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NASA NTRS1993

Sensitivity analysis of Lyapunov and Riccati equations with application to controls-structures integrated design

Controls-structure integrated design is a complicated multidisciplinary design optimization problem which involves the state equations pertaining to open-loop eigenvalues and control laws. In order to alleviate the intensity of the computation, this study uses the adjoint variable method to derive sensitivity equations for the eigenvalue, Liapunov, and Riccati equations. These individual sensitivity equations are then combined together to form the multidisciplinary sensitivity equations for the control structure integrated design problems. A set of linear sensitivity equations, proportional in number to the number of performance functions involved in the optimization process, are solved. This proposed approach may provide a great saving in computer resources. The validity of the newly developed sensitivity equations is verified by numerical examples.

Hou, Gene↗

NASA NTRS1981

Calculation of sensitivity derivatives in thermal problems by finite differences

The optimum design of a structure subject to temperature constraints is considered. When mathematical optimization techniques are used, derivatives of the temperature constraints with respect to the design variables are usually required. In the case of large aerospace structures, such as the Space Shuttle, the computation of these derivatives can become prohibitively expensive. Analytical methods and a finite difference approach have been considered in studies conducted to improve the efficiency of the calculation of the derivatives. The present investigation explores two possibilities for enhancing the effectiveness of the finite difference approach. One procedure involves the simultaneous solution of temperatures and derivatives. The second procedure makes use of the optimum selection of the magnitude of the perturbations of the design variables to achieve maximum accuracy.

Haftka, R. T.↗

NASA NTRS1998

Analysis and Design of Variable Stiffness Composite Cylinders

An investigation of the possible performance improvements of thin circular cylindrical shells through the use of the variable stiffness concept is presented. The variable stiffness concept implies that the stiffness parameters change spatially throughout the structure. This situation is achieved mainly through the use of curvilinear fibers within a fiber-reinforced composite laminate, though the possibility of thickness variations and discrete stiffening elements is also allowed. These three mechanisms are incorporated into the constitutive laws for thin shells through the use of Classical Lamination Theory. The existence of stiffness variation within the structure warrants a formulation of the static equilibrium equations from the most basic principles. The governing equations include sufficient detail to correctly model several types of nonlinearity, including the formation of a nonlinear shell boundary layer as well as the Brazier effect due to nonlinear bending of long cylinders. Stress analysis and initial buckling estimates are formulated for a general variable stiffness cylinder. Results and comparisons for several simplifications of these highly complex governing equations are presented so that the ensuing numerical solutions are considered reliable and efficient enough for in-depth optimization studies. Four distinct cases of loading and stiffness variation are chosen to investigate possible areas of improvement that the variable stiffness concept may offer over traditional constant stiffness and/or stiffened structures. The initial investigation deals with the simplest solution for cylindrical shells in which all quantities are constant around the circumference of the cylinder. This axisymmetric case includes a stiffness variation exclusively in the axial direction, and the only pertinent loading scenarios include constant loads of axial compression, pressure, and torsion. The results for these cases indicate that little improvement over traditional laminates exists through the use of curvilinear fibers, mainly due to the presence of a weak link area within the stiffness variation that limits the ultimate load that the structure can withstand. Rigorous optimization studies reveal that even though slight increases in the critical loads can be produced for designs with an arbitrary variation of the fiber orientation angle, the improvements are not significant when compared to traditional design techniques that utilize ring stiffeners and frames. The second problem that is studied involves arbitrary loading of a cylinder with a stiffness variation that changes only in the circumferential direction. The end effects of the cylinder are ignored, so that the problem takes the form of an analysis of a cross-section for a short cylinder segment. Various load cases including axial compression, pressure, torsion, bending, and transverse shear forces are investigated. It is found that the most significant improvements in load-carrying capability exist for cases which involve loads that also vary around the circumference of the shell, namely bending and shear forces. The stiffness variation of the optimal designs contribute to the increased performance in two ways: lowering the stresses in the critical areas through redistribution of the stresses; and providing a relatively stiff region that alters the buckling behavior of the structure. These results lead to an in-depth optimization study involving weight optimization of a fuselage structure subjected to typical design constraints. Comparisons of the curvilinear fiber format to traditional stiffened structures constructed of isotropic and composite materials are included. It is found that standard variable stiffness designs are quite comparable in terms of weight and load-carrying capability yet offer the added advantage of tailorability of distinct regions of the structure that experience drastically different loading conditions. The last two problems presented in this work involve the nonlinear phenomenon of long tubes under bending. Though this scenario is not as applicable to fuselage structures as the previous problems, the mechanisms that produce the nonlinear effect are ideally suited to be controlled by the variable stiffness concept. This is due to the fact that the dominating influence for long cylinders under bending is the ovalization of the cross-section, which is governed mainly by the stiffness parameters of the cylindrical shell. Possible improvement of the critical buckling moments for these structures is investigated using either a circumferential or axial stiffness variation. For the circumferential case involving infinite length cylinders, it is found that slight improvements can be observed by designing structures that resist the cross-sectional deformation yet do not detract from the buckling resistance at the critical location. The results also indicate that buckling behavior is extremely dependent on cylinder length. This effect is most easily seen in the solution of finite length cylinders under bending that contain an axial stiffness variation. For these structures, the only mechanism that exhibits improved response are those that effectively shorten the length of the cylinder, thus reducing the cross-sectional deformation due to the forced restraint at the ends. It was found that the use of curvilinear fibers was not able to achieve this effect in sufficient degree to resist the deformation, but that ring stiffeners produced the desired response admirably. Thus, it is shown that the variable stiffness concept is most effective at improving the bending response of long cylinders through the use of a circumferential stiffness variation.

Tatting, Brian F.↗

NASA NTRS1982

ACCESS computer program for the synthesis of large structural systems

The structural-synthesis computer code ACCESS-3, originally limited to the optimization of relatively simple problems involving truss, membrane, and shear panel elements, has been restructured to make it applicable to structures with a larger number of degrees-of-freedom, design variables, and constraints. The modifications made allow the use of six degrees-of-freedom per node and permit the out-of-core solution of large matrix equations encountered at the analysis stage. Also, finite elements which permit pure bending as well as combined bending and membrane (axial) behavior have been added to satisfy the need for a more comprehensive set of elements. Like its predecessor, the new version of the program combines the approximation concepts with primal or dual formulations to provide an efficient optimization tool.

Fleury, C.↗

NASA NTRS1992

Structural tailoring/analysis for hypersonic components - Executive system development

No direct analytical or integrated numerical tool exists today for the optimal design of a generic class of built-up actively cooled composite structure for applications in hypersonic propulsion ducts. The need exists for a numerical tool to perform the comprehensive design/analysis of a panel on the inlet wall under hypersonic flight conditions. Such a tool requires relatively complex multi-disciplinary analysis. One such numerical tool controlled by an executive system has been developed and is named as STAHYC (Structural Tailoring/Analysis for HYpersonic Components). A detailed account of the executive system development of STAHYC along with the results of one example inlet panel design problem is given in this paper.

Narayanan, G. V.↗

NASA NTRS1991

General shape optimization capability

A method is described for calculating shape sensitivities, within MSC/NASTRAN, in a simple manner without resort to external programs. The method uses natural design variables to define the shape changes in a given structure. Once the shape sensitivities are obtained, the shape optimization process is carried out in a manner similar to property optimization processes. The capability of this method is illustrated by two examples: the shape optimization of a cantilever beam with holes, loaded by a point load at the free end (with the shape of the holes and the thickness of the beam selected as the design variables), and the shape optimization of a connecting rod subjected to several different loading and boundary conditions.

Chargin, Mladen K.↗

NASA NTRS1999

Engineering Overview of a Multidisciplinary HSCT Design Framework Using Medium-Fidelity Analysis Codes

An objective of the HPCC Program at NASA Langley has been to promote the use of advanced computing techniques to more rapidly solve the problem of multidisciplinary optimization of a supersonic transport configuration. As a result, a software system has been designed and is being implemented to integrate a set of existing discipline analysis codes, some of them CPU-intensive, into a distributed computational framework for the design of a High Speed Civil Transport (HSCT) configuration. The proposed paper will describe the engineering aspects of integrating these analysis codes and additional interface codes into an automated design system. The objective of the design problem is to optimize the aircraft weight for given mission conditions, range, and payload requirements, subject to aerodynamic, structural, and performance constraints. The design variables include both thicknesses of structural elements and geometric parameters that define the external aircraft shape. An optimization model has been adopted that uses the multidisciplinary analysis results and the derivatives of the solution with respect to the design variables to formulate a linearized model that provides input to the CONMIN optimization code, which outputs new values for the design variables. The analysis process begins by deriving the updated geometries and grids from the baseline geometries and grids using the new values for the design variables. This free-form deformation approach provides internal FEM (finite element method) grids that are consistent with aerodynamic surface grids. The next step involves using the derived FEM and section properties in a weights process to calculate detailed weights and the center of gravity location for specified flight conditions. The weights process computes the as-built weight, weight distribution, and weight sensitivities for given aircraft configurations at various mass cases. Currently, two mass cases are considered: cruise and gross take-off weight (GTOW). Weights information is obtained from correlations of data from three sources: 1) as-built initial structural and non-structural weights from an existing database, 2) theoretical FEM structural weights and sensitivities from Genesis, and 3) empirical as-built weight increments, non-structural weights, and weight sensitivities from FLOPS. For the aeroelastic analysis, a variable-fidelity aerodynamic analysis has been adopted. This approach uses infrequent CPU-intensive non-linear CFD to calculate a non-linear correction relative to a linear aero calculation for the same aerodynamic surface at an angle of attack that results in the same configuration lift. For efficiency, this nonlinear correction is applied after each subsequent linear aero solution during the iterations between the aerodynamic and structural analyses. Convergence is achieved when the vehicle shape being used for the aerodynamic calculations is consistent with the structural deformations caused by the aerodynamic loads. To make the structural analyses more efficient, a linearized structural deformation model has been adopted, in which a single stiffness matrix can be used to solve for the deformations under all the load conditions. Using the converged aerodynamic loads, a final set of structural analyses are performed to determine the stress distributions and the buckling conditions for constraint calculation. Performance constraints are obtained by running FLOPS using drag polars that are computed using results from non-linear corrections to the linear aero code plus several codes to provide drag increments due to skin friction, wave drag, and other miscellaneous drag contributions. The status of the integration effort will be presented in the proposed paper, and results will be provided that illustrate the degree of accuracy in the linearizations that have been employed.

Weston, R. P.↗

NASA NTRS1991

Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

Hanks, Brantley R.↗

NASA NTRS2014

Supersonic Wing Optimization Using SpaRibs

This research investigates the advantages of using curvilinear spars and ribs, termed SpaRibs, to design a supersonic aircraft wing-box in comparison to the use of classic design concepts that employ straight spars and ribs. The objective is to achieve a more efficient load-bearing mechanism and to passively control the deformation of the structure under the flight loads. Moreover, the use of SpaRibs broadens the design space and allows for natural frequencies and natural mode shape tailoring. The SpaRibs concept is implemented in a new optimization MATLAB-based framework referred to as EBF3SSWingOpt. This optimization scheme performs both the sizing and the shaping of the internal structural elements, connecting the optimizer with the analysis software. The shape of the SpaRibs is parametrically defined using the so called Linked Shape method. Each set of SpaRibs is placed in a one by one square domain of the natural space. The set of curves is subsequently transformed in the physical space for creating the wing structure geometry layout. The shape of each curve of each set is unique; however, mathematical relations link the curvature in an effort to reduce the number of design variables. The internal structure of a High Speed Commercial Transport aircraft concept developed by Boeing is optimized subjected to stress, subsonic flutter and supersonic flutter constraints. The results show that the use of the SpaRibs allows for the reduction of the aircraft's primary structure weight without violating the constraints. A weight reduction of about 15 percent is observed.

Locatelli, David↗

NASA NTRS1989

Aeroservoelastic tailoring for lateral control enhancement

The need for effective aileron power for aircraft lateral control and turning maneuvers dates back to the Wright Brothers and their wing warping concept for active stabilization of their aircraft. Early researchers in Great Britain, Japan, Germany and the United States explored ways to increase the effectiveness of control aileron to generate a roll moment. The basic problem of aileron effectiveness and the interrelationship between structural distortion and the loads applied by the control surface is illustrated. A rigid wing/aileron surface will develop the capability to generate increased roll rates as airspeed increases. A flexible surface will become less effective as airspeed increases because of the twisting distortion created by the aft-mounted control surface. This tendency is further worsened by bending distortion of an aft swept wing. This study focuses its attention on the ability of a combined effort between structural redesign of a wing and sizing and placement of a control surface to create specified roll performance with a minimum hinge moment. This design optimization problem indicates the advantages of simultaneous consideration of structural design and control design.

Weisshaar, Terrence A.↗

NASA NTRS2005

Discrete Event Supervisory Control Applied to Propulsion Systems

The theory of discrete event supervisory (DES) control was applied to the optimal control of a twin-engine aircraft propulsion system and demonstrated in a simulation. The supervisory control, which is implemented as a finite-state automaton, oversees the behavior of a system and manages it in such a way that it maximizes a performance criterion, similar to a traditional optimal control problem. DES controllers can be nested such that a high-level controller supervises multiple lower level controllers. This structure can be expanded to control huge, complex systems, providing optimal performance and increasing autonomy with each additional level. The DES control strategy for propulsion systems was validated using a distributed testbed consisting of multiple computers--each representing a module of the overall propulsion system--to simulate real-time hardware-in-the-loop testing. In the first experiment, DES control was applied to the operation of a nonlinear simulation of a turbofan engine (running in closed loop using its own feedback controller) to minimize engine structural damage caused by a combination of thermal and structural loads. This enables increased on-wing time for the engine through better management of the engine-component life usage. Thus, the engine-level DES acts as a life-extending controller through its interaction with and manipulation of the engine s operation.

Litt, Jonathan S.↗

NASA NTRS1979

SCI model structure determination program (OSR) user's guide

The computer program, OSR (Optimal Subset Regression) which estimates models for rotorcraft body and rotor force and moment coefficients is described. The technique used is based on the subset regression algorithm. Given time histories of aerodynamic coefficients, aerodynamic variables, and control inputs, the program computes correlation between various time histories. The model structure determination is based on these correlations. Inputs and outputs of the program are given.

Source record↗

NASA NTRS1991

Control design variable linking for optimization of structural/control systems

In this study a method is presented to integrate the design space of structural/control system optimization problems in the case of state feedback control. Conventional structural sizing variables and elements of the feedback gain matrix are both treated as strictly independent design variables in the optimization by extending design variable linking concepts to the control gains. Examples which involve a variety of behavior constraints, including dynamic transient response and control force limits, are effectively solved by using the method presented.

Jin, I. M.↗

NASA NTRS1980

Screen printing technology applied to silicon solar cell fabrication

The process for producing space qualified solar cells in both the conventional and wraparound configuration using screen printing techniques was investigated. Process modifications were chosen that could be easily automated or mechanized. Work was accomplished to optimize the tradeoffs associated with gridline spacing, gridline definition and junction depth. An extensive search for possible front contact metallization was completed. The back surface field structures along with the screen printed back contacts were optimized to produce open circuit voltages of at least an average of 600 millivolts. After all intended modifications on the process sequence were accomplished, the cells were exhaustively tested. Electrical tests at AMO and 28 C were made before and after boiling water immersion, thermal shock, and storage under conditions of high temperature and high humidity.

Thornhill, J. W.↗

NASA NTRS2012

Follow on Researches for X-56A Aircraft at NASA Dryden Flight Research Center (Progress Report)

A lot of composite materials are used for the modern aircraft to reduce its weight. Aircraft aeroservoelastic models are typically characterized by significant levels of model parameter uncertainty due to composite manufacturing process. Small modeling errors in the finite element model will eventually induce errors in the structural flexibility and mass, thus propagating into unpredictable errors in the unsteady aerodynamics and the control law design. One of the primary objectives of X-56A aircraft is the flight demonstration of active flutter suppression, and therefore in this study, the identification of the primary and secondary modes is based on the flutter analysis of X-56A aircraft. It should be noted that for all three Mach number cases rigid body modes and mode numbers seven and nine are participated 89.1 92.4 % of the first flutter mode. Modal participation of the rigid body mode and mode numbers seven and nine for the second flutter mode are 94.6 96.4%. Rigid body mode and the first two anti-symmetric modes, eighth and tenth modes, are participated 93.2 94.6% of the third flutter mode. Therefore, rigid body modes and the first four flexible modes of X-56A aircraft are the primary modes during the model tuning procedure. The ground vibration test-validated structural dynamic finite element model of the X-56A aircraft is to obtain in this study. The structural dynamics finite element model of X-56A aircraft is improved using the parallelized big-bang big-crunch algorithm together with a hybrid optimization technique.

Structural Dynamic Model Tuning↗

NASA NTRSDate not supplied

Structural Sizing of a Tow-Steered Truss-Braced Wing Box Test Article

Tailoring of composite laminates is traditionally performed by changing the orientation of straight fibers in one or more plies. Modern automated fiber placement machines facilitate placement of bundles of curved fibers (tows) in a process called tow-steering, but additional variables must be used to define the shapes of tow-steered fiber paths. In this paper, the design of a tow-steered truss-braced wing test article called the Structural Wing Experiment Evaluating Truss-bracing 15-ft concept (SWEET-15) is discussed. The SWEET-15 test article is scaled to 18.6% of the span length and chord width of a full-scale vehicle. The test article is designed to withstand +2.5-g (positive limit) and -1.0-g (negative limit) maneuvering loads with a factor of safety of 1.5 under strength and buckling constraints. Design studies were performed using commercial finite element analysis and optimization software in conjunction with a tow-steering modeling tool called ATSCOOL (Automated Tool for Steered COmposite Optimizable Laminates) developed at NASA Langley Research center. A 6.4% weight reduction in the upper cover panels was achieved using a tow-steered layup configuration.

Composites↗

NASA NTRS1972

Computerized optimal control system design for reusable and expendable boost vehicles.

An optimization technique has been developed which combines the practical features of hybrid simulation of the dynamic system under study with the systematic approach of modern control theory where a mathematically formulated design criterion is optimized by functional minimization. Standard hybrid computer optimization methods using high-speed repetitive simulations and gradient minimization schemes have been extended to obtain time-varying optimal gain schedules and reduce the sensitivity of the optimized system to parameter and disturbance uncertainties. In this approach the performance index is expressed in meaningful engineering terms that reflect the interactions among all major disciplines, structures, control/actuation system design, aerodynamics and performance. The basic optimization technique is developed and its application to current aerospace control problems including the space shuttle is presented in detail. In the discussion of the application, the controllers resulting from the technique are compared with controllers developed by conventional methods. The paper concludes with a review of the advantages and disadvantages of the technique and plans for future applications.

Connor, C. L.↗

NASA NTRS2008

Static and Dynamic Structural Response of an Aircraft Wing with Damage Using Equivalent Plate Analysis

A process to generate an equivalent plate based on an optimization approach to predict the static and dynamic response of flight vehicle wing structures is proposed. Geometric-scale and frequency-scale factors are defined to construct an equivalent plate with any desired scale to use in simulation and wind tunnel experiments. It is shown that the stiffness and the displacements are scaled linearly with the geometric-scale factor, whereas the load is scaled as the square of the geometric-scale factor. The scaled stiffness of the reference flight vehicle is matched first to construct the equivalent plate. Then the frequency-scale factor is defined to scale the flight vehicle frequencies. The scaled flight vehicle frequencies are matched by placing arbitrary point masses along the equivalent plate geometry. Two simple stiffened-plate examples, one with damage and another without damage, were used to demonstrate the accuracy of the optimization procedure proposed. Geometric-scale factors ranging from 0.2 to 1.0 were used in the analyses. In both examples, the static and dynamic response of the reference stiffened-panel solution is matched accurately. The scaled equivalent plate predicted the first five frequencies of the stiffened panel very accurately. Finally, the proposed equivalent plate procedure was demonstrated in a more realistic typical aircraft wing structure. Two scale equivalent plate models were generated using the geometric-scale factors 1.0 and 0.2. Both equivalent plate models predicted the static response of the wing structure accurately. The equivalent plate models reproduced the first five frequencies of the wing structure accurately.

Krishnamurthy, T.↗