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.

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.

For a transient analysis with the second-order structure system, the unbalanced non-inertial forces are balanced out, while the inertia force is carried over to the next regular loading step. The kinetic status of the dynamic system is maintained, and no artificially unrealistic inertia force is introduced during rebalancing.

You can specify the maximum number of substeps (default = 5) 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. . . . . . . . . . . . .2D                  
   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   
   GLOBALLY ASSEMBLED MATRIX . . . . . . . . . . .SYMMETRIC  

                      L O A D   S T E P   O P T I O N S

   LOAD STEP NUMBER. . . . . . . . . . . . . . . .     1
   TIME AT END OF THE LOAD STEP. . . . . . . . . .  1.0000    
   AUTOMATIC TIME STEPPING . . . . . . . . . . . .    ON
      INITIAL NUMBER OF SUBSTEPS . . . . . . . . .    10
      MAXIMUM NUMBER OF SUBSTEPS . . . . . . . . .   100
      MINIMUM NUMBER OF SUBSTEPS . . . . . . . . .     5
      MAXIMUM NUMBER OF SUBSTEPS FOR MAPSOLVE. . .    50
   MAXIMUM NUMBER OF EQUILIBRIUM ITERATIONS. . . .    15
   STEP CHANGE BOUNDARY CONDITIONS . . . . . . . .    NO
   STRESS-STIFFENING . . . . . . . . . . . . . . .    ON
   TERMINATE ANALYSIS IF NOT CONVERGED . . . . . .YES (EXIT)  
   CONVERGENCE CONTROLS. . . . . . . . . . . . . .USE DEFAULTS
   PRINT OUTPUT CONTROLS . . . . . . . . . . . . .NO PRINTOUT
   DATABASE OUTPUT CONTROLS
      ITEM     FREQUENCY   COMPONENT
       ALL        ALL              

Mapping Substeps

The number of substeps used for mapping appears as follows:

 *** LOAD STEP     1   SUBSTEP    10  COMPLETED.    CUM ITER =    101
 *** TIME =  0.399110         REBALANCE FACTOR =   1.00000    


 *** Mechanical APDL BINARY FILE STATISTICS
  BUFFER SIZE USED= 16384
        0.375 MB WRITTEN ON ELEMENT SAVED DATA FILE: RznExample.esav
        0.125 MB WRITTEN ON ASSEMBLED MATRIX FILE: RznExample.full
        0.375 MB WRITTEN ON RESULTS FILE: RznExample.rst

 MAPSOLVE IS DONE SUCCESSFULLY IN 3 SUBSTEPS FOR MANUAL REZONING.

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

                                   13:06:16    09/20/2004

 LOAD  SUB-  NO.   NO.  TOTL  INCREMENT  TOTAL      VARIAB 1  VARIAB 2  VARIAB 3
 STEP  STEP  ATTMP ITER ITER  REBALANCE  REBALANCE  MONITOR   MONITOR   MONITOR
                              FACTOR     FACTOR     Wall       MxDs      MxPl

   1      8    2     7    93  0.35000   0.35000     5.4300   -.64291   0.78886E-30
   1      9    1     4    97  0.35000   0.70000     8.0600   -.81383   0.78886E-30
   1     10    1     4   101  0.30000    1.0000     11.260   -.93615   0.78886E-30

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).

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.

The reported stresses and strains represent the total stresses and strains from TIME = 0. However, the reported displacements are from the rezoned time or substep (when the element coordinates were updated via the REZONE command).

After the MAPSOLVE command has executed, the new mesh may be somewhat distorted, and the distortion may be even more significant if the residual forces are large. In such a case, more careful region selection and better remeshing are necessary.

If the rezoning process encounters convergence difficulties during the mapping (MAPSOLVE) stage of the rezoning process, try the following: