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Nonlinear Dialog Details

Incrementation

• 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 arc-length 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:

1. 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
2. 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 arc-length restart load factor is specified in an analysis controlled by the arc-length method then:

1. The maximum incremental arc-length parameter will be used to limit the step size of subsequent increments
2. The starting load factor will have no effect, i.e. the arc-length 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 arc-length 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 de-selecting 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 arc-length) 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 4-20, 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.

Geometric Nonlinearity

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.
• Co-rotational: Form of geometric nonlinearity in which large displacement effects are related to a set of axes that follow and rotate with the element.

Solution control

• 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.
• Non-symmetric solution: The non-symmetric solver (available in both frontal and multi-frontal direct solvers) is used in problems for which the stiffness matrix is non-symmetric. Non-symmetric stiffness matrices may be formed due to:

1. Frictional slidelines
2. Follower loads, when used in conjunction with co-rotational geometric nonlinearity
3. 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.

Automatic incrementation

• Stiffness ratio to switch to arc-length: This is the threshold value of the current stiffness parameter at which the solution will automatically switch from a constant load level to an arc-length 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 (arc-length control not invoked) and allow LUSAS to automatically switch to arc-length 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 arc-length 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.
• Arc-length calculation: When arc-length control is used, the loading varies during the iterations according to the method selected. Two algorithms based on the arc-length method are available in LUSAS:

1. Crisfield’s modified approach
2. Rheinboldt’s arc-length method

• Relative displacement arc-length procedure: Only to be used with the interface elements to provide an alternative arc-length 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 arc-length procedure with current stiffness: This is used in situations where undesired unloading or oscillation occurs in the presence of bifurcations. When using an arc-length procedure, this option forces the arc-length 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 arc-length 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.
• Arc-length restart load factor: The incremental-length value required to restart an analysis under arc-length control. When applying a restart with the structure near to collapse, it is advisable to use arc-length control. If the load-deflection response is very flat, it is impractical to restart, as normal, by specifying a load factor. Instead, it is better to specify an arc-length increment. An appropriate value can be obtained by looking at the output values of the arc-length (deltl) in the iterative log or output file – it can also be determined from prior arc-length increments. If the arc-length restart load factor is non-zero 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.
• Arc-length restart load change: The maximum value of the arc-length restart load factor for subsequent increments. If the arc-length 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*arc-length restart load factor).

See nonlinear load incrementation procedures

Termination criteria

• 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.

Step reduction

• 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.

Solution Strategy

• 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…

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).

Nonlinear iterative acceleration

• 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 2-6. 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).

Separate iterative loop for contact procedure

Incremental Lusas File Output

• Output file: The increment interval for output of results to the Solver output file. Non-zero 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. Non-zero 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 arc-length 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.

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