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Disclaimer MSC.Software Corporation reserves the right to
make changes in specifications and other information
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Revision 0. November 15, 2013
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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
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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
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PART Superelements 241
External Superelements 241
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
List Superelements 274
PART Superelements 274
External Superelements 275
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
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Baseline Residual Example 306
External Superelements 310
User Interface 327
List Superelements 329
PART Superelements 329
External Superelements 330
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
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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
List Superelements 470
PART Superelements 492
External Superelements 513
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
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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
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13 Practical Image Superelements
Using SEMPLN to define a mirror plane 737
Example Using SEBULK, SELOC, and SEMPLN 737
External Superelements 749
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
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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
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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
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List of Superelement Enhancements Released Since Version 69
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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
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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.
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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.
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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).
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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.
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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
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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
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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.
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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
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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).
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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 +=
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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 +=
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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 +=
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(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
+=
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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
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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
POINT ID. TYPE T1 T2 T3 R1 R2 R3
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
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(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+
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(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 =
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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
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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
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• 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:
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(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 –
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(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 = = = =
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(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.
• Phase 2 Processing
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.
• Phase 3 Processing
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 = = = =
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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
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(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
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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
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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
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• 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 – = =
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The MSC.Nastran output for this superelement matches the hand
calculations
F 12 K 12 U 1 U 2 –
=
F 12
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Data Recovery for Superelement 2
Following the same procedure, the data recovery for superelement 2
produces the following results:
(1-68)
(1-69)
1 MSC NASTRAN JOB CREATED ON 19-MAR-11 AT 16:09:34 MARCH 19, 2011
MSC NASTRAN 7/15/10 PAGE 29
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
POINT ID. TYPE T1 T2 T3 R1 R2 R3
2 G 1.000000E+00 0.0 0.0 0.0 0.0 0.0
POINT ID. TYPE T1 T2 T3 R1 R2 R3
1 G -2.500000E+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.
U g 2 U 3
U 4
U 5
0.0
3.5 – = =
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(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 – = =
1 MSC NASTRAN JOB CREATED ON 19-MAR-11 AT 16:09:34 MARCH 19, 2011
MSC NASTRAN 7/15/10 PAGE 38
DEFAULT SUPERELEMENT 2 , 1
0 SUPERELEMENT MODEL SUBCASE 1
5 G 0.0 0.0 0.0 0.0 0.0 0.0
POINT ID. TYPE T1 T2 T3 R1 R2 R3
4 G 3.000000E+00 0.0 0.0 0.0 0.0 0.0
POINT ID. TYPE T1 T2 T3 R1 R2 R3
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.
Main Index
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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
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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
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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
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• 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
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Main Index
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Introduction
The Superelement Map – SEMAP
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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
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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
SOL Number SOL Name Description
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analysis with options:
analysis with options:
SOL Number SOL Name Description
Main Index
43CHAPTER 2
Three Types of Superelements
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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
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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:
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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
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*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:
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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.)
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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
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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
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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
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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.
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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
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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
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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