If structural matrices are available externally, you can input the matrices directly into NX Nastran without providing all the modeling information. Normally this is not a recommended procedure since it requires additional work on your part. However, there are occasions where the availability of this feature is very useful and in some cases crucial. Some possible applications are listed below:
• Suppose you are a subcontractor on a classified project. The substructure that you are analyzing is attached to the main structure built by the main contractor. The stiffness and mass effects of this main structure are crucial to the response of your component, but geometry of the main structure is classified. The main contractor, however, can provide you with the stiffness and mass matrices of the classified structure. By reading these stiffness and mass matrices and adding them to your NX Nastran model, you can account for the effect of the attached structure without compromising security.
• Perhaps you are investigating a series of design options on a component attached to an aircraft bulkhead. Your component consists of 500 DOFs and the aircraft model consists of 100,000 DOFs. The flexibility of the backup structure is somewhat important. You can certainly analyze your component by including the full aircraft model (100,500 DOFs).
However, as an approximation, you can reduce the matrices for the entire aircraft down to a manageable size using dynamic reduction (see“Advanced Dynamic Analysis Capabilities”
). These reduced mass and stiffness matrices can then be read and added to your various component models. In this case, you may be analyzing a 2000-DOF system, instead of a 100,500-DOF system.
• The same concept can be extended to a component attached to a test fixture. If the finite element model of the fixture is available, then the reduced mass and stiffness matrices of the fixture can be input. Furthermore, there are times whereby the flexibility of the test fixture at the attachment points can be measured experimentally. The experimental stiffness matrix is the inverse of the measured flexibility matrix. In this instance, this experimental stiffness matrix can be input to your model.
One way of reading these external matrices is through the use of the direct matrix input feature in NX Nastran.
Direct Matrix Input
The direct matrix input feature can be used to input stiffness, mass, viscous damping, structural damping, and load matrices attached to the grid and/or scalar points in dynamic analysis. These matrices are referenced in terms of their external grid IDs and are input via DMIG Bulk Data entries. As shown inTable 2-3, there are seven standard kinds of DMIG matrices available in dynamic analysis.
Table 2-3. Types of DMIG Matrices in Dynamics
Matrix G Type P Type {P2g}. The four matrices K2GG, M2GG, B2GG, and K42GG must be real and symmetric. These matrices are implemented at the g-set level (see“The Set Notation System Used in Dynamic Analysis”for a description of the set notation for dynamic analysis). In other words, these terms are added to the corresponding structural matrices at the specified DOFs prior to the application of constraints (MPCs, SPCs, etc.).
The symbols for p-type matrices in standard mathematical format are [K2pp], [M2pp], and [B2pp].
The p-set is a union of the g-set and extra points. These matrices need not be real or symmetric.
The p-type matrices are used in applications such as control systems. Only the g-type DMIG input matrices are covered in this guide.
DMIG Bulk Data User Interface
In the Bulk Data Section, the DMIG matrix is defined by a single DMIG header entry followed by a series of DMIG data entries. Each of these DMIG data entries contains a column of nonzero terms for the matrix.
Header Entry Format:
1 2 3 4 5 6 7 8 9 10
DMIG NAME “0" IFO TIN TOUT POLAR NCOL
Column Entry Format:
6 = Symmetric (input only the upper or lower half) TIN Type of matrix being input:
1 = Real, single precision (one field is used per element) 2 = Real, double precision (one field per element)
3 = Complex, single precision (two fields are used per element) 4 = Complex, double precision (two fields per element)
TOUT Type of matrix to be created:
0 = Set by precision system cell (default) 1 = Real, single precision
2 = Real, double precision 3 = Complex, single precision 4 = Complex, double precision
POLAR Input format of Ai, Bi. (Integer = blank or 0 indicates real, imaginary format;
integer > 0 indicates amplitude, phase format.)
NCOL Number of columns in a rectangular matrix. Used only for IFO = 9.
GJ Grid, scalar, or extra point identification number for the column index or column number for IFO = 9.
CJ Component number for GJ for a grid point.
Gi Grid, scalar, or extra point identification number for the row index.
Field Contents Ci Component number for Gi for a grid point.
Ai, Bi Real and imaginary (or amplitude and phase) parts of a matrix element. If the matrix is real (TIN = 1 or 2), then Bi must be blank.
DMIG Case Control User Interface
In order to include these matrices, the Case Control must contain the appropriate K2GG, M2GG, B2GG, or K42GG command. (Once again, only the g-type DMIG input matrices are included in this guide.)
Examples
1. K2GG = mystiff
The above Case Control command adds terms that are defined by the DMIG Bulk Data entries with the name “mystiff ” to the g-set stiffness matrix.
2. M2GG = yourmass
The above Case Control command adds terms that are defined by the DMIG Bulk Data entries with the name “yourmass” to the g-set mass matrix.
3. B2GG = ourdamp
The above Case Control command adds terms that are defined by the DMIG Bulk Data entries with the name “ourdamp” to the g-set viscous damping matrix.
4. K42GG = strdamp
The above Case Control command adds terms that are defined by the DMIG Bulk Data entries with the name “strdamp” to the g-set structural damping matrix.
Use of the DMIG entry for inputting mass and stiffness is illustrated in one of the examples in
“Real Eigenvalue Analysis”.