def get_Shear_center(cos_value,
profile_constant,
thickness=[],
basic_point=[0, 0]):
bp = basic_point
if not is_point_in(bp, cos_value):
raise 'basic point not in profile,Choose another one'
Tk = thickness
Pc = profile_constant
c_x = copy.copy(cos_value)
k = profile_toolbox.if_clockwise(c_x)
if k > 0:
c_x.reverse()
cc = Open_Profile(c_x, Pc, thickness=Tk, Qx=0, Qy=1)
xx = get_Shear_center_x(cc, Shear_ST=cc.Shear_ST, basic_point=bp)
##--------------------------------------------------------------------------##
c_y = copy.copy(cos_value)
k = profile_toolbox.if_clockwise(c_y)
if k < 0:
c_y.reverse()
dd = Open_Profile(c_y, Pc, thickness=Tk, Qx=1, Qy=0)
yy = get_Shear_center_y(dd, Shear_ST=dd.Shear_ST, basic_point=bp)
aa = (xx + basic_point[0]).round(4)
bb = (yy + basic_point[1]).round(4)
return [aa, bb]
def get_Shear_center_y(profile_constant,
cos_value=[],
Shear_ST=[],
basic_point=[0, 0]):
y = 0
Sy = profile_constant.Sy
Iy = profile_constant.Iy
update = 0
Shear_flow = Shear_ST
mcos_value = cos_value
if mcos_value == []:
mcos_value = profile_constant.cos_value
k = profile_toolbox.if_clockwise(mcos_value)
if k > 0:
pass
if k < 0:
mcos_value.reverse()
Shear_flow.reverse()
update = 1
if Shear_flow:
for i in range(0, len(Shear_flow)):
ys = mcos_value[i][1]
ye = mcos_value[i + 1][1]
xs = mcos_value[i][0]
xe = mcos_value[i + 1][0]
yy = ye - ys
xx = xe - xs
length = math.sqrt(yy**2 + xx**2)
P_distance = dot_distance_line(mcos_value[i], mcos_value[i + 1],
basic_point)
Da = Shear_flow[i] * P_distance
y = y + syp.integrate(Da, (s, 0, length))
return y
else:
for i in range(0, len(Sy)):
ys = cos_value[i][1]
ye = cos_value[i + 1][1]
xs = cos_value[i][0]
xe = cos_value[i + 1][0]
yy = ye - ys
xx = xe - xs
length = math.sqrt(yy**2 + xx**2)
P_distance = dot_distance_line(cos_value[i], cos_value[i + 1],
basic_point)
Da = P_distance * Sy[i]
y = y + syp.integrate(Da, (s, 0, length))
return y / Iy * -1.0
def close_Shear_center(cos_value,
profile_constant,
thickness=[],
basic_point=[0, 0]):
'''
Only used when the profile with only one closed cell
'''
bp = basic_point
if not is_point_in(bp, cos_value):
raise 'basic point not in profile,Choose another one'
Pc = profile_constant
c_x = copy.copy(cos_value)
Tk1 = copy.copy(thickness)
k = profile_toolbox.if_clockwise(c_x)
if k > 0:
c_x.reverse()
Tk1.reverse()
cc = open_profile.Open_Profile(c_x, Pc, thickness=Tk1, Qx=0, Qy=1)
xx = close_Shear_center_x(cc,cos_value=c_x,Shear_ST = cc.Shear_ST,\
thickness = Tk1,basic_point = bp)
##--------------------------------------------------------------------------##
c_y = copy.copy(cos_value)
Tk2 = copy.copy(thickness)
k = profile_toolbox.if_clockwise(c_y)
if k < 0:
c_y.reverse()
Tk2.reverse()
dd = open_profile.Open_Profile(c_y, Pc, thickness=Tk2, Qx=1, Qy=0)
yy = close_Shear_center_y(dd,cos_value = c_y,Shear_ST = dd.Shear_ST,\
thickness = Tk2,basic_point = bp)
aa = (xx + basic_point[0]).round(4)
bb = (yy + basic_point[1]).round(4)
return [aa, bb]
def get_Shear_center_x(profile_constant,
cos_value=[],
Shear_ST=[],
basic_point=[0, 0]):
'''
If the Ixy do not equal to 0,
MUST use the shear flow to calculate
'''
x = 0
Sx = profile_constant.Sx
Ix = profile_constant.Ix
update = 0
Shear_flow = Shear_ST
mcos_value = cos_value
if mcos_value == []:
mcos_value = profile_constant.cos_value
k = profile_toolbox.if_clockwise(mcos_value)
if k < 0:
pass
if k > 0:
mcos_value.reverse()
Shear_flow.reverse()
update = 1
if Shear_flow:
for i in range(0, len(Shear_flow)):
ys = mcos_value[i][1]
ye = mcos_value[i + 1][1]
xs = mcos_value[i][0]
xe = mcos_value[i + 1][0]
yy = ye - ys
xx = xe - xs
length = math.sqrt(yy**2 + xx**2)
P_distance = dot_distance_line(mcos_value[i], mcos_value[i + 1],
basic_point)
Da = Shear_flow[i] * P_distance
x = x + syp.integrate(Da, (s, 0, length))
return x
##############################################################################3
else:
for i in range(0, len(Sx)):
ys = cos_value[i][1]
ye = cos_value[i + 1][1]
xs = cos_value[i][0]
xe = cos_value[i + 1][0]
yy = ye - ys
xx = xe - xs
length = math.sqrt(yy**2 + xx**2)
P_distance = dot_distance_line(cos_value[i], cos_value[i + 1],
basic_point)
Da = P_distance * Sx[i]
x = x + syp.integrate(Da, (s, 0, length))
# print('x--]]',Sx[i],'dis--]]',P_distance ,'[][][]',syp.integrate)(Da,(s,0,length))
return x / Ix
def close_Shear_center_x(profile_constant,cos_value = [],Shear_ST=[],thickness = [], \
basic_point = [0,0]):
'''
Attention that if without the Shear flow, the profile's Ixy must equal to ZERO
The Shear Flow used here is still the open-profile Shear Flow, NOT closed one.
'''
PSx = 0
Sxt = 0
Dst = 0
x1 = 0
x2 = 0
x3 = 0
mcos_value = cos_value
if mcos_value == []:
mcos_value = copy.copy(profile_constant.cos_value)
if thickness == []:
if len(mcos_value) == 2:
thickness = [1]
else:
thickness = np.ones(len(mcos_value) - 1)
thickness = thickness.tolist()
A = open_profile.Surround_Area(mcos_value, basic_point)
x_center = 0
Sx = profile_constant.Sx
Ix = profile_constant.Ix
Shear_flow = Shear_ST
k = profile_toolbox.if_clockwise(mcos_value)
if k < 0:
pass
if k > 0:
mcos_value.reverse()
Shear_flow.reverse()
thickness.reverse()
# print('---xxx-----reverse---xxx---in line-')
if Shear_flow:
for i in range(0, len(Shear_flow)):
ys = mcos_value[i][1]
ye = mcos_value[i + 1][1]
xs = mcos_value[i][0]
xe = mcos_value[i + 1][0]
yy = ye - ys
xx = xe - xs
length = math.sqrt(yy**2 + xx**2)
P_distance = dot_distance_line(mcos_value[i], mcos_value[i + 1],
basic_point)
qpds = Shear_flow[i] * P_distance
x1 = x1 + syp.integrate(qpds, (s, 0, length))
qtds = Shear_flow[i] / thickness[i] * 1.0
x2 = x2 + syp.integrate(qtds, (s, 0, length))
tt = 1.0 / thickness[i]
x3 = x3 + syp.integrate(tt, (s, 0, length))
# print('x1,x2,x3',x1,' ',x2,' ',x3)
x_center = x1 - 2 * A * x2 / x3
return x_center
else:
for i in range(0, len(Sx)):
ys = cos_value[i][1]
ye = cos_value[i + 1][1]
xs = cos_value[i][0]
xe = cos_value[i + 1][0]
yy = ye - ys
xx = xe - xs
length = math.sqrt(yy**2 + xx**2)
P_distance = dot_distance_line(cos_value[i], cos_value[i + 1],
basic_point)
x1 = P_distance * Sx[i]
PSx = PSx + syp.integrate(x1, (s, 0, length))
x2 = Sx[i] / thickness[i] * 1.0
Sxt = Sxt + syp.integrate(x2, (s, 0, length))
x3 = 1.0 / thickness[i]
Dst = Dst + syp.integrate(x3, (s, 0, length))
x_center = (Psx - 2 * A * Sxt / Dst) / Ix
return x_center
def close_Shear_center_y(profile_constant,cos_value = [],Shear_ST=[],thickness = [], \
basic_point = [0,0]):
'''
Attention that if without the Shear flow, the profile's Ixy must equal to ZERO
The Shear Flow used here is still the open-profile Shear Flow, NOT closed one.
'''
PSy = 0
Syt = 0
Dst = 0
y1 = 0
y2 = 0
y3 = 0
mcos_value = cos_value
if mcos_value == []:
mcos_value = profile_constant.cos_value
if thickness == []:
if len(mcos_value) == 2:
thickness = [1]
else:
thickness = np.ones(len(mcos_value) - 1)
thickness = thickness.tolist()
A = open_profile.Surround_Area(mcos_value, basic_point)
y_center = 0
Sy = profile_constant.Sy
Iy = profile_constant.Iy
Shear_flow = Shear_ST
# print(Shear_flow)
k = profile_toolbox.if_clockwise(mcos_value)
if k < 0:
mcos_value.reverse()
Shear_flow.reverse()
# print('--yyy------reverse----yyy---in_line-')
# print(mcos_value,'\n',Shear_flow)
if k > 0:
pass
if Shear_flow:
for i in range(0, len(Shear_flow)):
ys = mcos_value[i][1]
ye = mcos_value[i + 1][1]
xs = mcos_value[i][0]
xe = mcos_value[i + 1][0]
yy = ye - ys
xx = xe - xs
length = math.sqrt(yy**2 + xx**2)
P_distance = dot_distance_line(mcos_value[i], mcos_value[i + 1],
basic_point)
qpds = Shear_flow[i] * P_distance
y1 = y1 + syp.integrate(qpds, (s, 0, length))
qtds = Shear_flow[i] / thickness[i] * 1.0
y2 = y2 + syp.integrate(qtds, (s, 0, length))
tt = 1.0 / thickness[i]
y3 = y3 + syp.integrate(tt, (s, 0, length))
y_center = 2 * A * y2 / y3 - y1
return -1 * y_center
else:
for i in range(0, len(Sy)):
ys = cos_value[i][1]
ye = cos_value[i + 1][1]
xs = cos_value[i][0]
xe = cos_value[i + 1][0]
yy = ye - ys
xx = xe - xs
length = math.sqrt(yy**2 + xx**2)
P_distance = dot_distance_line(cos_value[i], cos_value[i + 1],
basic_point)
y1 = P_distance * Sy[i]
PSy = PSy + syp.integrate(y1, (s, 0, length))
y2 = Sy[i] / thickness[i] * 1.0
Syt = Syt + syp.integrate(y2, (s, 0, length))
y3 = 1.0 / thickness[i]
Dst = Dst + syp.integrate(y3, (s, 0, length))
y_center = (2 * A * PSy / Dst - PSy) / Iy
return y_center