Predefined solutions

Convenience classes and functions to define solution procedures.

class solution.predefined_solutions.BucklingAnalysisEigenPart(prb, staticAnalysisPart, name=None, printFlag=0, soeType: Optional[str] = None, solverType: Optional[str] = None, shift: float = 0.0)

Bases: solution.predefined_solutions.SolutionProcedure

Eigenvalue part of a linear buckling analysis.

setup()

Defines the solution procedure in the finite element problem object.

class solution.predefined_solutions.BucklingAnalysisStaticPart(prb, name=None, constraintHandlerType='transformation', maxNumIter=100, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType=None, soeType: Optional[str] = None, solverType: Optional[str] = None, solutionAlgorithmType='krylov_newton_soln_algo')

Bases: solution.predefined_solutions.SolutionProcedure

Static analysis part of a linear buckling analysis.

class solution.predefined_solutions.DisplacementControlBase(prb, node, dof, increment, numSteps, name, constraintHandlerType, maxNumIter, convergenceTestTol, printFlag, numberingMethod, convTestType, soeType, solverType, solutionAlgorithmType)

Bases: solution.predefined_solutions.SolutionProcedure

Base class for displacement control analysis.

Variables

  • dispControlNode – node whose response controls solution.

  • dispControlDof – degree of freedom that controls solution.

  • dispControlIncrement – first displacement increment.

class solution.predefined_solutions.FrequencyAnalysis(prb, name=None, printFlag=0, systemPrefix='sym_band', numberingMethod='rcm', shift: Optional[float] = None)

Bases: solution.predefined_solutions.SolutionProcedure

Return a natural frequency computation procedure.

class solution.predefined_solutions.IllConditioningAnalysis(prb, name=None, printFlag=0, systemPrefix='band_arpack', shift: float = 0.0)

Bases: solution.predefined_solutions.IllConditioningAnalysisBase

Procedure to obtain the modes associated with very small eigenvalues of the stiffness matrix.

class solution.predefined_solutions.IllConditioningAnalysisBase(prb, name=None, printFlag=0, systemPrefix='sym_band_eigen', shift: Optional[float] = None, numberingMethod='rcm')

Bases: solution.predefined_solutions.SolutionProcedure

Base class for ill-conditioning solution procedures.

class solution.predefined_solutions.LineSearchBase(prb, name, constraintHandlerType, maxNumIter, convergenceTestTol, printFlag, numSteps, numberingMethod, convTestType, lineSearchMethod, soeType, solverType, integratorType, solutionAlgorithmType)

Bases: solution.predefined_solutions.SolutionProcedure

Base class for line search solution aggregations.

Variables

lineSearchMethod – line search method to use (bisection_line_search, initial_interpolated_line_search, regula_falsi_line_search, secant_line_search).

setup()

Defines the solution procedure in the finite element problem object.

class solution.predefined_solutions.LinearBucklingAnalysis(prb, numModes, constraintHandlerType='transformation', numberingMethod='rcm', convTestType='norm_disp_incr_conv_test', convergenceTestTol=1e-08, maxNumIter=1000, soeType='band_gen_lin_soe', solverType='band_gen_lin_lapack_solver', solutionAlgorithmType='krylov_newton_soln_algo', eigenSOEType='band_arpackpp_soe', eigenSolverType='band_arpackpp_solver', printFlag=0)

Bases: object

Linear buckling analysis.

Variables

  • feProblem – XC finite element problem.

  • numModes – number of buckling modes to compute.

  • constraintHandlerType – type of the constraint handler to use.

  • numberingMethod – numbering method (plain or reverse Cuthill-McKee or alternative minimum degree).

  • convTestType – convergence test type for non linear analysis (norm unbalance,…).

  • convergenceTestTol – convergence tolerance (defaults to 1e-8).

  • maxNumIter – maximum number of iterations (defauts to 1000).

  • soeType – type of the system of equations object for the static part of the analysis.

  • solverType – type of the solver for the static part of the analysis.

  • solutionAlgorithmType – type of the solution algorithm for the static part of the analysis.

  • eigenSOEType – type of the system of equations object for the eigenproblem part of the analysis.

  • eigenSolverType – type of the solver for the eigenproblem part of the analysis.

analysisSetup()

Define the analysis object.

Parameters

analysisType – type of the analysis to perform.

setup()

Defines the solution procedure in the finite element problem object.

soluControlSetup()

Defines the solution control object.

solve()

Compute the linear buckling modes.

class solution.predefined_solutions.NewmarkBase(prb, timeStep, name, constraintHandlerType, maxNumIter, convergenceTestTol, printFlag, numSteps, numberingMethod, convTestType, soeType, solverType, gamma=0.5, beta=0.25, solutionAlgorithmType='newton_raphson_soln_algo', analysisType='direct_integration_analysis')

Bases: solution.predefined_solutions.SolutionProcedure

Base class for Newmark solvers.

Variables

  • gamma – gamma factor (used only for Newmark integrator).

  • beta – beta factor (used only for Newmark integrator).

solve(calculateNodalReactions=False, includeInertia=False, reactionCheckTolerance=1e-12)

Compute the solution (run the analysis).

Parameters

  • calculateNodalReactions – if true calculate reactions at nodes.

  • includeInertia – if true calculate reactions including inertia effects.

  • reactionCheckTolerance – tolerance when checking reaction values.

class solution.predefined_solutions.OrdinaryEigenvalues(prb, name=None, printFlag=0, systemPrefix='sym_band_lapack', numberingMethod='rcm', shift: Optional[float] = None)

Bases: solution.predefined_solutions.SolutionProcedure

Procedure to obtain the ordinary eigenvalues of the stiffness matrix of the finite element model.

class solution.predefined_solutions.PenaltyKrylovNewton(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_disp_incr_conv_test', integratorType: str = 'load_control_integrator', maxDim=6)

Bases: solution.predefined_solutions.SolutionProcedure

KrylovNewton algorithm object which uses a Krylov subspace

accelerator to accelerate the convergence of the modified newton method.

See appendix C. Analysis model script of the document “Finite Element Modeling of Gusset Plate Failure Using Opensees” Andrew J. Walker. Oregon State University

setup()

Defines the solution procedure in the finite element problem object.

class solution.predefined_solutions.PenaltyModifiedNewton(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='relative_total_norm_disp_incr_conv_test', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.PenaltyModifiedNewtonBase

Static solution procedure with a modified Newton algorithm and a penalty constraint handler.

class solution.predefined_solutions.PenaltyModifiedNewtonBase(prb, name, maxNumIter, convergenceTestTol, printFlag, numSteps, numberingMethod, convTestType='relative_total_norm_disp_incr_conv_test', soeType='sparse_gen_col_lin_soe', solverType='super_lu_solver', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.SolutionProcedure

Base class for penalty modified Newton solution aggregation.

class solution.predefined_solutions.PenaltyModifiedNewtonMUMPS(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='relative_total_norm_disp_incr_conv_test', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.PenaltyModifiedNewtonBase

Static solution procedure with a modified Newton algorithm, a penalty constraint handler and a MUMPS (parallel sparse direct solver) solver.

class solution.predefined_solutions.PenaltyModifiedNewtonUMF(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='relative_total_norm_disp_incr_conv_test', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.PenaltyModifiedNewtonBase

Static solution procedure with a modified Newton algorithm, a penalty constraint handler and a UMF (Unsimmetric multi-frontal method) solver.

class solution.predefined_solutions.PenaltyNewmarkNewtonRaphson(prb, timeStep, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_disp_incr_conv_test', soeType='profile_spd_lin_soe', solverType='profile_spd_lin_direct_solver', gamma=0.5, beta=0.25)

Bases: solution.predefined_solutions.NewmarkBase

Newmark solution procedure with a Newton Raphson algorithm and a penalty constraint handler.

class solution.predefined_solutions.PenaltyNewtonLineSearch(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='relative_total_norm_disp_incr_conv_test', lineSearchMethod='regula_falsi_line_search', integratorType='load_control_integrator')

Bases: solution.predefined_solutions.PenaltyNewtonLineSearchBase

Static solution procedure with a Newton line search algorithm and a penalty constraint handler.

class solution.predefined_solutions.PenaltyNewtonLineSearchBase(prb, name, maxNumIter, convergenceTestTol, printFlag, numSteps, numberingMethod, convTestType, lineSearchMethod, soeType, solverType, integratorType='load_control_integrator')

Bases: solution.predefined_solutions.LineSearchBase

Base class for penalty Newton line search solution aggregation.

class solution.predefined_solutions.PenaltyNewtonLineSearchMUMPS(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='relative_total_norm_disp_incr_conv_test', lineSearchMethod='regula_falsi_line_search', integratorType='load_control_integrator')

Bases: solution.predefined_solutions.PenaltyNewtonLineSearchBase

Static solution procedure with a Newton line search algorithm, a penalty constraint handler and a MUMPS (parallel sparse direct solver) solver.

class solution.predefined_solutions.PenaltyNewtonLineSearchUMF(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='relative_total_norm_disp_incr_conv_test', lineSearchMethod='regula_falsi_line_search', integratorType='load_control_integrator')

Bases: solution.predefined_solutions.PenaltyNewtonLineSearchBase

Static solution procedure with a Newton line search algorithm, a penalty constraint handler and a UMF (Unsimmetric multi-frontal method) solver.

class solution.predefined_solutions.PenaltyNewtonRaphson(prb, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_unbalance_conv_test', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.PenaltyNewtonRaphsonBase

Return a static solution procedure with a Newton Raphson algorithm and a penalty constraint handler.

class solution.predefined_solutions.PenaltyNewtonRaphsonBase(prb, name, maxNumIter, convergenceTestTol, printFlag, numSteps, numberingMethod, convTestType, soeType, solverType, integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.SolutionProcedure

Base class for penalty Newton-Raphson solution aggregation.

class solution.predefined_solutions.PenaltyNewtonRaphsonMUMPS(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_unbalance_conv_test', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.PenaltyNewtonRaphsonBase

Static solution procedure with a Newton algorithm, a penalty constraint handler and a MUMPS (parallel sparse direct solver) solver.

class solution.predefined_solutions.PenaltyNewtonRaphsonUMF(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_unbalance_conv_test', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.PenaltyNewtonRaphsonBase

Static solution procedure with a Newton algorithm, a penalty constraint handler and a UMF (Unsimmetric multi-frontal method) solver.

class solution.predefined_solutions.PenaltyStaticLinearBase(prb, name=None, printFlag=0, numSteps=1, numberingMethod='rcm', soeType='band_spd_lin_soe', solverType='band_spd_lin_lapack_solver', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.SolutionProcedure

Base class for linear static solution algorithm with a penalty constraint handler.

class solution.predefined_solutions.PlainKrylovNewton(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='simple', convTestType='energy_incr_conv_test', soeType='umfpack_gen_lin_soe', solverType='umfpack_gen_lin_solver', integratorType: str = 'load_control_integrator', maxDim=6)

Bases: solution.predefined_solutions.SolutionProcedure

KrylovNewton algorithm object which uses a Krylov subspace

accelerator to accelerate the convergence of the modified newton method.

See appendix C. Analysis model script of the document “Finite Element Modeling of Gusset Plate Failure Using Opensees” Andrew J. Walker. Oregon State University

setup()

Defines the solution procedure in the finite element problem object.

class solution.predefined_solutions.PlainLinearNewmark(prb, timeStep, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='simple', gamma=0.5, beta=0.25)

Bases: solution.predefined_solutions.NewmarkBase

Return a linear Newmark solution algorithm with a plain constraint handler.

class solution.predefined_solutions.PlainNewtonRaphson(prb, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_unbalance_conv_test', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.SolutionProcedure

Newton-Raphson solution algorithm with a plain constraint handler.

class solution.predefined_solutions.PlainNewtonRaphsonBandGen(prb, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_unbalance_conv_test', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.SolutionProcedure

Newton-Raphson solution algorithm with a plain constraint handler and a band general SOE solver.

class solution.predefined_solutions.PlainNewtonRaphsonMUMPS(prb, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_unbalance_conv_test', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.SolutionProcedure

Newton-Raphson solution algorithm with a plain constraint handler and a band general SOE solver.

class solution.predefined_solutions.PlainStaticModifiedNewton(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='relative_total_norm_disp_incr_conv_test', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.SolutionProcedure

Static solution procedure with a modified Newton solution algorithm with a plain constraint handler.

class solution.predefined_solutions.SimpleLagrangeStaticLinear(prb, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.SolutionProcedure

Linear static solution algorithm with a Lagrange constraint handler.

class solution.predefined_solutions.SimpleNewtonRaphsonDisplacementControl(prb, node, dof, increment, numSteps, name=None, maxNumIter=10, convergenceTestTol=1e-12, printFlag=0, numberingMethod='rcm', convTestType='norm_disp_incr_conv_test')

Bases: solution.predefined_solutions.DisplacementControlBase

Newton-Raphson solution algorithm with a plain constraint handler and a band general SOE solver.

class solution.predefined_solutions.SimpleStaticLinear(prb, name=None, printFlag=0, numSteps=1, numberingMethod='rcm', soeType='band_spd_lin_soe', solverType='band_spd_lin_lapack_solver', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.PenaltyStaticLinearBase

Return a linear static solution algorithm with a penalty constraint handler.

class solution.predefined_solutions.SimpleStaticLinearMUMPS(prb, name=None, printFlag=0, numSteps=1, numberingMethod='rcm', soeType='mumps_soe', solverType='mumps_solver', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.PenaltyStaticLinearBase

Return a linear static solution algorithm with a penalty constraint handler.

class solution.predefined_solutions.SimpleStaticLinearUMF(prb, name=None, printFlag=0, numSteps=1, numberingMethod='rcm', soeType='umfpack_gen_lin_soe', solverType='umfpack_gen_lin_solver', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.PenaltyStaticLinearBase

Return a linear static solution algorithm with a penalty constraint handler.

class solution.predefined_solutions.SimpleTransformationStaticLinear(prb, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.SolutionProcedure

Linear static solution algorithm with a transformation constraint handler.

class solution.predefined_solutions.SolutionProcedure(name=None, constraintHandlerType='plain', maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType=None, soeType: Optional[str] = None, solverType: Optional[str] = None, shift: Optional[float] = None, integratorType: str = 'load_control_integrator', solutionAlgorithmType='linear_soln_algo', analysisType='static_analysis')

Bases: object

Variables

  • solutionStrategy – object that aggregates all the component objects that define the type of analysis (constraint handler, DOF_Numberer, integrator, solution algorithm, system of equations, convergence test)

  • cHandler – constraint handler. Determines how the constraint equations are enforced in the analysis, how it handles the boundary conditions/imposed displacements

  • numberer – DOF numberer. Determines the mapping between equation numbers and degrees of freedom (how DOF are numbered)

  • integ –

    integrator, used to:

    • determine the predictive step for time t+dt

    • specify the tangent matrix and residual vector at any iteration

    • determine the corrective step based on the displacement increment

  • solutionAlgorithmType – type of the solution algorithm.

  • solAlgo –

    solution algorithm, which determines the sequence of steps taken to solve the non-linear equation:

    • linear

    • Newton Raphson (the tangent is updated at each iteration)

    • Newton with Line Search

    • Modified Newton Raphson (the tangent is not updated at

    each iteration) - Kyrlov-Newton - BFGS, for symetric systems - Broyden

  • soe – sparse system of equations: band general, band SPD, profile SPD, sparse general, umfPack, sparse SPD

  • solver – solver for the system of equations.

  • analysis – determines what type of analysis is to be performed

  • convergenceTestTol – convergence tolerance (defaults to 1e-9)

  • printFlag – if not zero print convergence results on each step.

  • numSteps – number of steps to use in the analysis (useful only when loads are variable in time).

  • numberingMethod – numbering method (plain or reverse Cuthill-McKee or alternative minimum degree).

  • convTestType – convergence test type for non linear analysis (norm unbalance,…).

  • integratorType – integrator type (see integratorSetup).

  • soeType – type of the system of equations object.

  • solverType – type of the solver.

  • maxNumIter – maximum number of iterations (defauts to 10)

  • numSteps – number of steps to use in the analysis (useful only when loads are variable in time).

  • solu –

  • solCtrl –

  • modelWrapper – model representation for the analysis.

  • shift – shift-and-invert mode (used with ARPACK).

analysisSetup()

Create the analysis object.

clear()

Wipe out the solution procedure.

constraintHandlerSetup()

Define the constraint handler and return a reference to it.

getConvergenceTest()

Return the convergence test.

getModelWrapperName()

Return the name for the model wrapper.

getSolutionStrategyName()

Return the name for the model wrapper.

integratorSetup()

Define the type of integrator to use in the analysis.

linearSolutionAlgorithm()

Return true if the solution algorithm is linear, false otherwise.

modelWrapperSetup()

Defines the model wrapper.

resetLoadCase()

Remove previous load from the domain.

setArcLengthIntegratorParameters(arcLength, alpha=1.0)

Set the values of the Arc-Length integrator.

Parameters

  • arcLength – radius of desired intersection with the equilibrium path.

  • alpha – scaling factor on the reference loads.

setPenaltyFactors(alphaSP=1000000000000000.0, alphaMP=1000000000000000.0)

Define the penalty factors to use with the penalty constraint handler.

Parameters

  • alphaSP – penalty factor on single points constraints (defaults to 1e15).

  • alphaMP – penalty factor on multi-poing constraints (defaults to 1e15).

setup()

Defines the solution procedure in the finite element problem object.

soluControlSetup()

Defines the solution control object.

solutionAlgorithmSetup()

Define the solution strategy.

solve(calculateNodalReactions=False, includeInertia=False, reactionCheckTolerance=1e-12)

Compute the solution (run the analysis).

Parameters

  • calculateNodalReactions – if true calculate reactions at nodes.

  • includeInertia – if true calculate reactions including inertia effects.

  • reactionCheckTolerance – tolerance when checking reaction values.

solveComb(combName, calculateNodalReactions=False, includeInertia=False, reactionCheckTolerance=1e-12)

Obtains the solution for the combination argument.

Parameters

  • combName – name of the combination to obtain the response for.

  • calculateNodalReactions – if true calculate reactions at nodes.

  • includeInertia – if true calculate reactions including inertia effects.

  • reactionCheckTolerance – tolerance when checking reaction values.

sysOfEqnSetup()

Defines the solver to use for the resulting system of equations.

class solution.predefined_solutions.SpectraLinearBucklingAnalysis(prb, numModes, constraintHandlerType='transformation', numberingMethod='rcm', convTestType='norm_disp_incr_conv_test', convergenceTestTol=1e-08, maxNumIter=1000, soeType='band_gen_lin_soe', solverType='band_gen_lin_lapack_solver', solutionAlgorithmType='krylov_newton_soln_algo', eigenSOEType='spectra_soe', eigenSolverType='spectra_solver', printFlag=0)

Bases: solution.predefined_solutions.LinearBucklingAnalysis

Linear buckling analysis that uses Spectra library to solve the eigenproblem part.

class solution.predefined_solutions.TRBDF2Base(prb, timeStep, name, constraintHandlerType, maxNumIter, convergenceTestTol, printFlag, numSteps, numberingMethod, convTestType, soeType, solverType, solutionAlgorithmType, analysisType)

Bases: solution.predefined_solutions.SolutionProcedure

Base class for TRBDF2 solvers.

solve(calculateNodalReactions=False, includeInertia=False, reactionCheckTolerance=1e-12)

Compute the solution (run the analysis).

Parameters

  • calculateNodalReactions – if true calculate reactions at nodes.

  • includeInertia – if true calculate reactions including inertia effects.

  • reactionCheckTolerance – tolerance when checking reaction values.

class solution.predefined_solutions.TRBDF3Base(prb, timeStep, name, constraintHandlerType, maxNumIter, convergenceTestTol, printFlag, numSteps, numberingMethod, convTestType, soeType, solverType, solutionAlgorithmType, analysisType)

Bases: solution.predefined_solutions.SolutionProcedure

Base class for TRBDF3 solvers.

solve(calculateNodalReactions=False, includeInertia=False, reactionCheckTolerance=1e-12)

Compute the solution (run the analysis).

Parameters

  • calculateNodalReactions – if true calculate reactions at nodes.

  • includeInertia – if true calculate reactions including inertia effects.

  • reactionCheckTolerance – tolerance when checking reaction values.

class solution.predefined_solutions.TransformationNewmarkNewtonRaphson(prb, timeStep, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_disp_incr_conv_test', soeType='profile_spd_lin_soe', solverType='profile_spd_lin_direct_solver', gamma=0.5, beta=0.25)

Bases: solution.predefined_solutions.NewmarkBase

Newmark solution procedure with a Newton Raphson algorithm and a transformation constraint handler.

class solution.predefined_solutions.TransformationNewtonLineSearch(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='relative_total_norm_disp_incr_conv_test', lineSearchMethod='regula_falsi_line_search', integratorType='load_control_integrator')

Bases: solution.predefined_solutions.TransformationNewtonLineSearchBase

Static solution procedure with a Newton line search algorithm and a transformation constraint handler.

class solution.predefined_solutions.TransformationNewtonLineSearchBase(prb, name, maxNumIter, convergenceTestTol, printFlag, numSteps, numberingMethod, convTestType, lineSearchMethod, soeType, solverType, integratorType='load_control_integrator')

Bases: solution.predefined_solutions.LineSearchBase

Base class for transformation Newton line search solution aggregation.

class solution.predefined_solutions.TransformationNewtonLineSearchMUMPS(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='relative_total_norm_disp_incr_conv_test', lineSearchMethod='regula_falsi_line_search', integratorType='load_control_integrator')

Bases: solution.predefined_solutions.TransformationNewtonLineSearchBase

Static solution procedure with a Newton line search algorithm, a transformation constraint handler and a MUMPS (parallel sparse direct solver) solver.

class solution.predefined_solutions.TransformationNewtonLineSearchUMF(prb, name=None, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='relative_total_norm_disp_incr_conv_test', lineSearchMethod='regula_falsi_line_search', integratorType='load_control_integrator')

Bases: solution.predefined_solutions.TransformationNewtonLineSearchBase

Static solution procedure with a Newton line search algorithm, a transformation constraint handler and a UMF (Unsimmetric multi-frontal method) solver.

class solution.predefined_solutions.TransformationNewtonRaphsonBandGen(prb, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_unbalance_conv_test', integratorType: str = 'load_control_integrator')

Bases: solution.predefined_solutions.SolutionProcedure

Newton-Raphson solution algorithm with a plain constraint handler and a band general SOE solver.

class solution.predefined_solutions.TransformationTRBDF2NewtonRaphson(prb, timeStep, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_unbalance_conv_test', soeType='profile_spd_lin_soe', solverType='profile_spd_lin_direct_solver')

Bases: solution.predefined_solutions.TRBDF2Base

TRBDF2 solution procedure with a Newton Raphson algorithm and a transformation constraint handler.

class solution.predefined_solutions.TransformationTRBDF3NewtonRaphson(prb, timeStep, name=None, maxNumIter=10, convergenceTestTol=1e-09, printFlag=0, numSteps=1, numberingMethod='rcm', convTestType='norm_unbalance_conv_test', soeType='profile_spd_lin_soe', solverType='profile_spd_lin_direct_solver')

Bases: solution.predefined_solutions.TRBDF3Base

TRBDF3 solution procedure with a Newton Raphson algorithm and a transformation constraint handler.

class solution.predefined_solutions.ZeroEnergyModes(prb, name=None, printFlag=0, systemPrefix='sym_band_eigen', shift: Optional[float] = None)

Bases: solution.predefined_solutions.IllConditioningAnalysisBase

Procedure to obtain the zero energy modes of the finite element model.

solution.predefined_solutions.frequency_analysis(prb, systemPrefix='sym_band', shift: Optional[float] = None)

Return a solution procedure that computes the natural frequencies of the model.

solution.predefined_solutions.ill_conditioning_analysis(prb)

Return a solution procedure that computes the modes that correspond to ill-conditioned degrees of freedom.

solution.predefined_solutions.ordinary_eigenvalues(prb)

Return a solution procedure that computes the ordinary eigenvalues of the model stiffness matrix.

solution.predefined_solutions.penalty_modified_newton(prb, maxNumIter=10, convergenceTestTol=0.0001, printFlag=0, convTestType='relative_total_norm_disp_incr_conv_test')

Return a simple static modified Newton solution procedure.

Parameters

  • maxNumIter – maximum number of iterations (defauts to 10)

  • convergenceTestTol – convergence tolerance (defaults to 1e-9)

  • printFlag – print message on each iteration

solution.predefined_solutions.penalty_newton_line_search_mumps(prb, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, convTestType='relative_total_norm_disp_incr_conv_test', lineSearchMethod='regula_falsi_line_search', integratorType='load_control_integrator')

Return a simple static modified Newton solution procedure.

Parameters

  • maxNumIter – maximum number of iterations (defauts to 10)

  • convergenceTestTol – convergence tolerance (defaults to 1e-9)

  • printFlag – print message on each iteration

  • integratorType – integrator type (see integratorSetup).

solution.predefined_solutions.penalty_newton_raphson(prb, maxNumIter=10, convergenceTestTol=0.0001, printFlag=0)

Return a penalty Newton-Raphson solution procedure.

Parameters

  • maxNumIter – maximum number of iterations (defauts to 10)

  • convergenceTestTol – convergence tolerance (defaults to 1e-9)

  • printFlag – print message on each iteration

solution.predefined_solutions.plain_krylov_newton(prb, maxNumIter=300, convergenceTestTol=1e-09, printFlag=0, maxDim=6)

Return a plain Krylov Newton solution procedure.

Parameters

  • maxNumIter – maximum number of iterations (defauts to 300)

  • convergenceTestTol – convergence tolerance (defaults to 1e-9)

  • printFlag – print message on each iteration

  • maxDim – max number of iterations until the tangent is reformed and the acceleration restarts (default = 6).

solution.predefined_solutions.plain_newton_raphson(prb, maxNumIter=10, convergenceTestTol=1e-09)
solution.predefined_solutions.plain_newton_raphson_band_gen(prb, maxNumIter=10)
solution.predefined_solutions.plain_newton_raphson_mumps(prb, maxNumIter=10)
solution.predefined_solutions.plain_static_modified_newton(prb, maxNumIter=150, convergenceTestTol=0.01, convTestType='relative_total_norm_disp_incr_conv_test', printFlag=0)

Return a simple static modified Newton solution procedure.

Parameters

  • maxNumIter – maximum number of iterations (defauts to 10)

  • convergenceTestTol – convergence tolerance (defaults to 1e-9)

  • printFlag – print message on each iteration

solution.predefined_solutions.simple_static_linear(prb)

Return a simple static linear solution procedure.

solution.predefined_solutions.simple_static_linear_mumps(prb)

Return a simple static linear solution procedure.

solution.predefined_solutions.simple_static_linear_umf(prb)

Return a simple static linear solution procedure.

solution.predefined_solutions.solveCombEstat2ndOrderLin(combName, solutionProcedure)
solution.predefined_solutions.solveStaticLinearComb(combName, solutionProcedure)
solution.predefined_solutions.solveStaticNoLinCase(combName, solutionProcedure)
solution.predefined_solutions.transformation_newton_line_search_mumps(prb, maxNumIter=150, convergenceTestTol=1e-09, printFlag=0, convTestType='relative_total_norm_disp_incr_conv_test', integratorType='load_control_integrator')

Return a simple static Newton-Raphson solution procedure.

Parameters

  • maxNumIter – maximum number of iterations (defauts to 10)

  • convergenceTestTol – convergence tolerance (defaults to 1e-9)

  • printFlag – print message on each iteration

  • convTestType – convergence test for non linear analysis (norm unbalance,…).

  • integratorType – integrator type (see integratorSetup).

solution.predefined_solutions.zero_energy_modes(prb)

Return a solution procedure that computes the zero energy modes of the model.