In design modeling, the BEAM element differs from other element types in that its properties must be referenced according to their word positions in the element property tables. The element property tables are internally generated in NX Nastran, and used to form the element-level structural matrices.
Note
By convention, field position identifiers are denoted as positive quantities on DVPRELi entries, EPT word positions are denoted as negative quantities.
The source of this difference is due to the generality of the PBEAM Bulk Data entry. Since a single entry can used to specify the BEAM’s cross-sectional properties for both ends and up to nine intermediate stations, a unique correspondence between a BEAM property and its field
position on the PBEAM entry is not assured. The only relation that is assured is the one between a property item and its word position in the element property table. This correspondence
requires that the engineer have some understanding of the structure of the EPT for the BEAM element and its relation to the data supplied on the PBEAM entry.
Note
Note that the numbering inFigure 2-6 applies to the “new” design sensitivity and optimization (Solution 200).
In general, the cross section of a BEAM element may be either constant, linear, or variable.
These three possibilities are shown inFigure 2-6, which is a schematic of the EPT configuration for each of these situations.
Figure 2-6. Element Property Table for BEAM Element
Item 1 inFigure 2-6is a diagram of the EPT for the BEAM element when the PBEAM entry furnishes data at end A only. End B data is built internally as a copy of end A properties. Since this structure is used by subsequent modules to generate the element mass and stiffness matrices, the design model must also define equal variations for both sets of data. Thus, for design sensitivity and optimization, you must prescribe EPT word positions 166-181 (end B) in addition to words 6-21 (end A). Otherwise, the ensuing incompatibility between end A and end B data will invalidate the subsequent analysis results.
Item 2 inFigure 2-6shows the structure of the EPT for a tapered beam. The data for ends A and B is determined based on the supplied PBEAM input. Additionally, the first intermediate station (Words 22-37) is internally generated and contains a copy of end B data. Your design model must then reference words 6-21 for end A, words 166-181 for end B, and the first intermediate station.
The most general case is shown in item 3 where, in addition to ends A and B, from one to nine intermediate stations are defined. As in item 2, the first available intermediate station always contains a copy of end B data. This must always be accounted for in the design model definition.
(Note that if nine intermediate stations are defined, there is no need to supply an additional copy of end B data since the next station is end B itself.)
To illustrate, consider the uniformly tapered beam element inFigure 2-7. The cross-sectional dimensions for a rectangular element can be described in terms of design variables b1, h1, b2, and h2as shown in the figure. An input data file using this element in a single-element design sensitivity test is given inListing 2-1. This example corresponds to a test of Item 2 inFigure 2-6.
Figure 2-7. Tapered Rectangular Beam Element The initial design is given by
Equation 2-12.
This design is input to the DEQATN entries to define the corresponding cross-sectional properties for the element.
In addition to the properties at ends A and B, the design model must also include a definition for the first intermediate station. The properties at end A are expressed as functions of Design Variables 1 and 2 via DVPREL2s 1-5, end B properties are expressed in terms of Design Variables 3 and 4 via DVPREL2s 6-10, and the first intermediate station by DVPREL2s 11-15.
In order to make identification of the EPT word positions easier, the PBEAM entry has been set up to define cross-sectional properties that are slightly different from the properties computed using the initial design variable values. The design model overrides the analysis model properties and the differences reported in a differences comparison table. Since the word positions in the EPT are also output, these results can be used to check the validity of the formulation.
Note
The design model should include stress recovery point locations. Serious design errors may result if you omit these from your design model formulation.
The difference comparison table associated with the design model override is shown inFigure 2-8. From the corresponding field IDs (FID) it can be seen that not only is the data for ends A and B in the expected word positions, but the intermediate station is also present as expected.
The analysis and design property columns indicate that it is indeed just a copy of the data for end B. Furthermore, the design model formulation appears to be correct judging from the number, location, and values of the design model override data.
Figure 2-8. Message Indicating an Analysis Model Override by the Design Model
$>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
$ BEAM MODELING TEST, VERSION 2
$
$ TAPERED BEAM WITH RECTANGULAR SECTION, DESIGN SENSITIVITY ANALYSIS. SINCE
$ BOTH ENDS A AND B ARE SPECIFIED ON THE PBEAM ENTRY, DESIGN CHANGES MUST
$ BE SPECIFIED NOT ONLY FOR THE ENDS, BUT ALSO FOR THE FIRST INTERMEDIATE
$ STATION, WHICH CONTAINS A COPY OF END B DATA.
$
----*----$ B * = STRESS RECOVERY LOCATIONS
$
DISP = ALL
DESOBJ(MIN) = 8 $ OBJECTIVE FUNCTION DEFINITION DESSUB = 10 $ CONSTRAINT SET SELECTION
$
$---MAT1 110 10.0E6 0.33 0.1 +M1
+M1 50000. 50000. 29000.
$ PBEAM ENTRY INPUT WITH SLIGHT ‘ERROR’ IN TERMS. THIS HELPS VALIDATE THE
DE-$ SIGN MODEL BECAUSE USER WARNING MESSAGE WILL BE ISSUED, CONFIRMING OVERRIDE.
$
PBEAM 100 110 2.01 .167 .667 +P11
+P11 0.0 1.01 0.0 -1.01 +P12
+P12 YES 1.0 0.51 .0104 .042 +P13
+P13 0.0 0.51 0.0 -0.51
$
SPC1 100 123456 1
FORCE 300 2 20000.0 0.0 0.0 -1.0
$DESVAR,ID, LABEL, XINIT, XLB, XUB, DELXV
DESVAR, 1, B1, 1.0, 0.1, 10.0
DESVAR, 2, H1, 2.0, 0.2, 20.0
$
$DVPREL2,ID, TYPE, PID, FID, PMIN, PMAX, EQID, , +
$+, DESVAR, DVID1, DVID2, ..., , , , , +
$DESVAR,ID, LABEL, XINIT, XLB, XUB, DELXV DESVAR, 3, B2, 0.5, 0.05, 10.0
DESVAR, 4, H2, 1.0, 0.1, 20.0
$
$DVPREL2,ID, TYPE, PID, FID, PMIN, PMAX, EQID, , +
$+, DESVAR, DVID1, DVID2, ..., , , , , +
$+, DTABLE, CID1, CID2, ...
DVPREL2,6, PBEAM, 100, -168, , , 101, , +
+, DESVAR, 3, 4
$...FIRST INTERMEDIATE STATION (COPY OF END B DATA): (A,I1,I2,C2,D2)
$
$DVPREL2,ID, TYPE, PID, FID, PMIN, PMAX, EQID, , +
$+, DESVAR, DVID1, DVID2, ..., , , , , +
$DRESP1,ID, LABEL, RTYPE, PTYPE, REGION, ATTA, ATTB, ATT1, +
$+, ATT2, ...
2.5 Relating Design Variables to Shape Changes
To use shape sensitivity and optimization in NX Nastran, you must define design variables, and relate them to allowable shape variations. The amount the design variable is changed during optimization results in a corresponding shape change.
The allowable shapes are defined using shape basis vectors. The engineer uses these to describe how the structure is allowed to change. The optimizer then determines how much the structure can change by modifying the design variables. There are four methods are available to describe these shape basis vectors:
• Manual grid variation.
• Direct input of shapes.
• Geometric boundary shapes.
• Analytic boundary shapes.
This section begins with a brief theoretical discussion of shape basis vectors, followed by an introduction to auxiliary models, which you can use in NX Nastran as an aid to shape basis vector generation. Following these discussions is an overview of the various modeling methods available as well as an example highlighting some of the differences among these various approaches.
Other examples can be found inExample Problems, Example Problems. Interested readers may also refer toExample Problemsfor details regarding shape sensitivity analysis.