S7-1NAS105, Section 7, May 2005 SECTION 7 SUPERELEMENT ANALYSIS

S7-2NAS105, Section 7, May 2005

S7-3NAS105, Section 7, May 2005 TABLE OF CONTENTS SectionPage WHAT IS A SUPERELEMENT?…………………………………………………………………7-9 ADVANTAGES OF SUPERELEMENT ANALYSIS……………………………………………7-10 DISADVANTAGES OF SUPERELEMENT ANALYSIS………………………………………7-12 HOW ARE SUPERELEMENTS DEFINED IN MSC.NASTRAN?……………………………7-13 MAIN BULK DATA SUPERELEMENT DEFINITION………………………………………….7-15 MAIN BULK DATA GRID POINT PARTITIONING…………………………………………….7-16 BULK DATA USED TO DEFINE PARTS……………………………………………………….7-17 BULK DATA USED TO DEFINE SUPERELEMENTS……………………………………… BULK DATA USED TO CONNECT PARTS……………………………………………………7-19 SEBNDRY ENTRYelement Boundary-Point Definition……………………………………….7-20 SECONCT ENTRY……………………………………………………………………………….7-21 SEEXCLD ENTRY……………………………………………………………………………… SEBULK ENTRY………………………………………………………………………………….7-24 SAMPLE PROBLEM- STEEL STAMPING…………………………………………………….7-26 SAMPLE PROBLEMSTEEL STAMPING SAMPLE SUPERELEMENT 1………………..7-28

S7-4NAS105, Section 7, May 2005 TABLE OF CONTENTS SectionPage SAMPLE PROBLEMSTEEL STAMPING SESET ENTRIES FOR MAIN BULK DATA SUPERELEMENTS…………………………………………………….7-33 PARTITIONED SOLUTIONS……………………………………………………………………7-34 THEORY OF STATIC CONDENSATION………………………………………………………7-36 CONVENTIONAL ANALYSIS……………………………………………………………………7-38 SUPERELEMENT ANALYSIS………………………………………………………………… BULK DATA FOR STATIC LOADS ON SUPERELEMENTS……………………………… SINGLE-POINT CONSTRAINSTS ON SUPERELEMENTS…………………………………7-50 MPCs AND RIGID ELEMENTS IN SUPERELEMENTS…………………………………… RIGID CONNECTION OF TWO SUPERELEMENTS…………………………………………7-53 SUPERELEMENT CASE CONTROL COMMANDS………………………………………….7-54 SUPER COMMAND………………………………………………………………………………7-55 EXPANDED VERSUS CONDENSED………………………………………………………….7-56 SUPER COMMAND EXAMPLEONE LOADING CONDITION…………………………….7-58 MULTIPLE LOADING CONDITIONS IN SUPERELEMENT CASE CONTROL – OPTION 1…………………………………………………………………7-59

S7-5NAS105, Section 7, May 2005 TABLE OF CONTENTS SectionPage MULTIPLE LOADING CONDITIONS IN SUPERELEMENT CASE CONTROL – OPTION 2……………………………………………………… REASONS TO USE OPTION 2 FOR MULTIPLE LOADINGS………………………………7-62 MULTIPLE LOADINGS – SAMPLE OF OPTION 1……………………………………………7-63 MULTIPLE LOADINGS – SAMPLE OF OPTION 2……………………………………………7-64 PARAMETERS IN CASE CONTROL………………………………………………………… SAMPLE SUPERELEMENT STATIC RUN INPUT……………………………………………7-66 SAMPLE SUPERELEMENT STATIC RUN INPUT USING PARTS………………………7-68 SUPERELEMENT REDUCTION METHODS AVAILABLE IN DYNAMIC ANALYSIS…….7-71 DEGREES OF REDUCTION…………………………………………………………………….7-72 COMPARISON OF REDUCTION METHODS…………………………………………………7-73 ADVANTAGES OF EACH REDUCTION METHOD………………………………………… CALCULATION OF NORMAL MODES USING STATIC REDUCTION ONLY……………7-75 CALCULATION OF NORMAL MODES USING DYNAMIC REDUCTION FOR SUPERELEMENT………………………………………………………………….7-76

S7-6NAS105, Section 7, May 2005 TABLE OF CONTENTS SectionPage FIXED BOUNDARY SOLUTIONS (PARAM, FIXEDB, -1)………………………………….7-78 PROCEDURES FOR SUPERELEMENT DYNAMIC REDUCTION…………………………7-79 SPECIFICATION OF FIXED AND FREE BOUNDARY DEGREES OF FREEDOM………7-81 REFERENCES FOR CMS……………………………………………………………………….7-82 SUPERELEMENT DYNAMICS EXAMPLE…………………………………………………….7-83 APPENDIX – THE CRAIG-BAMPTON MEDTHOD –HAND-SOLVED EXAMPLE…………7-100 DEFAULT CMS METHOD FIXED BOUNDARY CMS………………………………………7-101 SOLUTION BY HAND…………………………………………………………………………… SOLUTION USING MSC.NASTRAN SOL 103……………………………………………… SELECTED OUTPUT FROM MSC.NASTRAN………………………………………………

S7-7NAS105, Section 7, May 2005 TABLE OF CONTENTS SectionPage EXTERNAL SUPERELEMENTS…………………………………………………………………… CREATING AN EXTERNAL SUPERELEMENT…………………………………………………… ATTACHING AN EXTERNAL SUPERELEMENT………………………………………………… DATA RECOVERY FOR AN EXTERNAL SUPERELEMENT…………………………………… ATTACHING AN EXTERNAL SUPERELEMENT………………………………………………… SAMPLE PROBLEM………………………………………………………………………………… SAMPLE PROBLEM USING MATRIXDB………………………………………………………… SAMPLE PROBLEM USING DMGIOP2 PROGRAM………………………………………………7-132

S7-8NAS105, Section 7, May 2005

S7-9NAS105, Section 7, May 2005 WHAT IS A SUPERELEMENT? n Physical and mathematical representation u Physical – a superelement is a substructure: a finite element model of a portion of a structure u Mathematical – the physical model is replaced with boundary matrices: loads, mass, damping, and stiffness reduced from the interior points to the exterior or boundary points n When a model is divided into superelements, it is best to think of each superelement as having its own unique bulk data set (internally). n Each superelement is processed and the finite element model is replaced by reduced matrices which represent the mass, damping, stiffness and loadings on the superelement as seen by any adjacent parts of the model n Once a superelement is processed, the bulk data used to define it, along with all matrices used in processing it are not needed until performing data recovery on the superelement, or performing modifications on it. This data may be archived to reduce disk usage. n The reduced matrices are used to replace the physical model of the superelement

S7-10NAS105, Section 7, May 2005 ADVANTAGES OF SUPERELEMENT ANALYSIS n Large problems (i.e., allows solving problems that exceed your hardware capabilities) n Less CPU or wall clock time per run (reduced risk since each superelement may be processed individually) n Partial redesign requires only partial solution (cost). n Allows more control of resource usage n Partitioned input desirable u Organization u Repeated components n Partitioned output desirable u Organization u Comprehension n Components may be modeled by subcontractors.

S7-11NAS105, Section 7, May 2005 ADVANTAGES OF SUPERELEMENT ANALYSIS (Cont.) n Multi-step reduction for dynamic analysis n Zooming (or global-local analysis) n Allows for efficient configuration studies (What if...)

S7-12NAS105, Section 7, May 2005 DISADVANTAGES OF SUPERELEMENT ANALYSIS n Increased overhead due to DMAP compilation and database manipulation and storage n Mandatory static condensation may cancel other cost savings for small models. n All superelements must be linear. n Approximations must be made in dynamics for mass and damping through static, component mode, or generalized dynamic reduction.

S7-13NAS105, Section 7, May 2005 HOW ARE SUPERELEMENTS DEFINED IN MSC.NASTRAN? n Superelements are identified using numbers (SEID). n Each superelement (SEID > 0) is defined with its own set of grids, elements, constraints, loads, etc. n There are two ways to define superelements in MSC.NASTRAN, Main Bulk Data Superelements and PARTS (not currently supported for nonlinear analysis), which allow partitioned input files. n Main Bulk Data superelements are easiest thought of as a cookie–cutter approach. u All data provided in the Main Bulk Data section (Between the BEGIN BULK and either the first BEGIN SUPER = i or ENDDATA entry) is partitioned (divided) into a separate set for each superelement based on GRID point assignments made by the user n Partitioned bulk data superelements (PARTs) are defined in separate (self–contained) sections of the input file. The separate PARTs are assembled together based on coincident points. u Each PART is defined in a self–contained section which begins with a BEGIN SUPER=i entry and ends with either the next BEGIN SUPER=j entry of the ENDDATA

S7-14NAS105, Section 7, May 2005 HOW ARE SUPERELEMENTS DEFINED IN MSC.NASTRAN? n The residual structure is a superelement that contains grid points, elements, etc. (in the Main Bulk Data), which are not assigned to any other superelement. u Last superelement (SEID = 0) to be processed u Superelement on which the assembly analysis (nonlinear, transient response, frequency response, buckling, system modes, etc.) is performed n A superelement may also be defined as an image of a superelement or obtained from outside MSC.NASTRAN.

S7-15NAS105, Section 7, May 2005 MAIN BULK DATA SUPERELEMENT DEFINITION n Each superelement(SEID > 0) defined in the Main Bulk Data section is defined with its own set of grids, elements, constraints, loads, etc. u Interior grid points are assigned (partitioned) to a superelement by the user. u Exterior grid points, elements, loads, and constraints are automatically partitioned by the program based on interior grid point assignments.

S7-16NAS105, Section 7, May 2005 MAIN BULK DATA GRID POINT PARTITIONING n Bulk Data Entries n Only interior points need to be defined. n SESET takes precedence over GRID. u For the example shown above, Grid Point 47 will belong to the residual structure (SEID=0). n Elements, constraints, loads, etc., are automatically partitioned. n SESET THRU option allows open sets. n Points not assigned to any superelement belong to the residual structure by default. A model with no grid point assignments is defined as a residual structure-only model. Superelements are identified by an integer.

S7-17NAS105, Section 7, May 2005 BULK DATA USED TO DEFINE PARTS n Each PART is defined in a separate section of the input file n The section containing the data for a PART will begin with: BEGIN (BULK) SUPER = i u where i is the superelement id to be defined by the following input n The section containing the data for a PART will end with either: BEGIN (BULK) SUPER = j u where j is the superelement defined in the next section of the input file or ENDDATA u which indicates the end of the input file n The Bulk Data for each PART must be self–contained u It must contain all data defining elements, properties, materials, and loadings for that PART u Different PARTs may use the same id numbers for elements and GRID points, since each is in a self–contained input section.

S7-18NAS105, Section 7, May 2005 BULK DATA USED TO DEFINE SUPERELEMENTS ID test, problem SOL 101 CEND TITLE = SAMPLE INPUT FILE DEMONSTRATING PART INPUT SUBCASE 1 LOAD = 1 DISP = ALL BEGIN BULK $ $ MAIN BULK DATA – may be omitted if desired $ contains data defining residual structure and also any Main Bulk Data $ superelements $ $ any superelements defined in this section will be defined by $ using SESET entries or field 9 on the GRID entries $ BEGIN SUPER = 1 $ $ model data for PART 1 $ BEGIN SUPER = 2 $ $ model data for PART 2 $ ENDDATA Sample input stream

S7-19NAS105, Section 7, May 2005 BULK DATA USED TO CONNECT PARTS n Since PARTs are self–contained, it is necessary to connect them to each other and the Main Bulk Data superelements n The Program will automatically determine coincident grid points between each PART and any other PARTs or Main Bulk Data superelements n If desired, the automatic connection logic may be modified or overridden by using the following entries in the Main Bulk Data section n SEBNDRY – defines a set of points for a PART which may be used in the automatic search for attachments n SECONCT – Allows definition of a tolerance for connection and (if desired) manual listing of the grid points being connected n SEEXCLD – Allows you to provide a list of points to be excluded from the boundary search n SEBULK – the METHOD field on this entry controls whether the AUTO or MANUAL connection logic is used.

S7-20NAS105, Section 7, May 2005 SEBNDRY ENTRY Defines a list of grid points in a partitioned superelement for the automatic boundary search between a specified superelement or between all other superelements in the model. Format: Example 1: Example 2: FieldContents SEIDASuperelement Identification number. See Remark 2. (Integer 0) SEIDBSuperelement Identification. See Remark 3. (Integer 0 or Character All ; Default = ALL ) GIDAIIdentification number of a boundary grid point in superelement SEIDA. Remarks: 1. SEBNDRY may only be specified in the main Bulk Data Section and is not recognized after the BEGIN SUPER = n. 2. SEIDA AND SEIDB may reference partitioned superelements or superelements in the main Bulk Data Section

S7-21NAS105, Section 7, May 2005 SECONCT ENTRY Explicitly defines grid and scalar point connection procedures for a partitioned superelement. Format: Example: FieldContents SEIDAPartitioned superelement Identification number. See Remark 2. (Integer > 0) SEIDBIdentification number of superelement for connection to SEIDA. (Integer 0) TOLLocation tolerance to be used when searching for or checking boundary grid points. (Real; Default = 10E –5 ) LOCCoincident location check option for manual connection. (Character; YES or NO; Default = YES) GIDAIIdentification number of a grid or scalar point in superelement SEIDA, which will be connected to GIDBI. GIDBIIdentification number of a grid or scalar point in superelement SEIDB, which will be connected to GIDAI.

S7-22NAS105, Section 7, May 2005 SECONCT ENTRY (Cont.) Remarks: 1. SECONCT can only be specified in the main Bulk Data Section and is ignored after the BEGIN SUPER = n command. 2. TOL and LOC can be used to override the default values specified on the SEBULK entries. 3. The continuation entry is optional. 4. The (GIAI, GIBI) pair must both be grids or scalar points. 5. All six degrees of freedom of grid points will be defined as boundary degrees of freedom.

S7-23NAS105, Section 7, May 2005 SEEXCLD ENTRY Defines grids that will be excluded during the attachment of a partitioned superelement. Format: Example: FieldContents SEIDAPartitioned superelement Identification number. See Remark 2. (Integer > 0) SEIDBSuperelement Identification. (Integer > 0 or Character = ALL ) GIDAIIdentification number of a grid in superelement SEIDA to be executed from connection to superelement SEIDB. Remarks: 1. SEEXCLD can only be specified in the main Bulk Data Section and is ignored after the BEGIN SUPER = n command. 2. SEIDA and SEIDB may reference partitioned superelements or superelements defined in the main Bulk Data Section.

S7-24NAS105, Section 7, May 2005 SEBULK ENTRY Defines superelement boundary search options and a repeated, mirrored, or collector superelement. Format: Example: Field Contents SEID Superelement identification number. (Integer 0) TYPE Superelement type. (Character; No Default) PRIMARY Primary REPEAT Identical MIRROR Mirror COLLCTR Collector EXTERNAL External RSEID Identification number of the reference superelement, used if TYPE REPEAT and MIRROR. (Integer 0; Default 0) METHOD Method to be used when searching for boundary grid points. (Character: AUTO or MANUAL; Default = AUTO) TOL Location tolerance to be used when searching for boundary grid points. (Real; Default 10E–5) LOC Coincident location check option for manual connection option. (Character: YES or NO; Default = YES)

S7-25NAS105, Section 7, May 2005 SEBULK ENTRY (Cont.) Remarks: 1. The TYPE = REPEAT or MIRROR does not include superelements upstream of the reference superelement. A repeated or mirrored superelement can have boundaries, loads, constraints, and reduction procedures that are different than the reference superelement. 2. METHOD = MANUAL requires SECONCT entries. SEBNDRY and SEEXCLD, which reference SEID, will produce a fatal message. 3. SECONCT, SEBNDRY, and SEEXCLD entries can be used to augment the search procedure and/or override the global tolerance. 4. For combined automatic and manual boundary search, the METHOD = AUTO should be specified and connections should be specified on a SECONCT entry. 5. TOL and LOC are the default values that can be modified between two superelements by providing the required tolerance on the SECONCT entry. 6. TYPE = MIRROR also requires specification of a SEMPLN entry. 7. TYPE = COLLCTR indicates a collector superelement, which does not contain any grids or scalar points. 8. For TYPE = EXTERNAL, see also PARAM, EXTOUT, etc. description in Section 6 of the MSC.NASTRAN Quick Reference Guide.

S7-26NAS105, Section 7, May 2005 SAMPLE PROBLEM- STEEL STAMPING

S7-27NAS105, Section 7, May 2005 SAMPLE PROBLEM- STEEL STAMPING (Cont.) n Grid Points 1 and 2 fixed n Material properties: Steel t = 0.05 E = 29 x 10 6 psi = 0.3 = lb/in 3 (weight density) n Applied loads u 1 psi pressure on square portions u Normal force of 2 lb on Grids 93 and 104 u Opposing normal force of 2 lb on Grids 93 and 104

S7-28NAS105, Section 7, May 2005 SAMPLE PROBLEMSTEEL STAMPING SAMPLE SUPERELEMENT 1

S7-29NAS105, Section 7, May 2005 SAMPLE PROBLEM – STEEL STAMPING (Cont.) Grids 1 and 2 are fixed SteelD =.06 E = 20 x 10 6 psi D =. 3 =.283 lb./In 3 (weight density) Applied Loads 1. Pressure on square portions of 1 psi 2. Normal force of 2 lb on Grids points 93 and Opposing normal forces of 2lb on Grid points 93 and 104

S7-30NAS105, Section 7, May 2005 MODEL DEFINITION FOR SAMPLE PROBLEM BEGIN BULK $ $ ********************************** ********************************* $ BASIC MODEL DEFINITION - SAME FOR ALL RUNS $ ********************************** ********************************* $ GRDSET,,,,,,,6 GRID,1,,-.4,0.,0.,, GRID,3,,-.4,0.9,0. =,*2,=,=,*.9,== =1 GRID,2,,.4,0.,0.,, GRID,4,,.4,0.9,0. =,*2,=,=,*.9,== =1 GRID,9,,-3.6,3.6,0. =,*1,=,*.8,== =8 GRID,19,,-3.6,4.4,0. =,*1,=,*.8,== =8 GRID,29,,-3.6,5.2,0. GRID,30,,-2.8,5.2,0. GRID,31,,2.8,5.2,0. GRID,32,,3.6,5.2,0. GRID,33,,-5.2,6.,0. =,*1,=,*.8,== =4 GRID,39,,1.2,6.,0. =,*1,=,*.8,== =4 GRID,45,,-5.2,6.8,0. =,*1,=,*.8,== =4 GRID,51,,1.2,6.8,0. =,*1,=,*.8,== =4 GRID,57,,-5.2,7.6,0. =,*1,=,*.8,== =4 GRID,63,,1.2,7.6,0. =,*1,=,*.8,== =4 GRID,69,,-5.2,8.4,0. =,*1,=,*.8,== =4 GRID,75,,1.2,8.4,0. =,*1,=,*.8,== =4 GRID,81,,-5.2,9.2,0. =,*1,=,*.8,== =4 GRID,87,,1.2,9.2,0. =,*1,=,*.8,== =4 GRID,93,,-5.2,10.,0. =,*1,=,*.8,== =4 GRID,99,,1.2,10.,0. =,*1,=,*.8,== =4

S7-31NAS105, Section 7, May 2005 MODEL DEFINITION FOR SAMPLE PROBLEM (Cont.) $ $ ELEMENTS $ CQUAD4,1,1,1,2,4,3 =,*1,=,*2,*2,*2,*2 =1 CQUAD4,4,1,7,8,14,13 CQUAD4,6,1,9,10,20,19 =,*1,=,*1,*1,*1,*1 =2 CQUAD4,5,1,13,14,24,23 CQUAD4,10,1,14,15,25,24 = *1,=,*1,*1,*1,*1 =2 CQUAD4,14,1,19,20,30,29 CQUAD4,15,1,29,30,36,35 CQUAD4,16,1,27,28,32,31 CQUAD4,17,1,31,32,42,41 CQUAD4,18,1,33,34,46,45 =,*1,=,*1,*1,*1,*1 =3 CQUAD4,23,1,45,46,58,57 =,*1,=,*1,*1,*1,*1 =3 CQUAD4,28,1,57,58,70,69 =,*1,=,*1,*1,*1,*1 =3 CQUAD4,33,1,69,70,82,81 =,*1,=,*1,*1,*1,*1 =3 CQUAD4,38,1,81,82,94,93 =,*1,=,*1,*1,*1,*1 =3 CQUAD4,43,1,39,40,52,51 =,*1,=,*1,*1,*1,*1 =3 CQUAD4,48,1,51,52,64,63 =,*1,=,*1,*1,*1,*1 =3 CQUAD4,53,1,63,64,76,75 =,*1,=,*1,*1,*1,*1 =3 CQUAD4,58,1,75,76,88,87 =,*1,=,*1,*1,*1,*1 =3 CQUAD4,63,1,87,88,100,99 =,*1,=,*1,*1,*1,*1 =3 MAT1,1,30.+6,,.3,.283 PARAM,WTMASS, PSHELL,1,1,.05,1,,1 $ $ LOADINGS $ $ LOAD CASE 1 - PRESSURE LOAD $ PLOAD2,101,-1.,18,THRU,42 PLOAD2,101,-1.,43,THRU,67 $

S7-32NAS105, Section 7, May 2005 MODEL DEFINITION FOR SAMPLE PROBLEM (Cont.) $ LOAD CASE POINT LOADS AT CORNERS $ FORCE,201,93,,2.,0.,0.,1. FORCE,201,104,,2.,0.,0.,1. $ $ LOAD CASE 3 - OPPOSING POINT LOADS AT CORNERS $ FORCE,301,93,,2.,0.,0.,1. FORCE,301,104,,2.,0.,0.,-1. $ **************************************** *************************** $ END OF BASIC MODEL DEFINITION $ **************************************** *************************** ENDDATA

S7-33NAS105, Section 7, May 2005 SAMPLE PROBLEMSTEEL STAMPING SESET ENTRIES FOR MAIN BULK DATA SUPERELEMENTS $ FILE SESET.DAT $ $ DEFINE S.E. MEMBERSHIP OF GRID POINTS FOR SINGLE–LEVEL SUPERELEMEMT $ SAMPLE PROBLEM $ SESET,1,33,34,37,38 SESET,1,45,THRU,50 SESET,1,57,THRU,62 SESET,1,69,THRU,74 SESET,1,81,THRU,86 SESET,1,93,THRU,98 $ SESET,2,39,40,43,44 SESET,2,51,THRU,56 SESET,2,63,THRU,68 SESET,2,75,THRU,80 SESET,2,87,THRU,92 SESET,2,99,THRU,104 $ SESET,3,29,30 $ SESET,4,31,32 $ SESET,5,21,22 SESET,5,9,THRU,12 $ SESET,6,25,26 SESET,6,15,THRU,18 $ SESET,7,1,THRU,8 $

S7-34NAS105, Section 7, May 2005 PARTITIONED SOLUTIONS n For each superelement, its degrees-of-freedom (DOFs) are divided into two subsets: u Exterior DOFs (called the A-set): Designates the analysis DOFs, which are retained for subsequent processing (for Superelement 1, Grid Points 35 and 36) u Interior DOFs: Designates the DOFs that are reduced out during superelement processing and are omitted in subsequent processing (for Superelement 1 of the sample problem, Grid Points 33, 34, 37,38, 45–50, 57–62, 69–74, 81–86, 93–9 8). n The Main Bulk Data is partitioned by superelement (although the following operations are performed using tables, it is easier to think of them in terms of the Bulk Data). u All Bulk Data unique to the superelement is removed from the original input and placed into a unique set for the superelement. u Bulk Data that is shared or used by more than one superelement (ex: PSHELL, MAT1, etc.) is copied for each applicable superelement. n PARTs are already separated.

S7-35NAS105, Section 7, May 2005 PARTITIONED SOLUTIONS (Cont.) n For each superelement, the program produces a description in matrix terms of its behavior as seen at the boundary or exterior degrees of freedom. u A set of G-sized matrices is produced for each superelement based on the input data. l These matrices are reduced down to matrices representing the properties of the superelement as seen by the adjacent (attached) structure. n At the residual structure, the program combines and assembles the boundary matrices. u The BULK DATA for the RESIDUAL consists of all residual Main Bulk Data not assigned to any superelement plus any common data. n Solve for the residual structure displacements. n For each superelement, expand boundary (exterior) displacements to obtain its interior displacements.

S7-36NAS105, Section 7, May 2005 THEORY OF STATIC CONDENSATION After generating matrices and applying MPCs and SPCs, O-Set = Interior points (to be condensed out by the reduction) A-Set = exterior (or boundary) points (which are retained for further analysis) Partition Extract upper equation and pre-multiply by Let (Boundary Transformation) and(Fixed Boundary Displacements) then(Total Interior Displacements)

S7-37NAS105, Section 7, May 2005 THEORY OF STATIC CONDENSATION(Cont.) n Substitute expression for U o in the lower equation then (Boundary Stiffness) and (Boundary Loads) Solve for residual structure (Boundary displacements)

S7-38NAS105, Section 7, May 2005 CONVENTIONAL ANALYSIS Flowchart Generation Solution

S7-39NAS105, Section 7, May 2005 CONVENTIONAL ANALYSIS(Cont.) Generation

S7-40NAS105, Section 7, May 2005 CONVENTIONAL ANALYSIS(Cont.) Apply Constraints and Solve

S7-41NAS105, Section 7, May 2005 SUPERELEMENT ANALYSIS Flowchart DO LABELA I = 1, NSE Phase I GenerationAssemblyReduction LABELA Phase II Solution DO LABELB I = 1, NSE Phase III Data Recovery LABELB

S7-42NAS105, Section 7, May 2005 SUPERELEMENT ANALYSIS (Cont.) Generation –SEID = 1 Residual Structure

S7-43NAS105, Section 7, May 2005 SUPERELEMENT ANALYSIS (Cont.) Reduction – SEID = 1 Eliminate constraints: Compute boundary transformation:

S7-44NAS105, Section 7, May 2005 SUPERELEMENT ANALYSIS (Cont.) n Compute boundary stiffness: n Compute boundary loading: 0

S7-45NAS105, Section 7, May 2005 SUPERELEMENT ANALYSIS (Cont.) n Similarly – SEID = 2 0

S7-46NAS105, Section 7, May 2005 SUPERELEMENT ANALYSIS (Cont.) Residual Structure Assembly Solution 0

S7-47NAS105, Section 7, May 2005 SUPERELEMENT ANALYSIS (Cont.) Data Recovery – SEID = 1 Enforce (transform) boundary motion. Compute fixed-boundary motion. Compute total motion.

S7-48NAS105, Section 7, May 2005 BULK DATA FOR STATIC LOADS ON SUPERELEMENTS Main Bulk Data Superelements: u Loads applied to interior grid points are assigned to the superelement. u Loads applied to exterior grid points are assigned to the most downstream superelement, that is, the superelement for which the grid point is interior. u Loads applied to elements (PLOADi) are assigned in the same manner as elements. Note: A PLOAD entry may not reference the interior points of more than one superelement. Partitioned Superelements: u Any Loading–related entries must be defined in the partitioned data (in the area of the input file beginning with BEGIN SUPER =)

S7-49NAS105, Section 7, May 2005 STATIC LOADS ON MAIN BULK DATA SUPERELEMENTS Example SESET, 1, 4, 5, 6 u Grids 4, 5, and 6 are interior points to Superelement 1. u Point 3 is exterior to Superelement 1. u P 2 is assigned to Superelement 0. u W and P 1 is assigned to Superelement 1. Superelement 0 Superelement 1

S7-50NAS105, Section 7, May 2005 MAIN BULK DATA SUPERELEMENTS u Constraint entries applied to the interior points of a superelement are assigned to that superelement. u Constraint entries applied to the exterior points of a superelement are sent downstream. u Multiple boundary conditions are allowed for the residual structure only l For multiple boundary conditions, place grid points that will be constrained interior to the residual structure. l Each superelement may have only one SPC set per run. PARTITTIONED SUPERELEMENTS u All constraint–related bulk data entries for the interior points of a PART must be defined in the partitioned bulk data (BEGIN SUPER=). SINGLE-POINT CONSTRAINSTS ON SUPERELEMENTS

S7-51NAS105, Section 7, May 2005 SINGLE-POINT CONSTRAINSTS ON SUPERELEMENTS (Cont.) SESET, 1, 4,5, 6 u Grid Points 4, 5, and 6 are interior to Superelement 1. u Point 3 is exterior to Superelement 1. u SPC at 3 is assigned to Superelement 0. u SPC at 6 is assigned to Superelement 1. Superelement 0 Superelement 1

S7-52NAS105, Section 7, May 2005 MPCs AND RIGID ELEMENTS IN SUPERELEMENTS n Rigid elements and MPCs that connect only interior points are modeled conventionally. n Dependent degrees of freedom may not be exterior. n For MPCs and rigid elements that connect two superelements, u Place the upstream degrees of freedom in the dependent set. u Place the downstream degrees of freedom in the independent set. n Multiple multipoint constraint conditions are allowed for the residual structure only u For multiple multipoint constraints, place grid points that will be specified on these interior to the residual structure. u Each superelement may have only one MPC set per run. (Note: MPCADD may be used.)

S7-53NAS105, Section 7, May 2005 RIGID CONNECTION OF TWO SUPERELEMENTS METHOD 1 – RBAR METHOD 2 – MPC $ SEID GP1 GP2 GP3 ETC. SESET $ EID GA GB CNA CNB CMA CMB RBAR $ SEID GP1 GP2 GP3 ETC. SESET $ SID G C A G C A MPC –1. = = = *(1) = = *(1) = =(4) CSUPEXT 1 3 $ EID G1 G2 PLOTEL or Residual Structure ? SEID = 1 CBAR Rigid Connection

S7-54NAS105, Section 7, May 2005 SUPERELEMENT CASE CONTROL COMMANDS n SE-type (manual processing) – SEMG, SELG, SEKR, SELR, SEMR, SEDR, and SEALL – appear above the first SUBCASE if used u Control solution sequence execution u Make no requests for loads, constraints, or output u SEALL combines SEMG, SELG, SEKR, SELR, and SEMR u Not necessary in SOL 101 and higher (default is SEALL=ALL, which implies that all necessary processing will be performed) n Superelement processing order control – appear above the first SUBCASE if used u SEFINAL – Last superelements to be processed before residual structure – not recommended u SEEXCLUDE – Superelements not to be assembled downstream n Case Control partitioning – SUPER u Assigns a subcase(s) to a specific superelement(s) u Appears above or below subcase level

S7-55NAS105, Section 7, May 2005 SUPER COMMAND n Partitions (assigns) a subcase to a superelement(s) n Associates a superelement(s) with requests for parameters, loads, constraints, and output n Pre–V69 – If the Case Control Section does not contain a SUPER command, then loads, constraints, and output requests are applied to the residual structure only (the old default was SUPER = 0). n V69 The new default is SUPER=ALL. if no SUPER command is present, the subcases are assumed to apply to ALL superelements (if any SUPER commands occur in the Case Control, the default reverts to SUPER=0 for upward compatibility). n The SUPER command may reference a superelement or a SET of superelements. Note: The SET ID must be unique with respect to any superelement IDs. n Form of SUPER command SUPER = i, j where i = superelement ID or set of superelements j = load sequence number (a counter on loading conditions)

S7-56NAS105, Section 7, May 2005 EXPANDED VERSUS CONDENSED Conventional Case Control u Expanded u Condensed SUBCASE 10 SET 1 = 101 THRU 110 DISP = 1 LOAD = 100 SUBCASE 20 SET 1 = 101 THRU 110 DISP = 1 LOAD = 200 SUBCASE 30 SET 3 = 201 THRU 210 DISP = 3 LOAD = 200 SET 1 = 101 THRU 110 SET 3 = 201 THRU 210 DISP = 1 LOAD = 200 SUBCASE 10 LOAD = 100 SUBCASE 20 SUBCASE 30 DISP = 3

S7-57NAS105, Section 7, May 2005 EXPANDED VERSUS CONDENSED (Cont.) Superelement Case Control u Expanded – one loading condition u Condensed $ model with superelements 10, 20, 0 DISP = ALL SUBCASE 1 $ SE 10 SUPER = 10 LOAD = 100 SUBCASE 2 $ SE 20 SUPER = 20 LOAD = 100 SUBCASE 101 $ RESIDUAL STRUCTURE SET 999 = 0 SUPER = 999 LOAD = 100 BEGIN BULK SUBCASE 1 DISP = ALL LOAD = 100 BEGIN BULK

S7-58NAS105, Section 7, May 2005 SUPER COMMAND EXAMPLEONE LOADING CONDITION $ SEIDS 1, 2, 3, 4, 5, 0 DISP = ALL SUBCASE 10 SET 101 = 1, 4 SUPER = 101 SPC = 12 SUBCASE 20 SET 103 = 2, 5 SUPER = 103 SET 15 = 7, 9 ELFOR = 15 LOAD = 9 SUBCASE 30 SUPER = 0 ELSTRE = ALL

S7-59NAS105, Section 7, May 2005 MULTIPLE LOADING CONDITIONS IN SUPERELEMENT CASE CONTROL – OPTION 1 n Appears identical to conventional Case Control n For each loading, create one subcase (use the default SUPER=ALL) n Option 1 requires u All superelements must use the same loading, SPC, and MPC sets.

S7-60NAS105, Section 7, May 2005 MULTIPLE LOADING CONDITIONS IN SUPERELEMENT CASE CONTROL – OPTION 2 n For the residual structure u Define a subcase for each loading condition. n For each superelement (or set of superelements) u Define a subcase for each loading condition using a SUPER command identifying the superelement (or a set of superelements) and the loading sequence number. n SUBCOMs are treated as a new load sequence and, therefore, must have a SUPER command and the residual structure must have a corresponding subcase or subcom. n REPCASEs must immediately follow the subcase they reference and contain the same SUPER=i,j command.

S7-61NAS105, Section 7, May 2005 MULTIPLE LOADING CONDITIONS EXAMPLE -- OPTION 2 SEALL = ALL DISP = ALL SPC = 10 SUBCASE 1 $ SEID 10 LOAD SEQ 1 SUPER = 10, 1 LOAD = 100 SUBCASE 2 $ SEID 10 LOAD SEQ 2 SUPER = 10, 2 ELFORCE = ALL SUBCASE 12 $ SEID 20 LOAD SEQ 2 SUPER = 20, 2 LOAD = 200 SUBCASE 101 $ R.S. LOAD SEQUENCE 1 SUPER = 0,1 GPFOR = ALL SUBCASE 102 $ R.S. LOAD SEQUENCE 2 SUPER = 0,2 LOAD = 1000

S7-62NAS105, Section 7, May 2005 REASONS TO USE OPTION 2 FOR MULTIPLE LOADINGS n It allows different LOAD, SPC, MPC IDs, etc., for each superelement. n Each superelement may have unique output requests. n It may be the only way to perform an analysis if groups have not coordinated their efforts.

S7-63NAS105, Section 7, May 2005 MULTIPLE LOADINGS – SAMPLE OF OPTION 1 n Coordinated input allows for simple Case Control u P 1 and W 1 are applied for loading 1 u P 2 is applied for loading 2 SOL 101 TIME 5 CEND TITLE = SAMPLE OF OPTION 1 FOR MULTIPLE LOADINGS DISP = ALL $ DEFAULT CASE CONTROL BEFORE FIRST $ SUPER = ALL is now the default SUBCASE 1 LOAD = 1 SUBCASE 2 LOAD = 2 BEGIN BULK. ENDDATA Superelement 0 Superelement 1

S7-64NAS105, Section 7, May 2005 MULTIPLE LOADINGS – SAMPLE OF OPTION 2 n Uncoordinated input forces complicated Case Control u P 1 and W 1 are applied for loading 1 for Superelement 1. P 2 is applied for loading 1 on the residual structure. u P 1 is applied on the residual structure for loading 2. SOL 101 TIME 5 CEND TITLE = UNCOORDINATED INPUT FORCES COMPLEX CASE CONTROL DISP = ALL SET 99 = 0 SUBCASE 1 SUPER = 1,1 $ S.E. 1, LOAD CONDITION 1 LOAD = 1 SUBCASE 2 SUPER = 99,1 $ R.S., LOADING 1 LOAD = 2 SUBCASE 11 SUPER = 1,2 $ S.E. 1, LOAD CONDITION 2 $ NO LOADS APPLIED DIRECTLY ON S.E. 1 – SUBCASE ONLY FOR $ DATA RECOVERY SUBCASE 12 SUPER = 99,2 $ R.S., LOAD CONDITION 2 LOAD = 1 BEGIN BULK. ENDDATA Superelement 0 Superelement 1

S7-65NAS105, Section 7, May 2005 PARAMETERS IN CASE CONTROL n Allows changes between superelements on same run n Most, but not all, can be used in Case Control. n There is a hierarchical rule for what value used will be. u Subcase value first u Above subcase level value if not in a subcase u Bulk Data value if not in either of the above u Default value if not in any of the above l The default is taken from the main subDMAP if one exists. l If not in main subDMAP from the called subDMAP l If NDDL, the default is from the NDDL default table. n Recommendations u Specify the parameter value for each subcase (safe). or u Specify the default value above the subcase level and exceptions within subcases.

S7-66NAS105, Section 7, May 2005 SAMPLE SUPERELEMENT STATIC RUN INPUT ID SE, SAMPLE PROBLEM SOL 101 $ $ SUPERELEMENT STATICS – SAMPLE PROBLEM – STATIC SOLUTION $ USING SIMPLE CASE CONTROL $ SOL 101 $ SUPERELEMENT STATICS – SINGLE LEVEL TREE TIME 15 CEND TITLE = S.E. SAMPLE PROBLEM 1 SUBTITLE = S.E. STATICS – RUN 1 – MULTIPLE LOADS DISP = ALL PARAM,GRDPNT,0 SUBCASE 101 LABEL = PRESSURE LOAD LOAD = 101 $ SUBCASE 201 LABEL = 2# NORMAL LOADS LOAD = 201 $ SUBCASE 301 LABEL = OPPOSING LOADS LOAD = 301 $ BEGIN BULK PARAM,POST,0 $ INCLUDE seset.dat INCLUDE model.dat INCLUDE load1. dat $ ENDDATA File – se1s101.dat

S7-67NAS105, Section 7, May 2005 SAMPLE SUPERELEMENT STATIC RUN INPUT (Cont.) $ FILE LOAD1. DAT $ $ LOADINGS – FOR RUN SHOWING CONVENTIONAL CASE CONTROL $ $ LOAD CASE 1 – PRESSURE LOAD $ $ NOTE: THRU RANGE SHOULD INCLUDE ELEMENTS OF ONLY ONE SUPERELEMENT $ PLOAD2,101,–1.,18,THRU,42 PLOAD2,101,–1.,43,THRU,67 $ $ LOAD CASE 2 – 2 POINT LOADS AT CORNERS $ FORCE,201,93,,2.,0.,0.,1. FORCE,201,104,,2.,0.,0.,1. $ $ LOAD CASE 3 – OPPOSING POINT LOADS AT CORNERS $ FORCE,301,93,,2.,0.,0.,1. FORCE,301,104,,2.,0.,0.,–1. $ File – load1.dat

S7-68NAS105, Section 7, May 2005 SAMPLE SUPERELEMENT STATIC RUN INPUT USING PARTS $ file – se1s101p.dat SOL 101 CEND TITLE = S.E. SAMPLE PROBLEM 1 USING PARTs SUBTITLE = S.E. STATICS – RUN 1 – MULTIPLE LOADS DISP = ALL stress = all PARAM,GRDPNT,0 PARAM,WTMASS, SUBCASE 101 LABEL = PRESSURE LOAD LOAD = 101 $ SUBCASE 201 LABEL = 2# NORMAL LOADS LOAD = 201 $ SUBCASE 301 LABEL = OPPOSING LOADS LOAD = 301 BEGIN BULK include part0. dat $ main bulk data section begin super=1 $ include loadprt1. dat include part1. dat begin super=2 File – se1s101p.DAT $ include loadprt2. dat include part2. dat begin super=3 $ include part3. dat begin super=4 $ include part4. dat begin super=5 $ include part5. dat begin super=6 $ include part6. dat begin super=7 $ include part7. dat enddata

S7-69NAS105, Section 7, May 2005 SAMPLE SUPERELEMENT STATIC RUN INPUT USING PARTS $ $ file – loadprt1. dat $ loads on s.e. 1 $ $ LOAD CASE 1 – PRESSURE LOAD $ PLOAD2,101,–1.,18,THRU,42 $ $ LOAD CASE 2 – 2 POINT LOADS AT CORNERS $ FORCE,201,93,,2.,0.,0.,1. $ $ LOAD CASE 3 – OPPOSING POINT LOADS AT CORNERS $ FORCE,301,93,,2.,0.,0.,1. $ File – loadprt1.dat

S7-70NAS105, Section 7, May 2005 SAMPLE SUPERELEMENT STATIC RUN INPUT USING PARTS $ $ file – loadprt2. dat $ loads on s.e. 2 $ $ LOAD CASE 1 – PRESSURE LOAD $ PLOAD2,101,–1.,43,THRU,67 $ $ LOAD CASE 2 – 2 POINT LOADS AT CORNERS $ FORCE,201,104,,2.,0.,0.,1. $ $ LOAD CASE 3 – OPPOSING POINT LOADS AT CORNERS $ FORCE,301,104,,2.,0.,0.,–1. $ File – loadprt2.dat

S7-71NAS105, Section 7, May 2005 SUPERELEMENT REDUCTION METHODS AVAILABLE IN DYNAMIC ANALYSIS n Static reduction u Static condensation of stiffness and Guyan reduction of mass l Static reduction is the default n Dynamic reduction u Generalized dynamic reduction (GDR) (not recommended) u Component modal synthesis (CMS) l Analytical (All SE dynamic SOLs)

S7-72NAS105, Section 7, May 2005 DEGREES OF REDUCTION n Static reduction (default) u Interior masses relumped to boundary (Guyan) u Rigid body properties preserved u Important masses must be made exterior (boundary) n Generalized dynamic reduction – in addition to static reduction u Interior masses represented by approximate eigenvectors u Approximate natural frequencies and mode shapes may be output n Component mode reduction – in addition to static reduction u Interior masses represented by calculated eigenvectors of the component u Eigensolutions for each superelement may be output n All reductions are performed using a set of transformation vectors –these vectors are best thought of as Ritz vectors

S7-73NAS105, Section 7, May 2005 COMPARISON OF REDUCTION METHODS n Static reduction n Generalized dynamic reduction Approximate eigenvectors are used to represent the interior motion. n Component mode reduction Exact eigenvectors are used to represent the interior motion. 0 Local dynamic effects are ignored.

S7-74NAS105, Section 7, May 2005 ADVANTAGES OF EACH REDUCTION METHOD n Advantages of Component Mode Reduction over Static Reduction u Can use experimental results u More accurate for the same number of dynamic DOFs u Ideal for highly coupled and uncoupled structures n Advantages of Static Reduction over Component Mode Reduction u Cheaper u Less sophisticated

S7-75NAS105, Section 7, May 2005 CALCULATION OF NORMAL MODES USING STATIC REDUCTION ONLY n This is the default method used to reduce superelements is always be performed n Superelement mass, damping, and stiffness are reduced statically to exterior DOFs. n Case Control is similar to static analysis with the addition of a METHOD command under the residual structure subcase.

S7-76NAS105, Section 7, May 2005 CALCULATION OF NORMAL MODES USING DYNAMIC REDUCTION FOR SUPERELEMENT n Dynamic reduction of superelements is optional and is performed in addition to static (Guyan) reduction if requested n The behavior of a superelement is represented by its real modes in addition to the static shapes. n The superelement stiffness, mass, and damping are transformed using both physical and modal variables. n The superelement modes are computed if a METHOD command appears under the superelement subcase and SEQSETi entries are specified for the superelement (QSETi or SENQSET for PARTs). n The number of superelement modes computed (modal truncation) is controlled by the EIGRL entry. n The number of superelement modes sent downstream is controlled by the number of Q–set DOFs provided. n SEQSETi entries can reference GRID points or SPOINTs n By default, superelement modes are computed with all exterior degrees of freedom fixed (in the B-set). This is better known as the Craig-Bampton method.

S7-77NAS105, Section 7, May 2005 CALCULATION OF NORMAL MODES USING DYNAMIC REDUCTION FOR SUPERELEMENT (Cont.) n For free-free superelement component modes, all exterior DOFs should be specified on SECSETi entries (use of the SESUP is not recommended). u The rigid-body modes (f=0.0 Hz) are a linear combination of the static vectors and should not be included in the reduction. Either: l Do not calculate them (F1>0.0 on the EIGR or EIGRL entry). l Calculate them and hope that the program will remove them (see PARAM,ERSRC in the MSC.NASTRAN Users Manual). l Calculate them and remove them by using the SESUP entry. (For every exterior DOF listed on the SESUP entry, one eigenvector is thrown away.) n Mixed-boundary modes may be calculated by using the SECSETi and SEBSETi entries to describe the exterior DOFs to be unconstrained and constrained during CMS. u If 0.0 Hz mixed boundary modes exist, they must be handled in a similar manner to those in the free-free case. n For most problems, the default (Craig–Bampton) method will be adequate. The accuracy of the transformation is dependent on the number of component modes used, no matter which dynamic reduction method is used.

S7-78NAS105, Section 7, May 2005 FIXED BOUNDARY SOLUTIONS (PARAM, FIXEDB, -1) Statics n Allows output of the superelement component modes in dynamics where z implies superelement component modes v indicates the v-set ( 0 + R + C) n Allows checkout of one superelement at a time – displacements, stresses, deformed plots, etc. – any standard data recovery option. n In SOL 63 after checkout, PARAM,RESDUAL,–1 may be used to restart for system (residual structure) modes. 0.0 if FIXEDB = -1 Motion Due to Boundary Displacements Motion Due to Interior Loads Total Motion of Interior Points Superelement Modes (Are Printed if FIXEDB = -1)

S7-79NAS105, Section 7, May 2005 PROCEDURES FOR SUPERELEMENT DYNAMIC REDUCTION n Component boundary conditions u Fixed-fixed l Default – All exterior DOFs are automatically placed in the B-set. u Free-free l Specify all exterior DOFs in C-set. l Specify PARAM,INRLM,–1 in Case Control for more accuracy. u Mixed l Define exterior DOFs in C- and B-sets as desired.

S7-80NAS105, Section 7, May 2005 PROCEDURES FOR SUPERELEMENT DYNAMIC REDUCTION (Cont.) n Residual structure u If static reduction is desired, specify selected physical DOFs in the A-set. Note: If CMS has been performed for upstream superelements, the generalized coordinates from the superelements should be in the A-set in order to be included in the final solution. u If GDR or residual structure CMS is used, no physical DOFs in A- set are required.

S7-81NAS105, Section 7, May 2005 SPECIFICATION OF FIXED AND FREE BOUNDARY DEGREES OF FREEDOM Set Definition B Fixed during GDR or CMR C Free during GDR or CMR

S7-82NAS105, Section 7, May 2005 REFERENCES FOR CMS n W. C. Hurty, Dynamic Analysis of Structural Systems Using Component Modes, AIAA Journal, Vol. 3, No. 4, April 1965 (Based upon JPL Tech. Memo , January 1964). n R. H. MacNeal, A Hybrid Method of Component Mode Synthesis, Computers & Structures, Vol. 1, n R. R. Craig and M. C. C. Bampton, Coupling of Substructures for Dynamic Analysis, AIAA Journal, Vol. 6, No. 7, July n W. A. Benfield and R. F. Hruda, Vibration Analysis of Structures by Component Mode Substitution, presented at AIAA/ASME 11th Structures, Structural Dynamics, and Materials Conference, Denver, CO, April n S. Rubin, An Improved Component-Mode Representation, presented at AIAA/ASME 15th Structures, Structural Dynamics, and Materials Conference, Las Vegas, NV, April n R. R. Craig, Structural Dynamics: An Introduction to Computer Methods, John Wiley and Sons, New York, n E. D. Bellinger, Component Mode Synthesis for External Superelements, MSR-71, Los Angeles, May 1981, (SOLs 41, 42, 43).

S7-83NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE n Cantilever beam modeled with two superelements n Beam properties A = 5 in 2 I = in 4 n Material properties E = 10,000,000 psi p = 0.01 lb-sec 2 / in 4

S7-84NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) n Compute first five system modes using the following techniques: u Static reduction u Assume fixed exterior points. l Generalized dynamic reduction (GDR) l Component mode reduction (CMR) l GDR and CMR n Assume all free exterior points with CMR.

S7-85NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) $ FILE SEDYNBLK.DAT $ DYNRED,1,100. EIGR,37,MGIV,,,,5 SPC1,10,26,1001 SPC1,10,1345,1001,THRU,1011 SPC1,10,1345,2001,THRU,2016 RBE2,1001,1011,26,2001 GRID,1001,,0. =,(1),=,(2.),== =(9) GRID,2001,,20. =,(1),=,(2.),== =(14) CBAR,111,10,1001,1002,,1. =,(1),=,(1),(1),== =(8) CBAR,211,10,2001,2002,,1. =,(1),=,(1),(1),== =(13) PBAR,10,10,5., , MAT1,10,1.+4,,.3,.01 PARAM,COUPMASS,1 Bulk Data Input

S7-86NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) Static Reduction Only n For accuracy, assign six evenly-spaced points along the beam to the residual structure. n Without an ASETi entry, ALL DOFs in the residual structure belong to the A-set. n The SUPER=ALL and METHOD commands tell MSC.NASTRAN to perform CMS on all superelements, but the lack of SEQSET prevents it and a static reduction is performed. (System modes are found at the residual.) $ FILE = SEDYN1. DAT $ SOL 103 TIME 5 CEND TITLE = SUPERELEMENT CMS SAMPLE – RUN 1 SPC = 10 SEALL = ALL $ ONLY REQUIRED IF SOL

S7-87NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) Static Reduction Only (Cont.) SUPERELEMENT CMS SAMPLE – RUN 1 MAY 2, 1990 MSC.NASTRAN 1/ 4/ 89 PAGE 20 SUPERELEMENT 0 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E– E E E E E E E E E E E E E E E E E E E E E E+04

S7-88NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) Generalized Dynamic Reduction n Assign to the residual structure only the superelement endpoints that are assumed to be fixed for GDR. n Specify Q-set (SEQSET1) along with the corresponding variables (SPOINT). n Request GDR (DYNRED) for both superelements and eigensolution (METHOD) for the residual structure.

S7-89NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) $ FILE = SEDYN2. DAT $ SOL 103 TIME 5 CEND TITLE = SUPERELEMENT CMS SAMPLE – RUN 2 $SEALL = ALL $ ONLY REQUIRED IF SOL

S7-90NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) SUPERELEMENT CMS SAMPLE – RUN 2 JUNE 26, 1990 MSC. NASTRAN 10/ 20/ 89 PAGE 15 SUPERELEMENT 100 *** USER INFORMATION MESSAGE––– PROCESSING OF SUPERELEMENT 100 IS NOW INITIATED. ^^^ PHASE 1 – SUPERELEMENT GENERATION, ASSEMBLY AND REDUCTION. *** USER INFORMATION MESSAGE 4158––– STATISTICS FOR SYMMETRIC DECOMPOSITION OF DATA BLOCK SCRATCH FOLLOW NUMBER OF NEGATIVE TERMS ON FACTOR DIAGONAL = 2 *** USER INFORMATION MESSAGE 4181––– NUMBER OF ROOTS BELOW E+ 03 CYCLES IS 2 NUMBER OF GENERALIZED COORDINATES SET TO 6 SUPERELEMENT CMS SAMPLE – RUN 2 JUNE 26,1990 MSC.NASTRAN 10/20/ 89 PAGE 16 SUPERELEMENT 200 *** USER INFORMATION MESSAGE––– PROCESSING OF SUPERELEMENT 200 IS NOW INITIATED. ^^^ PHASE 1 – SUPERELEMENT GENERATION, ASSEMBLY AND REDUCTION. *** USER INFORMATION MESSAGE 4158––– STATISTICS FOR SYMMETRIC DECOMPOSITION OF DATA BLOCK SCRATCH FOLLOW NUMBER OF NEGATIVE TERMS ON FACTOR DIAGONAL = 3 *** USER INFORMATION MESSAGE 4181––– NUMBER OF ROOTS BELOW E+ 03 CYCLES IS 3 Generalized Dynamic Reduction (Cont.)

S7-91NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) NUMBER OF GENERALIZED COORDINATES SET TO 6 SUPERELEMENT CMS SAMPLE – RUN 2 JUNE 26, 1990 MSC.NASTRAN 10/ 20/ 89 PAGE 19 SUPERELEMENT 0 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E– E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

S7-92NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) Component Modal Synthesis n Assign to the residual structure only the superelement endpoints that are assumed to be fixed for calculation of component modes. n Specify Q-set (SEQSET1) for each superelement along with the corresponding modal variables (SPOINT). n Request eigensolution (METHOD) for both superelements and the residual structure. $ FILE = SEDYN3. DAT $ SOL 103 TIME 5 CEND TITLE = SUPERELEMENT CMS SAMPLE – RUN 3 SPC = 10 $SEALL = ALL $ ONLY REQUIRED IF SOL

S7-93NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) SUPERELEMENT CMS SAMPLE – RUN 3 MARCH 17, 1992 MSC.NASTRAN 11/ 20/ 91 PAGE 13 SUPERELEMENT 100 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E E E E E E E E E E E E E E E E E E E E E E E+06 SUPERELEMENT CMS SAMPLE – RUN 3 MARCH 17, 1992 MSC.NASTRAN 11/ 20/ 91 PAGE 16 SUPERELEMENT 200 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E E E E E E E E E E E E E E E E E E E E E E E+06 SUPERELEMENT CMS SAMPLE – RUN 3 MARCH 17, 1992 MSC.NASTRAN 11/ 20/ 91 PAGE 20 SUPERELEMENT 0 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E– E E E E E E E E E E E E E E E E E E E E E E+ 04 Component Modes Reduction (Cont.)

S7-94NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) GDR and CMR n Modified Case Control from GDR-only file set-up. In addition, eigensolution is requested for both superelements and the residual structure. $ FILE = SEDYN4. DAT $ SOL 103 TIME 5 CEND TITLE = SUPERELEMENT CMS SAMPLE – RUN 4 SEALL = ALL $ ONLY REQUIRED IF SOL

S7-95NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) SUPERELEMENT CMS SAMPLE – RUN 4 JUNE 26, 1990 MSC.NASTRAN 10/ 20/ 89 PAGE 15 SUPERELEMENT 100 USER INFORMATION MESSAGE––– PROCESSING OF SUPERELEMENT 100 IS NOW INITIATED. ^^^ PHASE 1 – SUPERELEMENT GENERATION, ASSEMBLY AND REDUCTION. USER INFORMATION MESSAGE 4158––– STATISTICS FOR SYMMETRIC DECOMPOSITION OF DATA BLOCK SCRATCH FOLLOW NUMBER OF NEGATIVE TERMS ON FACTOR DIAGONAL = 2 USER INFORMATION MESSAGE 4181––– NUMBER OF ROOTS BELOW E+ 03 CYCLES IS 2 NUMBER OF GENERALIZED COORDINATES SET TO 6 USER INFORMATION MESSAGE 5458, MODIFIED GIVENS METHOD IS FORCED BY USER. SUPERELEMENT CMS SAMPLE – RUN 4 JUNE 26, 1990 MSC.NASTRAN 10/ 20/ 89 PAGE 16 SUPERELEMENT 100 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E E E E E E E E E E E E E E E E E E E E E E E E E E SUPERELEMENT CMS SAMPLE – RUN 4 JUNE 26, 1990 MSC.NASTRAN 10/ 20/ 89 PAGE 18 SUPERELEMENT 200 USER INFORMATION MESSAGE––– PROCESSING OF SUPERELEMENT 200 IS NOW INITIATED. ^^^ PHASE 1 – SUPERELEMENT GENERATION, ASSEMBLY AND REDUCTION. USER INFORMATION MESSAGE 4158––– STATISTICS FOR SYMMETRIC DECOMPOSITION OF DATA BLOCK SCRATCH FOLLOW NUMBER OF NEGATIVE TERMS ON FACTOR DIAGONAL = 3 USER INFORMATION MESSAGE 4181––– NUMBER OF ROOTS BELOW E+ 03 CYCLES IS 3 NUMBER OF GENERALIZED COORDINATES SET TO 6 USER INFORMATION MESSAGE 5458, MODIFIED GIVENS METHOD IS FORCED BY USER. SUPERELEMENT CMS SAMPLE – RUN 4 JUNE 26, 1990 MSC.NASTRAN 10/ 20/ 89 PAGE 19 SUPERELEMENT 200 GDR and CMR (Cont.)

S7-96NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E E E E E E E E E E E E E E E E E E E E E E E E E E SUPERELEMENT CMS SAMPLE – RUN 4 JUNE 26, 1990 MSC.NASTRAN 10/ 20/ 89 PAGE 23 SUPERELEMENT 0 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E– E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E GDR and CMR (Cont.)

S7-97NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) CMS with Free-Free Components n Specify exterior points, which are unconstrained during CMS, with SECSET1 entries. n Recommend not using the SESUP entry or calculating 0.0 Hz component modes $ FILE = SEDYN5. DAT $ SOL 103 TIME 5 CEND TITLE = SUPERELEMENT CMS SAMPLE – RUN 5 SEALL = ALL $ ONLY REQUIRED IF SOL

S7-98NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) SUPERELEMENT CMS SAMPLE – RUN 5 MAY 2, 1990 MSC.NASTRAN 1/ 4/ 89 PAGE 16 SUPERELEMENT 100 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+ 07 SUPERELEMENT CMS SAMPLE – RUN 5 MAY 2, 1990 MSC.NASTRAN 1/ 4/ 89 PAGE 19 SUPERELEMENT 200 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+ 07 CMR with Free-Free Components (Cont.)

S7-99NAS105, Section 7, May 2005 SUPERELEMENT DYNAMICS EXAMPLE (Cont.) CMR with Free-Free Components (Cont.) SUPERELEMENT CMS SAMPLE – RUN 5 MAY 2, 1990 MSC.NASTRAN 1/ 4/ 89 PAGE 23 SUPERELEMENT 0 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E– E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+ 07 CMR with Free-Free Components (Cont.)

S7-100NAS105, Section 7, May 2005 APPENDIX 6A– THE CRAIG-BAMPTON MEDTHOD – HAND-SOLVED EXAMPLE

S7-101NAS105, Section 7, May 2005 DEFAULT CMS METHOD FIXED BOUNDARY CMS Description of Methodology (better known as Craig-Bampton CMS) n The superelement matrices are partitioned into two sets of degrees of freedom (DOFs). The first set (the B-set) represents the boundary points. The second set is the interior DOFs (the O-set). n A set of constraint modes is generated. Each constraint mode represents the motion of the model resulting from moving one boundary DOF 1.0 unit, while holding the other boundary DOF fixed. Therefore, there is one constraint mode for each boundary DOF (these vectors are known as G OAT in MSC.NASTRAN) n In matrix form, (P b is not actually applied.) n The first line gives

S7-102NAS105, Section 7, May 2005 DEFAULT CMS METHOD FIXED BOUNDARY CMS (Cont.) giving the following constraint modes: n Now the O-set equations are solved for the fixed-boundary modes (known as G OAQ in MSC.NASTRAN). As many fixed-boundary modes as are desired are found. Then they are concatenated with the constraint modes to form the generalized coordinates. n The mass and stiffness matrices are pre- and postmultiplied by these modes to obtain the generalized mass and stiffness where the F-set is the union of the B- and O-sets.

S7-103NAS105, Section 7, May 2005 DEFAULT CMS METHOD FIXED BOUNDARY CMS (Cont.) n These generalized matrices contain physical DOFs representing the boundaries and modal coordinates representing the fixed-boundary component modes. n At this point, these matrices can be treated like any other structural matrices, and data recovery can be performed for the component in a manner similar to using modal coordinates. That is, the displacements of the generalized coordinates are multiplied by the associated vectors and added together to obtain the component displacements. n The calculated modes for each superelement are internally scaled to have a maximum displacement = 1.0 in MSC.NASTRAN (regardless of the scaling requested by the user).

S7-104NAS105, Section 7, May 2005 SOLUTION BY HAND Component Modal Synthesis Sample Spring Stiffness = 1. Each Mass = 1. SESET,1,4,5 SESET,2,2 SPOINT, 1001,THRU,1010 SEQSET1,1,1001,1002 SEQSET1,2,1005 Theoretical solution for frequencies

S7-105NAS105, Section 7, May 2005 SOLUTION BY HAND (Cont.) n Superelement 1 Mass at Grid Point 3 belongs to the residual structure and is therefore exterior. n Grid Point 3 is the boundary point; solve for constraint modes. where

S7-106NAS105, Section 7, May 2005 SOLUTION BY HAND (Cont.) where n Solve for fixed-boundary modes. Note: Internally MSC.NASTRAN uses component modes scaled to a maximum deformation of 1.0. Output for the component modes is based on the normalization performed by the eigenvalue solution.

S7-107NAS105, Section 7, May 2005 SOLUTION BY HAND (Cont.) where 1001 and 1002 are scalar points used to represent Superelement 1s modes. Normalized to unit mass

S7-108NAS105, Section 7, May 2005 SOLUTION BY HAND (Cont.) Superelement 2 where 1005 is a scalar point used to represent Superelement 2s mode

S7-109NAS105, Section 7, May 2005 SOLUTION BY HAND (Cont.) Residual Structure u Before adding superelement:

S7-110NAS105, Section 7, May 2005 SOLUTION BY HAND (Cont.) n Add Superelement 1

S7-111NAS105, Section 7, May 2005 SOLUTION BY HAND (Cont.) n Add Superelement 2

S7-112NAS105, Section 7, May 2005 SOLUTION BY HAND (Cont.) n Apply constraints at DOF 1. n Solve which gives n Data recovery (grid point displacement for mode 1) Residual Structure

S7-113NAS105, Section 7, May 2005 SOLUTION BY HAND (Cont.) n Superelement 2 for exterior points n Superelement 1 for exterior points

S7-114NAS105, Section 7, May 2005 SOLUTION USING MSC.NASTRAN SOL 103 ID CMS1, SAMPLE PROBLEM FOR CMS SOL 103 TIME 10 CEND TITLE = SAMPLE PROBLEM FOR CMS SPC = 1 SUBCASE 1 DISP = ALL LABEL = CMS OF SUPERELEMENTS SET 1000 = 1,2 SUPER =1000 METHOD=2 $ GET 2 MODES SUBCASE 2 LABEL=SOLVE FOR RESIDUAL STRUCTURE MODES IF DESIRED METHOD = 1 DISP = ALL BEGIN BULK PARAM,FIXEDB,–1 PARAM,GRDPNT,0 EIGRL,1,,,10 EIGRL,2,,,2 $ ADD MODAL COORDINATES FOR S.E. 1 SPOINT,1001,THRU,1010 SEQSET1,1,0,1001,THRU,1004 SEQSET1,2,0,1005,THRU,1010 GRID,1,,0.,0.,0. =,(1),=,(10.),== =(3) CELAS2,1,1.,1,1,2,1 CELAS2,2,1.,2,1,3,1 CELAS2,3,1.,3,1,4,1 CELAS2,4,1.,4,1,5,1 $ DEFINE SUPERELEMENTS SESET,1,4,5 SESET,2,2 PARAM,AUTOSPC,YES SPC1,1,123456,1 CONM2,11,1,,1. CONM2,12,2,,1. CONM2,13,3,,1. CONM2,14,4,,1. CONM2,15,5,,1. ENDDATA The input data was run in MSC.NASTRAN:

S7-115NAS105, Section 7, May 2005 SELECTED OUTPUT FROM MSC.NASTRAN SAMPLE PROBLEM FOR CMS OCTOBER 3, 1989 MSC.NASTRAN 1/ 4/ 89 PAGE 18 SUPERELEMENT 1 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E– E– E– E E– E E E– E E+00 SUPERELEMENT 2 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E E E– E E+00 SUPERELEMENT 0 R E A L E I G E N V A L U E S MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED NO. ORDER MASS STIFFNESS E– E– E– E E– E E E– E E E E E– E E E E E– E E+00 SUPERELEMENT 0 SOLVE FOR RESIDUAL STRUCTURE MODES IF DESIRED SUBCASE 2 EIGENVALUE = E– 01 CYCLES = E– 02 R E A L E I G E N V E C T O R N O. 1 POINT ID. TYPE T1 T2 T3 R1 R2 R3 1 G G E– S E–01 – E– E– S

S7-116NAS105, Section 7, May 2005 SELECTED OUTPUT FROM MSC.NASTRAN (Cont.) SAMPLE PROBLEM FOR CMS OCTOBER 3, 1989 MSC.NASTRAN 1/ 4/ 89 PAGE 43 SUPERELEMENT 1 CMS OF SUPERELEMENT 1 SUBCASE 1 EIGENVALUE = E+ 00 CYCLES = E–01 R E A L E I G E N V E C T O R N O. 3 POINT ID. TYPE T1 T2 T3 R1 R2 R3 3 G – E– G – E– G E– S E– E– SAMPLE PROBLEM FOR CMS OCTOBER 3, 1989 MSC.NASTRAN 1/ 4/ 89 PAGE 48 SUPERELEMENT 2 CMS OF SUPERELEMENT 1 SUBCASE 1 EIGENVALUE = E–01 CYCLES = E–02 R E A L E I G E N V E C T O R N O. 1 POINT ID. TYPE T1 T2 T3 R1 R2 R3 1 G G E– G E– S E–

S7-117NAS105, Section 7, May 2005 EXTERNAL SUPERELEMENTS n In V70, the ability to use external superelements, complete with data recovery was added for SOLs 101 and 103. n In V70.5, these new external superelements have been extended into SOLs 101 thru 159 and data recovery for them exists in SOLs 101, 103, and 107 thru 112. n The procedure for this is as follows: u Create reduced model. u Read in reduced model as an external superelement. u Perform solution and data recovery of assembly. u Perform data recovery on external superelement.

S7-118NAS105, Section 7, May 2005 CREATING AN EXTERNAL SUPERELEMENT n A separate model file is used to create an external superelement. n The component must be modeled as the residual structure in this file. u upstream superelements are allowed in this file, but the residual structure (assembly) is the component with reduced matrices will be available for as an external superelement in subsequent runs. n Interface dof must be identified using ASETi, BSETi, and/or CSETi entries. n If you are using component modal synthesis, QSETi dof must be provided to represent the component modes. n Only one boundary condition may be used. n Only one SUBCASE is required. u If you are performing a static solution, multiple residual structure SUBCASEs may be specified, but they must be in the correct order for use when the component is attached.

S7-119NAS105, Section 7, May 2005 CREATING AN EXTERNAL SUPERLEMENT (Cont) n There are 4 ways the reduced data may be stored for use in future runs. n The format of the reduced data is controlled by PARAM,EXTOUT: u MATRIXDB = the reduced matrices are stored on the database. They do not contain connectivity data. u DMIGDB = the reduced matrices are stored on the database using DMIG format and can be automatically attached. u DMIGOP2 = the reduced matrices are written using OUTPUT2 format to a file (specified by PARAM,EXTUNIT – default=30). The matrices are stored using DMIG format. u DMIGPCH = the reduced matrices are written to the.pch file using DMIG format.

S7-120NAS105, Section 7, May 2005 ATTACHING AN EXTERNAL SUPERELEMENT n External superelements may be attached using partitioned bulk data or by using the CSUPER entry. n If you use the partitioned bulk data method to attach an external superelement: u You need an EXTRN entry in the partitioned bulk data section. u you need to provide the GRID and SPOINTs to attach the external superelement to. (Be careful to align the displacement coordinate systems properly – there is no checking). u If EXTOUT was MATRIXDB or DMIGDB when the superelement was created: l use FMS to attach the database and locate the matrices: ASSIGN SExxx=run1. MASTER DBLOCATE DATABLK=(EXTDB), convert(SEID=xx), LOGICAL=SExxx u If EXTOUT was DMIGOP2, then l you must assign the OUTPUT2 file in the FMS: ASSIGN INPUTT2=run1.OP2, unit=i l specify PARAM,EXTUNIT,i to point to the file

S7-121NAS105, Section 7, May 2005 ATTACHING AN EXTERNAL SUPERELEMENT (Cont) u If EXTOUT was DMIGPCH, include the.pch file from the previous run and use the following case control for the superelement: K2GG= KAAX P2G = PAX M2GG = MAAX B2GG = BAAx n At this point, the run will proceed normally, attaching the external superelement and solving the problem. n Standard data recovery is available for all superelements (except the external ones) during the solution run. n Data recovery for the external superelement run requires saving the database from the assembly run and performing a data recovery restart on the external superelement. This is controlled by PARAM,EXTDROUT: u EXTDROUT=MATRIXDB – solution for boundary displacements stored in database using the sequencing of the assembly model u EXTDROUT = DMIGDB – solution stored in database using DMIG (only applicable if EXTOUT was set to DMIGDB or DMIGOP2) u EXTDROUT = DMIGOP2 – writes DMIG to OUTPUT2 file selected by PARAM,EXTDRUNT (default = unit 31) – available only for EXTOUT=DMIGOP2 or DMIGDB

S7-122NAS105, Section 7, May 2005 DATA RECOVERY FOR AN EXTERNAL SUPERELEMENT n Performing data recovery on the external superelement requires using a restart from the run which created the reduced matrices. n The run requires the following FMS (or similar): u ASSIGN SE10=run1. MASTER RESTART, LOGICAL=SE10 $ read–only restart – not required ASSIGN RESID=run2. MASTER DBLOCATE DATABLK=(EXTDB), LOGICAL=RESID n The run also requires PARAM,EXTDR,YES

S7-123NAS105, Section 7, May 2005 ATTACHING AN EXTERNAL SUPERELEMENT EXTRN bulk data entry: Defines a boundary connection for an external superelement. Format: Example: Field Contents GIDi Grid identification number to which the exterior superelement matrices will be connected. Ci Component numbers. (Integer 0, blank, or 1 for scalar points; Integers 1 through 6 with no embedded blanks for grids.)

S7-124NAS105, Section 7, May 2005 ATTACHING AN EXTERNAL SUPERELEMENT (Cont) Remarks: 1. EXTRN can only be specified in partitioned Bulk Data Sections and is ignored in the main Bulk Data Section. 2. Connection grids must be specified in the partitioned Bulk Data Section following BEGIN SUPER = SEID. 3. THRU may be specified in fields 3, 5, or Pairs of blank fields may be entered to allow easier modification of the EXTRN entry.

S7-125NAS105, Section 7, May 2005 SAMPLE PROBLEM n The solution will be a modal transient, SOL 112. n The loading on this model is a pressure on the elements in Superelement 10 (the external superelement). n The solution will consist of 5 runs and will use the MATRIXDB method (the other approaches would also work fine). u Run1 – process SE 10 u Run 2 – Read in SE 10 as external u Run3 – define and process internal SE 11 u Run 4 – Define and solve residual structure u Run 5 – data recovery on external SE 10

S7-126NAS105, Section 7, May 2005 SAMPLE PROBLEM USING MATRIXDB SOL 112 $ superelement SSS modal transient CEND TITLE = Generate data to be attached as SE 10 PARAM,EXTOUT,MATRIXDB SUBCASE 1 loadset = 15 $ Define loading METHOD = 10 $ request cms param,resvec,yes $ request residual vectors SPC = 1 BEGIN BULK $ define loads $ lseq,15,1001,101 lseq,15,2001,201 pload2,101,1.,97,thru,112 force,201,1108,,1.,10.,0.,0. $ $ define modal coordinates for CMS $ SPOINT THRU QSET THRU $ $ define which dofs will be retained (i.e. which dofs will form the $ attachment to the system model when we bring it in as an external se) $ ASET THRU 1104 $ $ print dof map for connecting the external superelement to the $ system model, in se10.dat, with EXTRN entry. The MATRIXDB option $ requires the dofs specified in the subsequent se10. dat run be in $ ASET ascending order. This is obtained with these parameters in $ the f06 $ usetsel =128 will print only ASET dof $ PARAM USETPRT 0 PARAM USETSEL 128 $ EIGRL 10 4 PSHELL CQUAD $ $ model description occurs here... $ GRID GRID GRID ENDDATA Run1 – file run1_se10.dat

S7-127NAS105, Section 7, May 2005 SAMPLE PROBLEM USING MATRIXDB (Cont) ASSIGN SE10DB = run1_se10. MASTER DBLOCATE DB=(EXTDB), CONVERT(SEID=10), LOGI=SE10DB $ SOL 103 TIME 600 CEND TITLE = Add external data and call it SE 10 SET 99 = 10 SEALL = 99 $ process only SE 10 SUBCASE 1 SUPER = 10 $ process only SE 10 param,resvec,yes loadset=15 METHOD = 10 BEGIN BULK $ declare SE 10 as external $ SEBULK 10 EXTERNAL BEGIN SUPER = 10 $ $ set flag for data recovery $ PARAM EXTDROUTMATRIXDB $ dynamic loading definition lseq,15,1001,101 lseq,15,2001,201 $pload2,101,1.,97,thru,112 $force,201,1108,,1.,10.,0.,0. SPOINT THRU QSET THRU ASET THRU 1034 $ $ Connect external superelement to the system model: $ Note that for the MATRIXDB option the order of the $ grids must be in ASET ASCENDING order $ EXTRN EIGRL 10 4 GRID GRID GRID GRID GRID ENDDATA Run2 – file run2_se10ln.dat – read SE 10 as external

S7-128NAS105, Section 7, May 2005 SAMPLE PROBLEM USING MATRIXDB (Cont) ASSIGN MASTER=run2_se10in.MASTER RESTART, VERSION=1, KEEP SOL 112 TIME 600 CEND TITLE = Add in SE 11 ECHO = NONE MAXLINES = SET 99 = 10,11 SEALL = 99 SUBCASE 1 SUPER = 10 METHOD = 10 param,resvec,yes loadset = 15 SUBCASE 2 SUPER = 11 $ process only SE 11 METHOD = 11 param,resvec,yes loadset = 15 BEGIN BULK BEGIN SUPER = 11 $ $ dynamic loading definition lseq,15,1001,101 lseq,15,2001,201 $ define non–existant loads to allow upstream loads $ as place holders force,101,1007,,0.,1.,0.,0. force,201,1007,,0.,1.,0.,0. $ define modal coordinates for CMS $ SPOINT THRU QSET THRU $ $ define attachment points to the next SE – $ optional if they already exist in the model $ ASET THRU 1004 $ EIGRL 11 4 PSHELL CQUAD $ model of SE GRID GRID ENDDATA Run3 – file run2_se11. dat – define and process SE11

S7-129NAS105, Section 7, May 2005 SAMPLE PROBLEM USING MATRIXDB (Cont) ASSIGN MASTER=run2_se10in.MASTER RESTART, VERSION=2, KEEP SOL 112 TIME 600 $ $ insert dmap avoidance for error – see next page $ CEND TITLE = Solve residual structure SUBCASE 1 SUPER = 10 METHOD = 10 loadset = 15 param,extdrout,matrixdb SUBCASE 2 SUPER = 11 METHOD = 11 loadset = 15 SUBCASE 3 SUPER = 0 $ process only the residual METHOD = 90 tstep = 35 SPC = 1 loadset = 15 dload = 25 SPCFORCES(plot)=ALL BEGIN BULK $ tstep,35,100,.01 tload2,25,1001,,,0.,100.,10.,90. lseq,15,1001,101 lseq,15,2001,201 force,101,1,,0.,1.,0.,0. force,201,1,,0.,1.,0.,0. $ EIGRL 90 4 SPC PSHELL CQUAD CQUAD GRID GRID ENDDATA Run4 – file run4_resid.dat – define residual structure and solve

S7-130NAS105, Section 7, May 2005 SAMPLE PROBLEM USING MATRIXDB (Cont) ASSIGN EXT10=run1_se10. MASTER RESTART, LOGI=EXT10 $ ASSIGN SYSTEM=run2_se10in.MASTER DBLOCATE DB=(EXTDB), WHERE(SEID=10), LOGI=SYSTEM $ SOL 112 TIME 600 diag 56 CEND TITLE = Data Recovery for external data ECHO = NONE MAXLINES = $ $ tell NASTRAN this is a data recovery run for the external data $ PARAM,EXTDR,YES $ DISP = ALL SUBCASE 1 METHOD = 10 param,resvec,yes loadset = 15 tstep = 35 dload = 25 SPCFORCES(plot)=ALL $ BEGIN BULK ENDDATA Run5 – file run5_dr10. dat – perform data recovery on se 10

S7-131NAS105, Section 7, May 2005 SAMPLE PROBLEM USING MATRIXDB (Cont) n Plot of displacement GRID 1020

S7-132NAS105, Section 7, May 2005 SAMPLE PROBLEM USING DMGIOP2 PROGRAM assign file for use by dmigop2 $ assign output2=ext10.op2, unit=30, delete $ SOL 112 $ superelement SSS modal transient $ include alter for OTM – optional include alteria.v705 CEND TITLE = Generate data to be attached as SE 10 $ param,extout,dmigop2 $ SUBCASE 1 loadset = 15 METHOD = 10 param,resvec,yes $ request residual vectors SPC = 1 disp = all stress = all force = all BEGIN BULK $ $ parameter to create OTM using alter1ia.v705 param,drmh,yes $ $ define loadings – used for residual vectors (also stored in database) lseq,15,1001,101 lseq,15,2001,201 pload2,101,1.,97,thru,112 force,201,1108,,1.,10.,0.,0. $ $ define modal coordinates for CMS – allow for 6 modes $ SPOINT THRU QSET THRU $ $ define which dofs will be retained (i.e. which dofs will form the $ attachment to the system model when we create SE10 in se10.dat) $ ASET THRU 1104 $ EIGRL 10 4 $ model goes here.... $ ENDDATA $ Run 1 + file run1`_se.dat

S7-133NAS105, Section 7, May 2005 SAMPLE PROBLEM USING DMGIOP2 $ run 2 – se10. dat – locate external data and attach as $ superelement 10 $ –––––– $ attach file containing reduced matrices and OTM ASSIGN inputt2=ext10.op2, unit=30 $ SOL 103 diag 8,15,56 include alteria.v705 CEND TITLE = Add external data and call it SE 10 SET 99 = 10 SEALL = 99 SUBCASE 1 SUPER = 10 $ process only SE 10 param,resvec,yes loadset=15 METHOD = 10 BEGIN BULK $ declare SE 10 as external SEBULK 10 EXTERNAL BEGIN SUPER = 10 $ point to file used for INPUTT2 param,extunit,30 $ set flag for data recovery PARAM EXTDROUTDMIGOP2 param,extdrunt,31 $ dynamic loading definition lseq,15,1001,101 lseq,15,2001,201 $pload2,101,1.,97,thru,112 $force,201,1108,,1.,10.,0.,0. EXTRN $ identify exterior points (not needed if coincident points elsewhere ASET THRU 1104 $ define modal coordinates for CMS SPOINT THRU QSET THRU GRID GRID GRID GRID GRID ENDDATA Run2 – file run2_se10in.dat

S7-134NAS105, Section 7, May 2005 SAMPLE PROBLEM USING DMGIOP2 $ SE 10 is all ready in the run2_se10in.DBALL database $ $RESTART LOGI=SE10M ASSIGN MASTER=run2_se10in.MASTER RESTART, VERSION=1, KEEP SOL 112 TIME 600 include alteria.v705 CEND TITLE = Add in SE 11 SET 99 = 10,11 SEALL = 99 SUBCASE 1 SUPER = 10 METHOD = 10 param,resvec,yes loadset = 15 $ add new subcase (let the auto–restart logic work it out) SUBCASE 2 SUPER = 11 $ process only SE 11 METHOD = 11 param,resvec,yes loadset = 15 BEGIN BULK BEGIN SUPER = 11 lseq,15,1001,101 lseq,15,2001,201 $ define non–existant loads to allow upstream loads $ as place holders force,101,1007,,0.,1.,0.,0. force,201,1007,,0.,1.,0.,0. $ define modal coordinates for CMS SPOINT THRU QSET THRU $ $ attachment points to the next SE not needed if coincident points exist $ ASET THRU 1004 $ EIGRL 11 4 $ model of se 11 ENDDATA Run3 – file run3 se11.dat

S7-135NAS105, Section 7, May 2005 SAMPLE PROBLEM USING DMGIOP2 $ run4_resid.dat – add residual data and solve $ assign file for boundary solution $ assign output2=se10bndry.op2, unit=31, delete $ $ SE 10 and 11 are in the run2_se10 database. $ for a read–only restart (not required) assign oldrun=run2_se10in.MASTER restart, logical=oldrun $ SOL 112 TIME 600 include alteria.v705 CEND TITLE = Solve residual structure disp(plot)=all SUBCASE 1 disp=all stress = all force = all SUPER = 10 METHOD = 10 loadset = 15 param,extdrout,dmigop2 param,extdrunt,31 SUBCASE 2 SUPER = 11 METHOD = 11 loadset = 15 SUBCASE 3 SUPER = 0 $ process only the residual METHOD = 90 tstep = 35 SPC = 1 loadset = 15 dload = 25 BEGIN BULK tstep,35,100,.01 tload2,25,1001,,,0.,100.,10.,90. lseq,15,1001,101 lseq,15,2001,201 force,101,1,,0.,1.,0.,0. force,201,1,,0.,1.,0.,0. EIGRL 90 4 $ residual structure model ENDDATA Run4 – file run4-including data recovery of SE10 (OTM)

S7-136NAS105, Section 7, May 2005 SAMPLE PROBLEM USING DMGIOP2 $ run 5_dr10. dat – data recovery for external data $ ================================== $ $ Features demonstrated: $ –––––––––––––––––––––– $ Data recovery for the external data (that became SE 10) $ $ Notes: $ –––––– $ This deck must be run in MSC.NASTRAN version 70.5 or above. $ ASSIGN EXT10=run1_se10. MASTER RESTART, LOGI=EXT10 $ assign inputt2=se10bndry.op2, unit=31 $ SOL 112 TIME 600 diag 56 CEND TITLE = Data Recovery for external data $ $ tell NASTRAN this is a data recovery run for the external data $ PARAM,EXTDR,YES param,extdrunt,31 $ param,extdr,yes DISP = ALL SUBCASE 1 METHOD = 10 spc = 1 param,resvec,yes loadset=15 tstep = 35 dload = 25 SPCFORCES(plot)=ALL OUTPUT(XYPLOT) XTITLE = TIME IN SECS XGRID LINES = YES YGRID LINES = YES YTITLE = Z DISPLACEMENT TCURVE = DISPL of GRID 1120 XYPLOT DISP RESP/1120(T3) BEGIN BULK ENDDATA Run5 – file run5_dr10. dat – optional data recovery of SE 10