concentrated plasticity

[satyam]

hello everyone
I have modelled a space frame using 3d element concentrated plasticity element (Modified ibaraa model), during gravity analysis following error has occurred
WARNING BandGenLinLapackSolver::solve() -factorization failed, matrix singular U(i,i) = 0, i= 4
WARNING NewtonRaphson::solveCurrentStep() -the LinearSysOfEqn failed in solve()
StaticAnalysis::analyze() - the Algorithm failed at iteration: 0 with domain at load factor 0.1
OpenSees > analyze failed, returned: -3 error flag

I think the error is because of constraints. Can anyone suggest me how to define the constraints for zero length element for 3D case ?

proc rotSpring2DModIKModel {eleID nodeR nodeC K asPos asNeg MyPos MyNeg LS LK LA LD cS cK cA cD th_pP th_pN th_pcP th_pcN ResP ResN th_uP th_uN DP DN} {
#
# Create the zero length element
uniaxialMaterial Bilin $eleID $K $asPos $asNeg $MyPos $MyNeg $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;

element zeroLength $eleID $nodeR $nodeC -mat $eleID -dir 6

# Constrain the translational DOF with a multi-point constraint
# retained constrained DOF_1 DOF_2 ... DOF_n
equalDOF $nodeR $nodeC 1 2 3
#fix $nodeC 4
}

[selimgunay]

Currently the material is assigned only in the torsional direction and there is a hinge in every other dof. You need to assign the material in one of the horizontal translation dof and use equaldof in other directions

[satyam]

hi,
thanks for the reply
can u tell me how to define the dof for zerolength element in 3D case.

Actually, In the example posted on the website for the pushover analysis, the direction defined is 6 for the moment-rotation relationship for plane frame element. How the definition of direction will differ for 3D element.


############################################################################################
# rotSpring2DModIKModel.tcl

#
# This routine creates a uniaxial material spring with deterioration
#
# Spring follows: Bilinear Response based on Modified Ibarra Krawinkler Deterioration Model
#
# Written by: Dimitrios G. Lignos, Ph.D.
#
# Variables
# $eleID = Element Identification (integer)
# $nodeR = Retained/master node
# $nodeC = Constrained/slave node
# $K = Initial stiffness after the modification for n (see Ibarra and Krawinkler, 2005)
# $asPos = Strain hardening ratio after n modification (see Ibarra and Krawinkler, 2005)
# $asNeg = Strain hardening ratio after n modification (see Ibarra and Krawinkler, 2005)
# $MyPos = Positive yield moment (with sign)
# $MyNeg = Negative yield moment (with sign)
# $LS = Basic strength deterioration parameter (see Lignos and Krawinkler, 2009)
# $LK = Unloading stiffness deterioration parameter (see Lignos and Krawinkler, 2009)
# $LA = Accelerated reloading stiffness deterioration parameter (see Lignos and Krawinkler, 2009)
# $LD = Post-capping strength deterioration parameter (see Lignos and Krawinkler, 2009)
# $cS = Exponent for basic strength deterioration
# $cK = Exponent for unloading stiffness deterioration
# $cA = Exponent for accelerated reloading stiffness deterioration
# $cD = Exponent for post-capping strength deterioration
# $th_pP = Plastic rotation capacity for positive loading direction
# $th_pN = Plastic rotation capacity for negative loading direction
# $th_pcP = Post-capping rotation capacity for positive loading direction
# $th_pcN = Post-capping rotation capacity for negative loading direction
# $ResP = Residual strength ratio for positive loading direction
# $ResN = Residual strength ratio for negative loading direction
# $th_uP = Ultimate rotation capacity for positive loading direction
# $th_uN = Ultimate rotation capacity for negative loading direction
# $DP = Rate of cyclic deterioration for positive loading direction
# $DN = Rate of cyclic deterioration for negative loading direction
#
# References:
# Ibarra, L. F., and Krawinkler, H. (2005). �Global collapse of frame structures under seismic excitations,� Technical Report 152, The John A. Blume Earthquake Engineering Research Center, Department of Civil Engineering, Stanford University, Stanford, CA.
# Ibarra, L. F., Medina, R. A., and Krawinkler, H. (2005). �Hysteretic models that incorporate strength and stiffness deterioration,� International Journal for Earthquake Engineering and Structural Dynamics, Vol. 34, No.12, pp. 1489-1511.
# Lignos, D. G., and Krawinkler, H. (2010). �Deterioration Modeling of Steel Beams and Columns in Support to Collapse Prediction of Steel Moment Frames�, ASCE, Journal of Structural Engineering (under review).
# Lignos, D. G., and Krawinkler, H. (2009). �Sidesway Collapse of Deteriorating Structural Systems under Seismic Excitations,� Technical Report 172, The John A. Blume Earthquake Engineering Research Center, Department of Civil Engineering, Stanford University, Stanford, CA.
#
############################################################################################
#
proc rotSpring2DModIKModel {eleID nodeR nodeC K asPos asNeg MyPos MyNeg LS LK LA LD cS cK cA cD th_pP th_pN th_pcP th_pcN ResP ResN th_uP th_uN DP DN} {
#
# Create the zero length element
uniaxialMaterial Bilin $eleID $K $asPos $asNeg $MyPos $MyNeg $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;

element zeroLength $eleID $nodeR $nodeC -mat $eleID -dir 6

# Constrain the translational DOF with a multi-point constraint
# retained constrained DOF_1 DOF_2 ... DOF_n
equalDOF $nodeR $nodeC 1 2
}

[selimgunay]

It should be as follows:

element zeroLength $eleID $nodeR $nodeC -mat $eleID -dir 1

# Constrain the translational DOF with a multi-point constraint
# retained constrained DOF_1 DOF_2 ... DOF_n
equalDOF $nodeR $nodeC 2 3 4 5 6

[kesavapraba]

Dear Mr. Satyam
Did you solve the issue? I too face the same here.