def SolveStatic(
mbs,
simulationSettings=exudyn.SimulationSettings(),
updateInitialValues=False,
storeSolver=True,
showHints=False,
showCausingItems=True,
):
staticSolver = exudyn.MainSolverStatic()
if storeSolver:
mbs.sys[
'staticSolver'] = staticSolver #copy solver structure to sys variable
mbs.sys[
'simulationSettings'] = simulationSettings #link to last simulation settings
success = False
try:
success = staticSolver.SolveSystem(mbs, simulationSettings)
except:
pass
#print error message after except, to catch all errors
if not success:
# exudyn.Print not shown in Spyder at this time (because of exception?)
# exudyn.Print(SolverErrorMessage(staticSolver, mbs, isStatic=True, showCausingObjects=showCausingItems,
# showCausingNodes=showCausingItems, showHints=showHints))
print(
SolverErrorMessage(staticSolver,
mbs,
isStatic=True,
showCausingObjects=showCausingItems,
showCausingNodes=showCausingItems,
showHints=showHints))
raise ValueError("SolveStatic terminated due to errors")
elif updateInitialValues:
currentState = mbs.systemData.GetSystemState() #get current values
mbs.systemData.SetSystemState(
systemStateList=currentState,
configuration=exudyn.ConfigurationType.Initial)
return success
if exudynTestGlobals.useGraphics: #only start graphics once, but after background is set
exu.StartRenderer()
simulationSettings.staticSolver.numberOfLoadSteps = 10
simulationSettings.staticSolver.adaptiveStep = True
import numpy as np
testRefVal = 0
#compute eigenvalues manually:
calcEig = True
if calcEig:
from scipy.linalg import solve, eigh, eig #eigh for symmetric matrices, positive definite
staticSolver = exu.MainSolverStatic()
#staticSolver.SolveSystem(mbs, simulationSettings)
staticSolver.InitializeSolver(mbs, simulationSettings)
staticSolver.ComputeMassMatrix(mbs)
m = staticSolver.GetSystemMassMatrix()
#exu.Print("m =",m)
staticSolver.ComputeJacobianODE2RHS(mbs)
staticSolver.ComputeJacobianAE(mbs)
K = staticSolver.GetSystemJacobian()
#exu.Print("K =",K)
nODE2 = staticSolver.GetODE2size()
def ComputeODE2Eigenvalues(mbs,
simulationSettings=exudyn.SimulationSettings(),
useSparseSolver=False,
numberOfEigenvalues=0,
setInitialValues=True,
convert2Frequencies=False):
import numpy as np
#use static solver, as it does not include factors from time integration (and no velocity derivatives) in the jacobian
staticSolver = exudyn.MainSolverStatic()
#initialize solver with initial values
staticSolver.InitializeSolver(mbs, simulationSettings)
staticSolver.ComputeMassMatrix(mbs)
M = staticSolver.GetSystemMassMatrix()
staticSolver.ComputeJacobianODE2RHS(
mbs) #compute ODE2 part of jacobian ==> stored internally in solver
staticSolver.ComputeJacobianAE(
mbs) #compute algebraic part of jacobian (not needed here...)
jacobian = staticSolver.GetSystemJacobian() #read out stored jacobian
nODE2 = staticSolver.GetODE2size()
#obtain ODE2 part from jacobian == stiffness matrix
K = jacobian[0:nODE2, 0:nODE2]
if not useSparseSolver:
from scipy.linalg import eigh #eigh for symmetric matrices, positive definite; eig for standard eigen value problems
[eigenValuesUnsorted, eigenVectors
] = eigh(K,
M) #this gives omega^2 ... squared eigen frequencies (rad/s)
eigenValues = np.sort(
a=abs(eigenValuesUnsorted)) #eigh returns unsorted eigenvalues...
if numberOfEigenvalues > 0:
eigenValues = eigenValues[0:numberOfEigenvalues]
eigenVectors = eigenVectors[0:numberOfEigenvalues]
else:
if numberOfEigenvalues == 0: #compute all eigenvalues
numberOfEigenvalues = nODE2
from scipy.sparse.linalg import eigsh, csr_matrix #eigh for symmetric matrices, positive definite
Kcsr = csr_matrix(K)
Mcsr = csr_matrix(M)
#use "LM" (largest magnitude), but shift-inverted mode with sigma=0, to find the zero-eigenvalues:
#see https://docs.scipy.org/doc/scipy/reference/tutorial/arpack.html
[eigenValues, eigenVectors] = eigsh(A=Kcsr,
k=numberOfEigenvalues,
M=Mcsr,
which='LM',
sigma=0,
mode='normal')
#sort eigenvalues
eigenValues = np.sort(a=abs(eigenValues))
if convert2Frequencies:
eigenFrequencies = np.sqrt(eigenValues) / (2 * np.pi)
return [eigenFrequencies, eigenVectors]
else:
return [eigenValues, eigenVectors]