ZeroLengthImpact3D

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This command constructs a node-to-node zero-length contact element in 3D space.

element zeroLengthImpact3D $tag $slaveNode $masterNode $direction $initGap $frictionRatio $Kt $Kn $Kn2 $Delta_y $cohesion



$tag unique element object tag
$slaveNode Slave node tag
$masterNode Master node tag
$direction

1 if normal vector of master plane points to +X direction

2 if normal vector of master plane points to +Y direction

3 if normal vector of master plane points to +Z direction

$initGap Initial gap between master plane and slave plane
$frictionRatio Friction ratio
$Kt Penalty in tangential directions (parallel to master and slave planes)
$Kn Penalty in normal direction (normal to master and slave planes)
$Kn2 Penalty in normal direction after yielding based on Hertz impact model
$Delta_y Yield deformation based on Hertz impact model
$cohesion Cohesion, if no cohesion, it is zero


NOTES:

  1. This element has been developed on top of the “zeroLengthContact3D”. All the notes available in “zeroLengthContact3D” wiki page would apply to this element as well. It includes the definition of master and slave nodes, the number of degrees of freedom in the domain, etc.
  2. This element adds the capabilities of “ImpactMaterial” to “zeroLengthContact3D”, without the need for extra nodes and elements in the modeling process. That is the capability of having an "initial gap" in the normal direction and also the capability of considering energy dissipation due to impact in the normal direction.
  3. This element has been used to model the superstructure-abutment interaction in bridges at University of Connecticut (UConn) and University of Nevada, Reno (UNR). This element was found fast-converging and eliminating the need for many extra elements and nodes in the modeling process.



EXAMPLE SCRIPT:



You need to provide two input files of “example_cyclic_time.txt” and “example_cyclic_disp.txt” as input time and input displacement. 



# Prof. Arash E. Zaghi, Majid Cashany, @ UConn
#MAR,02,2012 ADRiK
#units kip, in,


# two blocks on top of each other:

#     y      (z=0.0)                        y     (z=10.0)     
#     |                                     |                 
#     31--------32                          34--------35      
#     |         |                           |         |       
#     21--------22                          24--------25
#
#     11--------12                          14--------15      
#     |         |                           |         |       
#     01--------02---->x                    04--------05---->x

    
#  x      (y=0.0)         x      (y=10.0)         x      (y=10.0)         x      (y=20.0)
#  |                      |                      |                      |
#  02--------05           12--------15           22--------25           32--------35
#  | master1 |            | master1 |            |  slave1 |            |  slave1 | 
#  01--------04---> z     11--------14---> z     21--------24---> z     31--------34---> z





wipe;
model BasicBuilder -ndm 3 -ndf 3;





# for plane of ( z=0.0) : 
node 01 0.0 0.0 0.0; 
node 02 10.0 0.0 0.0; 
node 11 0.0 10.0 0.0; 
node 12 10.0 10.0 0.0; 
node 21 0.0 10.0 0.0; 
node 22 10.0 10.0 0.0;
node 31 0.0 20.0 0.0; 
node 32 10.0 20.0 0.0;

# for plane of ( z=10.0) : 
node 04 0.0 0.0 10.0; 
node 05 10.0 0.0 10.0; 
node 14 0.0 10.0 10.0; 
node 15 10.0 10.0 10.0;
node 24 0.0 10.0 10.0; 
node 25 10.0 10.0 10.0; 
node 34 0.0 20.0 10.0; 
node 35 10.0 20.0 10.0; 

fix 01 1 1 1;
fix 02 1 1 1;
fix 04 1 1 1;
fix 05 1 1 1;




#nDMaterial ElasticIsotropic $matTag $E $v <$rho>
nDMaterial ElasticIsotropic 1 29000.0 0.3; #steel

#element stdBrick $eleTag $node1 $node2 $node3 $node4 $node5 $node6 $node7 $node8 $matTag
element stdBrick 1 12 11 01 02 15 14 04 05 1;#master1
element stdBrick 2 32 31 21 22 35 34 24 25 1;#slave1






################################################## implementation of new element: 
set direction 2; # direction of normal of contact surface
set initGap 0.5; # initial gap
set frictionRatio 0.1; # friction ratio 
set Kt 1.0e5; # penalty stiffness for tangential directions 
set Kn 1.0e5; # penalty stiffness for normal direction 
set Kn2 [expr $Kn * 0.1]; # penalty stiffness after yielding, based on Hertz impact model 
set Delta_y 0.1; # yield displacement based on Hertz impact model  
set cohesion 0.0; # cohesion

element zeroLengthImpact3D 2111 21 11 $direction $initGap $frictionRatio $Kt $Kn $Kn2 $Delta_y $cohesion;
element zeroLengthImpact3D 2212 22 12 $direction $initGap $frictionRatio $Kt $Kn $Kn2 $Delta_y $cohesion;
element zeroLengthImpact3D 2414 24 14 $direction $initGap $frictionRatio $Kt $Kn $Kn2 $Delta_y $cohesion;
element zeroLengthImpact3D 2515 25 15 $direction $initGap $frictionRatio $Kt $Kn $Kn2 $Delta_y $cohesion;
##################################################






#uniaxialMaterial Elastic $matTag $E;
uniaxialMaterial Elastic 6 1.0e-5;
uniaxialMaterial Elastic 7 1.0e-5;

#element zeroLength $eleTag $iNode $jNode -mat $matTag1 $matTag2 ... -dir $dir1 $dir2 ... <-orient $x1 $x2 $x3 $yp1 $yp2 $yp3> <-doRayleigh $rFlag>
element zeroLength 141 11 21 -mat 6 7 6 -dir 1 2 3; # springs with very low stiffness for convergance of Newton-Raphson method 
element zeroLength 142 12 22 -mat 6 7 6 -dir 1 2 3; # springs with very low stiffness for convergance of Newton-Raphson method 
element zeroLength 144 14 24 -mat 6 7 6 -dir 1 2 3; # springs with very low stiffness for convergance of Newton-Raphson method 
element zeroLength 145 15 25 -mat 6 7 6 -dir 1 2 3; # springs with very low stiffness for convergance of Newton-Raphson method 

puts "model is built";





file mkdir output;
recorder Node -file output/disp2Y.out -node 21 22 24 25 -dof 2 disp;
recorder Node -file output/disp1Y.out -node 11 12 14 15 -dof 2 disp;
recorder Element -file output/ele2212g.out -ele 2212 globalForce;


#recorder display $windowTitle $xLoc $yLoc $xPixels $yPixels <-file $fileName>
recorder display "animation" 10 10 800 800 -wipe;
prp 1.0 1.0 1.0;
vup -1.0 1.0 -1.0;#view-up vector (vup)
vpn 1.0 1.0 1.0;#view-plane normal (vpn)
viewWindow -15 15 -15 15;
display 1 3 1;





wipeAnalysis
#system ProfileSPD;
system BandGeneral;
#system BandSPD;
#system SparseGeneral -piv;
#system SparseGeneral;
#constraints Plain;
constraints Penalty 1.0e5 1.0e5;
test NormDispIncr 1.0e-8 1000;#test NormDispIncr $tol $iter <$pFlag>
numberer RCM;
#algorithm Linear;
#algorithm Newton;
#algorithm NewtonLineSearch 0.8;#algorithm NewtonLineSearch $ratio
#algorithm ModifiedNewton;
#algorithm Newton -initial;
algorithm KrylovNewton;
#algorithm BFGS 10;#algorithm BFGS <$count>; $count=number of iterations within a time step until a new tangent is formed
#algorithm Broyden 10;#algorithm Broyden <$count>; $count=number of iterations within a time step until a new tangent is formed

#timeSeries Path $tag -fileTime $fileTime -filePath $filePath <-factor $cFactor>;
timeSeries Path 1 -fileTime example_cyclic_time.txt -filePath example_cyclic_disp.txt;
#pattern Plain $patternTag $tsTag {...}
pattern Plain 1 1 {
            #sp $nodeTag $DOFtag $DOFvalue
            sp 31 2 1.0;
            sp 32 2 1.0;
            sp 34 2 1.0;
            sp 35 2 1.0;
}

#integrator LoadControl $lambda <$numIter $minLambda $maxLambda>;
set maxLambda [expr 0.01];
integrator LoadControl 0.0 1 $maxLambda $maxLambda;
analysis Static;

for {set i 1} {$i<=[expr int(80.0/$maxLambda)]} {incr i 1} {
 algorithm KrylovNewton;
set ok [analyze 1 ];                                     # actually perform analysis; returns ok=0 if analysis was successful


#nodeDisp $nodeTag <$dof>
set a2 [nodeDisp 25 2];
set a1 [nodeDisp 15 2];
puts "               disp. = [expr $a2-$a1]"
 
 
#puts "$i"
set success 1.0;
if {$ok != 0} {
                        set success 0.0;
                        puts "FAILURE: a miserable one!"
                        break
            }
}


if {$success == 1.0} {
                        puts "SUCCESS: enjoy!"
            }



REFERENCES:

Muthukumar, S., and DesRoches, R. (2006). “A Hertz Contact Model with Non-linear Damping for Pounding Simulation.” Earthquake Engineering and Structural Dynamics, 35, 811-828.

Muthukumar, S. (2003). “A Contact Element Approach with Hysteresis Damping for the Analysis and Design of Pounding in Bridges.” PhD Thesis, Georgia Institute of Technology. http://smartech.gatech.edu/

Nielson, B. (2005). “Analytical Fragility Curves for Highway Bridges in Moderate Seismic Zones.” PhD Thesis, Georgia Institute of Technology. http://smartech.gatech.edu/

Code Developed by: Arash E. Zaghi, Majid Cashany, University of Connecticut (UConn)

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