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At least 523 records · Page 29

Inducer Hydrodynamic Forces in a Cavitating Environment

Marshall Space Flight Center has developed and demonstrated a measurement device for sensing and resolving the hydrodynamic loads on fluid machinery. The device - a derivative of the six-component wind tunnel balance - senses the forces and moments on the rotating device through a weakened shaft section instrumented with a series of strain gauges. This rotating balance was designed to directly measure the steady and unsteady hydrodynamic loads on an inducer, thereby defining the amplitude and frequency content associated with operating in various cavitation modes. The rotating balance was calibrated statically using a dead-weight load system in order to generate the 6 x 12 calibration matrix later used to convert measured voltages to engineering units. Structural modeling suggested that the rotating assembly first bending mode would be significantly reduced with the balance s inclusion. This reduction in structural stiffness was later confirmed experimentally with a hammer-impact test. This effect, coupled with the relatively large damping associated with the rotating balance waterproofing material, limited the device s bandwidth to approximately 50 Hertz Other pre-test validations included sensing the test article rotating assembly built-in imbalance for two configurations and directly measuring the assembly mass and buoyancy while submerged under water. Both tests matched predictions and confirmed the device s sensitivity while stationary and rotating. The rotating balance was then demonstrated in a water test of a full-scale Space Shuttle Main Engine high-pressure liquid oxygen pump inducer. Experimental data was collected a scaled operating conditions at three flow coefficients across a range of cavitation numbers for the single inducer geometry and radial clearance. Two distinct cavitation modes were observed symmetric tip vortex cavitation and alternate-blade cavitation. Although previous experimental tests on the same inducer demonstrated two additional cavitation modes at lower inlet pressures, these conditions proved unreachable with the rotating balance installed due to the intense dynamic environment. The sensed radial load was less influenced by flow coefficient than by cavitation number or cavitation mode although the flow coefficient range was relatively narrow. Transition from symmetric tip vortex to alternate-blade cavitation corresponded to changes in both radial load magnitude and radial load orientation relative to the inducer. Sensed moments indicated that the effective load center moved downstream during this change in cavitation mode. An occurrence of "higher+rdex cavitation" was also detected in both the stationary pressures and the rotating balance data although the frequency of the phenomena was well above the reliable bandwidth of the rotating balance. In summary the experimental tests proved both the concept and device s capability despite the limitations and confirmed that hydrodynamically-induced forces and moments develop in response to the unbalanced pressure field, which is, in turn, a product of the cavitation environment.

Skelley, Stephen E.↗

Reliability and Creep/Fatigue Analysis of a CMC Component

High temperature ceramic matrix composites (CMC) are being explored as viable candidate materials for hot section gas turbine components. These advanced composites can potentially lead to reduced weight and enable higher operating temperatures requiring less cooling; thus leading to increased engine efficiencies. There is a need for convenient design tools that can accommodate various loading conditions and material data with their associated uncertainties to estimate the minimum predicted life as well as the failure probabilities of a structural component. This paper presents a review of the life prediction and probabilistic analyses performed for a CMC turbine stator vane. A computer code, NASALife, is used to predict the life of a 2-D woven silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC) turbine stator vane due to a mission cycle which induces low cycle fatigue and creep. The output from this program includes damage from creep loading, damage due to cyclic loading and the combined damage due to the given loading cycle. Results indicate that the trends predicted by NASALife are as expected for the loading conditions used for this study. In addition, a combination of woven composite micromechanics, finite element structural analysis and Fast Probability Integration (FPI) techniques has been used to evaluate the maximum stress and its probabilistic distribution in a CMC turbine stator vane. Input variables causing scatter are identified and ranked based upon their sensitivity magnitude. Results indicate that reducing the scatter in proportional limit strength of the vane material has the greatest effect in improving the overall reliability of the CMC vane.

Murthy, Pappu L. N.↗

TURBOMAT: A Probabilistic Turbomachinery Aeroelastic Analysis Tool

An integration of aeroelastic analysis procedures with probabilistic analysis methods enables us to design safe reliable engines with quantified reliability. Towards this goal, a graphical user interface (GUI) based tool that integrates the codes Aeroelastic analysis of propfans (ASTROP2) and Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) is developed. The tool entitled TURBOMachinery Aeroelastic Analysis Tool (TURBOMAT), is developed utilizing the MATrix Laboratory (Matlab) Guide (Graphical User Interface Development) tool box. TURBOMAT provides a user friendly computational environment for rapid assessment of Turbomachinery blades flutter characteristics, subjected to uncertain loading conditions with variability in material and aerodynamic properties. The tool is seen as an education tool for new students and young engineers starting their careers in structural Aeroelasticity who want to learn and understand aeroelastic aspects of turbomachinery components, fans, compressors and turbines, including uncertainties in loading and material properties.A typical fan blade configuration geometry was chosen to demonstrate the tool. The results are presented in the form of probabilistic density function (PDF), the cumulative distribution function (CDF) and sensitivity factors. Both first order fast probability integration (FPI) and the Monto Carlo (MC) techniques are used in the analysis and compared. The tool enabled us to quantify blade flutter reliability as well as the ranking of uncertain variables and their importance to blade flutter response.

Aeroelastic Analysis↗

Microscale Constitutive Model Sensitivity on Multiscale Modeling of Fiber Reinforced Composites

Fiber reinforced composites are desirable in applications where low weight and high strength are needed, but are susceptible to microscale variability during manufacturing, making failure predictions difficult. The impact microscale variability has on macroscale mechanical response is difficult to predict due to the computational efficiency needed to simulate many, large, high fidelity, microscale models. In this study, a multiscale approach was taken to model 3-point bend, 4-point bend, and tensile experiments of a unidirectional composite from only having microstructure scans of these samples and constituent properties from literature. These scans were sampled with different sized windows, and statistically equivalent microstructures were generated, then simulated for stiffness, strength, and fracture toughness using an efficient micromechanical. Mesoscale models were created where element sizes equaled microstructure size, and properties were assigned through sampling of microscale simulation results. First, this study showed the effect of using Weibull scaling on constituent matrix strength on macroscale response. Then, a comparison was made between different element sizes and experiments. Finally, model dimensions were fixed, and the effect of randomly distributed local properties alone was examined. Results showed that the scatter of strength and stiffness in the experiments could be predicted well using images of the microscale fiber morphologies and that using stochastic properties produced a 3% coefficient of variation of strength for all experiments.

statistical microstructure↗

Characterization of Two-Dimensionally Braided Composites Subject to Static and Fatigue Loading

This paper presents a characterization of damage processes in four different two-dimensionally braided architectures consisting of graphite fibers in an epoxy matrix, subjected to both static and fatigue loading. Both notched and unnotched specimens were tested from each architecture. Damage mechanisms in static compression testing were found to range from matrix cracking in an architecture controlled by shearing characteristics of the matrix to axial fiber bundle kinking and splitting in architectures controlled by unidirectional fiber bundles. In both static tension and tension-tension fatigue testing, it was found that all architectures sustained the same basic damage types and progression sequences. The first types of damage to occur were splits in the braider bundles and cracks in the resin rich areas. Once a sufficient density of this type of damage had occurred, the axial bundles began to disbond from the surrounding constituents, and continued to do so until ultimate failure. One architecture sustained an additional mode of failure, which involved splitting of the axial bundles along their length. Varied degrees of notch sensitivity were found among the different architectures. In one architecture, this was attributed to differences found in the stacking of the individual plys of the braided architecture. As the density of axial bundles adjacent to the notch increased, the rate of stiffness loss increased and the life decreased.

Burr, Scott T.↗

Process Research On Polycrystalline Silicon Material (PROPSM)

The performance-limiting mechanisms in large-grain (greater than 1 to 2 mm in diameter) polycrystalline silicon solar cells were investigated by fabricating a matrix of 4 sq cm solar cells of various thickness from 10 cm x 10 cm polycrystalline silicon wafers of several bulk resistivities. Analysis of the illuminated I-V characteristics of these cells suggests that bulk recombination is the dominant factor limiting the short-circuit current. The average open-circuit voltage of the polycrystalline solar cells is 30 to 70 mV lower than that of co-processed single-crystal cells; the fill-factor is comparable. Both open-circuit voltage and fill-factor of the polycrystalline cells have substantial scatter that is not related to either thickness or resistivity. This implies that these characteristics are sensitive to an additional mechanism that is probably spatial in nature. A damage-gettering heat-treatment improved the minority-carrier diffusion length in low lifetime polycrystalline silicon, however, extended high temperature heat-treatment degraded the lifetime.

Culik, J. S.↗

Applications of automatic differentiation in computational fluid dynamics

Automatic differentiation (AD) is a powerful computational method that provides for computing exact sensitivity derivatives (SD) from existing computer programs for multidisciplinary design optimization (MDO) or in sensitivity analysis. A pre-compiler AD tool for FORTRAN programs called ADIFOR has been developed. The ADIFOR tool has been easily and quickly applied by NASA Langley researchers to assess the feasibility and computational impact of AD in MDO with several different FORTRAN programs. These include a state-of-the-art three dimensional multigrid Navier-Stokes flow solver for wings or aircraft configurations in transonic turbulent flow. With ADIFOR the user specifies sets of independent and dependent variables with an existing computer code. ADIFOR then traces the dependency path throughout the code, applies the chain rule to formulate derivative expressions, and generates new code to compute the required SD matrix. The resulting codes have been verified to compute exact non-geometric and geometric SD for a variety of cases. in less time than is required to compute the SD matrix using centered divided differences.

Green, Lawrence L.↗

Wear and Friction Behavior of Metal Impregnated Microporous Carbon Composites

Metal-matrix composites have been prepared by pressure-infiltration casting of copper-base alloy melts into microporous carbon preforms. The carbon preforms contained varying proportions of amorphous carbon and graphite. Load dependence of the wear and friction behavior of the composite pins has been examined under ambient conditions against cast-iron plates, using a pin-on-plate reciprocating wear tester. The wear resistance of the composite is significantly improved, as compared with the base alloy. Contrary to the normally expected behavior, the addition of graphite to the amorphous carbon does not reduce the friction coefficient, especially at high loads. The wear and friction behavior of the composites is very sensitive to the size and distribution of the microstructural constituents.

Goller, Gultekin↗

Multi-Domain Routing in Delay Tolerant Networks

The goal of Delay Tolerant Networking (DTN) is to provide the missing ingredient for the ever-growing collection of communicating nodes in our solar system to become a Solar System Internet (SSI). Great strides have been made in modeling particular types of DTNs, such as schedule- or discovery-based. Now, analogously to the Internet, these smaller DTNs can be considered routing domains which must be stitched together to form the overall SSI. In this paper, we propose a framework for cross-domain routing in DTNs as well as methodologies for detecting these sub-domains. Example time-varying networks are given to demonstrate the techniques proposed. A basic component is the mathematical theory of sheaves, which unifies the underlying model of DTN routing algorithms, by giving rise to routing sheaves – these can be defined for the dynamic and scheduled networks as noted above, and can also be used to define the interfaces between these domains in order to route across them. An immediate application would be routing across discovery-based networks connected by scheduled networks. These DTN subdomains remain elusive, however, and need to become well-defined and properly sized for tractable computability. In particular, a balance must be determined between areas that are too large (i.e. large matrix computations) versus areas that are too small (i.e. “many” single-noded domains). Moreover, the connections between the domains should, at least locally, be chosen to optimize data flow and connectivity: we address this in three ways. First, tools from persistent homology are given to understand underlying structures, reminiscent of hierarchies in the Internet Protocol (IP) addressing. Second, we construct a notion of temporal graph curvature based on network geometry to analyze flows induced by dynamical processes on these networks. Finally, Schrodinger Bridges, a tool arising from statistical physics, are proposed as a method of constructing flows on time-evolving networks with desirable properties such as speed, robustness, and load sensitivity. We construct an approach to temporal hypergraphs to simultaneously model unicast, multicast, and broadcast, using the language of scheme theory, and then consider DTN network coding as a way to achieve network-level computation and organization. The paper concludes with a discussion and ideas for future work.

Alan Hylton↗

Delaminations Investigated With Ultrasonic Spectroscopy

A previous study suggested that the ultrasonic spectroscopy technique identified possible disbonds or delaminations in polymer matrix composite (PMC) rings sectioned from flywheel rotors (ref. 1). These results went unsubstantiated by other nondestructive evaluation (NDE) methods. To explain the results, PMC rings were further investigated with ultrasonic spectroscopy (ref. 2). The ultrasonic spectroscopy system utilizes a continuous-swept sine waveform as the input. After the swept sine wave traverses the material, the captured waveform is subjected to two fast Fourier transforms. The second fast Fourier transform along with equalization of the frequency spectrum, allows for evaluation of the fundamental resonant frequency. The full-thickness resonance, the resonance corresponding to the location of the intentional disbond, and the frequency spectrum were examined in an effort to characterize the sensitivity of the NDE method to various delamination conditions.

Cosgriff, Laura M.↗

Radiance, polarization, and ellipticity of the radiation in the earth's atmosphere

The complete radiation field including polarization is calculated for a model of the real atmosphere by the matrix operator method. The radiance, direction and amount of polarization, and ellipticity are obtained at the top and bottom of the atmosphere for three values of the surface albedo (0; 0.15 0.90) and five solar zenith angles. Scattering and absorption by molecules (including ozone) and by aerosols are taken into account together with the variation of the number density of these substances with height. All results are calculated for both a normal aerosol number and a distribution which is one-third of the normal amount at all heights. The calculated values show general qualitative agreement with the available experimental measurements. The position of the neutral points of the polarization in the principal plane is a sensitive indicator of the characteristics of the aerosol particles in the atmosphere, since it depends on the sign and value of the single scattered polarization for scattering angles around 20 deg and 160 deg for transmitted and reflected photons respectively.

Hitzfelder, S. J.↗

An Optical Oxygen Sensor for Long-Term Continuous Monitoring of Dissolved Oxygen in Perfused Bioreactors

For long-term growth of man1ITlalian cells in perfused bioreactors, it is essential to monitor the concentration of dissolved oxygen (DO) present in the culture medium to quantitate and control level of DO. Continuous measurement of the amount of DO in the cell culture medium in-line under sterile conditions in NASA's perfused bioreactor requires that the oxygen sensor provide increased sensitivity and be sterilizable and nontoxic. Additionally, long-term cell culture experiments require that the calibration be maintained several weeks or months. Although there are a number of sensors for dissolved oxygen on the market and under development elsewhere, very few meet these stringent conditions. An optical oxygen sensor (BOXY) based on dynamic fluorescent quenching and a pulsed blue LED light source was developed in our laboratory to address these requirements. Tris( 4,7 -diphenyl-l, 1 O-phenanthroline )ruthenium(II) chloride is employed as the fluorescent dye indicator. The sensing element consists of a glass capillary (OD 4.0 mm; ID 2.0 mm) coated internally with a thin layer of the fluorescent dye in silicone matrix and overlayed with a black shielding layer. Irradiation of the sensing element with blue light (blue LED with emission maximum at 475 nm) generates a red fluorescence centered at 626 nm. The fluorescence intensity is correlated to the concentration of DO present in the culture medium, following the modified non-linear Stern-Volmer equation. By using a pulsed irradiating light source, the problem of dye-bleaching, which is often encountered in long-term continuous measurements of tIns type, 'is minimized. To date we achieved sensor resolution of 0.3 mmHg at 50 mmHg p02, and 0.6 mmHg at 100 mmHg p02, with a response time of about one minute. Calibration was accomplished in sterile phosphate-buffered saline with a blood-gas analyzer (BGA) measurement as reference. Stand-alone software was also developed to control the sensor and bioreactor as well as to acquire data. Two HOXY sensors with a single calibration were employed to continuously monitor the DO in GTSF-2 medium during a Baby Hamster Kidney (BHK-21) cell culture in a Rotating Wall Perfused Vessel (RWPV) bioreactor for 90 days. HOXY sensors were located at the inlet to and outlet from the bioreactor. One of the sensors was placed between an oxygenator and the inlet to the bioreactor. The dissolved oxygen concentrations determined by both sensors were compared with those measured regularly with the BGA reference. The cell culture was maintained for 110 days. Sensor output was found to correlate well with the BGA data throughout the experiment, where the DO of the medium ranged between 25 and 50 mmHg at the bioreactor outlet and 90-130 mmHg at the bioreactor inlet. Measuring DO with the HOXY sensors versus the BGA reference indicated bias values of -2 mmHg and -15 mmHg, and precision values of +/-3mmHg and +/-16 mmHg at the bioreactor inlet and outlet, respectively.

Gao, F. G.↗

Impact Response of Thermoplastic Composites – Experiments and Modeling

This study investigates the impact response of thermoplastic composite materials. The material system under consideration is a carbon fiber reinforced low melt semi-crystalline resin TC1225 LMPAEK reinforced with T700G (T700/LMPAEK ). Several High Energy Dynamic Impact (HEDI) tests were performed wherein an aluminum projectile impacted T700/LMPAEK panels at different velocities. In the impact experiment studied herein, the projectile impacted the T700/LMAPEK panel at 73.2 m/s and rebounded. The ensuing damage to the T700/LMPAEK panel was characterized via ultrasonic C-scans, visualizing damage modes including matrix cracking and delaminations. Since the projectile rebounded, the fiber breakage damage mode was not evident. The impact event was modeled using a combined continuum damage mechanics and cohesive zone analysis approach with the commercially available hydrocode LS-DYNA®. The dynamic deformation and damage of the continuum, i.e., the plies in the T700/LMPAEK laminate, was modeled using a Deformation Gradient Decomposition (DGD) material model, i.e., MAT299 available within LS-DYNA. The interlaminar regions were treated as zero-thickness cohesive zones, wherein the dynamic delamination mechanics was modeled using a traction-separation formulation. Mixed-mode delamination growth was captured using the Benzegaggh-Kenane (B-K) traction-separation interpolation law. Strain-rate sensitivity of interlaminar fracture toughness was included using approximations based on published literature. The outcomes of the modeling effort are discussed herein which demonstrate good correlations with test data regarding panel deflection, panel-projectile interactions, damage modes and damage extent.

Impact modeling↗

Aeroelastic tailoring of composite wings with external stores

The use of an integrating matrix solution procedure allows the aeroelastic stability of a large number of wing/store combinations to be studied with relative speed and accuracy. Results are presented which show the effects of tailoring the orientation of the plies of laminated composite wings when external stores are present. The stores utilized take the form of concentrated masses that are varied in terms of size and location, and combinations of stores are also studied. It is seen that there are cases for which small changes in the laminate can produce large changes in the aeroelastic stability boundary, and for such situations care should be used in tailoring a wing. For a given wing, the choice fiber angle to optimize the aeroelastic performance is quite sensitive to both the size and location of the store.

Green, J. A.↗

Oxidation of Boron Nitride in Composites

Boron nitride (BN) is a prime candidate for fiber coatings in silicon carbide (SiC) fiber-reinforced SiC matrix composites. The properties of BN allow the fiber to impart beneficial composite properties to the matrix, even at elevated temperatures. The problem with BN is that it is readily attacked by oxygen. Although BN is an internal component of the composite, a matrix crack or pore can create a path for hot oxygen to attack the BN. This type of attack is not well understood. A variety of phenomena have been observed. These include borosilicate glass formation, volatilization of the BN, and under some conditions, preservation of the BN. In this study at the NASA Lewis Research Center, a series of BN materials and BN-containing model composites were methodically examined to understand the various issues dealing with the oxidation of BN in composites. Initial studies were done with a series of monolithic BN materials prepared by hot pressing and chemical vapor deposition (CVD). From these studies, we found that BN showed a strong orientation effect in oxidation and was extremely sensitive to the presence of water vapor in the environment. In addition, CVD material deposited at a high temperature showed much better oxidation behavior than CVD material deposited at a lower temperature.

Jacobson, Nathan S.↗

Distributed sensing of Composite Over-wrapped Pressure Vessels using Fiber-Bragg Gratings

The increasing use of advanced composite materials in the wide range of applications including Space Structures is a great impetus to the development of smart materials. These materials offer a wide range of possibilities within the space program. But before they can be reliably incorporated into space flight applications, additional understanding is required in the area of damage tolerance of these materials. Efforts to enhance our understanding of failure modes, mechanical properties, long and short term environmental effects, cyclic damage accumulation and residual strength are needed. Thus we have employed the use of fiber optical sensors which offers an excellent opportunity exploit these materials through monitoring and characterizing their mechanical properties and thus the integrity of structures made from such materials during their life cycle. Use of these optical innovations provides an insight into structures that have not been available in the past, as well as the technology available to provide real time health monitoring throughout its life cycle. The embedded fiber optical sensor shows a clearly detectable sensitivity to changes in the near strain and stress fields of the host structure promoted by mechanical or thermal loading or, in certain conditions, structural damage. The last ten years have seen a large increase in the use of FBG based monitoring systems in a broad range of applications. Fiber Bragg gratings are use to monitor the structural properties of composite pressure vessels. These gratings optically inscribed into the core of a single mode fiber are used as a tool to monitor the stress strain relation in composite structures. The fiber Bragg sensors are both embedded within the composite laminates and bonded to the surface of the vessel with varying orientations with respect to the carbon fiber in the epoxy matrix. The response of these fiber-optic sensors is investigated by pressurizing the cylinder up to its burst pressure of around 4400 psi. This is done at both ambient and cryogenic temperatures using water and liquid nitrogen. The recorded response is compared with the response from conventional strain gauge also present on the vessel. Additionally, several vessels were tested that had been damaged to simulate different type of events, such as cut tow, delimitation and impact damage.

Grant, Joseph↗

Monitoring of Time-Dependent System Profiles by Multiplex Gas Chromatography with Maximum Entropy Demodulation

The maximum entropy technique was successfully applied to the deconvolution of overlapped chromatographic peaks. An algorithm was written in which the chromatogram was represented as a vector of sample concentrations multiplied by a peak shape matrix. Simulation results demonstrated that there is a trade off between the detector noise and peak resolution in the sense that an increase of the noise level reduced the peak separation that could be recovered by the maximum entropy method. Real data originated from a sample storage column was also deconvoluted using maximum entropy. Deconvolution is useful in this type of system because the conservation of time dependent profiles depends on the band spreading processes in the chromatographic column, which might smooth out the finer details in the concentration profile. The method was also applied to the deconvolution of previously interpretted Pioneer Venus chromatograms. It was found in this case that the correct choice of peak shape function was critical to the sensitivity of maximum entropy in the reconstruction of these chromatograms.

Becker, Joseph F.↗

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.↗