vk.com/club152685050Rezoning | vk.com/id446425943

4.9. Step 6: Automatically Map Variables and Balance Residuals

Issue the MAPSOLVE command to map the solved node and element solutions automatically from the original mesh to the new mesh. The mapping operation also introduces extra substeps to balance the residuals and achieve equilibrium.

Assuming that you intend to continue the solution, MAPSOLVE is required and is the only rezoning command that you can issue after remeshing (REMESH,FINISH).

For further information, the following mapping topics are available:

4.9.1.Mapping Solution Variables

4.9.2.Balancing Residual Forces

4.9.3.Interpreting Mapped Results

4.9.4.Handling Convergence Difficulties

When the mapping operation has completed, proceed to Step 7: Perform a Multiframe Restart (p. 120).

4.9.1. Mapping Solution Variables

The program maps the solution variables (such as nodal displacements, and element stresses and strains) from the old mesh to the new mesh at the rezoned substep. The mapped variables must satisfy the strain-displacement relationships, constitutive laws, and the equilibrium equations. Algorithms inherent in the mapping scheme handle the first two conditions, but the mapped stress field is usually not in equilibrium due to the different mesh. Therefore, the out-of-balance forces (the residual forces) must

be balanced. Balancing occurs via additional substeps.

4.9.2. Balancing Residual Forces

Additional substeps are introduced automatically to reduce residuals to zero. During this stage, the

time is increased by only a tiny amount (TIME * 10-6, where TIME = the time of the current load step). Therefore, you can consider external loading to be unchanged.

The program always attempts to balance the residual forces within one substep. If it cannot, the program uses bisection logic (automatically, regardless of any manual settings) to use more substeps. A rebalance factor measures the balanced residuals and acts as the control factor during bisection (unlike a standard solution where time is the control factor.) A rebalance factor of zero means that no residuals are balanced yet, and a factor of 1 means that all residuals are balanced and the stress field is in equilibrium.

You can specify the maximum number of substeps--the default is five--to use during mapping (MAPSOLVE). Most problems should achieve balanced residual forces within a few substeps. If contact is included, more substeps may be necessary.

Output File

In the output file, the program presents MAPSOLVE command data as shown:

S O L U T I O N O P T I O N S

PROBLEM DIMENSIONALITY. . . . . . . . . . . . .2-D

DEGREES OF FREEDOM. . . . . . UX UY ROTZ

ANALYSIS TYPE . . . . . . . . . . . . . . . . .STATIC (STEADY-STATE)

MAPSOLVE FOR REZONING. . . . . . . . . . . .YES

NONLINEAR GEOMETRIC EFFECTS . . . . . . . . . .ON

STRESS-STIFFENING . . . . . . . . . . . . . . .ON

EQUATION SOLVER OPTION. . . . . . . . . . . . .SPARSE

NEWTON-RAPHSON OPTION . . . . . . . . . . . . .PROGRAM CHOSEN

vk.com/club152685050 | vk.com/id446425943 Step 6: Automatically Map Variables and Balance Residuals

GLOBALLY ASSEMBLED MATRIX . . . . . . . . . . .SYMMETRIC

Mapping Substeps

The number of substeps used for mapping appears as follows:

Monitor File

The 6th and 7th columns of the monitor file indicate the rebalance factor (rather than the time) for each mapping substep, as shown:

SOLUTION HISTORY INFORMATION FOR JOB: RznExample.mntr

Although multiple substeps may be necessary to balance all residuals, the program generates the restart file and saves the result in a results file for only the last converged mapping substep. (Only the last substep gives the balanced solution.) The program ignores any preexisting output specifications (set

via OUTRES or RESCONTROL commands, for example).

4.9.3. Interpreting Mapped Results

The mapped results are not simply the solution variables interpolated from the old mesh, but balanced results mapped from the old mesh. If the new mesh topology or density is very different from the old mesh, the mapped results may also be very different.