smillmorel
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233 lines
13 KiB
Text
233 lines
13 KiB
Text
# --------------------------------------------------------------------------------------------------
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# Example 2. 2D cantilever column, static pushover
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# element
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# Silvia Mazzoni & Frank McKenna, 2006
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#
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# ^Y
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# |
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# 2 __
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# | |
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# | |
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# | |
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# (1) LCol
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# | |
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# | |
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# | |
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# =1= _|_ -------->X
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#
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# SET UP ----------------------------------------------------------------------------
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# units: kip, inch, sec
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wipe; # clear memory of all past model definitions
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file mkdir Data; # create data directory
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model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm=#dimension, ndf=#dofs
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# define GEOMETRY -------------------------------------------------------------
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set LCol 432; # column length
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set Weight 2000.; # superstructure weight
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# define section geometry
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set HCol 60; # Column Depth
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set BCol 60; # Column Width
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# calculated parameters
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set PCol $Weight; # nodal dead-load weight per column
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set g 386.4; # g.
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set Mass [expr $PCol/$g]; # nodal mass
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# calculated geometry parameters
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set ACol [expr $BCol*$HCol*1000]; # cross-sectional area, make stiff
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set IzCol [expr 1./12.*$BCol*pow($HCol,3)]; # Column moment of inertia
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# nodal coordinates:
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node 1 0 0; # node#, X, Y
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node 2 0 $LCol
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# Single point constraints -- Boundary Conditions
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fix 1 1 1 1; # node DX DY RZ
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# nodal masses:
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mass 2 $Mass 1e-9 0.; # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes
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# Define ELEMENTS & SECTIONS -------------------------------------------------------------
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set ColMatTagFlex 2; # assign a tag number to the column flexural behavior
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set ColMatTagAxial 3; # assign a tag number to the column axial behavior
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set ColSecTag 1; # assign a tag number to the column section tag
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set BeamSecTag 2; # assign a tag number to the beam section tag
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# MATERIAL parameters
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set fc -4.; # CONCRETE Compressive Strength (+Tension, -Compression)
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set Ec [expr 57*sqrt(-$fc*1000)]; # Concrete Elastic Modulus (the term in sqr root needs to be in psi
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# COLUMN section
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# calculated stiffness parameters
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set EICol [expr $Ec*$IzCol]; # EI, for moment-curvature relationship
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set EACol [expr $Ec*$ACol]; # EA, for axial-force-strain relationship
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set MyCol 130000; # yield moment
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set PhiYCol 0.65e-4; # yield curvature
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set EIColCrack [expr $MyCol/$PhiYCol]; # cracked section inertia
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set b 0.01 ; # strain-hardening ratio (ratio between post-yield tangent and initial elastic tangent)
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uniaxialMaterial Steel01 $ColMatTagFlex $MyCol $EIColCrack $b; # bilinear behavior for flexure
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uniaxialMaterial Elastic $ColMatTagAxial $EACol; # this is not used as a material, this is an axial-force-strain response
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section Aggregator $ColSecTag $ColMatTagAxial P $ColMatTagFlex Mz; # combine axial and flexural behavior into one section (no P-M interaction here)
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# define geometric transformation: performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global-coordinate system
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set ColTransfTag 1; # associate a tag to column transformation
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geomTransf Linear $ColTransfTag ;
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# element connectivity:
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set numIntgrPts 5; # number of integration points for force-based element
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element nonlinearBeamColumn 1 1 2 $numIntgrPts $ColSecTag $ColTransfTag; # self-explanatory when using variables
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# Define RECORDERS -------------------------------------------------------------
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recorder Node -file Data/DFree.out -time -node 2 -dof 1 2 3 disp; # displacements of free nodes
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recorder Node -file Data/DBase.out -time -node 1 -dof 1 2 3 disp; # displacements of support nodes
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recorder Node -file Data/RBase.out -time -node 1 -dof 1 2 3 reaction; # support reaction
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recorder Drift -file Data/Drift.out -time -iNode 1 -jNode 2 -dof 1 -perpDirn 2 ; # lateral drift
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recorder Element -file Data/FCol.out -time -ele 2 globalForce; # element forces -- column
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recorder Element -file Data/ForceColSec1.out -time -ele 1 section 1 force; # Column section forces, axial and moment, node i
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recorder Element -file Data/DefoColSec1.out -time -ele 1 section 1 deformation; # section deformations, axial and curvature, node i
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recorder Element -file Data/ForceColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts force; # section forces, axial and moment, node j
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recorder Element -file Data/DefoColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts deformation; # section deformations, axial and curvature, node j
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# define GRAVITY -------------------------------------------------------------
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pattern Plain 1 Linear {
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load 2 0 -$PCol 0
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}
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# Gravity-analysis parameters -- load-controlled static analysis
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set Tol 1.0e-8; # convergence tolerance for test
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constraints Plain; # how it handles boundary conditions
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numberer Plain; # renumber dof's to minimize band-width (optimization), if you want to
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system BandGeneral; # how to store and solve the system of equations in the analysis
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test NormDispIncr $Tol 6 ; # determine if convergence has been achieved at the end of an iteration step
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algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
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set NstepGravity 10; # apply gravity in 10 steps
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set DGravity [expr 1./$NstepGravity]; # first load increment;
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integrator LoadControl $DGravity; # determine the next time step for an analysis
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analysis Static; # define type of analysis static or transient
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analyze $NstepGravity; # apply gravity
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# ------------------------------------------------- maintain constant gravity loads and reset time to zero
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loadConst -time 0.0
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puts "Model Built"
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# STATIC PUSHOVER ANALYSIS --------------------------------------------------------------------------------------------------
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#
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# we need to set up parameters that are particular to the model.
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set IDctrlNode 2; # node where displacement is read for displacement control
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set IDctrlDOF 1; # degree of freedom of displacement read for displacement contro
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set Dmax [expr 0.05*$LCol]; # maximum displacement of pushover. push to 10% drift.
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set Dincr [expr 0.001*$LCol]; # displacement increment for pushover. you want this to be very small, but not too small to slow down the analysis
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# create load pattern for lateral pushover load
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set Hload $Weight; # define the lateral load as a proportion of the weight so that the pseudo time equals the lateral-load coefficient when using linear load pattern
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pattern Plain 200 Linear {; # define load pattern -- generalized
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load 2 $Hload 0.0 0.0 0.0 0.0 0.0; # define lateral load in static lateral analysis
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}
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# ----------- set up analysis parameters
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# CONSTRAINTS handler -- Determines how the constraint equations are enforced in the analysis (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/617.htm)
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# Plain Constraints -- Removes constrained degrees of freedom from the system of equations (only for homogeneous equations)
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# Lagrange Multipliers -- Uses the method of Lagrange multipliers to enforce constraints
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# Penalty Method -- Uses penalty numbers to enforce constraints --good for static analysis with non-homogeneous eqns (rigidDiaphragm)
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# Transformation Method -- Performs a condensation of constrained degrees of freedom
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constraints Plain;
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# DOF NUMBERER (number the degrees of freedom in the domain): (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/366.htm)
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# determines the mapping between equation numbers and degrees-of-freedom
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# Plain -- Uses the numbering provided by the user
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# RCM -- Renumbers the DOF to minimize the matrix band-width using the Reverse Cuthill-McKee algorithm
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numberer Plain
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# SYSTEM (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/371.htm)
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# Linear Equation Solvers (how to store and solve the system of equations in the analysis)
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# -- provide the solution of the linear system of equations Ku = P. Each solver is tailored to a specific matrix topology.
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# ProfileSPD -- Direct profile solver for symmetric positive definite matrices
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# BandGeneral -- Direct solver for banded unsymmetric matrices
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# BandSPD -- Direct solver for banded symmetric positive definite matrices
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# SparseGeneral -- Direct solver for unsymmetric sparse matrices
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# SparseSPD -- Direct solver for symmetric sparse matrices
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# UmfPack -- Direct UmfPack solver for unsymmetric matrices
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system BandGeneral
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# TEST: # convergence test to
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# Convergence TEST (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/360.htm)
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# -- Accept the current state of the domain as being on the converged solution path
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# -- determine if convergence has been achieved at the end of an iteration step
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# NormUnbalance -- Specifies a tolerance on the norm of the unbalanced load at the current iteration
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# NormDispIncr -- Specifies a tolerance on the norm of the displacement increments at the current iteration
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# EnergyIncr-- Specifies a tolerance on the inner product of the unbalanced load and displacement increments at the current iteration
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set Tol 1.e-8; # Convergence Test: tolerance
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set maxNumIter 6; # Convergence Test: maximum number of iterations that will be performed before "failure to converge" is returned
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set printFlag 0; # Convergence Test: flag used to print information on convergence (optional) # 1: print information on each step;
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set TestType EnergyIncr ; # Convergence-test type
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test $TestType $Tol $maxNumIter $printFlag;
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# Solution ALGORITHM: -- Iterate from the last time step to the current (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/682.htm)
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# Linear -- Uses the solution at the first iteration and continues
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# Newton -- Uses the tangent at the current iteration to iterate to convergence
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# ModifiedNewton -- Uses the tangent at the first iteration to iterate to convergence
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set algorithmType Newton
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algorithm $algorithmType;
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# Static INTEGRATOR: -- determine the next time step for an analysis (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/689.htm)
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# LoadControl -- Specifies the incremental load factor to be applied to the loads in the domain
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# DisplacementControl -- Specifies the incremental displacement at a specified DOF in the domain
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# Minimum Unbalanced Displacement Norm -- Specifies the incremental load factor such that the residual displacement norm in minimized
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# Arc Length -- Specifies the incremental arc-length of the load-displacement path
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# Transient INTEGRATOR: -- determine the next time step for an analysis including inertial effects
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# Newmark -- The two parameter time-stepping method developed by Newmark
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# HHT -- The three parameter Hilbert-Hughes-Taylor time-stepping method
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# Central Difference -- Approximates velocity and acceleration by centered finite differences of displacement
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integrator DisplacementControl $IDctrlNode $IDctrlDOF $Dincr
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# ANALYSIS -- defines what type of analysis is to be performed (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/324.htm)
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# Static Analysis -- solves the KU=R problem, without the mass or damping matrices.
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# Transient Analysis -- solves the time-dependent analysis. The time step in this type of analysis is constant. The time step in the output is also constant.
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# variableTransient Analysis -- performs the same analysis type as the Transient Analysis object. The time step, however, is variable. This method is used when
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# there are convergence problems with the Transient Analysis object at a peak or when the time step is too small. The time step in the output is also variable.
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analysis Static
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# --------------------------------- perform Static Pushover Analysis
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set Nsteps [expr int($Dmax/$Dincr)]; # number of pushover analysis steps
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set ok [analyze $Nsteps]; # this will return zero if no convergence problems were encountered
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# ---------------------------------- in case of convergence problems
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if {$ok != 0} {
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# change some analysis parameters to achieve convergence
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# performance is slower inside this loop
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set ok 0;
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set controlDisp 0.0; # start from zero
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set D0 0.0; # start from zero
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set Dstep [expr ($controlDisp-$D0)/($Dmax-$D0)]
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while {$Dstep < 1.0 && $ok == 0} {
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set controlDisp [nodeDisp $IDctrlNode $IDctrlDOF ]
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set Dstep [expr ($controlDisp-$D0)/($Dmax-$D0)]
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set ok [analyze 1 ]
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if {$ok != 0} {
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puts "Trying Newton with Initial Tangent .."
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test NormDispIncr $Tol 2000 0
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algorithm Newton -initial
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set ok [analyze 1 ]
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test $TestType $Tol $maxNumIter 0
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algorithm $algorithmType
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}
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if {$ok != 0} {
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puts "Trying Broyden .."
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algorithm Broyden 8
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set ok [analyze 1 ]
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algorithm $algorithmType
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}
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if {$ok != 0} {
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puts "Trying NewtonWithLineSearch .."
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algorithm NewtonLineSearch .8
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set ok [analyze 1 ]
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algorithm $algorithmType
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}
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}
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}; # end if ok !0
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puts "DonePushover"
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