Explicit integrators for an adaptive time stepping algorithm

[filipov1]

Hi,
I have been working on creating an adaptive time stepping algorithm that not only switches between algorithms, but would ideally switch to explicit integration with a small step size in certain cases of very high nonlinearity.

Unfortunately, I am not able to obtain reasonable results with explicit integrators(compared to implicit), even when I am running a very simple elastic model.

I haven't been able to find much on explicit integrators except for some old forum posts. Does anyone have some sample tcl files that show implicit and explicit integration yielding similar results?

I am posting the simplified elastic model which I am using to validate my results, can anyone help with this.

Thank you for your help in advance!

- EF

# 1----------2----------4----------6
# 7 | | 8
# | |
# | |
# 3 5
wipe;
model basic -ndm 2 -ndf 3;
file mkdir data;

node 1 0 180
node 2 600 180
node 3 600 0
node 4 1200 180
node 5 1200 0
node 6 1800 180
node 7 0 180; # Nodes for Bearings
node 8 1800 180
# Single point constraints -- Boundary Conditions
fix 7 1 1 1
fix 3 1 1 1
fix 5 1 1 1
fix 8 1 1 1
# nodal masses:
mass 1 1500 0 0
mass 2 3000 0 0
mass 3 0 0 0
mass 4 3000 0 0
mass 5 0 0 0
mass 6 1500 0 0
mass 7 0 0 0
mass 8 0 0 0
# Define ELEMENTS -------------------------------------------------------------
geomTransf Linear 1;
# Bearing Materials
uniaxialMaterial Elastic 1 4000;
uniaxialMaterial Elastic 2 100000;
# connectivity: (make A very large, 10e6 times its actual value)
element elasticBeamColumn 1 3 2 3600000 40000 35000 1
element elasticBeamColumn 2 5 4 3600000 40000 35000 1
element elasticBeamColumn 3 1 2 5760000 30000 442368 1
element elasticBeamColumn 4 2 4 5760000 30000 442368 1
element elasticBeamColumn 5 4 6 5760000 30000 442368 1

# Horizontal Bearing Elements
element zeroLength 6 1 7 -mat 1 -dir 1
element zeroLength 7 6 8 -mat 1 -dir 1
# Vertical Bearing Elements
element zeroLength 8 1 7 -mat 2 -dir 2
element zeroLength 9 6 8 -mat 2 -dir 2
# Define RECORDERS -------------------------------------------------------------
recorder Node -file Data/FixedReactions.out -time -node 7 3 5 10 -dof 1 reaction
recorder Node -file Data/FixedDisp.out -time -node 7 3 5 10 -dof 1 disp
recorder Node -file Data/FreeDisp.out -time -node 1 2 4 6 -dof 1 disp
recorder Node -file Data/RBase.out -time -node 7 3 5 10 -dof 2 reaction
# define GRAVITY -------------------------------------------------------------
pattern Plain 1 Linear {
eleLoad -ele 3 -type -beamUniform -0.94 ;
eleLoad -ele 4 -type -beamUniform -0.94 ;
eleLoad -ele 5 -type -beamUniform -0.94 ;
}
constraints Transformation;
numberer Plain;
system BandGeneral;
test NormDispIncr 1.0e-8 6 1 ;
algorithm Newton;
integrator LoadControl 0.1;
analysis Static;
analyze 10;
loadConst -time 0.0;

# DYNAMIC ground-motion analysis -------------------------------------------------------------
set accelSeries "Series -dt 0.01 -filePath Paducah_KY_2475_06_part.txt -factor 5";
pattern UniformExcitation 2 1 -accel $accelSeries;
rayleigh 0. 0. 0. [expr 2*0.02/pow([eigen 1],0.5)];


wipeAnalysis;# clear previously-define analysis parameters
numberer RCM
constraints Plain

# FOR IMPLICIT ANALYSIS---------------------------
#system BandGeneral
#test NormDispIncr 1.0e-8 10 2
#algorithm Newton
#integrator Newmark 0.5 0.25

# FOR EXPLICIT ANALYSIS --------------------------
system Diagonal
algorithm Linear
integrator NewmarkExplicit 0.5
#integrator CentralDifference
#integrator CentralDifferenceNoDamping
analysis Transient
analyze 40000 0.001