SEARCH · Engineering Papers

Results for “fixed point method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

All sources NASA NTRS DOE OSTI

NASA NTRS1998

A New Approach to Overcoming Spatial Aliasing in Structural Damage Detection

Aircraft, reusable launch vehicles,unmanned aircraft, and other advanced structures are being built using lightweight composite materials/metals with design safety factors as low as 1.25. These advanced structures operate in uncertain and severe environments and are susceptible to damage such as delamination, fiber/matrix damage, hydrothermal strain in composite materials, and fatigue and cracking in metals. To ensure human safety and load-bearing integrity these structures must be inspected to detect and locate often invisible damage and faults before they become catastrophic. Conventional methods of non-destructive evaluation sometimes miss significant damage and are time consuming and expensive to perform. In contrast, vibrometry or vibration signature techniques are a global method of structural integrity monitoring that potentially can efficiently detect damage on large structures, including damage that is away from sensor locations, and in the interior of structures. However, a barrier problem in damage detection using vibration measurements is the need to measure the vibration response at a large number of points on the structure. Typically, model reduction or expansion procedures such as Guyan reduction or dynamic expansion are attempted to overcome the problem of insufficient measurements or spatial aliasing. These approaches depend on using information from the healthy model, and thus put error into the reduction used to represent the damaged structure. In this paper, a Frequency Response Function technique is used to detect damage to a fixed-free beam. The technique uses measured frequency response functions from the healthy structure as reference data, and then monitors vibration measurements during the life of the structure to detect damage. In an analytical simulation using a finite-element model of a beam, damage was located using only sparse measurements because the technique uses both rotation and translation measurements from the damaged structure.

Schulz, Mark J.↗

NASA NTRS2006

Repairing Fractured Bones by Use of Bioabsorbable Composites

A proposed method of surgical repair of fractured bones would incorporate recent and future advances in the art of composite materials. The composite materials used in this method would be biocompatible and at least partly bioabsorbable: that is, during the healing process following surgery, they would be wholly or at least partly absorbed into the bones and other tissues in which they were implanted. Relative to the traditional method, the proposed method would involve less surgery, pose less of a risk of infection, provide for better transfer of loads across fracture sites, and thereby promote better healing while reducing the need for immobilization by casts and other external devices. One requirement that both the traditional and proposed methods must satisfy is to fix the multiple segments of a broken bone in the correct relative positions. Mechanical fixing techniques used in the traditional method include the use of plates spanning the fracture site and secured to the bone by screws, serving of wire along the bone across the fracture site, insertion of metallic intramedullary rods through the hollow portion of the fractured bone, and/or inserting transverse rods through the bone, muscle, and skin to stabilize the fractured members. After the bone heals, a second surgical operation is needed to remove the mechanical fixture(s). In the proposed method, there would be no need for a second surgical operation. The proposed method is based partly on the observation that in the fabrication of a structural member, it is generally more efficient and reliable to use multiple small fasteners to transfer load across a joint than to use a single or smaller number of larger fasteners, provided that the stress fields of neighboring small fasteners do not overlap or interact. Also, multiple smaller fasteners are more reliable than are larger and fewer fasteners. However, there is a trade-off between structural efficiency and the cost of insertion time and materials. The proposed method is further based partly on the conjecture that through-the-thickness reinforcements could be excellent for fixing bone segments for surgical repair. The through-the-thickness reinforcements would superficially resemble nails in both form and function. Denoted small-diameter rods (SDRs) to distinguish them from other narrow rods, these reinforcements would be shot or otherwise inserted through adjacent segments of fractured bone to fix them in their correct relative positions (see figure). Shot insertion would be effected by use an applicator that would amount to a miniaturized and highly refined version of the pneumatic guns often used in carpentry to drive nails and brads. The applicator, envisioned to be about the size of a ball-point-pen, would be driven by pressurized carbon dioxide. To further promote stabilization of the segments, layers of bone glue could be applied to the fracture surfaces prior to insertion of the SDRs. The bone glue could be therapeutically loaded with chemicals to promote growth of bone and fight infection

Farley, Gary L.↗

NASA NTRS2005

Design Methods and Optimization for Morphing Aircraft

This report provides a summary of accomplishments made during this research effort. The major accomplishments are in three areas. The first is the use of a multiobjective optimization strategy to help identify potential morphing features that uses an existing aircraft sizing code to predict the weight, size and performance of several fixed-geometry aircraft that are Pareto-optimal based upon on two competing aircraft performance objectives. The second area has been titled morphing as an independent variable and formulates the sizing of a morphing aircraft as an optimization problem in which the amount of geometric morphing for various aircraft parameters are included as design variables. This second effort consumed most of the overall effort on the project. The third area involved a more detailed sizing study of a commercial transport aircraft that would incorporate a morphing wing to possibly enable transatlantic point-to-point passenger service.

Crossley, William A.↗

NASA NTRS2001

Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source

Although the single equivalent point dipole model has been used to represent well-localised bio-electrical sources, in realistic situations the source is distributed. Consequently, position estimates of point dipoles determined by inverse algorithms suffer from systematic error due to the non-exact applicability of the inverse model. In realistic situations, this systematic error cannot be avoided, a limitation that is independent of the complexity of the torso model used. This study quantitatively investigates the intrinsic limitations in the assignment of a location to the equivalent dipole due to distributed electrical source. To simulate arrhythmic activity in the heart, a model of a wave of depolarisation spreading from a focal source over the surface of a spherical shell is used. The activity is represented by a sequence of concentric belt sources (obtained by slicing the shell with a sequence of parallel plane pairs), with constant dipole moment per unit length (circumferentially) directed parallel to the propagation direction. The distributed source is represented by N dipoles at equal arc lengths along the belt. The sum of the dipole potentials is calculated at predefined electrode locations. The inverse problem involves finding a single equivalent point dipole that best reproduces the electrode potentials due to the distributed source. The inverse problem is implemented by minimising the chi2 per degree of freedom. It is found that the trajectory traced by the equivalent dipole is sensitive to the location of the spherical shell relative to the fixed electrodes. It is shown that this trajectory does not coincide with the sequence of geometrical centres of the consecutive belt sources. For distributed sources within a bounded spherical medium, displaced from the sphere's centre by 40% of the sphere's radius, it is found that the error in the equivalent dipole location varies from 3 to 20% for sources with size between 5 and 50% of the sphere's radius. Finally, a method is devised to obtain the size of the distributed source during the cardiac cycle.

NASA Discipline Cardiopulmonary↗

NASA NTRS2012

Wavefront Sensing for WFIRST with a Linear Optical Model

In this paper we develop methods to use a linear optical model to capture the field dependence of wavefront aberrations in a nonlinear optimization-based phase retrieval algorithm for image-based wavefront sensing. The linear optical model is generated from a ray trace model of the system and allows the system state to be described in terms of mechanical alignment parameters rather than wavefront coefficients. This approach allows joint optimization over images taken at different field points and does not require separate convergence of phase retrieval at individual field points. Because the algorithm exploits field diversity, multiple defocused images per field point are not required for robustness. Furthermore, because it is possible to simultaneously fit images of many stars over the field, it is not necessary to use a fixed defocus to achieve adequate signal-to-noise ratio despite having images with high dynamic range. This allows high performance wavefront sensing using in-focus science data. We applied this technique in a simulation model based on the Wide Field Infrared Survey Telescope (WFIRST) Intermediate Design Reference Mission (IDRM) imager using a linear optical model with 25 field points. We demonstrate sub-thousandth-wave wavefront sensing accuracy in the presence of noise and moderate undersampling for both monochromatic and polychromatic images using 25 high-SNR target stars. Using these high-quality wavefront sensing results, we are able to generate upsampled point-spread functions (PSFs) and use them to determine PSF ellipticity to high accuracy in order to reduce the systematic impact of aberrations on the accuracy of galactic ellipticity determination for weak-lensing science.

Jurling, Alden S.↗

NASA NTRS1973

On Lidar Sounding of the Atmosphere to Estimate Static and Dynamic Characteristics of Aerosol Inhomogeneities

1. A possible application of intensity fluctuations of a pulse light signal reflected by atmospheric aerosols is analyzed by the correlation method to evaluate static (medium sizes, shape) and dynamic (speed and direction of movement, lifetime) characteristics of aerosol inhomogeneities. The aerosol inhomogeneities are assumed to be expanded, pressed, disintegrated and originated constantly in accordance with random laws, the set of inhomogeneities as a whole traveling together with air masses and having predominant movement in wind direction. It is shown that the characteristics of aerosol inhomogeneities considered can be expressed by the coefficients of the correlation function expansion of the reflected signal fluctuation intensity in Tailor series. 2/ Correlation systems for evaluating static and dynamic characteristics of driving objects can be divided into two types according to the kind and quantity of used information: the systems with coordinates of the information removal "points" to be fixed in space, and the systems with a parallel simultaneous information removal at discrete moments of time. The systems for determination of wind direction considered in are the examples of the first type system. However, the operating information removal for two points is insufficient to estimate completely static and dynamic characteristics of inhomogenities, their quantity ought to be increased up to three of them for two-dimensional problem and up to four of them for three-dimensional problem as it is usually done in the ionospheric studies. The second type systems are used for the investigation of a medium shape and speed of the clouds according to photographs made from satellites. These systems are also used for solution of navigation problems. The use of optical quantum generators with a scanning beam is seen to increase greatly the working information removal in comparison with the first type systems. Nevertheless, scanning rate is not sufficient sometimes in order· to consider a general picture of aerosol inhomogeneities to be stationary. In this connection the use of the systems of second type treatment becomes a matter of essential difficulty. 3. Aerosol inhomogeneities simulation has been carried out on the basis of the digital computer experiments with the aim of estimating static and dynamic characteristics of inhomogeneities by an optical beam in the atmosphere at different scanning procedures. The dependence of determination accuracy of these characteristics on the type of chosen laws of aerosol particle distribution in the atmosphere, the parameters of inhomogeneities geometry, their speed and the law of scanning have been obtained.

Zuev, V. E.↗

NASA NTRS1984

Flight tests of the Digital Integrated Automatic Landing System (DIALS)

The design, development, implementation and flight tests of the Digital Integrated Automatic Landing System (DIALS) are discussed. The system was implemented and flight tested on the Transport Systems Research Vehicle (TSRV), a Boeing 737-100. The design uses modern optimal control methods. The direct digital design obtained uses a 10 Hz rate for the sampling of sensors and the control commands. The basic structure of the control law consists of a steady state Kalman filter followed by a control gain matrix. The sensor information used includes Microwave Landing System (MLS) position, attitude, calibrated airspeed, and body accelerations. The phases of the final approach considered are localized and steep glideslope capture (which may be performed simultaneously or independently), localizer and glideslope track, crab/decrab, and flare to touchdown. The system can capture, track, and flare from conventional, as well as steep, glideslopes ranging from 2.5 deg to 5.5 deg. All of the modes of the control law including the Kalman filters were implemented on the TSRV flight computers which use fixed point arithmetic with 16 bit words. The implementation considerations are described as well as an analysis of the flight test results.

Halyo, N.↗

NASA NTRS1981

Non-E x B ordered ion beams upstream of the earth's bow shock

The unexpected appearance of spin modulations in the fixed voltage electrostatic analyzer detectors on ISEE 1 and 2 has made it possible to study the plasma properties of the upstream ions in high time resolution. Using an isotropic flowing Maxwellian distribution to model the count rate modulations, estimates have been obtained of the local plasma temperature and three-dimensional flow velocity of the observed upstream ion population. It is found that in almost all of the observations of upstream particles there exist beam-like ions with temperatures in the range 5-80 eV. Their flow velocities cannot be ordered by E x B. This last point separates these observations from the previously reported reflected and diffuse populations of upstream ions. Mechanisms that can gyrophase bunch the ions reflected at the bow shock are discussed as a method of explaining the data.

Gurgiolo, C.↗

NASA NTRS2016

Spiral Lamber's Problem with Generalized Logarithmic Spirals

Lambert’s problem subject to a continuous acceleration is solved using the family of generalized logarithmic spirals. Thanks to the existence of two first integrals related to the energy and angular momentum surprising analogies with the Keplerian case are found. A minimum-energy spiral transfer exists. Increasing the value of the constant of the generalized energy yields pairs of conjugate spiral trajectories. The properties of such spirals are strongly connected with the properties of conjugate Keplerian orbits. When the generalized constant of the energy reaches a critical value the two solutions degenerate into a pair of parabolic spirals, one of which connects the two vectors through infinity. From that point the spiral transfers become hyperbolic. Generalized logarithmic spirals admit closed-form solutions to all the required magnitudes including the time of flight, providing a deep insight into the dynamics of the problem. In addition, the maximum acceleration along the transfer is found analytically so the solutions that violate the design constraints on the maximum thrust acceleration can be rejected without any further computations. When the time of flight is fixed there is still a degree of freedom in the solution, related to a control parameter. Resonant transfers appear naturally thanks to the symmetry properties of the generalized logarithmic spirals. The problem of designing a low-thrust transfer between two bodies can be reduced to solving the corresponding spiral Lambert’s problem. In order to show the versatility of the method it is applied to the design of an asteroid tour and to explore launch opportunities to Mars.\

Roa, Javier↗

NASA NTRS1991

Transformation of two and three-dimensional regions by elliptic systems

A reliable linear system is presented for grid generation in 2-D and 3-D. The method is robust in the sense that convergence is guaranteed but is not as reliable as other nonlinear elliptic methods in generating nonfolding grids. The construction of nonfolding grids depends on having reasonable approximations of cell aspect ratios and an appropriate distribution of grid points on the boundary of the region. Some guidelines are included on approximating the aspect ratios, but little help is offered on setting up the boundary grid other than to say that in 2-D the boundary correspondence should be close to that generated by a conformal mapping. It is assumed that the functions which control the grid distribution depend only on the computational variables and not on the physical variables. Whether this is actually the case depends on how the grid is constructed. In a dynamic adaptive procedure where the grid is constructed in the process of solving a fluid flow problem, the grid is usually updated at fixed iteration counts using the current value of the control function. Since the control function is not being updated during the iteration of the grid equations, the grid construction is a linear procedure. However, in the case of a static adaptive procedure where a trial solution is computed and used to construct an adaptive grid, the control functions may be recomputed at every step of the grid iteration.

Mastin, C. Wayne↗

NASA NTRS1994

Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

Jiang, Bo-Nan↗

NASA NTRS2024

X-57 Cruise Motor GVT Using Fixed-Base Correction Technique

The National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center (AFRC) completed a modal survey of the X-57 Maxwell aircraft cruise motor system to help inform cruise motor redesign efforts. X-57 Maxwell was an electric propulsion demonstrator aircraft developed by NASA to inform airworthiness standards for electrified-aircraft. The cruise motor system modal survey was completed in spring of 2023 utilizing the fixed-base correction (FBC) ground vibration test (GVT) technique developed by ATA Engineering, to decouple the motor modes from the aircraft modes. Previously during the full aircraft GVT, a detailed modal assessment of the cruise motors was not performed. Owing to the X-57 project’s phase in the aircraft development cycle when the motor redesign effort occurred, the cruise motor GVT could only be performed with the cruise motor system installed on the aircraft, with most of its installation hardware (wiring, baffling, sensors, etc.) attached. An impact hammer was used to provide excitation input at various locations within the tight confines of the cruise motor installation. To better support motor redesign efforts, the FBC methodology was utilized to fix, separate and de-couple the cruise motor modes from aircraft modal response. During the GVT, this required additional impact tap tests on candidate fixed-boundary points for each degree of freedom (DOF) to be fixed. Additional triaxial accelerometers installed at the candidate points were used to compute frequency response functions (FRFs) in X, Y, and Z directions to enable those DOFs to be numerically fixed. Test data was acquired using Hottinger Brüel & Kjær’s LAN-XI data acquisition hardware and BK Connect software. FBC post-test processing was performed using the Structural Modification Using Frequency Response Functions (SMURF) technique with ATA Engineering’s Interface between MATLAB, Analysis, Test (IMAT) software. Utilizing the FBC technique relieved test engineers from having to instrument the entire aircraft to identify and separate aircraft response from cruise motor modes of interest. The FBC technique also permitted structural analysis engineers to omit secondary components from their finite element model (FEM) of the cruise motor system. This FBC modal survey was successful, and the first time NASA AFRC utilized the FBC method on an aircraft rather than a test fixture, and also using an impact hammer rather than multiple shakers allowing significant project schedule and cost savings

Modal Survey↗

NASA NTRS1976

Space shuttle electromagnetic environment experiment. Phase A: Definition study

Methods for carrying out measurements of earth electromagnetic environment using the space shuttle as a measurement system platform are herein reported. The goal is to provide means for mapping intentional and nonintentional emitters on earth in the frequency range 0.4 to 40 GHz. A survey was made of known emitters using available data from national and international regulatory agencies, and from industry sources. The spatial distribution of sources, power levels, frequencies, degree of frequency re-use, etc., found in the survey, are here presented. A concept is developed for scanning the earth using a directive antenna whose beam is made to rotate at a fixed angle relative to the nadir; the illuminated area swept by the beam is of the form of cycloidal annulus over a sphere. During the beam's sojourn over a point, the receiver sweeps in frequency over ranges in the order of octave width using sweeping filter bandwidths sufficient to give stable readings.

Haber, F.↗

NASA NTRS1991

Experiments with conjugate gradient algorithms for homotopy curve tracking

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Irani, Kashmira M.↗

NASA NTRSDate not supplied

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↗

NASA NTRS1982

Engineering sciences area and module performance and failure analysis area

Photovoltaic-array/power-conditioner interface studies are updated. An experiment conducted to evaluate different operating-point strategies, such as constant voltage and pilot cells, and to determine array energy losses when the array is operated off the maximum power points is described. Initial results over a test period of three and a half weeks showed a 2% energy loss when the array is operated at a fixed voltage. Degraded-array studies conducted at NE RES that used a range of simulated common types of degraded I-V curves are reviewed. The instrumentation installed at the JPL field-test site to obtain the irradiance data was described. Experiments using an optical filter to adjust the spectral irradiance of the large-area pulsed solar simulator (LAPSS) to AM1.5 are described. Residential-array research activity is reviewed. Voltage isolation test results are described. Experiments performed on one type of module to determine the relationship between leakage current and temperature are reviewed. An encapsulated-cell testing approach is explained. The test program, data reduction methods, and initial results of long-duration module testing are described.

Ross, R. G., Jr.↗

NASA NTRS2003

Blind Leak Detection for Closed Systems

The current inspection technique for locating interstitial leaking in the Space Shuttle Main Engine nozzles is the application of a liquid leak check solution in the openings where the interstitials space between the tubing and the structural jacket vent out the aft end of the nozzle, while its cooling tubes are pressurized to 25 psig with Helium. When a leak is found, it is classified, and if the leak is severe enough the suspect tube is cut open so that a boroscope can be inserted to find the leak point. Since the boroscope can only cover a finite tube length and since it is impossible to identify which tube (to the right or left of the identified interstitial) is leaking, many extra and undesired repairs have been made to fix just one leak. In certain instances when the interstitials are interlinked by poor braze bonding, many interstitials will show indications of leaking from a single source. What is desired is a technique that can identify the leak source so that a single repair can be performed. Dr, Samuel Russell and James Walker, both with NASA/MSFC have developed a thermographic inspection system that addresses a single repair approach. They have teamed with Boeing/Rocketdyne to repackage the inspection processes to be suitable to address full scale Shuttle development and flight hardware and implement the process at NASA centers. The methods and results presented address the thermographic identification of interstitial leaks in the Space Shuttle Main Engine nozzles. A highly sensitive digital infrared camera (capable of detecting a delta temperature difference of 0.025 C) is used to record the cooling effects associated with a leak source, such as a crack or pinhole, hidden within the nozzle wall by observing the inner hot wall surface as the nozzle is pressurized, These images are enhanced by digitally subtracting a thermal reference image taken before pressurization. The method provides a non-intrusive way of locating the tube that is leaking and the exact leak source position to within a very small axial distance. Many of the factors that influence the inspectability of the nozzle are addressed; including pressure rate, peak pressure, gas type, ambient temperature and surface preparation. Other applications for this thermographic inspection system are the Reinforced-Carbon-Carbon (RCC) leading edge of the Space Shuttle orbiter and braze joint integrity.

Oelgoetz, Peter↗

NASA NTRS1993

Development and use of computational techniques in Army Aviation research and development programs for crash resistant helicopter technology

During the 1960's over 30 full-scale aircraft crash tests were conducted by the Flight Safety Foundation under contract to the Aviation Applied Technology Directorate (AATD) of the U.S. Army Aviation Systems Command (AVSCOM). The purpose of these tests were to conduct crash injury investigations that would provide a basis for the formulation of sound crash resistance design criteria for light fixed-wing and rotary wing aircraft. This resulted in the Crash Survival Design Criteria Designer's Guide which was first published in 1967 and has been revised numerous times, the last being in 1989. Full-scale aircraft crash testing is an expensive way to investigate structural deformations of occupied spaces and to determine the decelerative loadings experienced by occupants in a crash. This gave initial impetus to the U.S. Army to develop analytical methods to predict the dynamic response of aircraft structures in a crash. It was believed that such analytical tools could be very useful in the preliminary design stage of a new helicopter system which is required to demonstrate a level of crash resistance and had to be more cost effective than full-scale crash tests or numerous component design support tests. From an economic point of view, it is more efficient to optimize for the incorporation of crash resistance features early in the design stage. However, during preliminary design it is doubtful if sufficient design details, which influence the exact plastic deformation shape of structural elements, will be available. The availability of simple procedures to predict energy absorption and load-deformation characteristics will allow the designer to initiate valuable cost, weight, and geometry tradeoff studies. The development of these procedures will require some testing of typical specimens. This testing should, as a minimum, verify the validity of proposed procedures for providing pertinent nonlinear load-deformation data. It was hoped that through the use of these analytical models, the designer could optimize aircraft design for crash resistance from both a weight and cost increment standpoint, thus enhancing the acceptance of the design criteria for crash resistance.

Burrows, Leroy T.↗