def Solve_F90(XBINPUT, XBOPTS):
"""@brief Nonlinear dynamic structural solver using f90 solve routine."""
"Check correct solution code"
assert XBOPTS.Solution.value == 312, ('NonlinearDynamic (F90) requested' +\
' with wrong solution code')
"Initialise variables for static analysis"
XBINPUT, XBOPTS, NumNodes_tot, XBELEM, PosIni, PsiIni, XBNODE, NumDof \
= BeamInit.Static(XBINPUT, XBOPTS)
"Change solution code to NonlinearStatic"
XBOPTS.Solution.value = 112
"Set initial conditions as undef config"
PosDefor = PosIni.copy(order='F')
PsiDefor = PsiIni.copy(order='F')
"Solve static"
BeamLib.Cbeam3_Solv_NonlinearStatic(XBINPUT, XBOPTS, NumNodes_tot, XBELEM,\
PosIni, PsiIni, XBNODE, NumDof,\
PosDefor, PsiDefor)
"Change solution code back to NonlinearDynamic"
XBOPTS.Solution.value = 312
"Write deformed configuration to file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_def.dat'
if XBOPTS.PrintInfo == True:
sys.stdout.write('Writing file %s ... ' % (ofile))
fp = open(ofile, 'w')
fp.write('TITLE="Non-linear static solution: deformed geometry"\n')
fp.write('VARIABLES="iElem" "iNode" "Px" "Py" "Pz" "Rx" "Ry" "Rz"\n')
fp.close()
if XBOPTS.PrintInfo == True:
sys.stdout.write('done\n')
WriteMode = 'a'
BeamIO.OutputElems(XBINPUT.NumElems, NumNodes_tot.value, XBELEM, \
PosDefor, PsiDefor, ofile, WriteMode)
"Change solution code to NonlinearDynamic"
XBOPTS.Solution.value = 312
"Initialise variables for dynamic analysis"
Time, NumSteps, ForceTime, ForcedVel, ForcedVelDot,\
PosDotDef, PsiDotDef,\
OutGrids, PosPsiTime, VelocTime, DynOut\
= BeamInit.Dynamic(XBINPUT,XBOPTS)
"Write _force file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_force.dat'
fp = open(ofile, 'w')
BeamIO.Write_force_File(fp, Time, ForceTime, ForcedVel, ForcedVelDot)
fp.close()
"Write _vel file"
#TODO: write _vel file
"Write .mrb file"
#TODO: write .mrb file
"Solve dynamic using f90 solver"
BeamLib.Cbeam3_Solv_NonlinearDynamic(XBINPUT, XBOPTS, NumNodes_tot, XBELEM,\
PosIni, PsiIni, XBNODE, NumDof,\
PosDefor, PsiDefor,\
NumSteps, Time, ForceTime, ForcedVel, ForcedVelDot,\
PosDotDef, PsiDotDef,\
PosPsiTime, VelocTime, DynOut, OutGrids)
"Write _dyn file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_dyn.dat'
fp = open(ofile, 'w')
BeamIO.Write_dyn_File(fp, Time, PosPsiTime)
fp.close()
"Write _shape file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_shape.dat'
fp = open(ofile, 'w')
BeamIO.Write_shape_File(fp, len(Time), NumNodes_tot.value, Time, DynOut)
fp.close()
def Solve_Py(XBINPUT, XBOPTS, moduleName=None):
"""Nonlinear dynamic structural solver in Python. Assembly of matrices
is carried out with Fortran subroutines."""
"Check correct solution code"
assert XBOPTS.Solution.value == 312, ('NonlinearDynamic requested' +\
' with wrong solution code')
"Initialise beam"
XBINPUT, XBOPTS, NumNodes_tot, XBELEM, PosIni, PsiIni, XBNODE, NumDof \
= BeamInit.Static(XBINPUT,XBOPTS, moduleName)
# Solve static solution
XBOPTS.Solution.value = 112
PosDefor, PsiDefor = Solve_Py_Static(XBINPUT, XBOPTS, moduleName)
XBOPTS.Solution.value = 312
"Write deformed configuration to file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_def.dat'
if XBOPTS.PrintInfo == True:
sys.stdout.write('Writing file %s ... ' % (ofile))
fp = open(ofile, 'w')
fp.write('TITLE="Non-linear static solution: deformed geometry"\n')
fp.write('VARIABLES="iElem" "iNode" "Px" "Py" "Pz" "Rx" "Ry" "Rz"\n')
fp.close()
if XBOPTS.PrintInfo == True:
sys.stdout.write('done\n')
WriteMode = 'a'
BeamIO.OutputElems(XBINPUT.NumElems, NumNodes_tot.value, XBELEM, \
PosDefor, PsiDefor, ofile, WriteMode)
"Initialise variables for dynamic analysis"
Time, NumSteps, ForceTime, ForcedVel, ForcedVelDot,\
PosDotDef, PsiDotDef,\
OutGrids, PosPsiTime, VelocTime, DynOut\
= BeamInit.Dynamic(XBINPUT,XBOPTS, moduleName)
# Delete unused vars
del OutGrids, VelocTime
"Write _force file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_force.dat'
fp = open(ofile, 'w')
BeamIO.Write_force_File(fp, Time, ForceTime, ForcedVel, ForcedVelDot)
fp.close()
"Write _vel file"
#TODO: write _vel file
"Write .mrb file"
#TODO: write .mrb file
if XBOPTS.PrintInfo.value == True:
sys.stdout.write('Solve nonlinear dynamic case in Python ... \n')
"Initialise structural system tensors"
MglobalFull = np.zeros((NumDof.value, NumDof.value), ct.c_double, 'F')
CglobalFull = np.zeros((NumDof.value, NumDof.value), ct.c_double, 'F')
KglobalFull = np.zeros((NumDof.value, NumDof.value), ct.c_double, 'F')
FglobalFull = np.zeros((NumDof.value, NumDof.value), ct.c_double, 'F')
Asys = np.zeros((NumDof.value, NumDof.value), ct.c_double, 'F')
ms = ct.c_int()
cs = ct.c_int()
ks = ct.c_int()
fs = ct.c_int()
Mvel = np.zeros((NumDof.value, 6), ct.c_double, 'F')
Cvel = np.zeros((NumDof.value, 6), ct.c_double, 'F')
X = np.zeros(NumDof.value, ct.c_double, 'F')
DX = np.zeros(NumDof.value, ct.c_double, 'F')
dXdt = np.zeros(NumDof.value, ct.c_double, 'F')
dXddt = np.zeros(NumDof.value, ct.c_double, 'F')
Force_Dof = np.zeros(NumDof.value, ct.c_double, 'F')
Qglobal = np.zeros(NumDof.value, ct.c_double, 'F')
"Initialise rotation operators"
Unit = np.zeros((3, 3), ct.c_double, 'F')
for i in range(3):
Unit[i, i] = 1.0
Unit4 = np.zeros((4, 4), ct.c_double, 'F')
for i in range(4):
Unit4[i, i] = 1.0
Cao = Unit.copy('F')
Temp = Unit4.copy('F')
Quat = np.zeros(4, ct.c_double, 'F')
Quat[0] = 1.0
"Extract initial displacements and velocities"
BeamLib.Cbeam_Solv_Disp2State(NumNodes_tot, NumDof, XBINPUT, XBNODE,\
PosDefor, PsiDefor, PosDotDef, PsiDotDef,
X, dXdt)
"Approximate initial accelerations"
"Initialise accelerations as zero arrays"
PosDotDotDef = np.zeros((NumNodes_tot.value, 3), ct.c_double, 'F')
PsiDotDotDef = np.zeros((XBINPUT.NumElems,Settings.MaxElNod,3),\
ct.c_double, 'F')
"Force at the first time-step"
Force = (XBINPUT.ForceStatic + XBINPUT.ForceDyn * ForceTime[0]).copy('F')
"Assemble matrices for dynamic analysis"
BeamLib.Cbeam3_Asbly_Dynamic(XBINPUT, NumNodes_tot, XBELEM, XBNODE,\
PosIni, PsiIni, PosDefor, PsiDefor,\
PosDotDef, PsiDotDef, PosDotDotDef, PsiDotDotDef,\
Force, ForcedVel[0,:], ForcedVelDot[0,:],\
NumDof, Settings.DimMat,\
ms, MglobalFull, Mvel,\
cs, CglobalFull, Cvel,\
ks, KglobalFull, fs, FglobalFull,\
Qglobal, XBOPTS, Cao)
"Get force vector for unconstrained nodes (Force_Dof)"
BeamLib.f_fem_m2v(ct.byref(NumNodes_tot),\
ct.byref(ct.c_int(6)),\
Force.ctypes.data_as(ct.POINTER(ct.c_double)),\
ct.byref(NumDof),\
Force_Dof.ctypes.data_as(ct.POINTER(ct.c_double)),\
XBNODE.Vdof.ctypes.data_as(ct.POINTER(ct.c_int)) )
"Get RHS at initial condition"
Qglobal += -np.dot(FglobalFull, Force_Dof)
#Separate assembly of follower and dead loads"
tmpForceTime = ForceTime[0].copy('F')
Qforces = XbeamLib.LoadAssembly(XBINPUT, XBELEM, XBNODE, XBOPTS, NumDof, \
PosIni, PsiIni, PosDefor, PsiDefor, \
(XBINPUT.ForceStatic_foll + XBINPUT.ForceDyn_foll*tmpForceTime), \
(XBINPUT.ForceStatic_dead + XBINPUT.ForceDyn_dead*tmpForceTime), \
Cao, 1)[0]
Qglobal -= Qforces
"Initial Accel"
dXddt[:] = np.dot(np.linalg.inv(MglobalFull), -Qglobal)
"Record position of all grid points in global FoR at initial time step"
DynOut[0:NumNodes_tot.value, :] = PosDefor
"Position/rotation of the selected node in initial deformed configuration"
PosPsiTime[0, :3] = PosDefor[-1, :]
PosPsiTime[0, 3:] = PsiDefor[-1, XBELEM.NumNodes[-1] - 1, :]
"Get gamma and beta for Newmark scheme"
gamma = 0.5 + XBOPTS.NewmarkDamp.value
beta = 0.25 * np.power((gamma + 0.5), 2.0)
"Time loop"
for iStep in range(NumSteps.value):
if XBOPTS.PrintInfo.value == True:
sys.stdout.write(' Time: %-10.4e\n' % (Time[iStep + 1]))
sys.stdout.write(' SubIter DeltaF DeltaX ResLog10\n')
"calculate dt"
dt = Time[iStep + 1] - Time[iStep]
"Update transformation matrix for given angular velocity"
Temp = np.linalg.inv(Unit4 + 0.25 *
XbeamLib.QuadSkew(ForcedVel[iStep + 1, 3:]) * dt)
Quat = np.dot(
Temp,
np.dot(Unit4 - 0.25 * XbeamLib.QuadSkew(ForcedVel[iStep, 3:]) * dt,
Quat))
Quat = Quat / np.linalg.norm(Quat)
Cao = XbeamLib.Rot(Quat)
"Predictor step"
X += dt * dXdt + (0.5 - beta) * dXddt * dt**2
dXdt += (1.0 - gamma) * dXddt * dt
dXddt[:] = 0.0
"Force at current time-step"
Force = (XBINPUT.ForceStatic + \
XBINPUT.ForceDyn*ForceTime[iStep+1]).copy('F')
"Reset convergence parameters"
Iter = 0
ResLog10 = 1.0
"Newton-Raphson loop"
while ( (ResLog10 > XBOPTS.MinDelta.value) \
& (Iter < XBOPTS.MaxIterations.value) ):
"set tensors to zero"
Qglobal[:] = 0.0
Mvel[:, :] = 0.0
Cvel[:, :] = 0.0
MglobalFull[:, :] = 0.0
CglobalFull[:, :] = 0.0
KglobalFull[:, :] = 0.0
FglobalFull[:, :] = 0.0
"Update counter"
Iter += 1
if XBOPTS.PrintInfo.value == True:
sys.stdout.write(' %-7d ' % (Iter))
"nodal diplacements and velocities from state vector"
BeamLib.Cbeam3_Solv_State2Disp(XBINPUT, NumNodes_tot, XBELEM, XBNODE,
PosIni, PsiIni, NumDof, X, dXdt,\
PosDefor, PsiDefor, PosDotDef, PsiDotDef)
"update matrices"
BeamLib.Cbeam3_Asbly_Dynamic(XBINPUT, NumNodes_tot, XBELEM, XBNODE,\
PosIni, PsiIni, PosDefor, PsiDefor,\
PosDotDef, PsiDotDef, PosDotDotDef, PsiDotDotDef,\
Force, ForcedVel[iStep+1,:], ForcedVelDot[iStep+1,:],\
NumDof, Settings.DimMat,\
ms, MglobalFull, Mvel,\
cs, CglobalFull, Cvel,\
ks, KglobalFull, fs, FglobalFull,\
Qglobal, XBOPTS, Cao)
"Get force vector for unconstrained nodes (Force_Dof)"
BeamLib.f_fem_m2v(ct.byref(NumNodes_tot),\
ct.byref(ct.c_int(6)),\
Force.ctypes.data_as(ct.POINTER(ct.c_double)),\
ct.byref(NumDof),\
Force_Dof.ctypes.data_as(ct.POINTER(ct.c_double)),\
XBNODE.Vdof.ctypes.data_as(ct.POINTER(ct.c_int)) )
"Solve for update vector"
"Residual"
Qglobal += np.dot(MglobalFull, dXddt) \
+ np.dot(Mvel,ForcedVelDot[iStep+1,:]) \
- np.dot(FglobalFull, Force_Dof)
#Separate assembly of follower and dead loads
tmpForceTime = ForceTime[iStep + 1].copy('F')
Qforces = XbeamLib.LoadAssembly(XBINPUT, XBELEM, XBNODE, XBOPTS, NumDof, \
PosIni, PsiIni, PosDefor, PsiDefor, \
(XBINPUT.ForceStatic_foll + XBINPUT.ForceDyn_foll*tmpForceTime), \
(XBINPUT.ForceStatic_dead + XBINPUT.ForceDyn_dead*tmpForceTime), \
Cao,1)[0]
Qglobal -= Qforces
if XBOPTS.PrintInfo.value == True:
sys.stdout.write('%-10.4e ' % (max(abs(Qglobal))))
"Calculate system matrix for update calculation"
Asys = KglobalFull + \
CglobalFull*gamma/(beta*dt) + \
MglobalFull/(beta*np.power(dt,2.0))
"Solve for update"
DX[:] = np.dot(np.linalg.inv(Asys), -Qglobal)
"Corrector step"
X += DX
dXdt += DX * gamma / (beta * dt)
dXddt += DX / (beta * dt**2)
"Residual at first iteration"
if (Iter == 1):
Res0_Qglobal = max(max(abs(Qglobal)), 1)
Res0_DeltaX = max(max(abs(DX)), 1)
"Update residual and compute log10"
Res_Qglobal = max(abs(Qglobal))
Res_DeltaX = max(abs(DX))
ResLog10 = max(Res_Qglobal / Res0_Qglobal,
Res_DeltaX / Res0_DeltaX)
if XBOPTS.PrintInfo.value == True:
sys.stdout.write('%-10.4e %8.4f\n' % (max(abs(DX)), ResLog10))
"END Netwon-Raphson"
"update to converged nodal displacements and velocities"
BeamLib.Cbeam3_Solv_State2Disp(XBINPUT, NumNodes_tot, XBELEM, XBNODE,
PosIni, PsiIni, NumDof, X, dXdt,
PosDefor, PsiDefor, PosDotDef,
PsiDotDef)
PosPsiTime[iStep + 1, :3] = PosDefor[(NumNodes_tot.value - 1) / 2 +
1, :]
PosPsiTime[iStep + 1, 3:] = PsiDefor[-1, XBELEM.NumNodes[-1] - 1, :]
"Position of all grid points in global FoR"
i1 = (iStep + 1) * NumNodes_tot.value
i2 = (iStep + 2) * NumNodes_tot.value
DynOut[i1:i2, :] = PosDefor
"END Time loop"
"Write _dyn file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_dyn.dat'
fp = open(ofile, 'w')
BeamIO.Write_dyn_File(fp, Time, PosPsiTime)
fp.close()
"Write _shape file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_shape.dat'
fp = open(ofile, 'w')
BeamIO.Write_shape_File(fp, len(Time), NumNodes_tot.value, Time, DynOut)
fp.close()
if XBOPTS.PrintInfo.value == True:
sys.stdout.write(' ... done\n')
def Solve_F90(XBINPUT, XBOPTS):
"""@brief Nonlinear dynamic structural solver using f90 solve routine."""
#Check correct solution code
assert XBOPTS.Solution.value == 912, ('NonlinearDynamic (F90) requested' +\
' with wrong solution code')
#Initialise variables for static analysis
XBINPUT, XBOPTS, NumNodes_tot, XBELEM, PosIni, PsiIni, XBNODE, NumDof \
= BeamInit.Static(XBINPUT, XBOPTS)
#Change solution code to NonlinearStatic
XBOPTS.Solution.value = 112
#Set initial conditions as undef config
PosDefor = PosIni.copy(order='F')
PsiDefor = PsiIni.copy(order='F')
#Solve static
BeamLib.Cbeam3_Solv_NonlinearStatic(XBINPUT, XBOPTS, NumNodes_tot, XBELEM,\
PosIni, PsiIni, XBNODE, NumDof,\
PosDefor, PsiDefor)
#Change solution code back to NonlinearDynamic
XBOPTS.Solution.value = 912
#Write deformed configuration to file
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL912_def.dat'
if XBOPTS.PrintInfo == True:
sys.stdout.write('Writing file %s ... ' % (ofile))
fp = open(ofile, 'w')
fp.write('TITLE="Non-linear static solution: deformed geometry"\n')
fp.write('VARIABLES="iElem" "iNode" "Px" "Py" "Pz" "Rx" "Ry" "Rz"\n')
fp.close()
if XBOPTS.PrintInfo == True:
sys.stdout.write('done\n')
WriteMode = 'a'
BeamIO.OutputElems(XBINPUT.NumElems, NumNodes_tot.value, XBELEM, \
PosDefor, PsiDefor, ofile, WriteMode)
#Initialise variables for dynamic analysis
Time, NumSteps, ForceTime, ForcedVel, ForcedVelDot,\
PosDotDef, PsiDotDef,\
OutGrids, PosPsiTime, VelocTime, DynOut\
= BeamInit.Dynamic(XBINPUT,XBOPTS, NumNodes_tot)
# Delete unused variables.
del PosPsiTime, VelocTime
#Initialise quaternions for rigid-body dynamics
Quat = np.zeros(4, ct.c_double, 'F')
Quat[0] = 1.0
#Write _force file
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL912_force.dat'
fp = open(ofile, 'w')
BeamIO.Write_force_File(fp, Time, ForceTime, ForcedVel, ForcedVelDot)
fp.close()
#Solve dynamic using f90 solver
BeamLib.Xbeam_Solv_FreeNonlinDynamic(XBINPUT, XBOPTS, NumNodes_tot, XBELEM,\
PosIni, PsiIni, XBNODE, NumDof,\
PosDefor, PsiDefor, Quat,\
NumSteps, Time, ForceTime, ForcedVel, ForcedVelDot,\
PosDotDef, PsiDotDef, DynOut, OutGrids)
#Write _shape file
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL912_shape.dat'
fp = open(ofile, 'w')
BeamIO.Write_shape_File(fp, len(Time), NumNodes_tot.value, Time, DynOut)
fp.close()
#Write rigid-body velocities
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL912_rigid.dat'
fp = open(ofile, 'w')
BeamIO.Write_rigid_File(fp, Time, ForcedVel, ForcedVelDot)
fp.close()
def Solve_F90_steps(XBINPUT, XBOPTS):
"""@brief Nonlinear dynamic structural solver with time-steps controlled
in Python but solved using F90 routines at each time-step."""
"Check correct solution code"
assert XBOPTS.Solution.value == 312, ('NonlinearDynamic (F90) requested' +\
' with wrong solution code')
"Initialise variables for static analysis"
XBINPUT, XBOPTS, NumNodes_tot, XBELEM, PosIni, PsiIni, XBNODE, NumDof \
= BeamInit.Static(XBINPUT, XBOPTS)
"Change solution code to NonlinearStatic"
XBOPTS.Solution.value = 112
"Set initial conditions as undef config"
PosDefor = PosIni.copy(order='F')
PsiDefor = PsiIni.copy(order='F')
"Solve static"
BeamLib.Cbeam3_Solv_NonlinearStatic(XBINPUT, XBOPTS, NumNodes_tot, XBELEM,\
PosIni, PsiIni, XBNODE, NumDof,\
PosDefor, PsiDefor)
"Write deformed configuration to file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_def.dat'
if XBOPTS.PrintInfo == True:
sys.stdout.write('Writing file %s ... ' % (ofile))
fp = open(ofile, 'w')
fp.write('TITLE="Non-linear static solution: deformed geometry"\n')
fp.write('VARIABLES="iElem" "iNode" "Px" "Py" "Pz" "Rx" "Ry" "Rz"\n')
fp.close()
if XBOPTS.PrintInfo == True:
sys.stdout.write('done\n')
WriteMode = 'a'
BeamIO.OutputElems(XBINPUT.NumElems, NumNodes_tot.value, XBELEM, \
PosDefor, PsiDefor, ofile, WriteMode)
"Change solution code to NonlinearDynamic"
XBOPTS.Solution.value = 312
"Initialise variables for dynamic analysis"
Time, NumSteps, ForceTime, ForcedVel, ForcedVelDot,\
PosDotDef, PsiDotDef,\
OutGrids, PosPsiTime, VelocTime, DynOut\
= BeamInit.Dynamic(XBINPUT,XBOPTS)
"Write _force file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_force.dat'
fp = open(ofile, 'w')
BeamIO.Write_force_File(fp, Time, ForceTime, ForcedVel, ForcedVelDot)
fp.close()
"Write _vel file"
#TODO: write _vel file
"Write .mrb file"
#TODO: write .mrb file
"Save time-dependant variables with only one time step (2 time-steps)"
TimeElements = Time[0:2].copy('F')
Ftime = ForceTime[0:2].copy('F')
Fvel = ForcedVel[0:2, :].copy('F')
FvelDot = ForcedVelDot[0:2, :].copy('F')
"Create Output vectors, one for each time-step"
PosPsiTimeStep = PosPsiTime[0:2, :].copy('F')
VelocTimeStep = VelocTime[0:2, :].copy('F')
DynOutStep = DynOut[0:2 * NumNodes_tot.value, :].copy('F')
"Initialise and approximate initial accelerations as zero arrays"
PosDotDotDef = np.zeros((NumNodes_tot.value, 3), ct.c_double, 'F')
PsiDotDotDef = np.zeros((XBINPUT.NumElems,Settings.MaxElNod,3),\
ct.c_double, 'F')
"Start Time-loop"
for TimeStep in range(0, NumSteps.value):
"Update 2-step time arrays"
TimeElements = Time[TimeStep:TimeStep + 2]
Ftime = ForceTime[TimeStep:TimeStep + 2]
Fvel[:, :] = ForcedVel[TimeStep:TimeStep + 2, :]
FvelDot[:, :] = ForcedVelDot[TimeStep:TimeStep + 2, :]
"Solve dynamic step using f90 solver"
BeamLib.Cbeam3_Solv_NonlinearDynamicAccel(XBINPUT, XBOPTS, NumNodes_tot,\
XBELEM,PosIni, PsiIni, XBNODE, NumDof,\
PosDefor, PsiDefor,\
ct.c_int(1), TimeElements, Ftime, Fvel, FvelDot,\
PosDotDef, PsiDotDef,\
PosDotDotDef, PsiDotDotDef,\
PosPsiTimeStep, VelocTimeStep, DynOutStep, OutGrids)
"Append output information"
PosPsiTime[TimeStep + 1, :] = PosPsiTimeStep[1, :]
VelocTime[TimeStep + 1, :] = VelocTimeStep[1, :]
DynOut[(TimeStep)*NumNodes_tot.value:(TimeStep+1)*NumNodes_tot.value-1,\
: ] = DynOutStep[NumNodes_tot.value:2*NumNodes_tot.value-1]
"END Time-loop"
"Write _dyn file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_dyn.dat'
fp = open(ofile, 'w')
BeamIO.Write_dyn_File(fp, Time, PosPsiTime)
fp.close()
"Write _shape file"
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL312_shape.dat'
fp = open(ofile, 'w')
BeamIO.Write_shape_File(fp, len(Time), NumNodes_tot.value, Time, DynOut)
fp.close()
def Solve_Py(XBINPUT, XBOPTS):
"""Nonlinear dynamic structural solver in Python. Assembly of matrices
is carried out with Fortran subroutines."""
#Check correct solution code
assert XBOPTS.Solution.value == 912, ('NonlinearDynamic requested' +\
' with wrong solution code')
#Initialise beam
XBINPUT, XBOPTS, NumNodes_tot, XBELEM, PosIni, PsiIni, XBNODE, NumDof \
= BeamInit.Static(XBINPUT,XBOPTS)
#Solve static
XBOPTS.Solution.value = 112
PosDefor, PsiDefor = Solve_Py_Static(XBINPUT, XBOPTS)
XBOPTS.Solution.value = 912
#Write deformed configuration to file
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL912_def.dat'
if XBOPTS.PrintInfo == True:
sys.stdout.write('Writing file %s ... ' % (ofile))
fp = open(ofile, 'w')
fp.write('TITLE="Non-linear static solution: deformed geometry"\n')
fp.write('VARIABLES="iElem" "iNode" "Px" "Py" "Pz" "Rx" "Ry" "Rz"\n')
fp.close()
if XBOPTS.PrintInfo == True:
sys.stdout.write('done\n')
WriteMode = 'a'
BeamIO.OutputElems(XBINPUT.NumElems, NumNodes_tot.value, XBELEM, \
PosDefor, PsiDefor, ofile, WriteMode)
#Initialise variables for dynamic analysis
Time, NumSteps, ForceTime, Vrel, VrelDot,\
PosDotDef, PsiDotDef,\
OutGrids, PosPsiTime, VelocTime, DynOut\
= BeamInit.Dynamic(XBINPUT,XBOPTS)
# Delete unused variables.
del OutGrids, VelocTime
#Write _force file
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL912_force.dat'
fp = open(ofile, 'w')
BeamIO.Write_force_File(fp, Time, ForceTime, Vrel, VrelDot)
fp.close()
if XBOPTS.PrintInfo.value == True:
sys.stdout.write('Solve nonlinear dynamic case in Python ... \n')
#Initialise structural system tensors
MssFull = np.zeros((NumDof.value, NumDof.value), ct.c_double, 'F')
CssFull = np.zeros((NumDof.value, NumDof.value), ct.c_double, 'F')
KssFull = np.zeros((NumDof.value, NumDof.value), ct.c_double, 'F')
FstrucFull = np.zeros((NumDof.value, NumDof.value), ct.c_double, 'F')
ms = ct.c_int()
cs = ct.c_int()
ks = ct.c_int()
fs = ct.c_int()
Msr = np.zeros((NumDof.value, 6), ct.c_double, 'F')
Csr = np.zeros((NumDof.value, 6), ct.c_double, 'F')
X = np.zeros(NumDof.value, ct.c_double, 'F')
dXdt = np.zeros(NumDof.value, ct.c_double, 'F')
Force_Dof = np.zeros(NumDof.value, ct.c_double, 'F')
Qstruc = np.zeros(NumDof.value, ct.c_double, 'F')
#Initialise rigid-body system tensors
MrsFull = np.zeros((6, NumDof.value), ct.c_double, 'F')
CrsFull = np.zeros((6, NumDof.value), ct.c_double, 'F')
KrsFull = np.zeros((6, NumDof.value), ct.c_double, 'F')
FrigidFull = np.zeros((6, NumDof.value + 6), ct.c_double, 'F')
mr = ct.c_int()
cr = ct.c_int()
kr = ct.c_int()
fr = ct.c_int()
Mrr = np.zeros((6, 6), ct.c_double, 'F')
Crr = np.zeros((6, 6), ct.c_double, 'F')
Qrigid = np.zeros(6, ct.c_double, 'F')
#Initialise full system tensors
Q = np.zeros(NumDof.value + 6 + 4, ct.c_double, 'F')
DQ = np.zeros(NumDof.value + 6 + 4, ct.c_double, 'F')
dQdt = np.zeros(NumDof.value + 6 + 4, ct.c_double, 'F')
dQddt = np.zeros(NumDof.value + 6 + 4, ct.c_double, 'F')
Force_All = np.zeros(NumDof.value + 6, ct.c_double, 'F')
Msys = np.zeros((NumDof.value + 6 + 4, NumDof.value + 6 + 4), ct.c_double,
'F')
Csys = np.zeros((NumDof.value + 6 + 4, NumDof.value + 6 + 4), ct.c_double,
'F')
Ksys = np.zeros((NumDof.value + 6 + 4, NumDof.value + 6 + 4), ct.c_double,
'F')
Asys = np.zeros((NumDof.value + 6 + 4, NumDof.value + 6 + 4), ct.c_double,
'F')
Qsys = np.zeros(NumDof.value + 6 + 4, ct.c_double, 'F')
#Initialise rotation operators
Quat = np.zeros(4, ct.c_double, 'F')
Quat[0] = 1.0
Cao = XbeamLib.Rot(Quat)
ACoa = np.zeros((6, 6), ct.c_double, 'F')
Cqr = np.zeros((4, 6), ct.c_double, 'F')
Cqq = np.zeros((4, 4), ct.c_double, 'F')
Unit4 = np.zeros((4, 4), ct.c_double, 'F')
for i in range(4):
Unit4[i, i] = 1.0
#Extract initial displacements and velocities
BeamLib.Cbeam_Solv_Disp2State(NumNodes_tot, NumDof, XBINPUT, XBNODE,\
PosDefor, PsiDefor, PosDotDef, PsiDotDef,
X, dXdt)
#Initialise accelerations as zero arrays
PosDotDotDef = np.zeros((NumNodes_tot.value, 3), ct.c_double, 'F')
PsiDotDotDef = np.zeros((XBINPUT.NumElems,Settings.MaxElNod,3),\
ct.c_double, 'F')
#Populate state vector
Q[:NumDof.value] = X.copy('F')
dQdt[:NumDof.value] = dXdt.copy('F')
dQdt[NumDof.value:NumDof.value + 6] = Vrel[0, :].copy('F')
dQdt[NumDof.value + 6:] = Quat.copy('F')
#Force at the first time-step
Force = (XBINPUT.ForceStatic + XBINPUT.ForceDyn * ForceTime[0]).copy('F')
#Assemble matrices and loads for structural dynamic analysis
tmpVrel = Vrel[0, :].copy('F')
tmpQuat = Quat.copy('F')
BeamLib.Cbeam3_Asbly_Dynamic(XBINPUT, NumNodes_tot, XBELEM, XBNODE,\
PosIni, PsiIni, PosDefor, PsiDefor,\
PosDotDef, PsiDotDef, PosDotDotDef, PsiDotDotDef,\
Force, tmpVrel, 0*tmpVrel,\
NumDof, Settings.DimMat,\
ms, MssFull, Msr,\
cs, CssFull, Csr,\
ks, KssFull, fs, FstrucFull,\
Qstruc, XBOPTS, Cao)
BeamLib.f_fem_m2v(ct.byref(NumNodes_tot),\
ct.byref(ct.c_int(6)),\
Force.ctypes.data_as(ct.POINTER(ct.c_double)),\
ct.byref(NumDof),\
Force_Dof.ctypes.data_as(ct.POINTER(ct.c_double)),\
XBNODE.Vdof.ctypes.data_as(ct.POINTER(ct.c_int)) )
Qstruc -= np.dot(FstrucFull, Force_Dof)
#Assemble matrices for rigid-body dynamic analysis
BeamLib.Xbeam_Asbly_Dynamic(XBINPUT, NumNodes_tot, XBELEM, XBNODE,\
PosIni, PsiIni, PosDefor, PsiDefor,\
PosDotDef, PsiDotDef, PosDotDotDef, PsiDotDotDef,\
tmpVrel, 0*tmpVrel, tmpQuat,\
NumDof, Settings.DimMat,\
mr, MrsFull, Mrr,\
cr, CrsFull, Crr, Cqr, Cqq,\
kr, KrsFull, fr, FrigidFull,\
Qrigid, XBOPTS, Cao)
BeamLib.f_fem_m2v_nofilter(ct.byref(NumNodes_tot),\
ct.byref(ct.c_int(6)),\
Force.ctypes.data_as(ct.POINTER(ct.c_double)),\
ct.byref(ct.c_int(NumDof.value+6)),\
Force_All.ctypes.data_as(ct.POINTER(ct.c_double)) )
Qrigid -= np.dot(FrigidFull, Force_All)
#Separate assembly of follower and dead loads
tmpForceTime = ForceTime[0].copy('F')
tmpQforces,Dummy,tmpQrigid = XbeamLib.LoadAssembly(XBINPUT, XBELEM, XBNODE, XBOPTS, NumDof, \
PosIni, PsiIni, PosDefor, PsiDefor, \
(XBINPUT.ForceStatic_foll + XBINPUT.ForceDyn_foll*tmpForceTime), \
(XBINPUT.ForceStatic_dead + XBINPUT.ForceDyn_dead*tmpForceTime), \
Cao,1)
Qstruc -= tmpQforces
Qrigid -= tmpQrigid
#Assemble system matrices
Msys[:NumDof.value, :NumDof.value] = MssFull.copy('F')
Msys[:NumDof.value, NumDof.value:NumDof.value + 6] = Msr.copy('F')
Msys[NumDof.value:NumDof.value + 6, :NumDof.value] = MrsFull.copy('F')
Msys[NumDof.value:NumDof.value + 6,
NumDof.value:NumDof.value + 6] = Mrr.copy('F')
Msys[NumDof.value + 6:, NumDof.value + 6:] = Unit4.copy('F')
Qsys[:NumDof.value] = Qstruc
Qsys[NumDof.value:NumDof.value + 6] = Qrigid
Qsys[NumDof.value + 6:] = np.dot(Cqq, dQdt[NumDof.value + 6:])
#Initial Accel
dQddt[:] = np.dot(np.linalg.inv(Msys), -Qsys)
#Record position of all grid points in global FoR at initial time step
DynOut[0:NumNodes_tot.value, :] = PosDefor
#Position/rotation of the selected node in initial deformed configuration
PosPsiTime[0, :3] = PosDefor[-1, :]
PosPsiTime[0, 3:] = PsiDefor[-1, XBELEM.NumNodes[-1] - 1, :]
#Get gamma and beta for Newmark scheme
gamma = 0.5 + XBOPTS.NewmarkDamp.value
beta = 0.25 * (gamma + 0.5)**2
#Time loop
for iStep in range(NumSteps.value):
if XBOPTS.PrintInfo.value == True:
sys.stdout.write(' Time: %-10.4e\n' % (Time[iStep + 1]))
sys.stdout.write(' SubIter DeltaF DeltaX ResLog10\n')
#calculate dt
dt = Time[iStep + 1] - Time[iStep]
#Predictor step
Q += dt * dQdt + (0.5 - beta) * dQddt * dt**2
dQdt += (1.0 - gamma) * dQddt * dt
dQddt[:] = 0.0
#Force at current time-step
Force = (XBINPUT.ForceStatic + \
XBINPUT.ForceDyn*ForceTime[iStep+1]).copy('F')
#Reset convergence parameters
Iter = 0
ResLog10 = 1.0
#Newton-Raphson loop
while ( (ResLog10 > XBOPTS.MinDelta.value) \
& (Iter < XBOPTS.MaxIterations.value) ):
#set tensors to zero
MssFull[:, :] = 0.0
CssFull[:, :] = 0.0
KssFull[:, :] = 0.0
FstrucFull[:, :] = 0.0
Msr[:, :] = 0.0
Csr[:, :] = 0.0
Qstruc[:] = 0.0
MrsFull[:, :] = 0.0
CrsFull[:, :] = 0.0
KrsFull[:, :] = 0.0
FrigidFull[:, :] = 0.0
Mrr[:, :] = 0.0
Crr[:, :] = 0.0
Qrigid[:] = 0.0
Msys[:, :] = 0.0
Csys[:, :] = 0.0
Ksys[:, :] = 0.0
Asys[:, :] = 0.0
Qsys[:] = 0.0
#Update counter
Iter += 1
if XBOPTS.PrintInfo.value == True:
sys.stdout.write(' %-7d ' % (Iter))
#nodal diplacements and velocities from state vector
X = Q[:NumDof.value].copy('F')
dXdt = dQdt[:NumDof.value].copy('F')
BeamLib.Cbeam3_Solv_State2Disp(XBINPUT, NumNodes_tot, XBELEM, XBNODE,
PosIni, PsiIni, NumDof, X, dXdt,\
PosDefor, PsiDefor, PosDotDef, PsiDotDef)
#rigid-body velocities and orientation from state vector
Vrel[iStep + 1, :] = dQdt[NumDof.value:NumDof.value + 6].copy('F')
VrelDot[iStep + 1, :] = dQddt[NumDof.value:NumDof.value +
6].copy('F')
Quat = dQdt[NumDof.value + 6:].copy('F')
Quat = Quat / np.linalg.norm(Quat)
Cao = XbeamLib.Rot(Quat)
#Assemble matrices and loads for structural dynamic analysis
tmpVrel = Vrel[iStep + 1, :].copy('F')
tmpQuat = Quat.copy('F')
BeamLib.Cbeam3_Asbly_Dynamic(XBINPUT, NumNodes_tot, XBELEM, XBNODE,\
PosIni, PsiIni, PosDefor, PsiDefor,\
PosDotDef, PsiDotDef, PosDotDotDef, PsiDotDotDef,\
Force, tmpVrel, 0*tmpVrel,\
NumDof, Settings.DimMat,\
ms, MssFull, Msr,\
cs, CssFull, Csr,\
ks, KssFull, fs, FstrucFull,\
Qstruc, XBOPTS, Cao)
BeamLib.f_fem_m2v(ct.byref(NumNodes_tot),\
ct.byref(ct.c_int(6)),\
Force.ctypes.data_as(ct.POINTER(ct.c_double)),\
ct.byref(NumDof),\
Force_Dof.ctypes.data_as(ct.POINTER(ct.c_double)),\
XBNODE.Vdof.ctypes.data_as(ct.POINTER(ct.c_int)) )
#Assemble matrices for rigid-body dynamic analysis
BeamLib.Xbeam_Asbly_Dynamic(XBINPUT, NumNodes_tot, XBELEM, XBNODE,\
PosIni, PsiIni, PosDefor, PsiDefor,\
PosDotDef, PsiDotDef, PosDotDotDef, PsiDotDotDef,\
tmpVrel, 0*tmpVrel, tmpQuat,\
NumDof, Settings.DimMat,\
mr, MrsFull, Mrr,\
cr, CrsFull, Crr, Cqr, Cqq,\
kr, KrsFull, fs, FrigidFull,\
Qrigid, XBOPTS, Cao)
BeamLib.f_fem_m2v_nofilter(ct.byref(NumNodes_tot),\
ct.byref(ct.c_int(6)),\
Force.ctypes.data_as(ct.POINTER(ct.c_double)),\
ct.byref(ct.c_int(NumDof.value+6)),\
Force_All.ctypes.data_as(ct.POINTER(ct.c_double)) )
#Residual at first iteration
if (Iter == 1):
Res0_Qglobal = max(max(abs(Qsys)), 1)
Res0_DeltaX = max(max(abs(DQ)), 1)
#Assemble discrete system matrices with linearised quaternion equations
Msys[:NumDof.value, :NumDof.value] = MssFull.copy('F')
Msys[:NumDof.value, NumDof.value:NumDof.value + 6] = Msr.copy('F')
Msys[NumDof.value:NumDof.value +
6, :NumDof.value] = MrsFull.copy('F')
Msys[NumDof.value:NumDof.value + 6,
NumDof.value:NumDof.value + 6] = Mrr.copy('F')
Msys[NumDof.value + 6:, NumDof.value + 6:] = Unit4.copy('F')
Csys[:NumDof.value, :NumDof.value] = CssFull.copy('F')
Csys[:NumDof.value, NumDof.value:NumDof.value + 6] = Csr.copy('F')
Csys[NumDof.value:NumDof.value +
6, :NumDof.value] = CrsFull.copy('F')
Csys[NumDof.value:NumDof.value + 6,
NumDof.value:NumDof.value + 6] = Crr.copy('F')
Csys[NumDof.value + 6:,
NumDof.value:NumDof.value + 6] = Cqr.copy('F')
Csys[NumDof.value + 6:, NumDof.value + 6:] = Cqq.copy('F')
Ksys[:NumDof.value, :NumDof.value] = KssFull.copy('F')
Ksys[NumDof.value:NumDof.value +
6, :NumDof.value] = KrsFull.copy('F')
#Separate assembly of follower and dead loads
tmpForceTime = ForceTime[iStep + 1].copy('F')
tmpQforces,Dummy,tmpQrigid = XbeamLib.LoadAssembly(XBINPUT, XBELEM, XBNODE, XBOPTS, NumDof, \
PosIni, PsiIni, PosDefor, PsiDefor, \
(XBINPUT.ForceStatic_foll + XBINPUT.ForceDyn_foll*tmpForceTime), \
(XBINPUT.ForceStatic_dead + XBINPUT.ForceDyn_dead*tmpForceTime), \
Cao,1)
Qstruc -= tmpQforces
Qrigid -= tmpQrigid
#Compute residual
Qstruc += -np.dot(FstrucFull, Force_Dof)
Qrigid += -np.dot(FrigidFull, Force_All)
Qsys[:NumDof.value] = Qstruc
Qsys[NumDof.value:NumDof.value + 6] = Qrigid
Qsys[NumDof.value + 6:] = np.dot(Cqq, dQdt[NumDof.value + 6:])
Qsys += np.dot(Msys, dQddt)
#Calculate system matrix for update calculation
Asys = Ksys + \
Csys*gamma/(beta*dt) + \
Msys/(beta*dt**2)
#Compute correction
DQ[:] = np.dot(np.linalg.inv(Asys), -Qsys)
Q += DQ
dQdt += DQ * gamma / (beta * dt)
dQddt += DQ / (beta * dt**2)
#Update convergence criteria
if XBOPTS.PrintInfo.value == True:
sys.stdout.write('%-10.4e ' % (max(abs(Qsys))))
Res_Qglobal = max(abs(Qsys))
Res_DeltaX = max(abs(DQ))
ResLog10 = max(Res_Qglobal / Res0_Qglobal,
Res_DeltaX / Res0_DeltaX)
if XBOPTS.PrintInfo.value == True:
sys.stdout.write('%-10.4e %8.4f\n' % (max(abs(DQ)), ResLog10))
#END Netwon-Raphson
#update to converged nodal displacements and velocities
X = Q[:NumDof.value].copy('F')
dXdt = dQdt[:NumDof.value].copy('F')
BeamLib.Cbeam3_Solv_State2Disp(XBINPUT, NumNodes_tot, XBELEM, XBNODE,
PosIni, PsiIni, NumDof, X, dXdt,\
PosDefor, PsiDefor, PosDotDef, PsiDotDef)
PosPsiTime[iStep + 1, :3] = PosDefor[(NumNodes_tot.value - 1) / 2 +
1, :]
PosPsiTime[iStep + 1, 3:] = PsiDefor[-1, XBELEM.NumNodes[-1] - 1, :]
#Position of all grid points in global FoR
i1 = (iStep + 1) * NumNodes_tot.value
i2 = (iStep + 2) * NumNodes_tot.value
DynOut[i1:i2, :] = PosDefor
#Export rigid-body velocities/accelerations
if XBOPTS.OutInaframe.value == True:
Vrel[iStep + 1, :] = dQdt[NumDof.value:NumDof.value + 6].copy('F')
VrelDot[iStep + 1, :] = dQddt[NumDof.value:NumDof.value +
6].copy('F')
else:
Quat = dQdt[NumDof.value + 6:].copy('F')
Quat = Quat / np.linalg.norm(Quat)
Cao = XbeamLib.Rot(Quat)
ACoa[:3, :3] = np.transpose(Cao)
ACoa[3:, 3:] = np.transpose(Cao)
Vrel[iStep + 1, :] = np.dot(
ACoa, dQdt[NumDof.value:NumDof.value + 6].copy('F'))
VrelDot[iStep + 1, :] = np.dot(
ACoa, dQddt[NumDof.value:NumDof.value + 6].copy('F'))
#END Time loop
#Write _dyn file
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL912_dyn.dat'
fp = open(ofile, 'w')
BeamIO.Write_dyn_File(fp, Time, PosPsiTime)
fp.close()
#Write _shape file
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL912_shape.dat'
fp = open(ofile, 'w')
BeamIO.Write_shape_File(fp, len(Time), NumNodes_tot.value, Time, DynOut)
fp.close()
#Write rigid-body velocities
ofile = Settings.OutputDir + Settings.OutputFileRoot + '_SOL912_rigid.dat'
fp = open(ofile, 'w')
BeamIO.Write_rigid_File(fp, Time, Vrel, VrelDot)
fp.close()
if XBOPTS.PrintInfo.value == True:
sys.stdout.write(' ... done\n')