User Area > Advice
Nonlinear Dialog Details
 Nonlinear: Specifies the incremental
loading method to be used for the nonlinear analysis
(automatic or manual). When performing a nonlinear transient,
dynamic or creep analysis, manual incrementation must
be selected  parameters controlling the time step size,
number of time steps etc. must be set using the commands
in the Time Domain section. Automatic incrementation is
required when using load curves in order that the total
number of load increments may be specified.
 Starting load factor: This is the
factor by which the load level of the current load case will be multiplied for the first
iteration of the ensuing load increment. This load level will remain constant for the
increment if a constant load level procedure is used (i.e. no arclength control). It must
be nonzero for the first increment but may be respecified in subsequent load case
properties as zero if the new load factor is to be computed from the previous convergence
history (having also invoked adjust
load based on convergence history).
The following two alternative examples will apply the same load level at
the first increment:
 Specifying the load magnitude in the loadcase as 100 N and applying a starting load
factor of 0.1 will commence the loading of the structure with a load level of (0.1 *
100)N. The factor in this case indicates the proportion of the actual load to be applied
 Specifying the load magnitude as unity in the loadcase and applying a starting load
factor of 10. This will commence the loading of the structure with a (1 * 10) N load. The
factor in this case indicates the actual load to be applied
This parameter is otherwise known as slamda and has default values of 1.0 on the
first increment and 0.0 on subsequent increments.
 Maximum (absolute) change in load factor: This refers only to the first
iteration (iteration zero) of a variable load increment and limits the change of load
factor in an increment. It only has effect when the load level is automatically adjusted
following consideration of the iterations desired for convergence against those actually
performed and is used to stop excessive changes in load increment size when the actual and
desired number of iterations are significantly
different. It is also helpful in materially nonlinear analysis where an initial large
increment (to just below yield) is required followed by smaller increments to enable the
structure to gradually yield. This would be accomplished by setting the starting load
factor at the required level and the maximum change to be an order of magnitude smaller
(say). If zero is input, no limit is applied. For constant load level analyses, the value
should be set to the same value as slamda. A typical value for variable
incrementation would be zero to enable unrestricted change. This parameter is otherwise
known as dlamdx and the default value is 0. The current value is output to the
nonlinear log file as dlmda.
If a nonzero value of arclength
restart load factor is specified in an analysis controlled
by the arclength
method then:
 The maximum incremental arclength parameter will be used to limit the
step size of subsequent increments
 The starting load factor will have no effect, i.e. the arclength restart
load factor will be used to control the new increment
 Max total load factor: This is used
to terminate the solution when the current load factor reaches this maximum value and
applies to all automatic solution procedures. Note that if more than one termination
criterion has been specified, termination will occur following the first criterion to be
satisfied. This parameter is otherwise known as tlamdx and the default value is 1.
When automatic incrementation has been specified without
arclength procedures, the analysis will terminate exactly
at the specified value of the maximum load factor. See
termination
section for more details.
 Adjust load based on
convergence history: By default variable incrementation will be applied, in which the
starting load factor is automatically varied according to the iterative performance of the
solution. The variation is a function of the required number of iterations and a specified
desired iterative performance. Thus, where the number of iterations taken is less than the
desired value the incremented load factor will subsequently be increased, and conversely,
if the number of iterations is greater than the desired value, it will be decreased.
Alternatively, uniform incrementation may be requested by deselecting this toggle switch.
That is, for each increment the starting load factor will be multiplied by the specified
load components and added to the previous level.
 Iterations per increment:
This
specifies the number of desired iterations per load increment. When using automatic
variable incrementation, the loading variable (load or arclength) is varied according to
the actual number of iterations taken to converge on the preceding step. For example...
 If the actual number = the desired number
then the next load
increment will be the same as the previous
 If the actual number of iterations > the desired number
then the next load increment will be decreased
 If the actual number of iterations < the desired number
then the next load increment will be increased
Hence the rate of change of loading variable is adjusted depending on the degree of
nonlinearity present. If zero is input, the load variable will remain constant. Typical
values are 420, depending on the increment size and convergence value selected. This
parameter is otherwise known as itd and the default value is 4.
 Max time steps or increments:
This will terminate the solution when the specified number of further load increments has
been reached. Specifying zero in this field means that this termination criteria will not
be used. Note that if more than one termination criteria has been specified, termination
will occur following the first criterion to be satisfied. This parameter is otherwise
known as maxinc and the default value is 0.
Further details are available for load
incrementation and iterative
solution procedures.
Defines the type of geometric nonlinearity to be used in the analysis. The
default is for no geometric nonlinearity. Consult the LUSAS Element Library manual to
check which geometric nonlinearity type is supported for selected elements. The following
types are available:
 Total Lagrangian: A strain formulation that has its reference as the
initial configuration at the start of the analysis.
 Updated Lagrangian: A strain formulation that has its reference as the
end of the last converged increment.
 Eulerian: A strain formulation that has its reference as the current
configuration.
 Corotational: Form of geometric nonlinearity in which large displacement
effects are related to a set of axes that follow and rotate with the element.
 Continue solution after
convergence failure: This option forces the solution to continue the analysis even
after an increment has failed to converge. It is useful for writing the results of an
unconverged increment to the results file to visualise problem areas. This option should
be used with care and invokes the LUSAS option number 16.
 Continue solution if more
than one negative
pivot occurs: This forces the solution to continue
if more than one negative pivot is encountered at the
beginning of a new increment. This option should be used
with care, as it is likely to hide more fundamental analysis
problems. It invokes the LUSAS option number 62.
 Suppress initial
slideline penetration check: This will force LUSAS
to skip the initial check for contact at the start of
the solution. It invokes the LUSAS option number 186.
 Nonsymmetric solution: The nonsymmetric solver (available in both frontal and
multifrontal direct solvers) is used in problems for which the stiffness matrix is
nonsymmetric. Nonsymmetric stiffness matrices may be formed due to:
 Frictional slidelines
 Follower loads, when used in conjunction with corotational geometric
nonlinearity
 Mixed mode failure specified with the delamination elements
If this capability is required during an analysis it will be invoked
automatically by LUSAS. It invokes LUSAS option number 64.
 Stiffness
ratio to switch to arclength: This is the threshold
value of the current stiffness parameter at which the
solution will automatically switch from a constant load
level to an arclength procedure. The current
stiffness parameter varies between 1.0 (initially)
and 0.0 at a horizontal limit point for a "softening"
structure. For "stiffening" structures it will
commence at one and increase according to the degree of
stiffening experienced by the structure. It is therefore
a useful measure of structural collapse. This parameter
is otherwise known as cstif
and the default value is 0.4.
In general, it is recommended to start with load control (arclength control not invoked) and allow LUSAS to
automatically switch to arclength control as structural collapse is neared, i.e. once the
current stiffness parameter has fallen below the threshold value. Specifying a zero value
will suppress this automatic procedure and a constant load procedure will be maintained
for the entire solution. Note that the iterations per
increment must be given a positive value to use this facility and the switch to
"use arc length control" must be invoked.
 Use arc length control:
This switch controls
whether the load level is to be controlled by constant or arclength procedures. This
parameter is otherwise known as isurfc and, by default, the loading remains
constant during the iteration process unless the cstif threshold has been exceeded.
 Arclength calculation: When arclength control is used, the loading varies
during the iterations according to the method selected. Two algorithms based on the
arclength method are available in LUSAS:
 Crisfield’s modified approach
 Rheinboldt’s arclength method
 Relative displacement arclength procedure: Only to be used with the interface
elements to provide an alternative arclength procedure if convergence problems occur, in
which local relative displacements are used. This invokes the LUSAS option number 308. See
Theory Manual for details.
 Guide arclength
procedure with current stiffness: This is used in situations where undesired unloading
or oscillation occurs in the presence of bifurcations. When using an arclength procedure,
this option forces the arclength solution to be guided by the current stiffness parameter
instead of using the more usual minimum pivot (pivmn in the nonlinear log file). If
a bifurcation point is encountered, the arclength procedure could cause the solution to
oscillate about this point with no further progress being made. This option allows the
solution to continue on the fundamental path and overcomes such problems. This invokes the
LUSAS option number 164, but it is not applicable to the bracketing facility. See Theory
Manual for details.
 Use root with lowest residual norm: Only required to select the best solution
path when severe snap back is occurring. See Theory Manual for details. This invokes the
LUSAS option number 261.
 Arclength restart load factor: The
incrementallength value required to restart an analysis under arclength control. When
applying a restart with the structure near to collapse, it is advisable to use arclength
control. If the loaddeflection response is very flat, it is impractical to restart, as
normal, by specifying a load factor. Instead, it is
better to specify an arclength increment. An appropriate value can be obtained by looking
at the output values of the arclength (deltl) in the iterative log or output file
– it can also be determined from prior arclength increments. If the arclength
restart load factor is nonzero it will be used for the new load increment instead of the
starting load factor no matter what value of starting load factor is specified. This
parameter is otherwise known as dellst.
 Arclength restart load change: The maximum value of the arclength restart load
factor for subsequent increments. If the arclength restart load factor is nonzero this
value will be used to limit the size of subsequent increments instead of the maximum
change in the load factor no matter what value has been specified. This parameter is
otherwise known as delsmx and the default value is evaluated as (2*arclength
restart load factor).
See nonlinear load
incrementation procedures
 Terminate on value of limiting variable:
Terminates the solution by
limiting the maximum value permitted for a specified displacement degree of freedom. For
field analyses, the potential degree of freedom rather than displacement is used. Only
point features selected with the mouse will appear in the list box. Note that if more than
one termination criteria has been specified, termination will occur following the first
criterion to be satisfied.
The current value of the degree of freedom specified is
output to the nonlinear log file as ltdsp. If this termination criterion is
specified, then the value can be used to monitor the displacement/potential associated
with a key point in the structure.
 Point number: Although a point is selected it is actually the underlying node number
that is used in LUSAS. The displacement of this node is monitored throughout the analysis
and the solution terminated if the specified threshold limit is exceeded. This parameter
is otherwise known as mxnod and the default value is 0.
 Variable type: The displacement degree of freedom to be limited at node mxnod.
This parameter is otherwise known as mxvar and the default value is 0.
 Value: The maximum displacement permitted at the selected node mxnod, degree of
freedom mxvar. This parameter is otherwise known as rmxdsp and the default
value is 0.
 Allow step reduction: This switch controls how a load increment will be reduced
if convergence difficulties occur
 Maximum step reductions: The maximum number of times a step reduction can occur
on a single increment. If input as zero, step reduction will be suppressed. This parameter
is otherwise known as mxstr and the default value is 5
 Load reduction factor: Used to reduce the load increment on a step reduction.
This parameter is otherwise known as stpred and the default value is 0.5
 Load increase factor: Used to increase the original load increment if the maximum
step reductions have failed to achieve a solution. It is also known as stpfnl and
the default value is 2.0.
See nonlinear
incrementation procedures.
 Maximum number of iterations:
The maximum number of iterations permitted for each load increment. If the increment does
not converge within this number of iterations then for…
 Manual incrementation, the solution will be terminated because step reduction is not
applicable to this form of load incrementation
 Automatic incrementation, the solution will invoke the step
reduction facility
This parameter is otherwise known as nit and the default value is 12. Typical
values are between 620.
Further details are available for load
incrementation and iterative
solution procedures.
Nonlinear
convergence
 Maximum absolute residual: The limit for the maximum absolute value of
any residual. It is of limited use owing to its dependence upon the units being used. It
is a strict criteria and for some problems, especially those involving plasticity, it may
be very difficult to reduce locally large residuals and obtain convergence. However, in
sensitive geometrically nonlinear problems near bifurcation points, it can sometimes be
necessary to ensure that large residuals are completely eliminated. This parameter is
otherwise known as mar and the default value is a large number (i.e. ignore the
criterion).
 Residual RMS: The limit for the square root of the mean value of the
squares of all residuals. This is generally more applicable than the maximum absolute
residual, but is still dependent upon the units being used. This parameter is otherwise
known as rms and the default value is a large number (i.e. ignore the criterion).
 Incremental Displacement norm:
The limit for the sum
of the squares of the iterative displacements as a percentage of the sum of the squares of
the incremental displacements.
Only translational degrees of freedom are considered by
default but all degrees of freedom can be included by specifying the LUSAS option number
187. This norm is an incremental form of the displacement norm and the same
comments regarding usage apply. For analyses involving large numbers of increments, this
displacement criteria offers a more rigorous criteria than the displacement norm. Typical values of
slack and tight norms are (5.0  1.0) and (1.0  0.1) respectively. This parameter is
otherwise known as dtnrm and the default value is 1.0.
Note that in situations that incremental displacements are small,
this setting could cause an apparent convergence failure due to division
by small numbers. In such cases it is suggested to set a large number
for this value and check dpnrm instead.
 Residual
force norm: The limit for the sum of the squares of
all residual forces as a percentage of the sum of the
squares of all external forces, including reactions. By
default only translational degrees of freedom are considered
but all degrees of freedom can be included by specifying
the LUSAS option number 187. This is the most versatile
of the convergence criteria. Typical slack and tight values
are (10.0  5.0) and (0.1  0.00001) respectively. This
parameter is otherwise known as rdnrm and the default
value is 0.1.
 Displacement norm: The limit for the sum of the squares
of the iterative displacements as a percentage of the
sum of the squares of the total displacements. By default,
only translational degrees of freedom are considered but
all degrees of freedom can be included by specifying the
LUSAS option number 187. It is a useful measure of how
much the structure has moved during an iteration. Being
a scaled norm it is not affected by the units used. For
analyses involving large numbers of increments, this displacement
criteria offers a less rigorous criteria than the Incremental
displacement
norm. Typical values of slack and tight norms are
(5.0  1.0) and (0.1  0.001) respectively. This parameter
is otherwise known as dpnrm and the default value
is 1.0.
 Residual work norm: The limit for the work done by the residuals acting
on the iterative displacements as a percentage of the work done by the loads on iteration
zero of the increment. Since all freedoms are considered it is very versatile (the default
displacement and force norms consider only the translational freedoms). However, it should
be noted that a minimum detected potential energy need not necessarily coincide with the
equilibrate state. Typical values of slack and tight norms are (0.1  0.001) and (10^{6}
– 10^{9}) respectively. This parameter is otherwise known as wdnrm and
the default value is a large number (i.e. ignore the criterion).
 Maximum number of line searches: The maximum number of line searches that
can be performed in any iteration. This parameter is otherwise known as nalps and
the default value is 2. Typical values vary between 26. The current value for the number
of line searches in an iteration is specified in the nonlinear log file as nlsch.
 Line search tolerance factor: The threshold value beyond which line
search acceleration will be automatically invoked. This parameter is otherwise known as toline
and the default value is 0.75. The value must be between 0 and 1 and typical values vary
between 0.3 (low threshold) and 0.8 (high threshold)
 Maximum line search amplification factor: This parameter is otherwise
known as ampmx and the default value is 5.0.
 Maximum line search step length: This parameter is otherwise known as etmxa
and the default value is 25.0. The current value of the step length is specified in the
nonlinear log file as eta.
 Minimum line search step length: This parameter is otherwise known as etmna
and the default value is 0.0. The current value of the step length is specified in the
nonlinear log file as eta.
The selection of line search parameters is problem
dependent and largely a matter of experience. However, a maximum of 3 to 5 line search
iterations with a tolerance of 0.3 to 0.8 is usually sufficient (the closer the tolerance
is to unity, the more slack the minimum energy requirement).
See nonlinear
iterative procedures.
 Output file: The increment interval for output of results to the Solver output
file. Nonzero values will ensure that results are also automatically written on the last
increment or time step. Further control of the information output to the LUSAS output file
is available on the output dialog which can be found on the File> LUSAS Datafile form.
Because all result data is written to the results and restart files, the output file
results are not normally required. This parameter is otherwise known as incout and
the default value is 1.
 Plot file: The increment interval for output of results to the MODELLER results
file. Nonzero values will also ensure that results are automatically written on the last
increment or time step. The frequency may need to be increased for analyses involving
large numbers of time steps or increments to avoid large results files. This parameter is
otherwise known as incplt and the default value is 1.
 Restart file: The increment interval for output of results to the restart file.
The restart output facility enables failed or terminated analyses to be restarted from the
last saved restart results file. This is particularly useful where the termination of the
analysis was due to a failure of the solution process rather than that of the structure.
In this way, the solution may be restarted from the last converged increment with a
different or modified solution strategy. For example, a failed increment may be restarted
under either constant load or arclength control. This parameter is otherwise known as incrst
and the default value is 0.
 Max number of saved restarts: The maximum number of restart results to be saved.
For example, to save the latest two restart results throughout the problem, specify a
value of 2. This parameter is otherwise known as nrstsv and the default value is 0
 Log file: During the course of a nonlinear analysis, information is output to the
screen or a log file, so that the performance of the solution may be assessed. The
increment interval for the output of iterative results to the log file may be modified
with this variable. This parameter is otherwise known as inclog and the default
value is 1.
 History file: The increment interval for output of results to the selective
results history file. This parameter is otherwise known as inchis and the default
value is 1. This will only be invoked if selective results output is specified. In
problems where the restart facility is used, a separate history file is created for each
analysis.
Specifying a zero interval value for any of the results files will cause
no output to be written.
