Dynamic relaxation is not intended for general quasi-static analysis.
It's ok for applying preload when the preload produces only small
elastic strains or for initializing a system to a prescribed geometry[1].

You can do a quasi-static analysis by running a regular
explicit simulation, invoking time scaling and/or mass scaling as necessary to
crank out the results in a reasonable amount of time but you have to be careful.
For example, you should monitor the kinetic energy to help confirm
that inertial effects are small.  In other words, use the data in the glstat and
matsum files to show that the kinetic energy is small relative to the internal energy.

By time scaling, I mean applying the load more quickly than in the experiment in
order to reduce the simulation time but at the same time still not inducing
significant dynamic effects.  

See the file http://ftp.lstc.com/anonymous/outgoing/support/FAQ/mass_scaling for more 
information about the mass scaling approach.

To help reach steady state in an explicit analysis, you may be able to use global 
damping to good effect.  Run it undamped first to get a sense of the period of oscillation 
(plot displacement vs. time or stress vs. time).    After you've identified the period, 
you can calculate the global damping coefficient that corresponds to critical damping for 
that period  as 4*Pi/T   where T is the period.   This is equivalent to 2*omega, which is 
mentioned in the discussion of *DAMPING_GLOBAL in the Manual.    You'll want to apply, 
say 20% of that critical damping value during the window(s) of time where you're holding the 
load constant in order to get the oscillations to settle out and then, while the load is still 
constant, ramp down the damping value to zero.   What you want to see happen is that when damping 
goes to zero and the load is a constant, the solution is very close to steady state (oscillations 
are of small amplitude).  [jd, Ticket#2020061010000084]

Or, you can try an implicit, static analysis using LS-DYNA.
See the commands *control_implicit_... and Appendix M in the User's
Manual.  There are examples of implicit analysis on our "user" ftp site
in the ls-dyna/example directory.

See also: gravity.txt, readme.preload, mass_scaling, long_run_times, implicit.general,
          quick_initialization.


Note [1] 
*** Initializing to a prescribed geometry ***
1.   Write a file of nodal displacements from the final state 
of your first run.  


LS-PREPOST has an option to write the displacements using
Output > Nodal Displacements.
Note the d3plot does not contain nodal rotations and thus the rotations
are written as zero.  This could be a real problem for initialization of
shells and beams.

If you do a 'regular' dynamic relaxation run to get to the initialized state,
a file of prescribed displacements and rotations will automatically be 
written at the conclusion of the DR phase (drdisp.sif).

Example:
http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/typ2sol_dr_nrb.k (creates drdisp.sif) and 
typ2sol_presgeom_nrb.k (m=drdisp.sif run).


2.  In your second run, quickly initialize to the prescribed geometry 
written in step 1.  You need to set 
IDRFLG=2 in *control_dynamic_relaxation and include "m=filename" 
on the execution line where 
"filename" is the file created in step 1.    
Before the transient run begins, LS-DYNA will automatically 
run a precusor analysis of 100 timesteps wherein the nodes are displaced 
according to the data in "filename".