def execute(self):
# ------- node data ----------------
n = len(self.z)
node = np.arange(1, n+1)
x = np.zeros(n)
y = np.zeros(n)
z = self.z
r = np.zeros(n)
nodes = frame3dd.NodeData(node, x, y, z, r)
# -----------------------------------
# ------ reaction data ------------
# rigid base
node = self.kidx + 1 # add one because 0-based index but 1-based node numbering
rigid = float('inf')
reactions = frame3dd.ReactionData(node, self.kx, self.ky, self.kz, self.ktx, self.kty, self.ktz, rigid)
# -----------------------------------
# ------ frame element data ------------
element = np.arange(1, n)
N1 = np.arange(1, n)
N2 = np.arange(2, n+1)
roll = np.zeros(n-1)
# average across element b.c. frame3dd uses constant section elements
Az = 0.5*(self.Az[:-1] + self.Az[1:])
Asx = 0.5*(self.Asx[:-1] + self.Asx[1:])
Asy = 0.5*(self.Asy[:-1] + self.Asy[1:])
Jz = 0.5*(self.Jz[:-1] + self.Jz[1:])
Ixx = 0.5*(self.Ixx[:-1] + self.Ixx[1:])
Iyy = 0.5*(self.Iyy[:-1] + self.Iyy[1:])
E = 0.5*(self.E[:-1] + self.E[1:])
G = 0.5*(self.G[:-1] + self.G[1:])
rho = 0.5*(self.rho[:-1] + self.rho[1:])
elements = frame3dd.ElementData(element, N1, N2, Az, Asx, Asy, Jz,
Ixx, Iyy, E, G, roll, rho)
# -----------------------------------
# ------ options ------------
options = frame3dd.Options(self.shear, self.geom, self.dx)
# -----------------------------------
# initialize frame3dd object
tower = frame3dd.Frame(nodes, reactions, elements, options)
# ------ add extra mass ------------
# extra node inertia data
N = self.midx + 1
tower.changeExtraNodeMass(N, self.m, self.mIxx, self.mIyy, self.mIzz, self.mIxy, self.mIxz, self.mIyz,
self.mrhox, self.mrhoy, self.mrhoz, self.addGravityLoadForExtraMass)
# ------------------------------------
# ------- enable dynamic analysis ----------
tower.enableDynamics(self.nM, self.Mmethod, self.lump, self.tol, self.shift)
# ----------------------------
# ------ static load case 1 ------------
# gravity in the X, Y, Z, directions (global)
gx = 0.0
gy = 0.0
gz = -self.g
load = frame3dd.StaticLoadCase(gx, gy, gz)
# point loads
nF = self.plidx + 1
load.changePointLoads(nF, self.Fx, self.Fy, self.Fz, self.Mxx, self.Myy, self.Mzz)
# distributed loads
Px, Py, Pz = self.Pz, self.Py, -self.Px # switch to local c.s.
z = self.z
# trapezoidally distributed loads
EL = np.arange(1, n)
xx1 = np.zeros(n-1)
xx2 = z[1:] - z[:-1] - 1e-6 # subtract small number b.c. of precision
wx1 = Px[:-1]
wx2 = Px[1:]
xy1 = np.zeros(n-1)
xy2 = z[1:] - z[:-1] - 1e-6
wy1 = Py[:-1]
wy2 = Py[1:]
xz1 = np.zeros(n-1)
xz2 = z[1:] - z[:-1] - 1e-6
wz1 = Pz[:-1]
wz2 = Pz[1:]
load.changeTrapezoidalLoads(EL, xx1, xx2, wx1, wx2, xy1, xy2, wy1, wy2, xz1, xz2, wz1, wz2)
tower.addLoadCase(load)
# -----------------------------------
# run the analysis
displacements, forces, reactions, internalForces, mass, modal = tower.run()
iCase = 0
# mass
self.mass = mass.struct_mass
# natural frequncies
self.f1 = modal.freq[0]
self.f2 = modal.freq[1]
# deflections due to loading (from tower top and wind/wave loads)
self.top_deflection = displacements.dx[iCase, n-1] # in yaw-aligned direction
# shear and bending (convert from local to global c.s.)
Fz = forces.Nx[iCase, :]
Vy = forces.Vy[iCase, :]
Vx = -forces.Vz[iCase, :]
Mzz = forces.Txx[iCase, :]
Myy = forces.Myy[iCase, :]
Mxx = -forces.Mzz[iCase, :]
# one per element (first negative b.c. need reaction)
Fz = np.concatenate([[-Fz[0]], Fz[1::2]])
Vx = np.concatenate([[-Vx[0]], Vx[1::2]])
Vy = np.concatenate([[-Vy[0]], Vy[1::2]])
Mzz = np.concatenate([[-Mzz[0]], Mzz[1::2]])
Myy = np.concatenate([[-Myy[0]], Myy[1::2]])
Mxx = np.concatenate([[-Mxx[0]], Mxx[1::2]])
# axial and shear stress
##R = self.d/2.0
##x_stress = R*np.cos(self.theta_stress)
##y_stress = R*np.sin(self.theta_stress)
##axial_stress = Fz/self.Az + Mxx/self.Ixx*y_stress - Myy/self.Iyy*x_stress
# V = Vy*x_stress/R - Vx*y_stress/R # shear stress orthogonal to direction x,y
# shear_stress = 2. * V / self.Az # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
axial_stress = Fz/self.Az - np.sqrt(Mxx**2+Myy**2)/self.Iyy*self.d/2.0 #More conservative, just use the tilted bending and add total max shear as well at the same point, if you do not like it go back to the previous lines
shear_stress = 2. * np.sqrt(Vx**2+Vy**2) / self.Az # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
# hoop_stress (Eurocode method)
hoop_stress = hoopStressEurocode(self.z, self.d, self.t, self.L_reinforced, self.qdyn)
# von mises stress
self.stress = vonMisesStressUtilization(axial_stress, hoop_stress, shear_stress,
self.gamma_f*self.gamma_m*self.gamma_n, self.sigma_y)
# shell buckling
self.shell_buckling = shellBucklingEurocode(self.d, self.t, axial_stress, hoop_stress,
shear_stress, self.L_reinforced, self.E, self.sigma_y, self.gamma_f, self.gamma_b)
# global buckling
tower_height = self.z[-1] - self.z[0]
M = np.sqrt(Mxx**2 + Myy**2)
self.global_buckling = bucklingGL(self.d, self.t, Fz, M, tower_height, self.E,
self.sigma_y, self.gamma_f, self.gamma_b)
# fatigue
N_DEL = [365*24*3600*self.life]*len(z)
self.damage=np.zeros(z.size)
if any(self.M_DEL):
M_DEL = np.interp(z, self.z_DEL, self.M_DEL)
self.damage = fatigue(M_DEL, N_DEL, self.d, self.t, self.m_SN, self.DC, self.gamma_fatigue, stress_factor=1.0, weld_factor=True)
def execute(self):
# ------- node data ----------------
n = len(self.z)
node = np.arange(1, n+1)
x = np.zeros(n)
y = np.zeros(n)
z = self.z
r = np.zeros(n)
nodes = frame3dd.NodeData(node, x, y, z, r)
# -----------------------------------
# ------ reaction data ------------
# rigid base
node = self.kidx + 1 # add one because 0-based index but 1-based node numbering
rigid = float('inf')
reactions = frame3dd.ReactionData(node, self.kx, self.ky, self.kz, self.ktx, self.kty, self.ktz, rigid)
# -----------------------------------
# ------ frame element data ------------
element = np.arange(1, n)
N1 = np.arange(1, n)
N2 = np.arange(2, n+1)
roll = np.zeros(n-1)
# average across element b.c. frame3dd uses constant section elements
Az = 0.5*(self.Az[:-1] + self.Az[1:])
Asx = 0.5*(self.Asx[:-1] + self.Asx[1:])
Asy = 0.5*(self.Asy[:-1] + self.Asy[1:])
Jz = 0.5*(self.Jz[:-1] + self.Jz[1:])
Ixx = 0.5*(self.Ixx[:-1] + self.Ixx[1:])
Iyy = 0.5*(self.Iyy[:-1] + self.Iyy[1:])
E = 0.5*(self.E[:-1] + self.E[1:])
G = 0.5*(self.G[:-1] + self.G[1:])
rho = 0.5*(self.rho[:-1] + self.rho[1:])
elements = frame3dd.ElementData(element, N1, N2, Az, Asx, Asy, Jz,
Ixx, Iyy, E, G, roll, rho)
# -----------------------------------
# ------ options ------------
options = frame3dd.Options(self.shear, self.geom, self.dx)
# -----------------------------------
# initialize frame3dd object
tower = frame3dd.Frame(nodes, reactions, elements, options)
# ------ add extra mass ------------
# extra node inertia data
N = self.midx + 1
tower.changeExtraNodeMass(N, self.m, self.mIxx, self.mIyy, self.mIzz, self.mIxy, self.mIxz, self.mIyz,
self.mrhox, self.mrhoy, self.mrhoz, self.addGravityLoadForExtraMass)
# ------------------------------------
# ------- enable dynamic analysis ----------
tower.enableDynamics(self.nM, self.Mmethod, self.lump, self.tol, self.shift)
# ----------------------------
# ------ static load case 1 ------------
# gravity in the X, Y, Z, directions (global)
gx = 0.0
gy = 0.0
gz = -self.g
load = frame3dd.StaticLoadCase(gx, gy, gz)
# point loads
nF = self.plidx + 1
load.changePointLoads(nF, self.Fx, self.Fy, self.Fz, self.Mxx, self.Myy, self.Mzz)
# distributed loads
Px, Py, Pz = self.Pz, self.Py, -self.Px # switch to local c.s.
z = self.z
# trapezoidally distributed loads
EL = np.arange(1, n)
xx1 = np.zeros(n-1)
xx2 = z[1:] - z[:-1] - 1e-6 # subtract small number b.c. of precision
wx1 = Px[:-1]
wx2 = Px[1:]
xy1 = np.zeros(n-1)
xy2 = z[1:] - z[:-1] - 1e-6
wy1 = Py[:-1]
wy2 = Py[1:]
xz1 = np.zeros(n-1)
xz2 = z[1:] - z[:-1] - 1e-6
wz1 = Pz[:-1]
wz2 = Pz[1:]
load.changeTrapezoidalLoads(EL, xx1, xx2, wx1, wx2, xy1, xy2, wy1, wy2, xz1, xz2, wz1, wz2)
tower.addLoadCase(load)
# -----------------------------------
"""
print '*******************************************************************'
print '*******************************************************************'
#print 'tower: ', tower.__dict__
print "c_nodes: ", tower.__dict__['c_nodes'].__dict__
print "c_reactions: ", tower.__dict__['c_reactions'].__dict__
print "c_condensation: ", tower.__dict__['c_condensation'].__dict__
print "c_elements: ", tower.__dict__['c_elements'].__dict__
#print "loadCases: ", tower.__dict__['StaticLoadCase'].__dict__
print "c_extraInertia: ", tower.__dict__['c_extraInertia'].__dict__
print "c_other: ", tower.__dict__['c_other'].__dict__
print "c_extraMass: ", tower.__dict__['c_extraMass'].__dict__
"""
# run the analysis
displacements, forces, reactions, internalForces, mass, modal = tower.run()
iCase = 0
# mass
self.mass = mass.struct_mass
# natural frequncies
self.f1 = modal.freq[0]
self.f2 = modal.freq[1]
# deflections due to loading (from tower top and wind/wave loads)
self.top_deflection = displacements.dx[iCase, n-1] # in yaw-aligned direction
# shear and bending (convert from local to global c.s.)
Fz = forces.Nx[iCase, :]
Vy = forces.Vy[iCase, :]
Vx = -forces.Vz[iCase, :]
Mzz = forces.Txx[iCase, :]
Myy = forces.Myy[iCase, :]
Mxx = -forces.Mzz[iCase, :]
# one per element (first negative b.c. need reaction)
Fz = np.concatenate([[-Fz[0]], Fz[1::2]])
Vx = np.concatenate([[-Vx[0]], Vx[1::2]])
Vy = np.concatenate([[-Vy[0]], Vy[1::2]])
Mzz = np.concatenate([[-Mzz[0]], Mzz[1::2]])
Myy = np.concatenate([[-Myy[0]], Myy[1::2]])
Mxx = np.concatenate([[-Mxx[0]], Mxx[1::2]])
# axial and shear stress
##R = self.d/2.0
##x_stress = R*np.cos(self.theta_stress)
##y_stress = R*np.sin(self.theta_stress)
##axial_stress = Fz/self.Az + Mxx/self.Ixx*y_stress - Myy/self.Iyy*x_stress
# V = Vy*x_stress/R - Vx*y_stress/R # shear stress orthogonal to direction x,y
# shear_stress = 2. * V / self.Az # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
axial_stress = Fz/self.Az - np.sqrt(Mxx**2+Myy**2)/self.Iyy*self.d/2.0 #More conservative, just use the tilted bending and add total max shear as well at the same point, if you do not like it go back to the previous lines
shear_stress = 2. * np.sqrt(Vx**2+Vy**2) / self.Az # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
# hoop_stress (Eurocode method)
hoop_stress = hoopStressEurocode(self.z, self.d, self.t, self.L_reinforced, self.qdyn)
# von mises stress
self.stress = vonMisesStressUtilization(axial_stress, hoop_stress, shear_stress,
self.gamma_f*self.gamma_m*self.gamma_n, self.sigma_y)
# shell buckling
self.shell_buckling = shellBucklingEurocode(self.d, self.t, axial_stress, hoop_stress,
shear_stress, self.L_reinforced, self.E, self.sigma_y, self.gamma_f, self.gamma_b)
# global buckling
tower_height = self.z[-1] - self.z[0]
M = np.sqrt(Mxx**2 + Myy**2)
self.global_buckling = bucklingGL(self.d, self.t, Fz, M, tower_height, self.E,
self.sigma_y, self.gamma_f, self.gamma_b)
# fatigue
N_DEL = [365*24*3600*self.life]*len(z)
self.damage=np.zeros(z.size)
if any(self.M_DEL):
M_DEL = np.interp(z, self.z_DEL, self.M_DEL)
self.damage = fatigue(M_DEL, N_DEL, self.d, self.t, self.m_SN, self.DC, self.gamma_fatigue, stress_factor=1.0, weld_factor=True)
def execute(self):
#simplify nomenclature
gamma_f = self.IECpsfIns.gamma_f
gamma_m = self.IECpsfIns.gamma_m
gamma_n = self.IECpsfIns.gamma_n
gamma_b = self.IECpsfIns.gamma_b
gamma_g = self.IECpsfIns.gamma_g
##z = self.towerWindLoads.z # this should be the same for wind and wave
##Px = self.towerWindLoads.Px + self.towerWaveLoads.Px
##Py = self.towerWindLoads.Py + self.towerWaveLoads.Py
##Pz = self.towerWindLoads.Pz + self.towerWaveLoads.Pz
z =self.towerWWLoads.z
Px=self.towerWWLoads.Px
Py=self.towerWWLoads.Py
Pz=self.towerWWLoads.Pz
#Make it all along x
Px=np.sqrt(Px**2+Py**2)
Py *=0.
Twr = self.Twr_data.TwrObj
# #Augment with z etc as needed by JTwrUtilization
# Twr.nodes=self.Twrouts.nodes
# Twr.RNAmass=self.Twrouts.TopMass[0]
# Twr.CMzoff=self.Twrouts.TopMass[-1]
# Twr.RNA_Thrust=np.sqrt((self.RNA_F[0:2]**2).sum())
# Twr.RNA_M=self.RNA_F[3:]
# #GLUtil,EUshUtil=TwrUtil.JTwrUtilization(Twr,self.wind_dict,self.water_dict,wind_load=self.twr_wndload,water_load=self.twr_wtrload,ploton=False,gravity=self.gravity)#
# #max_GLUtil=np.nanmax(GLUtil)
# #max_EUUtil=np.nanmax(EUshUtil)
twr_z = self.Twr_data.nodes[2, :]
d_top = self.Dt
t_top = self.tt
twr_D = np.hstack((Twr.D, d_top)) # add top diameter
twr_t = np.hstack((Twr.t, t_top)) # add top thickness
twr_A = np.hstack((Twr.Area, np.pi/4.*(d_top**2-(d_top-2.*t_top)**2))) # add top diameter station
# twr_Amid = np.pi/4.*(twr_D-twr_t)**2 # Mid surface inscribed area (for torsion)
twr_Jyy = np.hstack((Twr.Jyy, np.pi/64.*(d_top**4-(d_top-2.*t_top)**4))) # add top diameter station
# if twr_z.size > twr_D.size: # this may include a fictitious z for the attachment to RNA (CMzoff)
# twr_z = twr_z[:-1] # pop the last element #Need to remove RNA joint, not part of tower
# n = twr_z.shape[0] # number of stations along the tower (removing top one in case there is a rigid link on top)
#Take care of the fact we get materials spearately for each tower element
rho = np.array([mat.rho for mat in Twr.mat]) # I wonder whether these 3 could be condensed into 1 loop instead of 3
E = np.array([mat.E for mat in Twr.mat])
fy = np.array([mat.fy for mat in Twr.mat])
#replicate the last item since mat was for elements not nodes
rho = np.hstack((rho, rho[-1]))
E = np.hstack((E, E[-1]))
fy = np.hstack((fy, fy[-1]))
#Calculate internal loads
# MTTg = Twr.RNAmass*self.gravity # [N] Tower top weight
n = len(z)
Vx = np.zeros(n)
Vy = np.zeros(n)
Fz = np.zeros(n)
Mx = np.zeros(n)
My = np.zeros(n)
Tz = np.zeros(n)
Vx[-1] = self.top_F[0]
Vy[-1] = self.top_F[1]
Fz[-1] = self.top_F[2]
Mx[-1] = self.top_M[0]
My[-1] = self.top_M[1]
Tz[-1] = self.top_M[2]
for i in reversed(range(n-1)):
delta_z=z[i+1]-z[i]
vol=frustum(twr_D[i],twr_D[i+1],delta_z)[0]-frustum(twr_D[i]-2.*twr_t[i], twr_D[i+1]-2.*twr_t[i+1], delta_z)[0]
Vx[i] = Vx[i+1] + 0.5*(Px[i] + Px[i+1])*delta_z
Vy[i] = Vy[i+1] + 0.5*(Py[i] + Py[i+1])*delta_z
Fz[i] = Fz[i+1] + 0.5*(Pz[i] + Pz[i+1])*delta_z - 0.5*(rho[i]+rho[i+1])*self.g*vol #This was missing self weight of tower shell
Mx[i] = Mx[i+1] + Vy[i+1]*(z[i+1]-z[i]) + (Py[i]/6.0 + Py[i+1]/3.0)*(z[i+1]-z[i])**2
My[i] = My[i+1] + Vx[i+1]*(z[i+1]-z[i]) + (Px[i]/6.0 + Px[i+1]/3.0)*(z[i+1]-z[i])**2
Tz[i] = Tz[i+1]
L_reinforced = self.L_reinforced*np.ones_like(twr_D)
# axial and shear stress (all stress evaluated on +x yaw side)
axial_stress = Fz/twr_A - np.sqrt(Mx**2+My**2)/twr_Jyy*twr_D/2.0
shear_stress = 2 * np.sqrt(Vx**2+Vy**2) / twr_A
#hoop_stress = hoopStressEurocode(self.towerWindLoads, self.towerWaveLoads,
# z, twr_D, twr_t, L_reinforced)
hoop_stress = hoopStressEurocode(z, twr_D, twr_t, L_reinforced,self.towerWWLoads.qdyn)
# von mises stress
VMutil = vonMisesStressUtilization(axial_stress, hoop_stress, shear_stress,
gamma_f*gamma_m*gamma_n, fy)
self.utilization.StressUtil = VMutil # utilization
# shell buckling
shell_buckling = shellBucklingEurocode(twr_D, twr_t, axial_stress, hoop_stress,
shear_stress, L_reinforced, E, fy, gamma_f, gamma_b)
self.utilization.EUshUtil = shell_buckling #utilization
# global buckling
tower_height = z[-1] - z[0]
tower_buckling = bucklingGL(twr_D, twr_t, Fz, My, tower_height, E, fy, gamma_f, gamma_b, gamma_g)
self.utilization.GLUtil = tower_buckling #utilization
def solve_nonlinear(self, params, unknowns, resids):
# ------- node data ----------------
z = params['z']
n = len(z)
node = np.arange(1, n+1)
x = np.zeros(n)
y = np.zeros(n)
r = np.zeros(n)
nodes = frame3dd.NodeData(node, x, y, z, r)
# -----------------------------------
# ------ reaction data ------------
# rigid base
node = params['kidx'] + np.ones(len(params['kidx']), dtype=int) # add one because 0-based index but 1-based node numbering
rigid = float('inf')
reactions = frame3dd.ReactionData(node, params['kx'], params['ky'], params['kz'], params['ktx'], params['kty'], params['ktz'], rigid)
# -----------------------------------
# ------ frame element data ------------
element = np.arange(1, n)
N1 = np.arange(1, n)
N2 = np.arange(2, n+1)
roll = np.zeros(n-1)
# average across element b.c. frame3dd uses constant section elements
Az = 0.5*(params['Az'][:-1] + params['Az'][1:])
Asx = 0.5*(params['Asx'][:-1] + params['Asx'][1:])
Asy = 0.5*(params['Asy'][:-1] + params['Asy'][1:])
Jz = 0.5*(params['Jz'][:-1] + params['Jz'][1:])
Ixx = 0.5*(params['Ixx'][:-1] + params['Ixx'][1:])
Iyy = 0.5*(params['Iyy'][:-1] + params['Iyy'][1:])
E = 0.5*(params['E'][:-1] + params['E'][1:])
G = 0.5*(params['G'][:-1] + params['G'][1:])
rho = 0.5*(params['rho'][:-1] + params['rho'][1:])
elements = frame3dd.ElementData(element, N1, N2, Az, Asx, Asy, Jz,
Ixx, Iyy, E, G, roll, rho)
# -----------------------------------
# ------ options ------------
options = frame3dd.Options(params['shear'], params['geom'], params['dx'])
# -----------------------------------
# initialize frame3dd object
tower = frame3dd.Frame(nodes, reactions, elements, options)
# ------ add extra mass ------------
# extra node inertia data
N = params['midx'] + np.ones(len(params['midx']), dtype=int)
tower.changeExtraNodeMass(N, params['m'], params['mIxx'], params['mIyy'], params['mIzz'], params['mIxy'], params['mIxz'], params['mIyz'],
params['mrhox'], params['mrhoy'], params['mrhoz'], params['addGravityLoadForExtraMass'])
# ------------------------------------
# ------- enable dynamic analysis ----------
tower.enableDynamics(params['nM'], params['Mmethod'], params['lump'], params['tol'], params['shift'])
# ----------------------------
# ------ static load case 1 ------------
# gravity in the X, Y, Z, directions (global)
gx = 0.0
gy = 0.0
gz = -params['g']
load = frame3dd.StaticLoadCase(gx, gy, gz)
# point loads
nF = params['plidx'] + np.ones(len(params['plidx']), dtype=int)
load.changePointLoads(nF, params['Fx'], params['Fy'], params['Fz'], params['Mxx'], params['Myy'], params['Mzz'])
# distributed loads
Px, Py, Pz = params['Pz'], params['Py'], -params['Px'] # switch to local c.s.
z = params['z']
# trapezoidally distributed loads
EL = np.arange(1, n)
xx1 = np.zeros(n-1)
xx2 = z[1:] - z[:-1] - np.ones(n-1)*1e-6 # subtract small number b.c. of precision
wx1 = Px[:-1]
wx2 = Px[1:]
xy1 = np.zeros(n-1)
xy2 = z[1:] - z[:-1] - np.ones(n-1)*1e-6
wy1 = Py[:-1]
wy2 = Py[1:]
xz1 = np.zeros(n-1)
xz2 = z[1:] - z[:-1] - np.ones(n-1)*1e-6
wz1 = Pz[:-1]
wz2 = Pz[1:]
load.changeTrapezoidalLoads(EL, xx1, xx2, wx1, wx2, xy1, xy2, wy1, wy2, xz1, xz2, wz1, wz2)
tower.addLoadCase(load)
# -----------------------------------
# run the analysis
displacements, forces, reactions, internalForces, mass, modal = tower.run()
iCase = 0
# mass
unknowns['mass'] = mass.struct_mass
# natural frequncies
unknowns['f1'] = modal.freq[0]
unknowns['f2'] = modal.freq[1]
# deflections due to loading (from tower top and wind/wave loads)
unknowns['top_deflection'] = displacements.dx[iCase, n-1] # in yaw-aligned direction
# shear and bending (convert from local to global c.s.)
Fz = forces.Nx[iCase, :]
Vy = forces.Vy[iCase, :]
Vx = -forces.Vz[iCase, :]
Mzz = forces.Txx[iCase, :]
Myy = forces.Myy[iCase, :]
Mxx = -forces.Mzz[iCase, :]
# one per element (first negative b.c. need reaction)
Fz = np.concatenate([[-Fz[0]], Fz[1::2]])
Vx = np.concatenate([[-Vx[0]], Vx[1::2]])
Vy = np.concatenate([[-Vy[0]], Vy[1::2]])
Mzz = np.concatenate([[-Mzz[0]], Mzz[1::2]])
Myy = np.concatenate([[-Myy[0]], Myy[1::2]])
Mxx = np.concatenate([[-Mxx[0]], Mxx[1::2]])
# axial and shear stress
##R = self.d/2.0
##x_stress = R*np.cos(self.theta_stress)
##y_stress = R*np.sin(self.theta_stress)
##axial_stress = Fz/self.Az + Mxx/self.Ixx*y_stress - Myy/self.Iyy*x_stress
# V = Vy*x_stress/R - Vx*y_stress/R # shear stress orthogonal to direction x,y
# shear_stress = 2. * V / self.Az # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
axial_stress = Fz/params['Az'] - np.sqrt(Mxx**2+Myy**2)/params['Iyy']*params['d']/2.0 #More conservative, just use the tilted bending and add total max shear as well at the same point, if you do not like it go back to the previous lines
shear_stress = 2. * np.sqrt(Vx**2+Vy**2) / params['Az'] # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
# hoop_stress (Eurocode method)
hoop_stress = hoopStressEurocode(params['z'], params['d'], params['t'], params['L_reinforced'], params['qdyn'])
# von mises stress
unknowns['stress'] = vonMisesStressUtilization(axial_stress, hoop_stress, shear_stress,
params['gamma_f']*params['gamma_m']*params['gamma_n'], params['sigma_y'])
# shell buckling
unknowns['shell_buckling'] = shellBucklingEurocode(params['d'], params['t'], axial_stress, hoop_stress,
shear_stress, params['L_reinforced'], params['E'], params['sigma_y'], params['gamma_f'], params['gamma_b'])
# global buckling
tower_height = params['z'][-1] - params['z'][0]
M = np.sqrt(Mxx**2 + Myy**2)
unknowns['global_buckling'] = bucklingGL(params['d'], params['t'], Fz, M, tower_height, params['E'],
params['sigma_y'], params['gamma_f'], params['gamma_b'])
# fatigue
N_DEL = [365*24*3600*params['life']]*len(z)
unknowns['damage']=np.zeros(z.size)
if any(params['M_DEL']):
M_DEL = np.interp(z, params['z_DEL'], params['M_DEL'])
unknowns['damage'] = fatigue(M_DEL, N_DEL, params['d'], params['t'], params['m_SN'], params['DC'], params['gamma_fatigue'], stress_factor=1.0, weld_factor=True)
def solve_nonlinear(self, params, unknowns, resids):
# ------- node data ----------------
z = params['z']
n = len(z)
node = np.arange(1, n+1)
x = np.zeros(n)
y = np.zeros(n)
r = np.zeros(n)
nodes = frame3dd.NodeData(node, x, y, z, r)
# -----------------------------------
# ------ reaction data ------------
# rigid base
node = params['kidx'] + np.ones(len(params['kidx']), dtype=np.int_) # add one because 0-based index but 1-based node numbering
rigid = float('inf')
reactions = frame3dd.ReactionData(node, params['kx'], params['ky'], params['kz'], params['ktx'], params['kty'], params['ktz'], rigid)
# -----------------------------------
# ------ frame element data ------------
element = np.arange(1, n)
N1 = np.arange(1, n)
N2 = np.arange(2, n+1)
roll = np.zeros(n-1)
# average across element b.c. frame3dd uses constant section elements
# TODO: Use nodal2sectional
Az = params['Az']
Asx = params['Asx']
Asy = params['Asy']
Jz = params['Jz']
Ixx = params['Ixx']
Iyy = params['Iyy']
E = params['E']*np.ones(Az.shape)
G = params['G']*np.ones(Az.shape)
rho = params['rho']*np.ones(Az.shape)
elements = frame3dd.ElementData(element, N1, N2, Az, Asx, Asy, Jz, Ixx, Iyy, E, G, roll, rho)
# -----------------------------------
# ------ options ------------
options = frame3dd.Options(params['shear'], params['geom'], params['dx'])
# -----------------------------------
# initialize frame3dd object
cylinder = frame3dd.Frame(nodes, reactions, elements, options)
# ------ add extra mass ------------
# extra node inertia data
N = params['midx'] + np.ones(len(params['midx']), dtype=np.int_)
cylinder.changeExtraNodeMass(N, params['m'], params['mIxx'], params['mIyy'], params['mIzz'], params['mIxy'], params['mIxz'], params['mIyz'],
params['mrhox'], params['mrhoy'], params['mrhoz'], params['addGravityLoadForExtraMass'])
# ------------------------------------
# ------- enable dynamic analysis ----------
cylinder.enableDynamics(params['nM'], params['Mmethod'], params['lump'], params['tol'], params['shift'])
# ----------------------------
# ------ static load case 1 ------------
# gravity in the X, Y, Z, directions (global)
gx = 0.0
gy = 0.0
gz = -gravity
load = frame3dd.StaticLoadCase(gx, gy, gz)
# point loads
nF = params['plidx'] + np.ones(len(params['plidx']), dtype=int)
load.changePointLoads(nF, params['Fx'], params['Fy'], params['Fz'], params['Mxx'], params['Myy'], params['Mzz'])
# distributed loads
Px, Py, Pz = params['Pz'], params['Py'], -params['Px'] # switch to local c.s.
z = params['z']
# trapezoidally distributed loads
EL = np.arange(1, n)
xx1 = xy1 = xz1 = np.zeros(n-1)
xx2 = xy2 = xz2 = np.diff(z) - 1e-6 # subtract small number b.c. of precision
wx1 = Px[:-1]
wx2 = Px[1:]
wy1 = Py[:-1]
wy2 = Py[1:]
wz1 = Pz[:-1]
wz2 = Pz[1:]
load.changeTrapezoidalLoads(EL, xx1, xx2, wx1, wx2, xy1, xy2, wy1, wy2, xz1, xz2, wz1, wz2)
cylinder.addLoadCase(load)
# Debugging
#cylinder.write('temp.3dd')
# -----------------------------------
# run the analysis
displacements, forces, reactions, internalForces, mass, modal = cylinder.run()
iCase = 0
# mass
unknowns['mass'] = mass.struct_mass
# natural frequncies
unknowns['f1'] = modal.freq[0]
unknowns['f2'] = modal.freq[1]
# deflections due to loading (from cylinder top and wind/wave loads)
unknowns['top_deflection'] = displacements.dx[iCase, n-1] # in yaw-aligned direction
# shear and bending, one per element (convert from local to global c.s.)
Fz = forces.Nx[iCase, 1::2]
Vy = forces.Vy[iCase, 1::2]
Vx = -forces.Vz[iCase, 1::2]
Mzz = forces.Txx[iCase, 1::2]
Myy = forces.Myy[iCase, 1::2]
Mxx = -forces.Mzz[iCase, 1::2]
# Record total forces and moments
unknowns['base_F'] = -1.0 * np.array([reactions.Fx.sum(), reactions.Fy.sum(), reactions.Fz.sum()])
unknowns['base_M'] = -1.0 * np.array([reactions.Mxx.sum(), reactions.Myy.sum(), reactions.Mzz.sum()])
unknowns['Fz_out'] = Fz
unknowns['Vx_out'] = Vx
unknowns['Vy_out'] = Vy
unknowns['Mxx_out'] = Mxx
unknowns['Myy_out'] = Myy
unknowns['Mzz_out'] = Mzz
# axial and shear stress
d,_ = nodal2sectional(params['d'])
qdyn,_ = nodal2sectional(params['qdyn'])
##R = self.d/2.0
##x_stress = R*np.cos(self.theta_stress)
##y_stress = R*np.sin(self.theta_stress)
##axial_stress = Fz/self.Az + Mxx/self.Ixx*y_stress - Myy/self.Iyy*x_stress
# V = Vy*x_stress/R - Vx*y_stress/R # shear stress orthogonal to direction x,y
# shear_stress = 2. * V / self.Az # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
unknowns['axial_stress'] = Fz/params['Az'] - np.sqrt(Mxx**2+Myy**2)/params['Iyy']*d/2.0 #More conservative, just use the tilted bending and add total max shear as well at the same point, if you do not like it go back to the previous lines
unknowns['shear_stress'] = 2. * np.sqrt(Vx**2+Vy**2) / params['Az'] # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
# hoop_stress (Eurocode method)
L_reinforced = params['L_reinforced'] * np.ones(Fz.shape)
unknowns['hoop_stress_euro'] = hoopStressEurocode(params['z'], d, params['t'], L_reinforced, qdyn)
# Simpler hoop stress used in API calculations
unknowns['hoop_stress'] = hoopStress(d, params['t'], qdyn)
def solve_nonlinear(self, params, unknowns, resids):
# ------- node data ----------------
z = params['z']
n = len(z)
node = np.arange(1, n + 1)
x = np.zeros(n)
y = np.zeros(n)
r = np.zeros(n)
nodes = frame3dd.NodeData(node, x, y, z, r)
# -----------------------------------
# ------ reaction data ------------
# rigid base
node = params['kidx'] + np.ones(
len(params['kidx']), dtype=np.int_
) # add one because 0-based index but 1-based node numbering
rigid = float('inf')
reactions = frame3dd.ReactionData(node, params['kx'], params['ky'],
params['kz'], params['ktx'],
params['kty'], params['ktz'], rigid)
# -----------------------------------
# ------ frame element data ------------
element = np.arange(1, n)
N1 = np.arange(1, n)
N2 = np.arange(2, n + 1)
roll = np.zeros(n - 1)
# average across element b.c. frame3dd uses constant section elements
# TODO: Use nodal2sectional
Az = params['Az']
Asx = params['Asx']
Asy = params['Asy']
Jz = params['Jz']
Ixx = params['Ixx']
Iyy = params['Iyy']
E = params['E'] * np.ones(Az.shape)
G = params['G'] * np.ones(Az.shape)
rho = params['rho'] * np.ones(Az.shape)
elements = frame3dd.ElementData(element, N1, N2, Az, Asx, Asy, Jz, Ixx,
Iyy, E, G, roll, rho)
# -----------------------------------
# ------ options ------------
options = frame3dd.Options(params['shear'], params['geom'],
params['dx'])
# -----------------------------------
# initialize frame3dd object
cylinder = frame3dd.Frame(nodes, reactions, elements, options)
# ------ add extra mass ------------
# extra node inertia data
N = params['midx'] + np.ones(len(params['midx']), dtype=np.int_)
cylinder.changeExtraNodeMass(N, params['m'], params['mIxx'],
params['mIyy'], params['mIzz'],
params['mIxy'], params['mIxz'],
params['mIyz'], params['mrhox'],
params['mrhoy'], params['mrhoz'],
params['addGravityLoadForExtraMass'])
# ------------------------------------
# ------- enable dynamic analysis ----------
cylinder.enableDynamics(params['nM'], params['Mmethod'],
params['lump'], params['tol'], params['shift'])
# ----------------------------
# ------ static load case 1 ------------
# gravity in the X, Y, Z, directions (global)
gx = 0.0
gy = 0.0
gz = -gravity
load = frame3dd.StaticLoadCase(gx, gy, gz)
# point loads
nF = params['plidx'] + np.ones(len(params['plidx']), dtype=int)
load.changePointLoads(nF, params['Fx'], params['Fy'], params['Fz'],
params['Mxx'], params['Myy'], params['Mzz'])
# distributed loads
Px, Py, Pz = params['Pz'], params['Py'], -params[
'Px'] # switch to local c.s.
z = params['z']
# trapezoidally distributed loads
EL = np.arange(1, n)
xx1 = xy1 = xz1 = np.zeros(n - 1)
xx2 = xy2 = xz2 = np.diff(
z) - 1e-6 # subtract small number b.c. of precision
wx1 = Px[:-1]
wx2 = Px[1:]
wy1 = Py[:-1]
wy2 = Py[1:]
wz1 = Pz[:-1]
wz2 = Pz[1:]
load.changeTrapezoidalLoads(EL, xx1, xx2, wx1, wx2, xy1, xy2, wy1, wy2,
xz1, xz2, wz1, wz2)
cylinder.addLoadCase(load)
# Debugging
#cylinder.write('temp.3dd')
# -----------------------------------
# run the analysis
displacements, forces, reactions, internalForces, mass, modal = cylinder.run(
)
iCase = 0
# mass
unknowns['mass'] = mass.struct_mass
# natural frequncies
unknowns['f1'] = modal.freq[0]
unknowns['f2'] = modal.freq[1]
# deflections due to loading (from cylinder top and wind/wave loads)
unknowns['top_deflection'] = displacements.dx[
iCase, n - 1] # in yaw-aligned direction
# shear and bending, one per element (convert from local to global c.s.)
Fz = forces.Nx[iCase, 1::2]
Vy = forces.Vy[iCase, 1::2]
Vx = -forces.Vz[iCase, 1::2]
Mzz = forces.Txx[iCase, 1::2]
Myy = forces.Myy[iCase, 1::2]
Mxx = -forces.Mzz[iCase, 1::2]
# Record total forces and moments
unknowns['base_F'] = -1.0 * np.array(
[reactions.Fx.sum(),
reactions.Fy.sum(),
reactions.Fz.sum()])
unknowns['base_M'] = -1.0 * np.array(
[reactions.Mxx.sum(),
reactions.Myy.sum(),
reactions.Mzz.sum()])
unknowns['Fz_out'] = Fz
unknowns['Vx_out'] = Vx
unknowns['Vy_out'] = Vy
unknowns['Mxx_out'] = Mxx
unknowns['Myy_out'] = Myy
unknowns['Mzz_out'] = Mzz
# axial and shear stress
d, _ = nodal2sectional(params['d'])
qdyn, _ = nodal2sectional(params['qdyn'])
##R = self.d/2.0
##x_stress = R*np.cos(self.theta_stress)
##y_stress = R*np.sin(self.theta_stress)
##axial_stress = Fz/self.Az + Mxx/self.Ixx*y_stress - Myy/self.Iyy*x_stress
# V = Vy*x_stress/R - Vx*y_stress/R # shear stress orthogonal to direction x,y
# shear_stress = 2. * V / self.Az # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
unknowns['axial_stress'] = Fz / params['Az'] - np.sqrt(
Mxx**2 + Myy**2
) / params[
'Iyy'] * d / 2.0 #More conservative, just use the tilted bending and add total max shear as well at the same point, if you do not like it go back to the previous lines
unknowns['shear_stress'] = 2. * np.sqrt(Vx**2 + Vy**2) / params[
'Az'] # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
# hoop_stress (Eurocode method)
L_reinforced = params['L_reinforced'] * np.ones(Fz.shape)
unknowns['hoop_stress_euro'] = hoopStressEurocode(
params['z'], d, params['t'], L_reinforced, qdyn)
# Simpler hoop stress used in API calculations
unknowns['hoop_stress'] = hoopStress(d, params['t'], qdyn)
def solve_nonlinear(self, params, unknowns, resids):
# ------- node data ----------------
z = params['z']
n = len(z)
node = np.arange(1, n + 1)
x = np.zeros(n)
y = np.zeros(n)
r = np.zeros(n)
nodes = frame3dd.NodeData(node, x, y, z, r)
# -----------------------------------
# ------ reaction data ------------
# rigid base
node = params['kidx'] + np.ones(
len(params['kidx']), dtype=int
) # add one because 0-based index but 1-based node numbering
rigid = float('inf')
reactions = frame3dd.ReactionData(node, params['kx'], params['ky'],
params['kz'], params['ktx'],
params['kty'], params['ktz'], rigid)
# -----------------------------------
# ------ frame element data ------------
element = np.arange(1, n)
N1 = np.arange(1, n)
N2 = np.arange(2, n + 1)
roll = np.zeros(n - 1)
# average across element b.c. frame3dd uses constant section elements
Az = 0.5 * (params['Az'][:-1] + params['Az'][1:])
Asx = 0.5 * (params['Asx'][:-1] + params['Asx'][1:])
Asy = 0.5 * (params['Asy'][:-1] + params['Asy'][1:])
Jz = 0.5 * (params['Jz'][:-1] + params['Jz'][1:])
Ixx = 0.5 * (params['Ixx'][:-1] + params['Ixx'][1:])
Iyy = 0.5 * (params['Iyy'][:-1] + params['Iyy'][1:])
E = 0.5 * (params['E'][:-1] + params['E'][1:])
G = 0.5 * (params['G'][:-1] + params['G'][1:])
rho = 0.5 * (params['rho'][:-1] + params['rho'][1:])
elements = frame3dd.ElementData(element, N1, N2, Az, Asx, Asy, Jz, Ixx,
Iyy, E, G, roll, rho)
# -----------------------------------
# ------ options ------------
options = frame3dd.Options(params['shear'], params['geom'],
params['dx'])
# -----------------------------------
# initialize frame3dd object
tower = frame3dd.Frame(nodes, reactions, elements, options)
# ------ add extra mass ------------
# extra node inertia data
N = params['midx'] + np.ones(len(params['midx']), dtype=int)
tower.changeExtraNodeMass(N, params['m'], params['mIxx'],
params['mIyy'], params['mIzz'],
params['mIxy'], params['mIxz'],
params['mIyz'], params['mrhox'],
params['mrhoy'], params['mrhoz'],
params['addGravityLoadForExtraMass'])
# ------------------------------------
# ------- enable dynamic analysis ----------
tower.enableDynamics(params['nM'], params['Mmethod'], params['lump'],
params['tol'], params['shift'])
# ----------------------------
# ------ static load case 1 ------------
# gravity in the X, Y, Z, directions (global)
gx = 0.0
gy = 0.0
gz = -params['g']
load = frame3dd.StaticLoadCase(gx, gy, gz)
# point loads
nF = params['plidx'] + np.ones(len(params['plidx']), dtype=int)
load.changePointLoads(nF, params['Fx'], params['Fy'], params['Fz'],
params['Mxx'], params['Myy'], params['Mzz'])
# distributed loads
Px, Py, Pz = params['Pz'], params['Py'], -params[
'Px'] # switch to local c.s.
z = params['z']
# trapezoidally distributed loads
EL = np.arange(1, n)
xx1 = np.zeros(n - 1)
xx2 = z[1:] - z[:-1] - np.ones(
n - 1) * 1e-6 # subtract small number b.c. of precision
wx1 = Px[:-1]
wx2 = Px[1:]
xy1 = np.zeros(n - 1)
xy2 = z[1:] - z[:-1] - np.ones(n - 1) * 1e-6
wy1 = Py[:-1]
wy2 = Py[1:]
xz1 = np.zeros(n - 1)
xz2 = z[1:] - z[:-1] - np.ones(n - 1) * 1e-6
wz1 = Pz[:-1]
wz2 = Pz[1:]
load.changeTrapezoidalLoads(EL, xx1, xx2, wx1, wx2, xy1, xy2, wy1, wy2,
xz1, xz2, wz1, wz2)
tower.addLoadCase(load)
# -----------------------------------
# run the analysis
displacements, forces, reactions, internalForces, mass, modal = tower.run(
)
iCase = 0
# mass
unknowns['mass'] = mass.struct_mass
# natural frequncies
unknowns['f1'] = modal.freq[0]
unknowns['f2'] = modal.freq[1]
# deflections due to loading (from tower top and wind/wave loads)
unknowns['top_deflection'] = displacements.dx[
iCase, n - 1] # in yaw-aligned direction
# shear and bending (convert from local to global c.s.)
Fz = forces.Nx[iCase, :]
Vy = forces.Vy[iCase, :]
Vx = -forces.Vz[iCase, :]
Mzz = forces.Txx[iCase, :]
Myy = forces.Myy[iCase, :]
Mxx = -forces.Mzz[iCase, :]
# one per element (first negative b.c. need reaction)
Fz = np.concatenate([[-Fz[0]], Fz[1::2]])
Vx = np.concatenate([[-Vx[0]], Vx[1::2]])
Vy = np.concatenate([[-Vy[0]], Vy[1::2]])
Mzz = np.concatenate([[-Mzz[0]], Mzz[1::2]])
Myy = np.concatenate([[-Myy[0]], Myy[1::2]])
Mxx = np.concatenate([[-Mxx[0]], Mxx[1::2]])
# axial and shear stress
##R = self.d/2.0
##x_stress = R*np.cos(self.theta_stress)
##y_stress = R*np.sin(self.theta_stress)
##axial_stress = Fz/self.Az + Mxx/self.Ixx*y_stress - Myy/self.Iyy*x_stress
# V = Vy*x_stress/R - Vx*y_stress/R # shear stress orthogonal to direction x,y
# shear_stress = 2. * V / self.Az # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
axial_stress = Fz / params['Az'] - np.sqrt(
Mxx**2 + Myy**2
) / params['Iyy'] * params[
'd'] / 2.0 #More conservative, just use the tilted bending and add total max shear as well at the same point, if you do not like it go back to the previous lines
shear_stress = 2. * np.sqrt(Vx**2 + Vy**2) / params[
'Az'] # coefficient of 2 for a hollow circular section, but should be conservative for other shapes
# hoop_stress (Eurocode method)
hoop_stress = hoopStressEurocode(params['z'], params['d'], params['t'],
params['L_reinforced'],
params['qdyn'])
# von mises stress
unknowns['stress'] = vonMisesStressUtilization(
axial_stress, hoop_stress, shear_stress,
params['gamma_f'] * params['gamma_m'] * params['gamma_n'],
params['sigma_y'])
# shell buckling
unknowns['shell_buckling'] = shellBucklingEurocode(
params['d'], params['t'], axial_stress, hoop_stress, shear_stress,
params['L_reinforced'], params['E'], params['sigma_y'],
params['gamma_f'], params['gamma_b'])
# global buckling
tower_height = params['z'][-1] - params['z'][0]
M = np.sqrt(Mxx**2 + Myy**2)
unknowns['global_buckling'] = bucklingGL(params['d'], params['t'], Fz,
M, tower_height, params['E'],
params['sigma_y'],
params['gamma_f'],
params['gamma_b'])
# fatigue
N_DEL = [365 * 24 * 3600 * params['life']] * len(z)
unknowns['damage'] = np.zeros(z.size)
if any(params['M_DEL']):
M_DEL = np.interp(z, params['z_DEL'], params['M_DEL'])
unknowns['damage'] = fatigue(M_DEL,
N_DEL,
params['d'],
params['t'],
params['m_SN'],
params['DC'],
params['gamma_fatigue'],
stress_factor=1.0,
weld_factor=True)