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Step Control

FrontISTR structural analysis proceeds by switching boundary conditions, loads, contact, and element activation on a step-by-step basis. This page explains the time span, substeps, convergence criteria, and how to choose between fixed increments and automatic increments/cutback for each step.

Terminology for Analysis Time

This page distinguishes analysis time using the following terms.

  • Current time: Total elapsed time from the start of the analysis.
  • Step time: Elapsed time from the start of the current step.
  • Time span: The analysis time advanced in one step.
  • Relative time: Step time divided by the time span. It is 0 at the start of the step and 1 at the end of the step.
  • Time increment: Increment from the current time to the next time at which equilibrium is solved.

Definitions of terms related to analysis time

Figure 4.7.1 Definitions of terms related to analysis time

Feature Overview

Step control is organized according to the following aspects.

Aspect Role Main Specification
Increment method Determines whether a step advances with fixed increments or whether the time increment is adjusted according to convergence !STEP
Step type Determines whether the step is a static analysis or a viscous analysis including viscoelasticity or creep !STEP
Conditions to activate Selects groups of boundary conditions, loads, contact, and element activation for each step Data lines of !STEP
Convergence criteria Adjusts criteria such as residuals, Lagrange multipliers, and displacement increments for each step !STEP
Output time Specifies times at which calculation and output must occur when automatic increments are used !TIME_POINTS and !STEP

For static analysis, fixed increments or automatic increments/cutback can be selected. In dynamic analysis, conditions can also be switched using multiple !STEP entries, and it is recommended to specify both the fixed time increment and the step time span with !STEP. In !DYNAMIC, n_step and t_delta are treated as defaults when !STEP is omitted or for backward compatibility. Automatic increments/cutback can be used with nonlinear implicit methods. Time control for heat conduction analysis is handled not by !STEP but by the time-step specification in !HEAT.

Conditions activated in a step are specified by group ID. Because boundary conditions, loads, contact, and element activation can be switched by step, staged loading, switching of contact conditions, and analyses involving construction sequences can be represented in a single analysis control file. For selection of element activation/deactivation modes, see Element Activation/Deactivation.

Choosing Step Control

Choose the increment method based on the nonlinearity of the analysis and the required output times.

  • For linear analyses or analyses completed in a single step, detailed adjustment of increment control is often unnecessary.
  • For nonlinear static analyses in which loads and responses vary smoothly, fixed increments are often sufficient. If convergence is difficult, reduce the time increment.
  • For analyses involving the onset or release of contact, progression of yielding, large deformation, or abrupt changes in material nonlinearity, automatic increments/cutback should be considered first. Increments can be increased in regions that converge easily and reduced in regions that are difficult to converge.
  • If results are required at specific times while using automatic increments, use an output-time list together with them.

Adjust convergence criteria to balance analysis stability and computation time. Tightening the convergence criteria improves equilibrium accuracy but increases the number of iterations. In analyses involving contact or Lagrange multipliers, not only the ordinary residual criterion but also the number of contact iterations and the Lagrange-multiplier criterion affect how the calculation proceeds.

Step Control for Static Analysis

Static analysis consists of one or more analysis steps. The iteration over steps is called the step loop, and the iteration that solves one step by dividing it into time increments is called the substep loop. At each substep, equilibrium is calculated using the load factor, boundary conditions, contact state, and other conditions at the specified time.

With fixed increments, the time increment within the step advances by the specified value. If convergence fails, the analysis terminates at that point.

With automatic increments/cutback, the next base time-increment value dtime_base is updated from the convergence status of the preceding substep. If convergence fails, the previously saved state is restored and the same time range is recalculated using a smaller time increment.

Increment-control flow

Figure 4.7.2 Increment-control flow

The flow of automatic increments/cutback is as follows.

  1. At the start of a step, the initial time increment is used as dtime_base.
  2. Determine the actual time increment so that it does not pass the step end time or the next output time.
  3. Calculate equilibrium at the time advanced from the current time by the time increment.
  4. If the calculation converges, advance the time and increase or decrease the next dtime_base according to the convergence status.
  5. If the calculation does not converge, restore the state, reduce dtime_base using the cutback reduction ratio, and recalculate.
  6. When the current time reaches the step end time, finish that step.

Whether to increase or decrease the increment is determined from the iteration status of the preceding substep. The three representative quantities used for this decision are as follows.

Quantity Meaning
N_max Maximum number of Newton-method iterations
N_sum Total number of Newton-method iterations; equal to N_max when there are no contact iterations
N_cont Number of contact iterations

If the state in which any of N_max, N_sum, or N_cont exceeds its decrease-side threshold continues for the specified number of times, the time increment is reduced. Conversely, if the state in which all three remain within their increase-side thresholds continues for the specified number of times, the time increment is increased. When increasing it, the increment is adjusted so as not to exceed the upper limit.

With automatic increments/cutback, the analysis terminates as failed in the following cases.

  • The upper limit on the number of substeps is reached before the step end time.
  • The base time-increment value falls below the lower limit on the time increment.
  • The upper limit on consecutive cutbacks is reached.

The following example enables automatic increments and sets an initial time increment of 0.01, a step time span of 2.5, a lower time-increment limit of 1E-5, an upper time-increment limit of 0.3, and a maximum of 200 substeps. Automatic-increment parameter set AP1 and output-time list TP1, containing total times 1.5, 2.7, and 3.9, are assigned to the step.

!AUTOINC_PARAM, NAME=AP1
0.25, 10, 50, 10, 1
1.25,  1,  1,  1, 2
0.25,  5
!TIME_POINTS, TIME=TOTAL, NAME=TP1
1.5
2.7
3.9
!STEP, INC_TYPE=AUTO, SUBSTEPS=200, AUTOINCPARAM=AP1, TIMEPOINTS=TP1
0.01, 2.5, 1E-5, 0.3

For the input format and default value of each parameter, see !STEP, !AUTOINC_PARAM, and !TIME_POINTS.

Step Control for Dynamic Analysis

For direct time integration in dynamic analysis, specify the solution method and time-integration parameters with !DYNAMIC, and specify analysis steps, boundary-condition and load groups, and the increment method with !STEP. If !STEP is omitted, the analysis is treated as a single-step analysis in which all boundary conditions and loads are active.

With fixed increments, on the second line of !STEP specify DTIME, ETIME to control the time increment and step time span for each step. Defining multiple !STEP entries allows the active boundary-condition and load groups to be switched by step. In !DYNAMIC, t_delta and n_step are treated as defaults for legacy single-step input in which !STEP is omitted and for backward compatibility. For new input, it is recommended to specify the time conditions explicitly with !STEP even when fixed increments are used.

When using automatic increments, specify !STEP, INC_TYPE=AUTO and provide the initial time increment, step time span, lower time-increment limit, and upper time-increment limit on the !STEP data line. With a nonlinear implicit method, the time increment is increased or decreased according to the state of Newton iterations and contact iterations; if convergence fails, the preceding state is restored and the calculation is repeated with a smaller time increment.

The time-integration method and coefficients such as those of the Newmark-β method are specified with !DYNAMIC. For the input format, see !DYNAMIC and !STEP.

Step Control for Heat Conduction Analysis

The time step for heat conduction analysis is specified with !HEAT. !HEAT specifies a set of values including the time step, end time, minimum time step, maximum temperature change, number of iterations, and convergence criterion.

Time control for heat conduction analysis operates through a mechanism separate from !STEP, INC_TYPE=AUTO for structural static analysis. Therefore, when adjusting the time step in heat conduction analysis, do not use !STEP; use the !HEAT specification instead. For the input format, see !HEAT.

Specifying Output Times

Because the time increment changes according to convergence when automatic increments are used, the times at which results are output may not be known in advance. !TIME_POINTS is a list of times used to adjust the time increment so that equilibrium is always calculated and results can be output at the specified times.

A time list can be specified either as total time from the start of the analysis or as step time from the start of the step. Use total time when specifying common times across multiple steps, and step time when specifying the same relative output positions for each step.

For each step, the time list to use is referenced from !STEP. When used together with automatic increments, the time increment is shortened so that it does not pass the next output time or the step end time. For the input format, see !TIME_POINTS.