord)
counter += 1
q4.append(q4_shear + q4_shear_yy + q4_shear_yy + X[1])
#region five
y = np.linspace(0,-self.ha/2.,num = 100)
q5 =[]
for i in range(len(y)):
q5_shear = self.shear(Sy,Izz,self.tsp,1,self.integrate,0,y[i],-5,-5,0)
q5_shear_yy = (-Sx/Iyy)*self.tsp*(-self.ha/2-z_coord)*y[i]
q5.append(q5_shear + q5_shear_yy + X[1] - X[0] + X2[1] - X2[0])
#region six
theta = np.linspace(-m.pi/2,0,num = 100)
q6 = []
shear6 = 0
for i in range(len(theta)):
a = (self.ha/2)-(self.ha/2)*m.cos(abs(theta[i]))
if a <= abs(dist_stringers[12][0]):
shear6 = (-Sy/Izz)*area_st*dist_stringers[12][1] + (-Sx/Iyy)*area_st*(dist_stringers[12][0] - z_coord)
shear6_zz = self.shear(Sy,Izz,self.tsk,(self.ha/2)**2, self.integrateSin, 0, theta[i],-5, -5,0)
shear6_yy = (-Sx/Iyy)*self.tsk*(-1*(self.ha/2+z_coord)*self.ha/2)*theta[i]
shear6_yy += self.shearyy(Sx,Iyy,self.tsk,(self.ha/2)**2,self.integrateCos, 0,theta[i],-5,-5,0)
q6.append((shear6_zz + shear6_yy + shear6 + q4[-1] - q5[-1] + X2[0]))
theta = np.linspace(0,m.pi/2,num = 100)
x = []
y = []
for i in theta:
zst, yst = (self.ha/2)*(1-m.cos(i)), (self.ha/2)*m.sin(i)
x.append(-zst)
y.append(yst)
x = np.array(x)
y = np.array(y)
q2_y = np.linspace(0,self.ha/2.,num = 100)
q2_z = np.full((100,1),-self.ha/2)
x = np.append(x,q2_z)
y = np.append(y,q2_y)
length_schuin = np.sqrt((self.ha/2.)**2 + (self.Ca - self.ha/2.)**2.)
s = np.linspace(0,m.sqrt((self.Ca-self.ha/2.)**2+(self.ha/2.)**2),num = 100)
alpha = m.atan((self.ha/2)/(self.Ca - self.ha/2.))
for i in s:
x = np.append(x,-1*(self.Ca-(length_schuin - i)*m.cos(alpha)))
y = np.append(y,((length_schuin - i)*m.sin(alpha)))
for i in s[::-1]:
x = np.append(x,-1*(self.Ca-(length_schuin - i)*m.cos(alpha)))
y = np.append(y,(-1*(length_schuin - i)*m.sin(alpha)))
q2_y = np.linspace(0,-self.ha/2.,num = 100)
q2_z = np.full((100,1),-self.ha/2)
x = np.append(x,q2_z)
y = np.append(y,q2_y)
for i in theta[::-1]:
zst, yst = (self.ha/2)*(1-m.cos(i)), (self.ha/2)*m.sin(i)
x = np.append(x,-zst)
y = np.append(y,-yst)
x = np.array(x)
y = np.array(y)
data = np.array(q1) # first derivative
data = np.append(data,q2)
data = np.append(data,q3)
data = np.append(data,q4[::-1])
data = np.append(data,q5)
data = np.append(data,q6)
return data, x, y
def Plot(self, data, x, y):
points = np.array([x, y]).T.reshape(-1, 1, 2)
segments = np.concatenate([points[:-1], points[1:]], axis=1)
fig, axis = plt.subplots(1, 1)
norm = plt.Normalize(data.min(), data.max())
line_col = LineCollection(segments, cmap='rainbow', norm=norm)
# Set the values used for colormapping
line_col.set_array(data)
line_col.set_linewidth(2)
line = axis.add_collection(line_col)
fig.colorbar(line, ax=axis, label=r'q = $N/m $')
# Use a boundary norm instead
axis.set_xlim(0.05, -0.5)
axis.set_ylim(-0.15, 0.15)
axis.set_xlabel('z [m]')
axis.set_title('Shear flow distribution')
axis.set_ylabel('y [m]')
plt.show()
if __name__ == "__main__":
#Sy = -4985.0292997
#Sz = -73359.55813566
#T = -1743.7425962
Sy = 56576.054162008
Sz = -39021.131846804834
T = 1291.9302730065012
#Sy = -71552.22303513
#Sx = 202054.57756203
#T = -1184.42632407
a = ShearFlow(1)
data, x, y = a.Print_shear(Sy, Sz, T)
a.Plot(data, x, y)