Mesh sensitivity study - Cantilever Bridge Column

[polimeruvijay]

Dear OpenSEES Community Members

I am doing convergence study, for a cantilever column, by varying number of nonlinear beam column elements(Convergence study means, when varying the number of elements, How far the stress strains and load displacement values are varying??), My objective from this convergence study is to find the number of nonlinear beam column elements for reasonable accuracy

I am using the below mentioned is part of the code for the analysis, which is taken from Pushover analysis of Portal frame example. In the code, if analysis failed to converge (i.e. OK !=0) We are trying the analysis with other algorithms (Examples: Newton, Broyden, NewtonLineSearch).

My problem here is, When I increase number of elements, the load displacement values and stress strain values are increasing continuously, no convergence is found between any two simulations (each simulation is analyzed with different number of elements). I was not able to find the number of elements for analysis.

Please suggest, what modifications are necessary to get convergence??

## ---------------------------------------------------------------------------------------
if {$ok != 0} {
# if analysis fails, we try some other stuff, performance is slower inside this loop
set ok 0;
set controlDisp 0.0;
set D0 0.0; # analysis starts from zero
set Dstep [expr ($controlDisp-$D0)/($Dmax-$D0)]
while {$Dstep < 1.0 && $ok == 0} {
set controlDisp [nodeDisp $IDctrlNode $IDctrlDOF ]
set Dstep [expr ($controlDisp-$D0)/($Dmax-$D0)]
set ok [analyze 1 ]
if {$ok != 0} {
puts "Trying Newton with Initial Tangent .."
test NormDispIncr $Tol 100 0
algorithm Newton -initial
set ok [analyze 1 ]
test $TestType $Tol $maxNumIter 0
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying Broyden .."
algorithm Broyden 8
set ok [analyze 1 ]
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying NewtonWithLineSearch .."
algorithm NewtonLineSearch .8
set ok [analyze 1 ]
algorithm $algorithmType
}
}; # end while loop
}; # end if ok !0

puts "Pushover Done. Control Disp=[nodeDisp $IDctrlNode $IDctrlDOF]"


## --------------------------------------------------------------------------------------

Thank you

Sincerely

[fmk]

mesh sensitivity does not always work even for elastic problems! e.g. finding the stress at a tip of a crack or corner in a continuum problem, the value it keeps going up as you make the mesh finer.

if you stop and think why it is not working here it may help you become a better modeler.

[polimeruvijay]

Dear Frank

Thank you very much for your prompt reply,

I understood that you are talking about the concept of stress singularities (please correct me if I am wrong). I checked for stress-strain convergence at other-points, there is no issue, I was able to get convergence and got the appropriate mesh size needed for the analysis.

But the point at which singularity is occurring is the critical point in my analysis. I want the stress-strain values at that point only, since it need to report the stresses and strains at the critical point.

could you please give some idea of, how to deal with stress singularities?

Thank you

Sincerely