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

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

K. J. Bathe and S. Gracewski, "On Nonlinear Dynamic Analysis Using Substructuring and Mode Superposition", J. Computers
& Structures, 13, 699707, 1981.
