### Tech Briefs

ADINA Substructuring in Analyses with Local Nonlinearities

The ADINA substructuring capability can be very efficient when the analysis involves only local nonlinearities; for the theory used, see references given below. Here we present two examples of the use of substructuring.

The first example pertains to a metal forming problem in which elastic upper rollers are pushed down to deform a sheet that rests on elastic lower rollers, see figure below.

Nonlinearities occur only at the points of contact and in the sheet to be formed.

The analysis was performed using no substructuring and using the substructuring described in the figure. The statistics of both solutions are shown in the table. Here some savings are seen but not very large savings.

Solution Statistics for Example 1

 Substructuring No. of equations Memory used Memory usage reduction factor Solution time (50 steps) Solution time reduction factor No Yes 87,672 87,672 351 MB 142 MB - 2.5 66 min 27 min - 2.4

Our second example illustrates the solution efficiency that can be reached when using substructuring. A building frame structure is analyzed. Nonlinearities are only considered in the contact region at the bottom floor. Hence, only a small portion (0.3% of the total height, shown in green) of the entire building frame is modeled in the master structure, in which contact surfaces are assigned.

Comparing the solution times used with and without substructuring, it is seen that the use of substructuring is very efficient in this case.

Solution Statistics for Example 2

 Substructuring No. of equations Memory used Memory usage reduction factor Solution time (50 steps) Solution time reduction factor No Yes 513,645 513,645 1,750 MB 309 MB - 5.7 611 min 10 min - 61

Hence, it is seen that the ADINA substructuring capability is a simple, flexible and effective modeling option that is useful for the analysis of problems in which only local nonlinearities need to be accounted for.

References

1. K. J. Bathe, Finite Element Procedures, Prentice Hall, 1996.

2. K. J. Bathe and S. Gracewski, "On Nonlinear Dynamic Analysis Using Substructuring and Mode Superposition", J. Computers & Structures, 13, 699-707, 1981.