Node-Based Submodeling

The submodeling capability can be used in the dynamic procedures using explicit integration (in Abaqus/Explicit) and in the dynamic procedures using direct integration (in Abaqus/Standard). The following combinations of procedures between the global model and the submodel can be considered: explicit dynamic, implicit dynamic, dynamic coupled thermal-stress, and coupled thermal-stress. In dynamic problems in which inertial forces are significant, the global model and the submodel need to be run for the same step time intervals.

In Abaqus/Explicit a quasi-static analysis is performed as a dynamic procedure. For this case and for the static analyses performed in Abaqus/Standard, the time step of the global model and submodel can be different. The time variable of the driven nodes from the global analysis must be scaled to the step time of the submodel analysis to match the time variable of the amplitude functions generated at the driven nodes to the step time used in the submodel.

For significantly dynamic problems in Abaqus/Explicit, a sufficiently large number of intervals need to be written to the results or output database file for the global model. Preferably the displacement results for the nodes that are used to drive the submodel should be saved for each increment. This caution is necessary in particular for problems with elastic material properties to avoid possible aliasing (under sampling), which can cause solution distortion in the submodel. These requirements do not apply to quasi-static problems.

In Abaqus/Standard it is possible to study the submodel's linearized response corresponding to a particular point in time in the global solution by using a static, linear perturbation procedure in the submodel analysis. You can select the increment in the global analysis step that is to be used as the basis for calculating the values for the driven variables. If you do not select an increment in a static linear perturbation step, the last increment of the selected step in the global analysis is used as the basis for calculating the values for the driven variables. You cannot select an increment in a general submodel step.

BOUNDARY, SUBMODEL, STEP=step, INC=increment

Load module: Create Boundary Condition: choose Other for the Category and Submodel for the Types for Selected Step: select region: Global step number: step, Global increment: increment

The submodeling capability can be used in the frequency domain. In this case the global model can be run using the mode-based or direct-solution steady-state dynamic procedure and the submodel can be run only using the direct-solution steady-state dynamic procedure. A frequency-domain submodel cannot be driven with a time-domain global model or vice versa. Mode-based steady-state dynamics cannot be used at the submodel level.

The only restriction on the specification of the frequency range in the submodel is that the minimum and maximum frequency should lie within the range of calculated frequencies in the global model. Abaqus interpolates the solution variables from the global model in the frequency domain, as well as spatially, before applying them to the submodel. The results will be most accurate if the frequencies at which the response in the submodel is requested match the frequencies at which the response was calculated in the global model. This is particularly true in the vicinity of the eigenfrequencies of the global model.

In the global model you must write both the amplitude and the phase of the nodal displacements to the results file so that Abaqus can apply the real and imaginary parts of the solution at the driven nodes in the submodel. If you are using the output database to drive the submodel, you need to request only nodal displacement output since displacement output to the output database includes both real and imaginary parts.

It is possible to mix general steps and linear perturbation steps in both the global and the submodel analyses. Abaqus allows general analysis steps to be treated as linear perturbation steps during submodeling, and vice versa.

STEP
** Apply preload
STATIC
 0.1, 1.0
…
** Write out results for nodes needed to
** interpolate to the submodel's boundary
NODE FILE, NSET=DETAIL
 U
END STEP
STEP
** Calculate modes and frequencies
FREQUENCY
…
** The NODE FILE option is repeated because
** this is the first linear perturbation step
NODE FILE, NSET=DETAIL
 U
END STEP
STEP
** Dynamic response of preloaded system
MODAL DYNAMIC
 0.01, 5.0
…
END STEP

** Define submodel boundary (driven nodes)
SUBMODEL
PERIM
STEP
** Preload
STATIC
 0.1, 1.0
BOUNDARY, SUBMODEL, STEP=1
…
END STEP
STEP
** Local static response to global dynamic step
STATIC
 0.01, 5.0
BOUNDARY, SUBMODEL, STEP=3
…
END STEP

RESTART, READ, STEP=3
** Read state at end of initial preload
** (could equally well use RESTART, READ, STEP=1)
STEP
** Add more preload
STATIC
 0.2, 1.0
…
END STEP

RESTART, READ, STEP=2
** Read state at end of step 2
STEP
** Add more preload
STATIC
 0.2, 1.0
BOUNDARY, SUBMODEL, STEP=4
…
END STEP

RESTART, READ, STEP=1
** Read state at end of preload step
STEP
** Add more preload
STATIC
 0.2, 1.0
BOUNDARY, SUBMODEL, STEP=4
…
END STEP

During general analysis steps Abaqus works in terms of total solution variables such as the displacements, $u$ . In linear perturbation steps Abaqus works in terms of the displacement perturbation, $\mathrm{\Delta }u$ , about a base state, ${u|}_0$ . When general analysis steps and linear perturbation steps are reinterpreted in the submodel analysis, the global analysis results are treated as defined in Table 1.

In this table

$u_s$

is the current value of a driven variable in the submodel at any time during a general, nonlinear, analysis step;

$\mathrm{\Delta }{u}_s$

is the value of the perturbation of a driven variable in the submodel during a linear perturbation step;

$u_g$ and $\mathrm{\Delta }{u}_g$

are the corresponding values of the same (geometrically interpolated) variable in the global model;

${u_g|}_0$

is the “base state” value of the variable during a linear perturbation step in the global analysis;

${u_s|}_0$

is the “base state” value of the variable during a linear perturbation step in the submodel analysis;

${u_g|}_i$

is the value of $u_g$ at increment i of the global analysis step; and

${\mathrm{\Delta }{u}_g|}_i$

is the value of $\mathrm{\Delta }{u}_g$ at increment i of the global analysis step.

Additional assumptions must be made for the shell-to-solid case when a general procedure on the global model drives a linear perturbation procedure on the submodel and vice versa. The assumptions depend on the geometric formulation used (linear or nonlinear) and on the procedure combination. For details and governing equations for these cases, see Submodeling analysis.