The NX Nastran Design Sensitivity and Optimization User’s Guide contains a comprehensive description of the NX Nastran design sensitivity and optimization capability. This section contains supplementary information on the aeroelastic aspects of this capability and is divided into subsections on analysis, response evaluation, sensitivity, and optimization.
Multidisciplinary Analysis
For an optimization procedure to be of maximum benefit, it must be able to simultaneously take into account of all the conditions that impact the design. For this reason, the design sensitivity and optimization capability in NX Nastran is based on a multidisciplinary analysis capability that includes statics, normal modes, buckling, direct and modal frequency, modal transient, static aeroelastic, and flutter analyses. The static aeroelastic and flutter analysis capabilities present in the multidisciplinary analysis and design solution sequence (SOL 200) contain the full capabilities of the static aeroelastic (SOL 144) and flutter (SOL 145) solution sequences. It is necessary in SOL 200 to designate the type of analysis being performed for each subcase using the ANALYSIS Case Control command. ANALYSIS = SAERO is used for static aeroelasticity, while ANALYSIS = FLUTTER is used for flutter analysis.
Response Evaluation
For a sensitivity value to be computed, the user must designate it on a DRESP1 entry and either constrain it on a DCONSTR entry or identify it as the design objective using the DESOBJ Case Control command. Further, the DCONSTR set must be selected by either a DESSUB or a DESGLB Case Control command. For static aeroelasticity, the DRESP1 entry can be used to invoke standard static analysis responses, specifically, RTYPE = DISP, STRAIN, STRESS, FORCE, CSTRAIN, CSTRESS, and/or CFAILURE, as well as two responses, RTYPE = STABDER and/or TRIM, that are unique to static aeroelasticity. The STABDER response requests a stability derivative response and therefore selects one of the components of an AESTAT or AESURF aerodynamic extra point. The selected response type can correspond to a restrained or unrestrained derivative (seeStatic Aeroelasticity), based on the value of the ATTB field. The utility of this request is that it is possible to determine how a key aeroelastic parameter, such as lift curve slope,CLa, varies when a structural change is made. More significant perhaps, it is possible to include design requirements on these stability derivatives in an NX Nastran design optimization study.
The TRIM response on the DRESP1 entry requests a particular aerodynamic extra point by referencing an AESTAT or AESURF entry ID. The associated response is the magnitude of the aerodynamic extra point for the maneuver condition defined for the subcase. It is to be expected that the sensitivity of this response to a particular structural parameter is small. The response can have utility in limiting the range over which an aerodynamic value can vary during an optimization task; e.g., by limiting an elevator rotation to be less than 20 degrees, therefore, unrealistic designs can be precluded.
A final DRESP1 response type related to aeroelasticity is for flutter (RTYPE = FLUTTER). The entry selects damping values from an aerodynamic flutter analysis as response quantities. The ATTi (i = 1,2,3 and 4) fields of this entry allow for a precise selection of the damping values from the available responses; i.e., ATT1 specifies a SET1 entry that selects the mode set, ATT2 specifies an FLFACT entry that selects the set of densities, ATT3 specifies an FLFACT entry that selects a set of Mach numbers, and ATT4 specifies an FLFACT entry that specifies a list of velocities. The requested data must exist from the analysis at precisely the Mach number, density, and velocity triplets specified by the FLFACT data. The effective use of this capability requires knowledge of the flutter characteristics of the vehicle so that the subset of the analysis results that are selected for design are both reasonable and comprehensive. For example, it
would make little sense to try and alter the structure to modify undesirable damping values that result from the rigid body response of the vehicle. Similarly, most damping values are noncritical and can be safely excluded from the design task.
NX Nastran can also construct synthetic responses that can be a function of DRESP1 response values, design variables values, user-defined constants, and grid locations. This is done using a combination of the DRESP2 entry to define the quantities that contribute to the synthetic response and a DEQATN entry that provides the equation that defines the synthetic response. A particular aeroelastic application of this capability is the construction of a response that predicts the roll performance of the vehicle as a function of the ratio of two stability derivatives:
Obtaining adequate roll performance is often a design driver for air-combat vehicles and typically entails enhancing the torsional stiffness of a wing. By use of the above relationship, this requirement can be incorporated into an NX Nastran design task. An example of this is given inAeroelastic Optimization of FSW Airplane (Example HA200A).
Sensitivity Analysis
The specification of response quantities as described in the preceding subsection is a means towards the end of obtaining information for the structural design task. The first type of information that is available is sensitivity results wherein the rate of change of a particular response quantity rj, with respect to a change in a design variable xj, is produced:
Defining the Design Variables in the NX Nastran Design Sensitivity and Optimization User’s
Guide (Moore, Version 68) contains a detailed description of design sensitivity analysis while in
thisAeroelastic Design Sensitivities and Optimizationprovides a description of the calculations required to provide these sensitivities for aeroelastic responses. This section provides guidelines useful in obtaining desired sensitivity information.
The user selects sensitivity analysis by setting PARAM,OPTEXIT equal to 4. An example of the output obtained with this option is given inAeroelastic Optimization of FSW Airplane (Example HA200A).
The NX Nastran implementation of design sensitivity analysis requires that the responses specified on DRESP1 and DRESP2 entries must be “constrained” in order for design sensitivity to occur. Further, the constrained responses have to pass through screening criteria that are applied in NX Nastran in order to limit the number of responses that are used in a design sensitivity and/or optimization task.
The constraint specification begins with a DESSUB Case Control command that identifies the constraint set that is to be applied to a particular subcase. The command invokes DCONADD and/or DCONSTR Bulk Data entries, where the optional DCONADD entry is used to collect DCONSTR sets applicable in the subcase and the DCONSTR entry selects the DRESPi entries and specifies lower and upper limits on the response value.
The screening procedure selects the constraints that are greater than a threshold value with a further limitation that only a limited number of responses of a given type will be retained (see the Defining the Analysis Disciplines in the NX Nastran Design Sensitivity and Optimization
to reduce the threshold value and/or increase the number of retained responses. For sensitivity analysis, a trick that can be used to force the retention of a response is to specify identical upper and lower limits on the DCONSTR entry associated with the response.
Optimization
Once you have specified the design variables, a design objective, and design constraints, you can use NX Nastran to determine the design that provides the minimum (or maximum) value of the objective while satisfying the imposed constraints. This is a powerful tool for the aeroelastician in that it provides a systematic means of finding an improved design. An optimization task exploits any deficiencies in the analysis in a way that helps it achieve its goals. Again, see the
NX Nastran Design Sensitivity and Optimization User’s Guide for guidelines on performing
optimization tasks, including means of gaining insight into the performance of the optimizer. One user guideline that is relevant here is that the use of 0.0 as a limiting value on the DCONSTR entry should be avoided, if possible. NX Nastran uses a normalized value for the constraint that entails dividing the response value by the constraint limit. Specifying a limit of 0.0 then produces a division-by-zero problem that NX Nastran avoids by substituting a small number for the limit. In the context of aeroelasticity, the user would be inclined to apply an upper bound of 0.0 to a DRESP1 entry that has an RTYPE of FLUTTER. This would ensure a negative damping level. It is recommended that a DRESP2 entry be used to offset the flutter response from zero and also to scale the response so that the constraint varies over a wider range than the unscaled response. The DRESP2 response is of the form:
where g is the flutter response, OFFSET is the offset value (typically 0.3) and GFACT is the scaling factor (typically 0.1). The DCONSTR entry would then impose an upper bound limit of -OFFSET/GFACT on the DRESP2 response, and this would be equivalent to restricting the flutter damping value to be negative.