Hipótesis General

If the model includes PARTs, you must use the SETREE or DTI,SETREE entries if you want a multilevel tree is. Models containing PARTs are automatically treated as single-level, unless one of these entries appears in the Main Bulk Data Section. Otherwise, the SETREE and

DTI,SETREE define a tree in the same manner as models defined in the Main Bulk Data Section only. Once again, these entries must be in the Main Bulk Data Section of the input file.

The SETREE entry actually provides a list of all superelements immediately upstream from a single superelement in the tree. One SETREE is required for each superelement that has any upstream connections.

1 2 3 4 5 6 7 8 9 10

SETREE SEID SEUP1 SEUP2 SEUP3 SEUP4 SEUP5 SEUP6 SEUP7

SEUP8 SEUP9

-etc.-The following set of SETREE entries accomplishes the same tree as the above DTI,SETREE forFigure 7-28.

SETREE,0,1,2,4 SETREE,2,5 SETREE,5,6 SETREE,4,3

In this set, the first entry states that superelements 1, 2, and 4 are directly above the residual structure. The second entry states that superelement 5 is directly above superelement 2, and so on.

Either the SETREE or the DTI,SETREE can be used, and if both entries are in the input file, the SETREE takes precedence. Also note that these entries must be in the Main Bulk Data Section if they are used. Verify that all superelements you want to include in the analysis are listed on the SETREE (or DTI,SETREE) entries, because superelements that are not listed are placed directly above the residual structure.

7.4 Example: Multilevel Problem Solved by Hand

An example solved by hand is the best demonstration of how multilevel superelements are processed. Because solving large problems by hand is not practical, only the simplest of problems can be used. In this case, we use a fixed-fixed beam that is divided into multilevel superelements.

We only look at motion in the horizontal direction in the plane of the paper. The model is shown below.

For this example, we use the following SESET and DTI,SETREE entries.

SESET,1,6,7 $ used only if model is main bulk data only SESET,2,4,5 $ used only if model is main bulk data only DTI,SETREE,1,2,0,1,2

Using this superelement definition, the following model for superelement 1 is created. The program removes grid points 6 and 7 (interior points) from the bulk data. The program then removes all elements connected to those points and makes a copy of grid point 5, which is the exterior point for this superelement. Any loads and constraints associated with grid points 5 and 6 or the elements in superelement 1 are also placed in the bulk data for the model.

The first step in processing the superelement is to generate the G-sized matrices for this component. When dealing with a multilevel configuration, there are two sets of matrices generated for each superelement.

The first set of matrices created represents the physical properties of the superelement (plus any K2GG, K42GG, M2GG, B2GG, or P2G matrices). The first set of matrices are G-sized and are defined by the letter J. For example, the physical stiffness matrix is called KJJ. The following stiffness and loading matrices are generated for superelement 1.

Equation 7-1.

The program then creates assembly G-sized matrices by combining these J matrices with the reduced matrices from upstream superelements. Because superelement 1 has no upstream superelements, the J and G matrices are the same. (Note that for this situation, where two matrices are identical, NX Nastran stores only one matrix in the database and creates a pointer for the second matrix, which points to the stored data. Therefore, the database files do not become excessively large.)

If there were any MPC-type relations (MPCs, RBE2, RBAR, etc), the program would apply and process these relations, and the G matrices would be reduced to N matrices.

The program then applies constraints to the matrices. For superelement 1, grid point 7 is constrained; thus, terms associated with this grid point are removed from the matrices to apply that constraint. After applying the constraints, the matrices are defined for the Fset.

Equation 7-2.

At this point, the static condensation is performed. The matrices are partitioned into A and O set DOFs and then transformed.

Equation 7-3.

Superelement 1 is now processed, and only the set of A sized matrices are required to continue the solution.

SUPERELEMENT 2

The physical model for superelement 2 is shown below. This model contains interior points 4 and 5, any remaining elements that are connected to them, a copy of exterior point 3, and the reduced matrices representing superelement 1.

Once again, the J matrices are generated for the physical model of the superelement.

Equation 7-4.

Now we add the reduced matrices from superelement 1. Superelement 1 is connected to grid point 5, so its reduced matrices are added to the terms for that grid point. The reduced stiffness of .5 units is added to the existing term in that position (1.0) to get the assembly stiffness of 1.5 in that DOF. The reduced load of 2.0 units is added to the physical load on grid 5 (3.0 units), resulting in an assembly load of 5.0 units on that point. The resulting assembly stiffness and loading matrices are shown below.

Equation 7-5.

This superelement has no MPCs and constraints applied, so we proceed to the reduction process.

Equation 7-6.