Msc Nastran 2013.1 Superelements Guide

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Main Index
Superelements User’s Guide
1 Introduction and Fundamentals
Why Use Superelements? 4 Reduced Cost 4
Quicker Turnaround 4
Reduced Risk 4
Security 5
Fundamentals of Superelement Analysis 7
Partitioned Solutions 10
Static Condensation Process 11
Conventional Analysis 17
Superelement Analysis 19
2 How to Define a Superelement
Introduction 40
Defining List Superelements 44
List Superelement Definition on Element ID – the SEELT entry 46
Interior versus Exterior Points 47Superelement Partitioning 54
Main Index
Defining Parts 71
The Bulk Data Section Using PARTs 71Format of the Input File When PARTs are Used 72
Connecting PARTs to Other PARTs 78
Defining and Attaching External Superelements 94
Discussion of 2-step vs. 3-step methods 94
Definition of External Points 102
Creating External Superelements with EXTSEOUT 105
Using EXTSEOUT (2-Step) External Superelements 114
Using PARAM,EXTOUT (3-Step) External Superelements 126
The Superelement Map – SEMAP 138
Contents of the Superelement MAP – List Superelement 138
Contents of the Superelement MAP – PART Superelement 141
3 Single Level Superelement Analysis
Introduction 150
Comparison of Methods 223
4 Loads, Constraints, Case Control, and Parameters in Static Analysis
Introduction 228
List Superelements 229
PART Superelements 234
External Superelements 234
Main Index
Boundary Conditions in Static Analysis 242 Single Point Constraints (SPCs) 242
Grid Point Singularity Processing 243
Multipoint Constraints (MPCs) and Rigid Elements 244
Case Control 260
Parameter Controls 274
Special Considerations 276 SNORM for PART or External Superelements 276
5 Inertia Relief Analysis Using Superelements
Introduction 282
Interface for Inertia Relief Using Superelements 284
Manual Definition of Reference Points 284
Automatic Definition of Reference Points 286
Inertia Relief Examples (Freedom) 287
Baseline Residual Example 288
List Superelement Example 292
Comparison of results 297
Introduction 300
Internal Case Control Partitioning 301 Use of Load Sequences 301
Main Index
Baseline Residual Example 306
User Interface 327
Example – Multi-Level Superelement (Freedom) 339
Baseline Residual Solution 340
List Superelement Solution 341
PART Superelement Solution 345
External Superelement Solution 349
Comparison of Results 369
Introduction 372
375 Part Superelement Diagnostic Output 387
Sorted Bulk Data 387
List (SESET) Superelement Diagnostic Output 391
Sorted Bulk Data 391
Main Index
Controlling Results Output with SEDR 405
9 Introduction to Dynamic Analysis Using Superelements
Introduction 408
Dynamic Reduction – Component Modes Synthesis 413
Illustrative Example 450
Nastran Set Definitions – The USET Table 458
10 Input and Output for Dynamic Reduction
Introduction 464
Single Level Dynamic Reduction 468
Multi-Level Superelement Component Modes Synthesis Connection 517
Multi-Level Modal Reduction Example (fly swatter) 518
11 Dynamic Loading on Superelements
Introduction 542
Indirect Reference to EXCITEDID: LOADSET / LSEQ Method 554
Superelement Damping 559
Non-Superelement Solution 560
PART Superelement LOADSET / LSEQ Reference to EXCITEDID 581
PART Superelement Direct Reference to EXCITEDID 587
Frequency Response Illustrative Example 593
Non-Superelement Solution 593
List Superelement Direct Reference to EXCITEDID 609
PART Superelement LOADSET / LSEQ Reference to EXCITEDID 612
PART Superelement Direct Reference to EXCITEDID 618
External Superelement Dynamic Loading 624
Residual Vectors 624
Applying the Time History to the External Loading 627
Combining External Superelement Dynamic Loads with Residual Dynamic Loads
629 External Superelements and Damping 632
12 External Superelement Examples
Manual Connections 636
Static Examples 642
Static Examples Using 3-Step Method 650
Modal Examples 660 Modal Examples Using 2-Step Method (EXTSEOUT) 660
Modal Examples Using 3-Step Method 668
Transient Response Examples 676
Transient Response Examples Using 3-Step Method 683
Frequency Response Examples 695 Frequency Response Examples Using 2-Step Method (EXTSEOUT) 695
Main Index
13 Practical Image Superelements
Using SEMPLN to define a mirror plane 737
Example Using SEBULK, SELOC, and SEMPLN 737
Example using SECONCT 751
Multiple Image Example for Electronic Components 756 Baseline Solution (Full Model) 756
CSUPER Image Superelement Solution 757
PART Superelement Image Solution 762
External Superelement Image Solution 766
Comparison of Results 774
Introduction 778
Simple Linkage Example 781
Additional Reference Material 790
Introduction 792
Main Index
Introduction 812
Applying Loads on Upstream Superelements in Nonlinear Statics 824
Superelement Loading in SOL 106 824
Superelement Loading in SOL 400 830
Practical Buckling Example – Isolating and Individual Panel 833
Superelements in Heat Transfer 840
18 Random Vibration with Superelements
Introduction 846
External Superelement 869
Electronics Board Example 884
19 Output with XYPLOT
PART Superelement Example 920 CSUPER Example 926
Main Index
Illustrative Example: Modal Frequency Response 944
Illustrative Example: Random Vibration 950
APPENDICES
External Superelement 2
Main Bulk Data Section 4
PART Superelement 4
Processing Order 5

List of Superelement Enhancements Released Since Version 69
Main Index
2
Introduction to this Guide In finite element analysis, demand for computer resources has always exceeded existing capabilities. In
the early days of computers, when engineers were solving 3 x 3 problems by hand, computers were able
to handle problems as large as 11 x 11. Once engineers discovered this ability, the size of engineering
problems quickly grew to exceed the capacity of the existing systems. This process has repeated itself
time and time again. Today modern computers are capable of solving problems involving more than
100,000,000 equations with 100,000,000 unknowns, which is still not enough to satisfy the needs of
many engineers as more detail is added to finite element models and higher fidelity solutions are
required.
The limits on hardware resources, combined with budget restrictions (large runs and stochastic variations can be time-consuming), limits the ability of engineers to solve large, complicated problems with high
fidelity meshes. A solution to these problems (both hardware and time budget), can be achieved for many
models by using superelements in MSC.Nastran.
By using superelements, the analyst can not only analyze larger models (including those which exceed
the capacity of your hardware), but he can also become more efficient in performing the analysis, thus
allowing more analytical design cycles or iterations in the analysis. Another benefit of superelements
efficiency can be realized when models are subjected to probabilistic or stochastic analysis by varying portions of the structure. In design optimization, the use of superelements has become automated to help
reduce the overall optimization costs through a process called Automated External Superelement
Optimization (AESO) which is briefly described in Chapter 15: Design Sensitivity and Optimization
with Superelements, and more fully described in the Design Sensitivity and Optimization User’s Guide.
The principle used in superelement analysis is often referred to as substructuring. That is, the model is
divided into a series of components, each of which is processed independently resulting in a set of
matrices that are reduced to a boundary and describe the behavior of the component as seen by the rest
of the structure. Often these components are comprised of logical groupings of elements (an engine, a
wing, a fender, the exhaust system, etc.), hence the term superelement.
The reduced boundary matrices for the individual superelements are combined to form assembly
matrices which are referred to as the residual matrices. The residual matrices are solved using standard
techniques for calculating displacements (and velocities, accelerations for dynamic solutions). The
residual solution is then imposed on the boundary of each superelement so that the data recovery
(calculation of displacements, stresses, etc.) for the boundary can be combined with the data recovery for
the body loads on the superelement.
In static analysis the theory used in superelement processing is exact. In dynamics the reduction of the
stiffness is exact, but approximations occur during the reduction of the mass and damping matrices. The
dynamic solution can be improved dramatically by augmenting the static reduction with additional
dynamic degrees of freedom in a method called component modal synthesis, which is described in
Chapter 10: Input and Output for Dynamic Reduction.
In buckling analysis, the reduction of the differential stiffness uses the same theory as the static reduction,
but doesn’t provide an accurate solution compared to the non-reduced system. Unfortunately, there is no
improvement available as in dynamic analysis, however, a savvy user can use this to his advantage as
Main Index
3CHAPTER 1
3CHAPTER 1
described in Practical Buckling Example – Isolating and Individual Panel (Ch. 17). Superelements can be
used in nonlinear analysis, but the superelement is limited to a linear reduction in its initial orientation.
This User’s Guide is intended to be tutorial in format. That is, the emphasis is on how to use
superelements, not on the theory of superelements. Sufficient theory is presented for those who wish tounderstand the operations. Hand-solved samples are included to help the user understand the operations
involved when superelements are used. Sample MSC.Nastran input files and selected output are also
presented at appropriate points for clarity. All of the example files used in this guide are also delivered
with the standard MSC.Nastran delivery in the “install_dir/doc/seug/chapter#/subject” subdirectories.
This User’s Guide presumes that the reader is experienced in finite element analysis and wants to add
superelement technology to his repertoire of skills. The Guide is arranged so that an experienced finite
element analyst can start at the beginning and read only the information applicable to the type of analysis
desired. Overall information on superelements is presented first, followed by information for static
analysis, followed by dynamics and other features. It is recommended that the user read the first 3
chapters for foundation as well as Chapter 4 because much of the information presented in the section
on statics is applicable in subsequent chapters. However, an engineer should be able to read the
applicable sections without having to read unnecessary information.
Note: Even though the theory of static condensation is exact for static solutions, the numeric
conditioning of the structural matrices can affect the overall solution. If the superelement
stiffness matrices are well conditioned, then there will be only miniscule differences
between a residual-only solution and a superelement solution.
Main Index
Why Use Superelements?
Why Use Superelements? Efficiency is the primary reason to use superelements. A finite element model is rarely analyzed only
once. Often the model is modified and re-analyzed time and time again. By analyzing only the part of the structure which changes, the user can save significant time. Without using superelements, each analysis
can cost the price of a complete solution. Here is a partial list of the advantages of superelements:
Reduced Cost
Instead of solving the entire model each time, superelements offer the advantage of incremental
processing. On restarts this advantage is magnified by the need to process only the parts of the structure directly affected by the change. This means that if the user thinks ahead when defining superelements, it
is possible to achieve performance improvements on the order of anywhere from 2 to 30 times faster than
non-superelement methods (or more).
Because superelements can be processed individually with less computer resources required than a
complete, non-superelement solution, it is often possible to submit individual superelement processing
runs using fast queues (or on local workstations instead of servers), rather than waiting and running the
complete problem at once using an overnight queue. As stochastic and Monte Carlo simulations are
becoming more popular to understand the robustness of a structural design, fast solutions are a must.
Reduced Risk
Processing a model without using superelements is an all-or-nothing proposition. If an error occurs, the entire model must be processed again once the error is corrected. When using superelements, each
superelement need be processed only once, unless a change requires reprocessing the superelement. If an
error occurs during processing, only the affected superelement and the residual structure (final
superelement to be processed) need be reprocessed. The superelements that did not have an error do not
need to be processed again until a change is made to those superelements.
Large Problem Capabilities All computers have hardware limits. MSC.Nastran is designed so that problem size will not be limited
by the program. This means that limits on available disk space or memory are the only limitations that
should be encountered by a user. When the size of a model becomes too large to be processed on a
computer without using superelements, the user can use multiple computer resources to process each
superelement, or process one superelement at a time on a single computer resource. The reduced matrices
for each superelement can be stored on separate drives and brought together for the residual solution.
Main Index
5CHAPTER 1
Introduction and Fundamentals
Then data recovery can be done on each superelement separately, if desired. This process frees file space
and reduces disk usage and storage costs.
Partitioned Input and Output
Because superelements can be processed individually, separate analysis groups or organizations can
model individual parts of the structure and perform model checks without information from other groups.
An excellent example is the International Space Station which has many contractors working on the
structure. Each contractor models his own components and sends either complete or reduced models toa system integrator, who assembles the models to represent the many possible configurations, performs
analysis for each configuration, and sends results back to the individual contractors for their use. The
partitioned output format used in superelements allows for segmented data recovery; i.e., data recovery
can be requested for only the desired segments of the structure.
Security
Many companies work on proprietary or secure projects. These may range from keeping a new design from the competition, to keeping material data proprietary, to working on a highly confidential defense
program. Even when working on open programs, there is a need to send a representation of the model to
others so that they may perform a coupled analysis of an assembly which incorporates the component.
The use of external superelements allows users to send reduced boundary matrices that contain no
geometric information about the actual component-only mass, stiffness, damping and loads as seen at the
boundary. Upon receiving a set of reduced matrices in any format that can be read by MSC.Nastran, an
engineer can define an external superelement using those matrices and attach the foreign structure to his
model.
Automation with High Performance Computing
As models become larger and users demand high fidelity system level responses, the discipline of High
Performance Computing (HPC) has become a primary consideration for industries such as the
automotive industry. There are many techniques involved in HPC, including efficient use of CPU core
memory (i.e. L1, L2, L3 cache), shared memory parallel (SMP) schemes for enhanced matrix solutiontimes using multi-core CPU machines, and distributed memory parallel (DMP) schemes used to take
advantage of compute clusters with many different machines linked with a high-speed intranet to split
Note: Prior to MSC.Nastran Version 2005.5, there was a memory limit of 2 Gigawords (8
Gigabytes) because of a 32 bit integer address used by MSC.Nastran (“i4”). Beginning in
MSC.Nastran Version 2005.5, this limitation was removed by providing the option to use
a 64 bit integer address (“i8), thus making the number of words available for memory
address = 2^64, which is, in effect, an unlimited memory address. The higher memory can
be made available by specifying MODE=i8 on the command line. (note: the “mode”
keyword cannot be specified in an rc file as of MSC.Nastran v2010, so the user must
specify the “mode” keyword on the command line).
Main Index
Why Use Superelements?
and recombine solutions. While many of the schemes are purely mathematical (cache memory, SMP),
the distributed computing utilizes superelement technology as its core method for splitting and
recombining the solution of a large model. There are several schemes available to the user, such as
Geometric Domain Decomposition which automatically splits the model into superelements based on
GRID connectivity, Matrix Domain Decomposition which automatically splits the model into
superelements based on matrix characteristics, and Automated Component Modes Synthesis (ACMS)
which automatically splits the model based on GRID or Matrix characteristics and adds a Component
Modes Synthesis calculation for improved dynamic characteristics. While distributed HPC is based on
superelement technology, the discipline of HPC is beyond the scope of this document and will be covered
in another manual.
8/9/2019 Msc Nastran 2013.1 Superelements Guide
Fundamentals of Superelement Analysis
Superelement analysis can be described as a form of substructuring. That is, a model can be divided intosuperelements by the user in such a way that MSC.Nastran will process each superelement independently
of all other superelements. The processing of each superelement results in a reduced set of matrices
(mass, damping, stiffness, and loading) that represent the properties of the superelement as seen at its
connections to adjacent structures. Once all superelements have been processed, these reduced matrices
are assembled in what is known as the residual structure, and the assembly solution is performed. Data
recovery for each superelement is performed by expanding the solution at the attachment points, using
the same transformation that was used to perform the original reduction on the superelement.
Superelements can consist of physical data (elements and grid points) or can be defined as an image of another superelement or as an external superelement (a set of matrices from an external source to be
attached to the model). Figure 1-1 demonstrates a simplified illustration of condensing a structure to its
boundaries, solving a reduced system, and back-expanding the solution to obtain the data recovery for
the superelement. Example files are available to the user in the following installation directory and file
names: /doc/seug/chapter1/clamp-baseline.bdf, clamp-seset.bdf, and clamp-part-se.bdf.
Figure 1-1 Simplified Depiction of Superelement Reduction, Solution, and Data Recovery
The following figures illustrate the possible types of superelement. In Figure 1-2, a model of a portion
of a gear is shown. The physical model of one tooth can be represented as a superelement. This type is
called a primary superelement-one where the actual geometry for the superelement is defined in the bulk
data. Other gear teeth, as shown in Figure 1-2, are images of the first (primary) tooth. An image superelement is a superelement that uses the geometry of another superelement to describe it for
MSC.Nastran. These image superelements can save processing time in that they are able to re-use the
Main Index
reduced stiffness, mass, and damping matrices from their primary superelement, which reduces the
amount of calculations needed. Full data recovery is available for image superelements. An image
superelement can be an identical image, as shown in Figure 1-2, or a mirror image, as shown in
Figure 1-3. In Figure 1-3, the right side of the plate is a mirror image copy of the primary. Please note that images can have their own unique loadings. Only the stiffness, mass and damping is identical to the
primary. Another type of superelement is the external superelement, where a part of the model is
represented by using matrices from an outside source (the matrices can come from another MSC.Nastran
run). For these matrices no internal geometry information is available; only the grid points to which the
matrices are attached are known. An external superelement is shown in Figure 1-4. In this figure the finite
element model is on the left and the external superelement is represented by the dashed lines on the right.
Figure 1-2 A Primary Superelement and Several Identical Images
Figure 1-3 A Primary Superelement and its Mirror Image Superelement
Main Index
9CHAPTER 1
Figure 1-4 An External Superelement
In static analysis the theory used in superelement processing is exact. In dynamics the reduction of the
stiffness is exact, but approximations occur during the reduction of the mass and damping matrices. The
dynamic solution can be improved dramatically by augmenting the static reduction with additional
dynamic degrees of freedom in a method called component modal synthesis, which is described in
Chapter 10: Input and Output for Dynamic Reduction.
Main Index
Partitioned Solutions
Partitioned Solutions
Key Concepts in Superelement Partitions There are several key concepts that must be understood in the superelement formulation and processing;
these are:
• The input is partitioned into a separate set for processing each superelement. When MSC.Nastran is processing the bulk data for a model, the input is partitioned into a
separate set for each superelement, based on user instructions. The input used to accomplish this
partitioning is discussed in Chapter 2: How to Define a Superelement. Once the bulk data is partitioned into separate sets, each superelement is processed individually.
The degrees-of-freedom (DOFs) for each superelement are partitioned into sets in a manner
identical to that used in conventional analysis. That is, all DOFs for a superelement are
combined to create a G-set. Then MPCs and R-elements are used to define the M- and N-sets,
etc. (see Constraint and Set Notation (Ch. 1) in the MSC Nastran Reference Manual for a
complete description of MSC.Nastran sets). The only change in the definition of sets is the
definition of exterior DOFs. For each superelement the exterior DOFs are defined as the A-set,
which can contain physical and modal degrees of freedom.
• Boundary / Exterior DOFs are best described as those that are retained or kept for further analysis. A superelement’s exterior DOFs are best described as those that are retained
for further analysis, or you can think of them as boundary or attachment DOFs, where the
superelement connects to other superelements or the residual. Note that exterior DOF are not
required to attach to any other DOF. Structural matrices are assembled for each superelement,
and the matrices go through reduction processing until the only remaining terms are for the A-set
or attachment DOFs. These reduced matrices are used to represent the properties of the
superelement when it is attached to the rest of the model.
• Interior DOFs can be thought of as those that are condensed out during superelement processing. All DOFs of a superelement that are not exterior are called
interior DOFs (the omitted or O-set). These are the DOFs that are condensed out of the matrices
during the reduction process. Using either static or dynamic reduction, the stiffness, mass,
damping, and loading on these interior DOFs are transferred to the exterior DOFs.
• Each superelement is processed individually. The reduction process is best illustrated
using the process known as static condensation. For illustration purposes, we will ignore
Lagrange DOF in this discussion, since they are not compatible with superelement processing. In
static condensation we will start with the superelement matrices after all MPCs, R-elements, and
Main Index
11CHAPTER 1
SPCs have been processed. The set of DOFs remaining at this point are in terms of the F-set
(DOFs that are not constrained), which contains the O- and A-sets as subsets. Although the
interior DOFs include the M- and S-sets also, the interior DOFs in this guide will often be oftenreferred to as the O-set.
Static Condensation Process
The key to superelement processing is the reduction of the omitted DOF to the equivalent boundary
matrices as shown in the following figure:
Figure 1-5 Pictorial Example of Static Condensation
Note: Lagrange Rigid Element Processing. Typically, the dependent dof associated with
RBE’s are placed in the “mr” set, while the dependent dof associated with MPC’s are
placed in the “mp” set; which collectively define the M-Set. However, if the user specifies
RIGID=LAGRAN in the case control, the dependent dof are carried into the ASET as part
of the “lm” dof. Currently the MSC.Nastran processing does not handle the
RIGID=LAGRAN for superelements. Further discussion on this subject can be found in Nastran Set Definitions – The USET Table (Ch. 9).
Main Index
A comprehensive description of the equations used by MSC.Nastran can be found in Dynamic Reduction
and Component Mode Synthesis in SubDMAP SEMR3 (Ch. 1) in the MSC Nastran Reference Manual .A
more simplified presentation of the static condensation theory is included here for completeness. It is
assumed that the reader has some familiarity with the MSC.Nastran set notation – for more information on set notation, please refer to Degree-of-Freedom Sets (Ch. 7) in the MSC Nastran Quick Reference
Guide.
In this formulation we will start with the superelement matrices after all M-set (MPCs and Rigid
elements), and S-Set (active SPCs and permanent constraints on grid entries) have been processed. The
set of DOFs remaining at this point are in terms of the F-set (dof that are not constrained), which contains
the O- and A-sets as subsets. Although, in general, the interior dof may also include the M- and S-sets
also, the interior dof in this guide will often be often referred to as the O-set.
The static equation for the F-set is
(1-1)
This equation may be expanded to show the A-set and O-set partitions as
(1-2)
where the bar over a term ( and ) indicates that the sub-matrix represents the associated matrix
of terms for that set before the reduction operation. In a static solution, the T-set is equivalent to the A-
set and is defined as the “retained physical dof.” So, for a static solution the previous equation becomes:
(1-3)
If we look at the upper part of the equation, we obtain
(1-4)
(1-5)
K oo K oa K oa
T K aa
K oo U o K ot U t + P o =
K oo 1 –
U o total
K oo – 1 –
P o +=
Main Index
13CHAPTER 1
We can break up the total solution into two parts: the Fixed Boundary Solution , , and the
Free Boundary Solution, . To simplify the equation we define the physical boundary
transformation matrix between the exterior and interior motion as .
(1-6)
Physically, the matrix represents the influence coefficients to the free boundary solution, also
referred to as the Constraint Modes. That is, each column of this matrix represents the motion of the
interior points when one boundary dof is moved one unit while the other boundary points are held constrained. Therefore, the transformation matrix has one column for each exterior (boundary) dof (the
Aset for the superelement), and the number of rows are equal to the number of interior dof (the O-set for
the superelement). The constraint modes are discussed further in Example of Constraint Modes (Ch. 9)
which includes a graphic example.
When the constraints mode influence coefficients are multiplied by the boundary displacements of the
residual solution, the free boundary solution is obtained:
(1-7)
Where is the partition from the residual structure solution of the physical dof to the superelement
boundary dof.
In addition to the free boundary solution, the fixed boundary solution of the superelement must be
calculated in order to obtain the total solution for the superelement:
(1-8)
This matrix represents the static solution for the displacements of the superelement when the loads are
applied and the exterior points are held fixed. Based on these definitions, the total displacement of the
interior points can be defined as
(1-9)
U o f ree
Note: Computational Cost of Constraint Modes
The calculation of the constraint modes – more specifically – is typically the highest
cost associated with a static superelement solution because of the cost of calculating the
matrix . Even in dynamic solutions the cost associated with the constraint modes
is often a significant cost of the overall solution.
Got
1 – P o = =
U o total U o free U o f ixed +=
Main Index
A physical representation of this equation demonstrates the concepts of fixed boundary solution and free
boundary solution for a cantilever beam example.
Figure 1-6 Pictorial representation of fixed boundary solution and free boundary solution
Continuing with the reduction theory – we rewrite the equation for the lower part of Equation 1-3 as:
(1-10)
From which, we can obtain the reduced stiffness and boundary loading of the superelement:
(1-11)
(1-12)
The residual structure consists of all components of the model that were not assigned to any other
superelement, plus the assembly of the reduced superelement matrices. Each superelement is processed
in this manner, and its associated matrices are reduced to the exterior dofs. Once all superelements have
been processed, the reduced matrices are assembled into a system matrix during the residual structure
processing.
Thus, the total assembled stiffness matrix of the residual structure, , is represented by
K ot T
Got U t U o o + K t t U t + P t =
K t t P t
K t t K ot T
Got K t t +=
P t Got T
P o P t +=
(1-13)
The system or assembly solution is performed using the assembled matrices for the residual structure.
Once the assembly solution is known, the boundary solution is found for each superelement. This
boundary solution is used to calculate the interior displacements for each superelement, then standard
data recovery is available for all superelements, including the residual structure. Any output that is
available in standard (non-superelement) analysis is available in superelement analysis. The difference
is that the output is now partitioned by superelement.
K gg K j j K aa +=
Main Index
16
Manual Solution of a Small Superelement Example The following small problem is used to demonstrate how a static analysis is performed using
superelements. The solution to the problem is first shown using conventional analysis, then by using superelements.
Figure 1-7 Small NON-Superelement Example
For this example we are looking only at motion along the axis of the points, thus the problem is simplified
to contain only five DOFs. Note: this example is solved in MSC.Nastran and provided as part of the
documentation. The conventional analysis model is: /doc/seug/chapter1/simple-conventional.bdf and
the superelement solution is: /doc/seug/chapter1/simple-superelement.bdf.
The output for the simple-conventional.bdf file is as follows. Note that this .f06 listing, and other listings in this book may remove page headings and slightly re-arrange the format slightly to fit the page, so the
actual .f06 output format may be slightly different than shown
Main Index
17CHAPTER 1
Listing 1-1 MSC.Nastran Output for the Simple Example w/o Superelements
Conventional Analysis
In conventional analysis the problem is formulated in matrix form, constraints are applied, and the
resulting reduced problem is solved. The five-by-five stiffness matrix is as follows:
MSC NASTRAN JOB CREATED ON 19-MAR-11 AT 16:09:34 MARCH 19, 2011 MSC NASTRAN 7/15/10 PAGE 10
DEFAULT
0 BASELINE MODEL SUBCASE 1

1 G 0.0 0.0 0.0 0.0 0.0 0.0
2 G 2.500000E+00 0.0 0.0 0.0 0.0 0.0
3 G 4.000000E+00 0.0 0.0 0.0 0.0 0.0
4 G 3.500000E+00 0.0 0.0 0.0 0.0 0.0
5 G 0.0 0.0 0.0 0.0 0.0 0.0

POINT ID. TYPE T1 T2 T3 R1 R2 R3
2 G 1.000000E+00 0.0 0.0 0.0 0.0 0.0
3 G 2.000000E+00 0.0 0.0 0.0 0.0 0.0
4 G 3.000000E+00 0.0 0.0 0.0 0.0 0.0

1 G -2.500000E+00 0.0 0.0 0.0 0.0 0.0
5 G -3.500000E+00 0.0 0.0 0.0 0.0 0.0
F O R C E S I N S C A L A R S P R I N G S ( C E L A S 1 )
ELEMENT FORCE ELEMENT FORCE ELEMENT FORCE ELEMENT FORCE
ID. ID. ID. ID.
1 -2.500000E+00 2 -1.500000E+00 3 5.000000E-01 4 3.500000E+00
Main Index
18
(1-14)
Each row (or column) in the above matrix represents the terms associated with one DOF in the model.
The terms are in ascending order; that is, the first column represents DOF 1, and the last column
represents DOF 5. Replacing the springs by their numeric values, we have
(1-15)
We now apply the constraints to the problem. In finite element analysis, constraints are applied by removing the associated rows and columns from the matrix; therefore, after applying constraints we have
the static equation for the constrained structure
(1-16)
Solving the equations provides the solution for the free dof:
(1-18)
K 45 – K 45
=
K 23 K 23 K 34+ K – 34
K 34 K 45+
(1-19)
The constraint forces are obtained by partitioning the G-set stiffness matrix and solution vector as
follows:
Element Data Recovery
For this example, we can calculate the element forces based upon:
(1-22)
The CELAS1 convention for calculating element force is (Refer to Eq. (3-64) in the MSC Nastran Reference Manual ) :
(1-23)
(1-24)
The remainder of the elements forces can be calculated similarly.
(1-25)
(1-26)
(1-27)
Superelement Analysis We now formulate and solve the same problem using superelements, as shown in Figure 1-8. Because
the method of defining superelements has not been discussed yet, some of what follows has not been
U g
U 1
U 2
U 3
U 4
U 5
F 1
F 5
F 12 K 12 U 1 U 2 – =
F 12 1.0 0.0 2.5 – 2.5 = =
F 23 1.5 – =
F 34 0.5 =
F 45 3.5 =
20
defined. However, as you read further, more of the information will become clear. First a flowchart
showing the order of processing used to perform superelement analysis is shown in Figure 1-9, Flowchart
for Superelmeent Processing.
Figure 1-9 Flowchart for Superelmeent Processing
Main Index
21CHAPTER 1
Continuing with the superelement solution for our simple example, the definitions of the model shown
in Figure 1-8:
• Superelement 1 (SEID = 1)
• Grid points 1 and 2 are interior points. (These grid points are condensed out during the Phase
1 operations for superelement 1.)
• Elements and are interior or belong to superelement 1.
• The constraint at grid point 1 is contained in superelement 1.
• The load applied on grid point 2 is in superelement 1.
Note: Note to advanced users: in the MSC.Nastran SubDMAP listings, the parameter LPFLG is
used to control entry and processing within a superelement loop. Also, several of the
MALTER statements are strategically placed at the top and bottom of superelement loops
as follows:
$MALTER:QUALIFIERS SET
$MALTER:ELEMENT STRUCTURAL DAMPING GENERATION (KJJZ, BJJX, MJJX, K4JJ)
$MALTER:AFTER TOTAL SUPERELEMENT STIFFNESS, VISCOUS DAMPING, AND MASS
$MALTER:FORMULATED, STRUCTURAL + DIRECT INPUT (KJJ, BJJ, MJJ)
$MALTER:AFTER SUPERELEMENT LAD GENERATION (PJ)
$MALTER:AFTER UPSTREAM SUPERELEMENT MATRIX AND LOAD ASSEMBLY
$MALTER:(KGG, BGG, MGG, K4GG, PG)
$MALTER:AFTER SUPERELEMENT MATRIX AND LOAD REDUCTION TO A-SET,
$MALTER:STATIC AND DYNAMIC (KAA, MAA, BAA, K4AA, PA)
ENDIF $ EXTER $MALTER:BOTTOM OF PHASE 1 SUPERELEMENT LOOP
$MALTER:AFTER SUPERELEMENT DISPLACEMENT RECOVERY (UG)
$ SET THE FOLLOWING FOR DBCPATH
ENDIF $ MALTER:BOTTOM OF SUPERELEMENT DATA RECOVERY LOOP
Main Index
22
• Grid point 3 is exterior to superelement 1. (After all reduction [Phase 1] is completed for
superelement 1, all that remains is a set of matrices representing the superelement attached to
grid point 3.)
• Grid points 4 and 5 are interior to superelement 2.
• Grid point 3 is exterior to superelement 2.
• The load on grid point 4 is in superelement 2.
• Elements and are interior to or belong to superelement 2.
• The constraint on grid point 5 is contained in superelement 2.
• Residual structure (R.S. OR SEID = 0)
• Grid point 3 is interior to the residual structure.
• There are no elements left to belong to the residual structure.
• The load on grid point 3 is in the residual structure.
• Superelements 1 and 2 are processed independently, then the reduced matrices are assembled
at the residual.
Phase 1 Processing of Superelement 1
After the model is divided into superelements, the data for superelement 1 contains the following
information:
Figure 1-10 Simple Model, Superelement 1 Partition
Based on this model, is the exterior DOF and belongs to the A-set for superelement 1. Therefore, we
want to generate matrices for superelement 1, apply any constraints, and reduce the matrices to the
exterior DOF. The G-set for this superelement consists of the DOFs associated with grid points 1, 2, and
3. The following are the G-sized matrices:
u3
(1-28)
(1-29)
The boxed superscript 1 ( ) shown on the matrices indicates that they belong to superelement 1. Notice
that the force on grid point 3, , is not included in the Superelement Processing because the force is
applied to an exterior point, it is not included in the superelement, but is accounted for in the residual
structure. This fact is indicated in the matrix for the loading by placing a bar over the P3 term and
indicating that this represents only loading on grid point 3 associated with superelement 1.
Looking at the model, we see that grid point 1 is constrained. Because that grid point is interior to the
superelement, the constraint is applied as a part of the processing for superelement 1. The resulting
(reduced) stiffness matrix is
0 (1-30)
This matrix is now divided into interior (O-set) and exterior (A-set) DOFs, and a static condensation is
performed to reduce the matrices to the exterior DOFs.
First we compute the boundary transformation for superelement 1 becomes (recall equation (1-6)):
1 (1-31)
The physical meaning of this equation is that if Point 3 is moved +1.0 units, then Point 2 will move 0.5
units. This is exactly as expected considering that Point 1 is constrained.
Now, we use the transformation to compute the reduced stiffness at the boundary:
(1-32)
Again, the results make sense because there are two springs in series, for which the equation is readily available in text books or online services such as Wikipedia
(http://en.wikipedia.org/wiki/Hooke%27s_law#Derivation) :
K 12
– K 12
K 23
+ K 23
1 1 – 0
1 – 2 1 –
0 1 – 1
K f f 1 K 12 K 23+ K 23 –
K 23 – K 23
K oo K ot
2 1 –
1 – 1 = = =
1 –
Main Index
24
(1-33)
Now we have to reduce the applied loadings to the boundary. After applying the constraint to the loading
matrix, we have
(1-34)
Referring back to 1-12, the loads reduction to the boundary becomes:
(1-35)
Inspection reveals that this also makes sense. If grid points 1 and 3 are constrained, then ½ of the load
would be distributed to each point.
Phase 1 Processing of Superelement 2
After the model is divided into superelements, the data for superelement 1 contains the following
information:
Figure 1-11 Simple Model, Superelement 2 Partition
Degree of freedom is the exterior dof and belongs to the A-set for superelement 2. The reduction of
the stiffness and loads to the exterior dof follows. Since this is similar to superelement 1, only the critical
equations are shown.
P 3 1
+ 0.5 1.0 0.0 + 0.5 = = = =
(1-36)
(1-37)
Again, since grid point 3 is exterior to superelement 2, the load is not part of the load vector for
superelement 2. Recall, forces on exterior points are not included in the superelement matrices.
The constraint will be applied, this time at dof 5, thus the boundary transformation will be calculated and
applied to the stiffness and loads matrices, resulting in the following:
(1-38)
(1-39)
(1-40)
The transformation and reduced matrices make sense. If grid point 3 is moved 1.0 unit, grid point 4 willmove 0.5 units. As before, the stiffness is two springs in series, resulting in a combined stiffness of 0.5,
and the load of 3.0 units at grid point 4 gives a 1.5 unit reaction at point 3 if it is constrained.
Residual Structure Processing
The remaining dof, or in this case grid point 3, is defined as the residual structure.
• Phase 1 Processing
The phase 1 matrices are generated for the residual structure, based on any elements or loads remaining,
then the reduced matrices from the superelements are added at the appropriate dof.
After the combined (or assembled) matrix for the residual is formed, and constraints applicable to the
remaining DOFs are applied and the residual structure problem is solved as part of phase 2 operations.
K – 34
K 34
K + 45
K – 45
1 1 – 0
1 – 2 1 –
0 1 – 1
P t 2
P 3 2
+ 0.5 3 0.0 + 1.5 = = = =
26
Phase 3 represents the data recovery. In this case, since there is only one grid, the data recovery is trivial.
In the general case, the data recovery for the residual will include the residual element stresses, strains,
forces, etc.
Figure 1-1, depicts how the superelements feed into the residual structure. The individual components
that are assembled to make up the residual are shown on the left. The resulting assembly model is shown
on the right, where the system stiffness is: . The residual structure for this model contains
no elements, only one grid point, the physical load on that point, and the reduced matrices from the
superelements.
Figure 1-12 Simple Model, Residual Structure
Because all physical constraints have been applied at the superelement level, no reduction is performed
at the residual level for this model. If there were a physical model for the residual, then it would also go
through the application of constraints and a reduction to a final set of analysis matrices. Therefore, the
assembly matrix is the result of adding the superelement matrices together at grid point 3, or
(1-41)
(1-42)
(1-43)
Where the matrices and represent the reduced superelement stiffness matrices, and the
matrix represents the stiffness matrix resulting from any elements in the residual structure. In
this problem there are no elements in the residual structure; therefore, is null. Since there are
no SPCs or MPCs in the residual structure, there are not eliminations or reductions require, so
K K 1 K 2+=
K gg 0
K t t 2
(1-44)
Similarly, the loading matrix is the physical loadings applied on the residual, plus the reduced superelement loads. Because grid point 3 was in the residual, its load was not applied to the upstream
superelements, so the 2.0 unit force on grid point 3 is finally included at this point.
(1-45)
(1-46)
Now that the stiffness and loading matrices have been generated and reduced, we are ready to solve the
residual structure problem for the physical (T-set) displacements. This is referred to as the Phase 2
solution:
(1-47)
(1-48)
Now that the residual solution vector is available, the data recovery can be performed. In this case, there
is no additional data recovery for the residual structure since there are no elements, SPC constraints, or
MPC constraints. The data recovery will be performed for the superelements in the subsequent sections.
Review of the MSC.Nastran output from file /doc/seug/chapter1/simple-superelement.bdf. confirms the
solution.
Listing 1-2 MSC.Nastran Output for the Residual Structure of the Simple Example with
Superelements
Detailed explanations of the output will be provided in subsequent chapters.
K t t 0
P t =
U 3 0 1 1 --- 4.0 4.0 = =
1 MSC NASTRAN JOB CREATED ON 19-MAR-11 AT 16:09:34 MARCH 19, 2011 MSC NASTRAN 7/15/10 PAGE 22
DEFAULT SUPERELEMENT 0 , 1
0 SUPERELEMENT MODEL SUBCASE 1

Main Index
28
Data Recovery for Superelement 1
The first part of the Phase 3 data recovery involves partitioning the residual solution to the superelement
boundary. In this case, it is trivial since there is only one residual dof. The next step for superelement
data recovery is to calculate the solution vector for the interior dof. The interior solution has two components:
• Free boundary displacements
The free boundary displacements are based on the boundary solution of the residual structure (i.e. the
external dof are, in general, free dof in the residual). For this example, the only unknown becomes
based on the external dof boundary displacements (i.e. the T-set), or
Figure 1-13 Simple Example – Superelement 1 Free Boundary Displacement Data
Recovery
(1-49)
(1-50)
(1-51)
• Fixed boundary displacements
The fixed boundary solution is the solution vector for the interior dof when the T-set is fixed.
u2 t
Figure 1-14 Simple Example – Superelement 1 Fixed Boundary Displacement Data
Recovery
(1-52)
(1-53)
(1-54)
• Total interior solution:
The total interior solution is the summation of the free boundary solution and the fixed boundary solution
(1-55)
(1-56)
• The F-set (free set) displacements
The solution vector for the degrees of freedom allowed to move is obtained by merging the T-set and O-
Set:
(1-57)
uo
o
P o se id
U o
30
• The G-set displacements
The total solution vector for all dof in the superelement is calculated by merging the SPC constraints and
back-expansion of the MPC dependent dof. In this example, there are only SPCs, so the total solution
vector becomes:
• Constraint Forces
The constraint forces are obtained by partitioning the G-set stiffness matrix and solution vector as
follows:
(1-62)
(1-63)
• Element Data Recovery
For this example, we can calculate the element forces based upon:
(1-64)
U s seid
F 1 1 – 0 2.5
4.0
2.5 – = =
Main Index
31CHAPTER 1
The MSC.Nastran output for this superelement matches the hand calculations
F 12 K 12 U 1 U 2 – =
F 12
Main Index
32
Data Recovery for Superelement 2
Following the same procedure, the data recovery for superelement 2 produces the following results:
(1-68)
(1-69)
DEFAULT SUPERELEMENT 1 , 1 0 SUPERELEMENT MODEL SUBCASE 1

1 G 0.0 0.0 0.0 0.0 0.0 0.0
2 G 2.500000E+00 0.0 0.0 0.0 0.0 0.0
3 G 4.000000E+00 0.0 0.0 0.0 0.0 0.0

2 G 1.000000E+00 0.0 0.0 0.0 0.0 0.0

1 G -2.500000E+00 0.0 0.0 0.0 0.0 0.0
ID. ID. ID. ID.
U g 2 U 3
U 4
U 5
0.0
3.5 – = =
(1-70)
(1-71)
The MSC.Nastran output for this superelement matches the hand calculations:
Listing 1-4 MSC.Nastran output for Simple Example – Superelement 2
F 34 1.0 3.5 4.0 – 0.5 – = =
F 45 1.0 0.0 3.5 – 3.5 – = =
DEFAULT SUPERELEMENT 2 , 1
0 SUPERELEMENT MODEL SUBCASE 1

5 G 0.0 0.0 0.0 0.0 0.0 0.0

4 G 3.000000E+00 0.0 0.0 0.0 0.0 0.0

5 G -3.500000E+00 0.0 0.0 0.0 0.0 0.0
ID. ID. ID. ID.
Main Index
34
List of Superelement Enhancements Released Since Version 69
Superelement technology is constantly being advanced by the development staff of MSC.Nastran and New versions of MSC.Nastran are released periodically. This guide has been prepared with minimal
reference to the version number and is consistent with the MSC.Nastran 2010. The previous version of
this guide was released in conjunction with the MSC Nastran 2001. There have been several significant
releases in the meantime and it is felt to be of historical interest to show how each of these releases add
to the Superelement capability. It is also of great practical interest to those who are not using the most
recent release to see which of the capabilities described in this Guide are not available to them. The major
enhancements since Version 69 are identified here. Discussions of each of these topics are included in
this Guide.
Version 69
• Multilevel Superelements
• Upward Compatibility
• MSC/PATRAN Interface
• Sample Files
Version 69.1
• External Superelements for SOL 101 and SOL 103 – 3 Step Method
• PARAMs added: EXTOUT, EXTDROUT, EXTDR
• Support for MATRIXDB, DMIGDB, DMIGOP2, DMIGPCH
• Addition of EXTERNAL to SEBULK entry
• EXTRN bulk data entry introduced
Version 70.0
Version 70.5
• Use of External Superelements in Aeroelastic Analysis
• Coupled Fluid-Structure Models with Interface DOFs in Superelements
• PARAM, FLUIDSE
• Data Recovery support added for SOL 107 through 112
• CSUPER-type support for external SE via EXTOUT PARAMs
• PARAM,VMOPT,1 to support virtual mass at GSET level
• Better component mode handling byu bypassing INREL module
Version 70.7
• Differential Stiffness for Upstream Superelements
• External Superelement Data Recovery for SOL 146
• Modal Damping for Upstream Superelements, PARAM,SESDAMP,YES
• Add Modal Damping to Structural Damping for Superelements, PARAM,KDAMP,-1
• Special Superelement Reserved for Fluid Elements, PARAM,FLUIDSE, seid • Reduced Data Recovery Matrices, PARAM,MINIGOA
• Automated QSET Generation, PARAM,NQSET,n
Version 2001
• Simplified Static Loading Data in Dynamic Analysis (removal of LOADSET/LSEQ
restrictions)
• WEIGHTCHECK Mass Summation Output Including Upstream Superelements
• Parallel Processing Enhancements: Geometric Domain Decomposition
Main Index
36
Version 2004
• Enhancements to External Superelements – 2 Step Method • EXTSEOUT Cast Control
• BNDFIX/BNDFIX1, BNDFREE, BNDFREE1
• Residual Vector Enhancements
• Modal Participation Factors for Fluid Superelement
• Control of Superelement Differential Stiffness Calculation, PARAM,SEKD
• Adams Flexible Body Support, ADMSMNF
• Punch File Identification of Superelement ID
Version 2004R3 (2004.5)
• ACMS compatible with Superelements, Including External Superelements
Version 2005
Version 2005R2 (2005.1)
• ADMSMNF Support in SOL 600
• USET Support for MATMOD Option 16
• Support for Fixed Boundary Displacements in SOL 101 for EXTSEOUT Assembly Runs
• Support for Data Recovery with EXTSEOUT(DMIGPCH) option
Version 2005R3 (2005.5) / MDR1
• BSETi/BNDFIXi and CSETi/BNDFREEi Entries can be commingled
• Enhancements to EXTSEOUT • ASMBULK AUTO and MANQ options
Main Index
37CHAPTER 1
• DMIGSFIX option to Define DMIG Matrix Names
• Automatic QSET numbering scheme with PARAM AUTOQSET • Automatic OTM output for PLOTEL elements
• MATDB name equivalent to MATRIXDB
Version 2007 / MDR2
Version 2007.1 / MDR2.1
• EXTSEOUT support for OUTPUT4 with MATRIXOP4
• Merged Superelement Output, PARAM,FULLSEDR
Version 2010
• SOL 400 Support for Linear Solutions with Superelements
Main Index
38
Main Index

Introduction
The Superelement Map – SEMAP
Now that the basic concept of superelements has been explained, we can focus on how to define
superelements in MSC.Nastran. Superelements are defined using the Bulk Data Section of the input fileand controlled via File Management Section (FMS), Executive Control, PARAMeters, and Case Control.
There are three methods available for defining superelements:
• List Superelement: Commonly referred to as “SESET” superelements
• PART Superelement: Commonly referred to as “BEGIN SUPER” superelements
• External Superelement: Commonly referred to as “EXTSEOUT” or “EXTOUT” or “DMIG”
superelements
The purpose of this chapter is to describe the input required to define each type of superelement as well
as discuss some of the advantages and disadvantages of each method.
Note: BEGIN SUPER vs. BEGIN BULK Superelement Partitioning
MSC.Nastran maintains two distinct paths for superelement processing in the solution
sequences. When a BEGIN SUPER entry is present the program uses the more modern
SEP1X module to make the SEMAP table used to control partition of superelements. When there is a BEGIN BULK entry but no BEGIN SUPER entries a parallel path using the older
SEP1 module is used instead. For a more detailed discussion of these two methods, please
refer to the Superelement Analysis (p. 394) in the MSC Nastran Reference Manual .
Main Index
41CHAPTER 2
Superelement vs. Residual
Each superelement in MSC.Nastran is identified by an integer identification known as the SEID. Each
SEID must be a unique positive integer (with the exception of the residual structure, which is known as superelement 0). If no superelements are defined, the model is assumed to be a residual-structure-only
model, and a conventional (non-superelement) solution is performed. By default, all superelement
solution sequences perform a conventional solution if no superelements are defined. The superelement
solution sequences for MSC.Nastran are as follows:
Table 2-1 Solution Sequences that Support Superelements
SOL Number SOL Name Description
101 SESTATIC Statics with options:
Linear steady state heat transfer.
Alternate reduction.
Inertia relief.
Static analysis.
Alternate reduction.
Inertia relief.
107 SEDCEIG Direct complex modes 108 SEDFREQ Direct frequency response
109 SEDTRAN Direct transient response
110 SEMCEIG Modal complex eigenvalues
111 SEMFREQ Modal frequency response
112 SEMTRAN Modal transient response
128 SENLRHM Nonlinear harmonic response 129 NLTRAN Nonlinear or linear transient response
144 AESTAT Static Aeroelastic response
145 SEFLUTTER Aerodynamic flutter
146 SEAERO Aeroelastic response
analysis with options:
analysis with options:
Main Index
43CHAPTER 2
Three Types of Superelements
As mentioned in the Introduction to this chapter, MSC.Nastran has 3 basic methods for defining
superelements:
• List Superelements: as the name implies, List Superelements are defined by specifying a list
(or set) in the main Bulk Data section of the input file. These are often referred to as “SESET”
superelements because the most common way of defining them is with the SESET bulk data
entry. When superelements are defined using this approach, the model defined in this section of
the input is cut apart into separate components (each component is a superelement). A good way
to describe this is to say that the program is using a cookie-cutter approach with the model,
taking a model and dividing it into superelement lists for processing. Many models of this type
could be run as a stand-alone, or “one shot” model without superelement processing. However,
a savvy user who has repeated components can use the List Superelements to efficiently image
(copy, repeat, mirror) parts of the model.
• PART Superelements: PART superelements are defined by defining each superelement in its
own Partitioned Bulk Data section. These separate sections of the bulk data are self-contained in
that each section contains all geometry, elements, properties, constraints, parameters, and
loading data for that component of the model. When PARTs are used the program works in a
manner similar to an assembly process. That is, a series of separate components are assembled into the final finite element model, i.e. the residual structure.
• External superelements: External Superelements are similar to PART superelements in many
respects, except rather than solving the model in a single run, the superelement can be processed
and output for use at a later time. There are many advantages of external superelements: 1) the
reduced matrices are compact and can be added to another structure while maintaining full
fidelity of the component behavior on the system, 2) they can be easily re-used as many times as
necessary at a very low runtime cost, 3) they can protect design information (proprietary
geometry) and material information (composite layup), 4) key results can be monitored without
the need for full data recovery, 5) files can be easily shared and maintained across different
organizations or design groups.
The three approaches can be used independently or together depending upon the application. In versions
prior to Version 69, only the list superelements were available. Input files from versions prior to Version
69 of MSC.Nastran can be used in later versions, and any superelement input will be treated as before.
Once PARTs are defined, the program uses a different set of rules to partition the Main Bulk Data Section
into superelements. The modern external superelements were first introduced with PARAMs in V69.1 and enhanced to include convenient case control commands in V2004. A list of enhancements by
version can be found in List of Superelement Enhancements Released Since Version 69.
Main Index
44
Defining List Superelements As the name implies List Superelements are defined by specifying a list or set; but List Superelements
As the name implies, List Superelements are defined by specifying a list or set; but List Superelements
can only be defined in the main Bulk Data section of the MSC.Nastran input file. The superelement
processing partitions the model into separate sections based on a list of interior grid points and/or
elements defined by the user. The Main Bulk Data Section is defined as the ‘first’ bulk data input section
which occurs after BEGIN BULK or BEGIN SUPER [=0].
List Superelements can be defined on the GRID entry, the SESET entry, or the SEELT entry. In addition,
a superelement can be defined as a copy of another superelement (image superelement) or by using
matrices from an external source (external superelement) by using the CSUPER entry. Refer to
Chapter 13: Practical Image Superelements for more details on image superelements.
Any grid points defined in the main bulk data that are not assigned to a superelement, using either a
SESET, GRID, or a SEELT entry will automatically be assigned to the residual structure (SEID = 0).
For list superelements defined with BEGIN BULK: if SPOINTs or EPOINTs exist in the input stream,
they are automatically and permanently assigned to the residual structure and cannot be reassigned to be
interior to a superelement. However, if the user specifies BEGIN SUPER, then SPOINTs and EPOINTs
can be assigned to any superelement. The reason is that BEGIN BULK and BEGIN SUPER undergo
different superelement processing as described in the Superelement Analysis (Ch. 1) in the MSC Nastran
Reference Manual
List Superelement Definition with the SESET Entry
The SESET entry can be used to define the interior GRIDs associated to a Superelement. The user
simply defines the SESET, its SEID and the associated GRID list for the interior GRIDs.
Defines interior grid points for a superelement.
Format:
Example:
1 2 3 4 5 6 7 8 9 10
SESET SEID G1 G2 G3 G4 G5 G6 G7
SESET 5 2 17 24 25 165
Main Index
45CHAPTER 2
Alternate Format and Example:
The SESET entry takes precedence over the SEID field on the GRID entry defined below. SESET
defines grid and scalar points to be included as interior to a superelement. SESET may be used as the
primary means of defining superelements or it may be used in combination with SEELT entries which
define elements interior to a superelement. For additional comments on the SESET entry, please refer
to the SESET (Ch. ) in the MSC Nastran Quick Reference Guide.
There is no limit on the number of SESET entries that can be used to define a superelement, and the
THRU option on the SESET entry, can have open sets. That is, not all grid points in the range specified
need to exist. If a nonexistent grid point is referenced by an SESET entry, that part of the entry is ignored.
If BEGIN SUPER is used and SEELT is present, then SEELT will take precedence over both the SESET
entry and GRID entry SEID field.
List Superelement Definition with the GRID Entry An interior superelement GRID can also be defined on the GRID entry in the SEID field.
Defines the location of a geometric grid point, the directions of its displacement, and its permanent
single-point constraints.
Field Contents
SEID Superelement identification number. Must be a primary superelement. (Integer > 0)
Gi Grid or scalar point identification numbers. (0 < Integer < 1000000; G1 < G2)
GRID Grid Point
1 2 3 4 5 6 7 8 9 10
GRID ID CP X1 X2 X3 CD PS SEID
GRID 2 3 1.0 -2.0 3.0 316
Main Index
*See the GRDSET entry for default options for the CP, CD, PS, and SEID fields.
List Superelement Definition on Element ID – the SEELT entry
As an alternative to defining the superelement based on GRID ids, the superelement can be defined based on element ids using the SEELT entry. If the main bulk data section is defined with BEGIN SUPER
[=0] instead of BEGIN BULK , then the SEELT entry can be used to define the elements which belong
to each superelement. The advantage is that sometimes it is easier to define element ranges rather than
GRID ranges for large models. Refer to the note on superelement processing based on BEGIN SUPER
vs. BEGIN BULK Superelement Partitioning.
Reassigns superelement boundary elements to an upstream superelement
Format:
Field Contents
lD Grid point identification number. (0 < Integer < 100,000,000, see Remark 9.)
CP Identification number of coordinate system in which the location of the grid
point is defined. (Integer > 0 or blank*)
X1, X2, X3 Location of the grid point in coordinate system CP. (Real; Default = 0.0)
CD Identification number of coordinate system in which the displacements,
degrees- of-freedom, constraints, and solution vectors are defined at the grid
point. (Integer > -1 or blank, see Remark 3.)*
PS Permanent single-point constraints associated with the grid point. (Any of
the Integers 1 through 6 with no embedded blanks, or blank*.)
SEID Superelement identification number. (Integer > 0; Default = 0)
Note: Note that a SESET entry will override the definition on the GRID entry. Also, theGRDSET entry can be used to define the default SEID for all GRIDs in the main bulk data
section.
1 2 3 4 5 6 7 8 9 10
SEELT SEID EID1 EID2 EID3 EID4 EID5 EID6 EID7
Main Index
47CHAPTER 2
Example:
Alternate Format and Example:
The SEELT entry can also be used to assign elements connected entirely to boundary GRIDs to the
upstream superelement.
Interior versus Exterior Points
Any GRID point assigned to a superelement by the user is interior to that superelement. Exterior grid
points are defined by the program based on processing order. If a grid point is connected to a
superelement but is interior to a downstream superelement (one which is processed later), that grid point
is exterior to the upstream superelement. Processing order can be defined by either the user or the
program. Other than Chapter 7: Multi-Level Superelement Analysis, we will limit the discussion in this
Guide to what is known as a single-level processing tree, where all exterior points of the superelements are assigned as interior to the residual structure.
Simple Example using Cantilever Plate
To illustrate the concept of interior vs. exterior grid points, we can use the cantilever plate as an example.
In this case, we want to define two superelements and a residual as shown in Figure 2-1; the non-
superelement model for this can be found at: /doc/seug/chapter2/cantilever-beam/baseline.bdf, and the
corresponding SESET model is in the same directory in file seset.bdf.
SEELT 2 147 562 937
SEELT SEID EID1 “THRU
Field Contents
“THRU” option EID1 < EID2.)
Figure 2-1 Simple Example use to define List Superelements
We will define the interior grids for each superelement with the SESET entry. Note that this example
demonstrates both forms of the SESET entry (simple list and “thru” list).
The resulting superelement definition is shown in Figure 2-2.
Figure 2-2 Example Model Superelement Interior Grid Definition
Considering superelement 10, the grid definitions are as follows:
Table 2-2 Sample SESET Entries used to define a List Superelement
$ Tip.10
$ Base.20
Main Index
49CHAPTER 2
Figure 2-3 Interior and Exterior Grids for Superelement 10
Note that GRID 107 and 207 are exterior to Superelement 10 and interior to Superelement 0 (the residual). The .f06 file clearly lists the interior and exterior GRID definitions as well as the list of
elements for each superelement
Listing 2-1 Superelement Summary Based on List Superelements with BEGIN BULK
Note that instead of SESET, this example could have been defined by using BEGIN SUPER (instead of
BEGIN BULK) and the following SEELT definition: SEELT,10,7,thru,10. In this case the superelement
processing would have gone through the ‘new’ superelement processing and the output would have been
SUPERELEMENT 10

SUPERELEMENT 10
LIST OF EXTERIOR POINTS ( TOTAL NO. OF EXTERIOR POINTS = 2 )
INDEX -1- -2- -3- -4- -5- -6- -7- -8- -9- -10-
1 107 207
LIST OF ELEMENT ID-S ( TOTAL NO. OF ELEMENTS = 4 )
INDEX -1- -2- -3- -4- -5- -6- -7- -8- -9- -10-
1 7 8 9 10
Main Index
50
different as shown in Listing 2-2. See also the Note on BEGIN SUPER vs. BEGIN BULK Superelement
Partitioning
Listing 2-2 Superelement Summary Based on List Superelements with BEGIN SUPER
Demonstration of Defining Interior Points in Patran
The cantilever plate example in the previous section can be easily defined in Patran. It is presumed that
the user has a working knowledge of Patran and groups. First, to define the superelements, the user opens
the proper form in Patran by selecting the Meshing tab and the Superelement Icon
0 SUPERELEMENT 10
LIST OF EXTERIOR POINTS ( TOTAL NO. OF EXTERIOR POINT = 2 )
INDEX -1- -2- -3- -4- -5- -6- -7- -8- -9- -10-
1 1B 2B
0 SUPERELEMENT 10
LIST OF INTERIOR POINTS ( TOTAL NO. OF INTERIOR POINT = 8 )
INDEX -1- -2- -3- -4- -5- -6- -7- -8- -9- -10-
1 108 109 110 111 208 209 210 211
0 SUPERELEMENT 10
LIST OF ELEMENTS ( TOTAL NO. OF ELEMENTS = 4 )
INDEX -1- -2- -3- -4- -5- -6- -7- -8- -9- -10-
1 7 8 9 10
Main Index
51CHAPTER 2
Figure 2-4 Opening the Create Superelement form in Patran
Next the user simply selects the group which will define each superelement. The “dot” in the “SE.10” will tell Patran to honor the number “10” as the SEID when it exports the MSC.Nastran bdf SESET
entries.
Figure 2-5 Patran Superelement Definition Based on Groups
By default, Patran will automatically detect grids 107 and 207 as the superelement exterior dof. There
are some special cases where the user may want to redefine the exterior dof and they are covered later in
this Guide
When creating an analysis job, the user must specify if superelements are desired, otherwise Patran will
not write a superelement model. By default, a PART superelement model is written, but the user can also
chose a list (SESET) superelement model as shown in the example below.
Main Index
53CHAPTER 2
Figure 2-6 Patran Analysis Setup to Write a List (SESET) Superelement Input File
Main Index
Superelement Partitioning
Each superelement is processed as an independent model. To achieve this, MSC.Nastran creates separate
bulk data for each superelement. In the case of Part Superelements, this is naturally performed based on
p p y p
the user directive BEGIN SUPER = SEID. However, for list superelements, MSC.Nastran must interrogate and partition the bulk data into its constituent superelements.
List superelements are partitioned based on user input. Recall that list superelements are defined with
SESET entries, or GRID entries with and SEID specified on field 9, or by defining BEGIN SUPER in
conjunction with SEELT in the main bulk data section.
The partitioning process for list superelements is described as follows.
• First the processing order is defined for the model; i.e. which superelement will be processed first. For single-level superelements, the processing order is not important. However, for multi-
level superelements, the tip superelements must be processes first, followed by the collector
superelements in a hierarchy that will feed into the residual structure. Once the processing order
is defined, the bulk data is partitioned for each superelement based on the processing order.
• All interior grid points assigned to the superelement are placed in the bulk data section for its
associated superelement. These grids are also removed from the residual structure bulk data.
• All elements connected to the interior grid points of the superelement are placed in its associated bulk data section. These elements are removed from the residual bulk data.
• All exterior points are stored with the superelement bulk data. These grids remain in residual
bulk data section and may also be defined in other superelement bulk data sections.
• Any loading entries specific to the interior grid points and/or interior elements are removed from
the residual bulk data and associated with the superelement bulk data. Any information removed
from the residual bulk data and associated to a superelement is not available for use in any other
superelement.
• Any loads that are specific to grids interior to the residual structure are retained in the residual
bulk data section and processes with the residual structure. (Refer to the simple example in
Superelement Analysis (Ch. 1)).
• Copies are made of common data. For example, property entries can be applicable to elements
in multiple superelements. Also loadings such as PLOAD4 and GRAV could apply to multiple
superelements. Common data is not removed from the residual bulk data, but it i

Msc Nastran 2013.1 Superelements Guide

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