# -------------------------------------------------------------------------------------------------- # Example 3. 2D Cantilever -- EQ ground motion # Silvia Mazzoni & Frank McKenna, 2006 # execute this file after you have built the model, and after you apply gravity # # Uniform Earthquake ground motion (uniform acceleration input at all support nodes) set GMdirection 1; # ground-motion direction set GMfile "BM68elc.acc" ; # ground-motion filenames set GMfact 1.5; # ground-motion scaling factor # set up ground-motion-analysis parameters set DtAnalysis [expr 0.01*$sec]; # time-step Dt for lateral analysis set TmaxAnalysis [expr 10. *$sec]; # maximum duration of ground-motion analysis -- should be 50*$sec # DYNAMIC ANALYSIS PARAMETERS # CONSTRAINTS handler -- Determines how the constraint equations are enforced in the analysis (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/617.htm) # Plain Constraints -- Removes constrained degrees of freedom from the system of equations # Lagrange Multipliers -- Uses the method of Lagrange multipliers to enforce constraints # Penalty Method -- Uses penalty numbers to enforce constraints # Transformation Method -- Performs a condensation of constrained degrees of freedom constraints Transformation ; # DOF NUMBERER (number the degrees of freedom in the domain): (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/366.htm) # determines the mapping between equation numbers and degrees-of-freedom # Plain -- Uses the numbering provided by the user # RCM -- Renumbers the DOF to minimize the matrix band-width using the Reverse Cuthill-McKee algorithm numberer Plain # SYSTEM (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/371.htm) # Linear Equation Solvers (how to store and solve the system of equations in the analysis) # -- provide the solution of the linear system of equations Ku = P. Each solver is tailored to a specific matrix topology. # ProfileSPD -- Direct profile solver for symmetric positive definite matrices # BandGeneral -- Direct solver for banded unsymmetric matrices # BandSPD -- Direct solver for banded symmetric positive definite matrices # SparseGeneral -- Direct solver for unsymmetric sparse matrices (-piv option) # SparseSPD -- Direct solver for symmetric sparse matrices # UmfPack -- Direct UmfPack solver for unsymmetric matrices system SparseGeneral -piv # TEST: # convergence test to # Convergence TEST (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/360.htm) # -- Accept the current state of the domain as being on the converged solution path # -- determine if convergence has been achieved at the end of an iteration step # NormUnbalance -- Specifies a tolerance on the norm of the unbalanced load at the current iteration # NormDispIncr -- Specifies a tolerance on the norm of the displacement increments at the current iteration # EnergyIncr-- Specifies a tolerance on the inner product of the unbalanced load and displacement increments at the current iteration # RelativeNormUnbalance -- # RelativeNormDispIncr -- # RelativeEnergyIncr -- set Tol 1.e-8; # Convergence Test: tolerance set maxNumIter 10; # Convergence Test: maximum number of iterations that will be performed before "failure to converge" is returned set printFlag 0; # Convergence Test: flag used to print information on convergence (optional) # 1: print information on each step; set TestType EnergyIncr; # Convergence-test type test $TestType $Tol $maxNumIter $printFlag; # Solution ALGORITHM: -- Iterate from the last time step to the current (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/682.htm) # Linear -- Uses the solution at the first iteration and continues # Newton -- Uses the tangent at the current iteration to iterate to convergence # ModifiedNewton -- Uses the tangent at the first iteration to iterate to convergence # NewtonLineSearch -- # KrylovNewton -- # BFGS -- # Broyden -- set algorithmType ModifiedNewton algorithm $algorithmType; # Static INTEGRATOR: -- determine the next time step for an analysis (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/689.htm) # LoadControl -- Specifies the incremental load factor to be applied to the loads in the domain # DisplacementControl -- Specifies the incremental displacement at a specified DOF in the domain # Minimum Unbalanced Displacement Norm -- Specifies the incremental load factor such that the residual displacement norm in minimized # Arc Length -- Specifies the incremental arc-length of the load-displacement path # Transient INTEGRATOR: -- determine the next time step for an analysis including inertial effects # Newmark -- The two parameter time-stepping method developed by Newmark # HHT -- The three parameter Hilbert-Hughes-Taylor time-stepping method # Central Difference -- Approximates velocity and acceleration by centered finite differences of displacement set NewmarkGamma 0.5; # Newmark-integrator gamma parameter (also HHT) set NewmarkBeta 0.25; # Newmark-integrator beta parameter integrator Newmark $NewmarkGamma $NewmarkBeta # ANALYSIS -- defines what type of analysis is to be performed (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/324.htm) # Static Analysis -- solves the KU=R problem, without the mass or damping matrices. # Transient Analysis -- solves the time-dependent analysis. The time step in this type of analysis is constant. The time step in the output is also constant. # variableTransient Analysis -- performs the same analysis type as the Transient Analysis object. The time step, however, is variable. This method is used when # there are convergence problems with the Transient Analysis object at a peak or when the time step is too small. The time step in the output is also variable. analysis Transient # define DAMPING-------------------------------------------------------------------------------------- # apply Rayleigh DAMPING from $xDamp # D=$alphaM*M + $betaKcurr*Kcurrent + $betaKcomm*KlastCommit + $beatKinit*$Kinitial set xDamp 0.02; # 2% damping ratio set lambda [eigen 1]; # eigenvalue mode 1 set omega [expr pow($lambda,0.5)]; set alphaM 0.; # M-prop. damping; D = alphaM*M set betaKcurr 0.; # K-proportional damping; +beatKcurr*KCurrent set betaKcomm [expr 2.*$xDamp/($omega)]; # K-prop. damping parameter; +betaKcomm*KlastCommitt set betaKinit 0.; # initial-stiffness proportional damping +beatKinit*Kini # define damping rayleigh $alphaM $betaKcurr $betaKinit $betaKcomm; # RAYLEIGH damping # --------------------------------- perform Dynamic Ground-Motion Analysis # Uniform EXCITATION: acceleration input set IDloadTag 400; # load tag set dt 0.01; # time step for input ground motion set GMfatt 1.0; # data in input file is in g Unifts -- ACCELERATION TH set AccelSeries "Series -dt $dt -filePath $GMfile -factor $GMfatt"; # time series information pattern UniformExcitation $IDloadTag $GMdirection -accel $AccelSeries ; # create Unifform excitation set Nsteps [expr int($TmaxAnalysis/$DtAnalysis)]; set ok [analyze $Nsteps $DtAnalysis]; # actually perform analysis; returns ok=0 if analysis was successful if {$ok != 0} { ; # if analysis was not successful. # change some analysis parameters to achieve convergence # performance is slower inside this loop # Time-controlled analysis set ok 0; set controlTime [getTime]; while {$controlTime < $TmaxAnalysis && $ok == 0} { set ok [analyze 1 $DtAnalysis] set controlTime [getTime] set ok [analyze 1 $DtAnalysis] if {$ok != 0} { puts "Trying Newton with Initial Tangent .." test NormDispIncr $Tol 1000 0 algorithm Newton -initial set ok [analyze 1 $DtAnalysis] test $TestType $Tol $maxNumIter 0 algorithm $algorithmType } if {$ok != 0} { puts "Trying Broyden .." algorithm Broyden 8 set ok [analyze 1 $DtAnalysis] algorithm $algorithmType } if {$ok != 0} { puts "Trying NewtonWithLineSearch .." algorithm NewtonLineSearch .8 set ok [analyze 1 $DtAnalysis] algorithm $algorithmType } } }; # end if ok !0 puts "Ground Motion Done. End Time: [getTime]"