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At least 127 records · Page 7

Improved Sizing of Impact Damage in Composites Based on Thermographic Response

Impact damage in thin carbon fiber reinforced polymer composites often results in a relatively small region of damage at the front surface, with increasing damage near the back surface. Conventional methods for reducing the pulsed thermographic responses of the composite tend to underestimate the size of the back surface damage, since the smaller near surface damage gives the largest thermographic indication. A method is presented for reducing the thermographic data to produce an estimated size for the impact damage that is much closer to the size of the damage estimated from other NDE techniques such as microfocus x-ray computed tomography and pulse echo ultrasonics. Examples of the application of the technique to experimental data acquired on specimens with impact damage are presented. The method is also applied to the results of thermographic simulations to investigate the limitations of the technique.

Winfree, William P.↗

Use of a New Portable Instrumented Impactor on the NASA Composite Crew Module Damage Tolerance Program

Damage tolerance performance is critical to composite structures because surface impacts at relatively low energies may result in a significant strength loss. For certification, damage tolerance criteria require aerospace vehicles to meet design loads while containing damage at critical locations. Data from standard small coupon testing are difficult to apply to larger more complex structures. Due to the complexity of predicting both the impact damage and the residual properties, damage tolerance is demonstrated primarily by testing. A portable, spring-propelled, impact device was developed which allows the impact damage response to be investigated on large specimens, full-scale components, or entire vehicles. During impact, both the force history and projectile velocity are captured. The device was successfully used to demonstrate the damage tolerance performance of the NASA Composite Crew Module. The impactor was used to impact 18 different design features at impact energies up to 35 J. Detailed examples of these results are presented, showing impact force histories, damage inspection results, and response to loading.

Jackson, Wade C.↗

Integration of Earth Remote Sensing into the NOAA/NWS Damage Assessment Toolkit

Following the occurrence of severe weather, NOAA/NWS meteorologists are tasked with performing a storm damage survey to assess the type and severity of the weather event, primarily focused with the confirmation and assessment of tornadoes. This labor‐intensive process requires meteorologists to venture into the affected area, acquire damage indicators through photos, eyewitness accounts, and other documentation, then aggregation of data in order to make a final determination of the tornado path length, width, maximum intensity, and other characteristics. Earth remote sensing from operational, polar‐orbiting satellites can support the damage assessment process by helping to identify portions of damage tracks that are difficult to access due to road limitations or time constraints by applying change detection techniques. In addition, higher resolution commercial imagery can corroborate ground‐based surveys by examining higher‐resolution commercial imagery. As part of an ongoing collaboration, NASA and NOAA are working to integrate near real‐time Earth remote sensing observations into the NOAA/NWS Damage Assessment Toolkit, a handheld application used by meteorologists in the survey process. The team has recently developed a more streamlined approach for delivering data via a web mapping service and menu interface, allowing for caching of imagery before field deployment. Near real‐time products have been developed using MODIS and VIIRS imagery and change detection for preliminary track identification, along with conduits for higher‐resolution Landsat, ASTER, and commercial imagery as they become available. In addition to tornado damage assessments, the team is also investigating the use of near real‐time imagery for identifying hail damage to vegetation, which also results in large swaths of damage, particularly in the central United States during the peak growing season months of June, July, and August. This presentation will present an overview of recent activities, challenges and successes, best practices, and opportunities for future work and collaboration.

Molthan, Andrew↗

Investigation of Spiral Bevel Gear Condition Indicator Validation via AC-29-2C Combining Test Rig Damage Progression Data with Fielded Rotorcraft Data

This is the final of three reports published on the results of this project. In the first report, results were presented on nineteen tests performed in the NASA Glenn Spiral Bevel Gear Fatigue Test Rig on spiral bevel gear sets designed to simulate helicopter fielded failures. In the second report, fielded helicopter HUMS data from forty helicopters were processed with the same techniques that were applied to spiral bevel rig test data. Twenty of the forty helicopters experienced damage to the spiral bevel gears, while the other twenty helicopters had no known anomalies within the time frame of the datasets. In this report, results from the rig and helicopter data analysis will be compared for differences and similarities in condition indicator (CI) response. Observations and findings using sub-scale rig failure progression tests to validate helicopter gear condition indicators will be presented. In the helicopter, gear health monitoring data was measured when damage occurred and after the gear sets were replaced at two helicopter regimes. For the helicopters or tails, data was taken in the flat pitch ground 101 rotor speed (FPG101) regime. For nine tails, data was also taken at 120 knots true airspeed (120KTA) regime. In the test rig, gear sets were tested until damage initiated and progressed while gear health monitoring data and operational parameters were measured and tooth damage progression documented. For the rig tests, the gear speed was maintained at 3500RPM, a one hour run-in was performed at 4000 in-lb gear torque, than the torque was increased to 8000 in-lbs. The HUMS gear condition indicator data evaluated included Figure of Merit 4 (FM4), Root Mean Square (RMS) or Diagnostic Algorithm 1(DA1), + 3 Sideband Index (SI3) and + 1 Sideband Index (SI1). These were selected based on their sensitivity in detecting contact fatigue damage modes from analytical, experimental and historical helicopter data. For this report, the helicopter dataset was reduced to fourteen tails and the test rig data set was reduced to eight tested gear sets. The damage modes compared were separated into three cases. For case one, both the gear and pinion showed signs of contact fatigue or scuffing damage. For case two, only the pinion showed signs of contact fatigue damage or scuffing. Case three was limited to the gear tests when scuffing occurred immediately after the gear run-in. Results of this investigation highlighted the importance of understanding the complete monitored systems, for both the helicopter and test rig, before interpreting health monitoring data. Further work is required to better define these two systems that include better state awareness of the fielded systems, new sensing technologies, new experimental methods or models that quantify the effect of system design on CI response and new methods for setting thresholds that take into consideration the variance of each system.

spiral bevel gears↗

Model-Based Fatigue Prognosis of Fiber-Reinforced Laminates Exhibiting Concurrent Damage Mechanisms

Prognostics of large composite structures is a topic of increasing interest in the field of structural health monitoring for aerospace, civil, and mechanical systems. Along with recent advancements in real-time structural health data acquisition and processing for damage detection and characterization, model-based stochastic methods for life prediction are showing promising results in the literature. Among various model-based approaches, particle-filtering algorithms are particularly capable in coping with uncertainties associated with the process. These include uncertainties about information on the damage extent and the inherent uncertainties of the damage propagation process. Some efforts have shown successful applications of particle filtering-based frameworks for predicting the matrix crack evolution and structural stiffness degradation caused by repetitive fatigue loads. Effects of other damage modes such as delamination, however, are not incorporated in these works. It is well established that delamination and matrix cracks not only co-exist in most laminate structures during the fatigue degradation process but also affect each other's progression. Furthermore, delamination significantly alters the stress-state in the laminates and accelerates the material degradation leading to catastrophic failure. Therefore, the work presented herein proposes a particle filtering-based framework for predicting a structure's remaining useful life with consideration of multiple co-existing damage-mechanisms. The framework uses an energy-based model from the composite modeling literature. The multiple damage-mode model has been shown to suitably estimate the energy release rate of cross-ply laminates as affected by matrix cracks and delamination modes. The model is also able to estimate the reduction in stiffness of the damaged laminate. This information is then used in the algorithms for life prediction capabilities. First, a brief summary of the energy-based damage model is provided. Then, the paper describes how the model is embedded within the prognostic framework and how the prognostics performance is assessed using observations from run-to-failure experiments

Prognostics↗

Kinetic Damage from Meteorites

A Near Earth object impacting into Earth's atmosphere may produce damaging effects at the surface due to airblast, thermal pulse, or kinetic impact in the form of meteorites. At large sizes (greater than many tens of meters), the damage is amplified by the hypersonic impact of these large projectiles moving with cosmic velocity, leaving explosively produced craters. However, much more common is simple "kinetic" damage caused by the impact of smaller meteorites moving at terminal speeds. As of this date a handful of instances are definitively known of people or structures being directly hit and/or damaged by the kinetic impact of meteorites. Meteorites known to have struck humans include the Sylacauga, Alabama fall (1954) and the Mbale meteorite fall (1992). Much more common is kinetic meteorite damage to cars, buildings, and even a post box (Claxton, Georgia - 1984). Historical accounts indicate that direct kinetic damage by meteorites may be more common than recent accounts suggest (Yau et al., 1994). In this talk we will examine the contemporary meteorite flux and estimate the frequency of kinetic damage to various structures, as well as how the meteorite flux might affect the rate of human casualties. This will update an earlier study by Halliday et al (1985), adding variations expected in meteorite flux with latitude (Le Feuvre and Wieczorek, 2008) and validating these model predictions of speed and entry angle with observations from the NASA and SOMN fireball networks. In particular, we explore the physical characteristics of bright meteors which may be used as a diagnostic for estimating which fireballs produce meteorites and hence how early warning of such kinetic damage may be estimated in advance through observations and modeling.

Cooke, William↗

Kinetic Damage from Meteorites

A Near Earth object impacting into Earth's atmosphere may produce damaging effects at the surface due to airblast, thermal pulse, or kinetic impact in the form of meteorites. At large sizes (>many tens of meters), the damage is amplified by the hypersonic impact of these large projectiles moving with cosmic velocity, leaving explosively produced craters. However, much more common is simple "kinetic" damage caused by the impact of smaller meteorites moving at terminal speeds. As of this date a handful of instances are definitively known of people or structures being directly hit and/or damaged by the kinetic impact of meteorites. Meteorites known to have struck humans include the Sylacauga, Alabama fall (1954) and the Mbale meteorite fall (1992). Much more common is kinetic meteorite damage to cars, buildings, and even a post box (Claxton, Georgia - 1984). Historical accounts indicate that direct kinetic damage by meteorites may be more common than recent accounts suggest (Yau et al., 1994). In this talk we will examine the contemporary meteorite flux and estimate the frequency of kinetic damage to various structures, as well as how the meteorite flux might affect the rate of human casualties. This will update an earlier study by Halliday et al (1985), adding variations expected in meteorite flux with latitude (Le Feuvre and Wieczorek, 2008) and validating these model predictions of speed and entry angle with observations from the NASA and SOMN fireball networks. In particular, we explore the physical characteristics of bright meteors which may be used as a diagnostic for estimating which fireballs produce meteorites and hence how early warning of such kinetic damage may be estimated in advance through observations and modelling.

Cooke, William↗

Exploration of Failure and Potential Damage Markers in Ti-6Al-4V

To improve prognostics for predicting component life, coupon tests were conducted on Ti-6Al-4V to investigate the development of damage. Various test types were employed (tension, creep, stress relaxation, and fatigue) under a wide range of temperatures and loading rates to engage various amounts of time-dependent and damage behavior. Both stiffness degradation and Poisson’s ratio were monitored to see if they were useful in indicating the initiation and accumulation of damage and subsequently the onset of failure. Stiffness exhibited large decreases with increasing strain when calculated using engineering stress and strain. However, minimal stiffness change was observed when using the true-stress and true- strain values. Detailed microscopy and image analysis were performed to document the actual physical damage that occurred within the various specimens. Two types of damage were observed: shallow surface cracks and internal pores. The severity of damage was greater in the region of localized necking and diminished further away from the neck. The area fraction of pores was higher in the necked region, yet even there it did not exceed more than a few percent and, in most cases, was significantly lower. It was observed that conditions that induced more time-dependent deformation (e.g., slower strain rate testing) resulted in a larger number of pores and larger pore sizes. The pores were always found to occur in the softer β-phase. The severity of observed damage was inconsistent with the large drop in engineering stiffness, but was more aligned with stiffness changes from the true-stress and -strain values. Poisson’s ratio was monitored on every test and showed promise as a damage indicator. It was found to be more sensitive than either the ultimate tensile strength or the inception of tertiary creep. However, calculation of Poisson’s ratio was found to be more involved than expected because of anisotropy and the presence of strain gradients along the specimen at large applied strains. First, the material had a moderate texture and resulted in anisotropy of the strains. Second, the evolution of Poisson’s ratio as a function of axial strain showed strange and unexpected behaviors, which necessitated more extensive analyses of its development. This led to an investigation on the use of small versus large strain approaches and the importance of making consistent measurements; that is, axial and transverse strain measurements over the same volume of material. Additionally, finite element analysis of a tensile sample indicated that non- uniform strain occurred in the sample prior to attaining the maximum strength. This, along with the location at which transverse strain was measured, had a significant influence on the resulting values of Poisson’s ratio. Based on this, lessons learned are offered for future testing.

Ti-6Al-4V↗

Characterizing Damage Accumulation in CMCs

Silicon carbide / silicon carbide ceramic matrix composites (SiC/SiC CMCs) are structural ceramics that are well-suited for the extreme environment conditions of aerospace applications largely due to their low weight, creep resistance, damage tolerance, and high specific strength. In CMCs, the initiation and evolution of damage is influenced by a number of factors including characteristics of the constituent landscape (porosity, interfacial properties, and geometric distribution of CMC constituents), thermo-mechanical loading parameters, and environmental conditions. However, much is still unknown about these factors and the interactions between them. In order to accurately predict the lifetimes of these advanced composites, it is critical to understand the evolution of damage and to characterize which early damage mechanisms (and their relationship to key microstructural features) subsequently lead to crack coalescence and macroscopic failure. This research focuses on the use of a multi-modal, experimental approach to examine the relative activity of surface and subsurface damage mechanisms in CMCs. The impact of fabrication choices on the evolution of damage to final failure, and the influence of constituent architecture on early damage mechanisms, are investigated. This approach combines acoustic emission (AE) with microscale deformation tracking via digital image correlation inside a scanning electron microscope (SEM-DIC). The potential application of this combined approach towards characterization of damage in SiC/SiC CMCs under more complex testing conditions is explored.

Swaminathan, Bhavana↗

Benchmarking Mixed Mode Failure in Progressive Damage and Failure Analysis Methods

The verification and validation of progressive-damage-analysis finite element methods are difficult but critical tasks to undertake during their development. Verification exercises assess whether a predictive analysis tool produces results that are consistent with the fundamental concepts and assumptions of the tool under evaluation. Ideally, closed-form analytical solutions can be derived for which method verification results can be compared. Problems selected for computational tool verification are often simple and isolate individual features of the tool. In the case of progressive damage finite element methods, verifications should be performed to evaluate the ability of the model to predict the initiation of damage and its growth through the finite element mesh under a variety of conditions. Mabson et al. proposed a test case of a unidirectional, fiber-reinforced plate with a center crack subjected to tensile loads to evaluate matrix crack propagation predictions. The problem was modeled using the Abaqus Hashin continuum damage mechanics (CDM) model for fiber-reinforced composites. Different combinations of matrix strengths and element sizes were used in the simulations, and the results were compared to a closed-form solution based on linear elastic fracture mechanics (LEFM). It was determined that the Abaqus CDM model could predict the LEFM solution of Mode I cracks only when the finite element mesh density met specific requirements based on the material properties. This paper presents closed-form LEFM solutions for a center notch mixed mode (CNMM) verification problem. Parametric finite element analyses were developed using progressive damage analysis methods of both the Discrete Damage Mechanics (DDM) and CDM classes. The progressive damage analysis methods applied in the analyses of the CNMM problem include CompDam and the Floating Node Method. Analyses were conducted with various mode mixities and element sizes to verify that the damage models were working as intended and to identify any limits of applicability.

Leone, Frank↗

The Effect of Impact Damage Next to Holes on the Bearing Strength of Carbon Fiber Laminates

This study was undertaken as a follow-on to a previous study that examined the effect of hole quality in the bearing strength of carbon fiber laminates. After the author of that previous study had established that hole quality had little effect on the ultimate bearing strength for carbon fiber laminates, the question was raised as to the effects of impact damage next to a hole on the bearing strength of that hole. While this is an unlikely scenario, it is still possible that this may occur on a launch vehicle structure and thus warranted study. After a literature review, results of a few studies on the hole-impact interaction with respect to resulting damage for carbon fiber laminates were found, but none that specifically addressed the resulting bearing strength. In reference 2, it was found that the holes and impact could interact to develop matrix splits. However, the lay-ups used in this study consisted of clumped plies [04/904]S, which are much more prone to matrix splitting than a laminate that would actually be used in practice (such as a lay-up of [0/90]4S). This study also focused on the analytical aspects of the problem rather than the experimental results. Reference 3 also used [04/904]S laminates (clumped plies) and examined the damage morphology, determining that, as the impact damage neared the hole, the damage zone became more asymmetrical. The effect this would have on bearing strength was not addressed. The experimental work presented in this study was to develop empirical data relating holeimpact damage effects on the resulting bearing strength of a commonly used (quasi-isotropic) lay-up of carbon fiber laminate. The emphasis was not on the morphology of the resulting damage, as it was in references 2 and 3, but rather on the practical aspects of how this damage affected the bearing strength and how this compared to the companion study1 on the effect of hole quality on the bearing strength of the laminate.

Nettles, A. T.↗

Testing of a Multi-Stringer Post-Buckled Panel with Incremental Damage Detection

A multi-stringer panel was designed and tested to produce a failure mode of skin-stiffener delamination due to compression loading of a post-buckled skin to support the validation of high-fidelity progressive damage failure analysis modeling. The test procedure included multiple methods of data acquisition ranging from multiple strain gages, front and back digital image correlation, passive thermography, acoustic emission, and ultrasonic inspection to capture key events and damage progression prior to catastrophic failure. Detailed data showing the initial stiffness, onset of skin buckling, buckled mode shape, damage initiation load, damage propagation morphology, and peak load was captured. Two panel configurations were tested. The first had a Teflon insert placed in the interface between the skin and the stiffener flanges adjacent to the center skin bay. The second was subjected to impact damage to the skin-stiffener flange. In each case, continuously-loaded-to-failure tests were conducted first with passive thermography being used exclusively to determine key damage events. Then, incrementally loaded tests were completed where ultrasonic inspections were conducted between each increment. The amount of load applied between each increment was determined based on the in-situ damage detection provided by the passive thermography system. The results of the testing showed a complex delamination growth pattern which migrated between ply interfaces through matrix splits in the upper skin ply of the panel. The result of the testing produced very detailed data which will prove to be useful for validation of delamination growth and migration predictions from progressive damage failure analysis methods.

Jason Action↗

Probabilistic Blast Damage Modeling Uncertainties and Sensitivities

Blast overpressure is the predominant source of ground damage posed by potentially hazardous asteroid strikes. Estimates of the extent, severity, and likelihoods of potential blast damage regions will be one of the key metrics needed to mount civil defense or disaster response plans in the face of an impending impact. However, there are many inherent sources of uncertainty in evaluating the damage, both in characterizing the properties of the incoming object and in the approaches used to model the entry/impact and resulting damage, which make it difficult to produce a single ‘accurate’ or ‘best guess’ prediction of ground damage. The current 2021 PDC hypothetical impact scenario poses a particular challenge due to its short warning time. The need for rapid disaster response to prepare for an immanent impact, combined with lack of observational opportunities to refine basic knowledge about the object’s basic size and properties, make understanding the range and relative likelihood of consequences particularly critical. The potential damage caused by these blasts can be evaluated using a range of modeling and simulation approaches and levels of fidelity. Fast-running engineering-level models can be used to run large numbers of probabilistically sampled cases covering wide variations of uncertain properties or parameters. High-fidelity simulations, on the other hand, can capture more detailed/accurate blast physics, but can only be performed for a small selection of specific cases, requiring many assumptions to be made about the initial object and its unpredictable entry/breakup characteristics. In order to provide a more complete picture of the potential threat for effective disaster response, both types of analysis need to be employed together. In this approach, high-fidelity simulations are used to refine and anchor engineering models, and the probabilistic engineering models are used to evaluate broad parameters spaces and guide selection of the most pertinent simulation cases for a given scenario. This presentation expands upon the probabilistic asteroid impact risk assessments being performed as part of the 2021 PDC hypothetical impact exercise, focusing on key aspects of blast damage modeling uncertainties and sensitivities. We review the current modeling and simulation approaches employed in the current assessment, compare the relative levels of uncertainty stemming from each main element of the problem (i.e., knowledge of the asteroid properties, modeling of the atmospheric entry/breakup and airburst, and estimates of the ground damage from the resulting blasts waves), and highlight any notable trends and sensitivities for the current scenario case.

SMD↗

Simulation of Radiation-Induced DNA Damage With the Code RITRACKS

INTRODUCTION DNA damage is one of the most physiologically important effects of ionizing radiation. Clustered DNA damage events, like double-strand breaks (DSBs), have the most notable biological consequences. DNA damage types depend on both the track structure of the radiation and the spatial organization of the DNA. High linear energy transfer (LET) charged nuclei, found in galactic cosmic rays (GCR), are known to produce large numbers of complex DNA damage events. The human genome is packaged into chromatin, which can take on locus-dependent and cell type-dependent spatial conformations that correspond to epigenetic states, such as more open, extended structures in transcriptionally active chromatin. These epigenetic differences can affect DNA break patterns in response to ionizing radiation, potentially creating distinct DNA repair and signaling outcomes across the genome in different cells. MATERIAL AND METHODS The code RITRACKS (Relativistic Ion Tracks), which simulates stochastic radiation track structures and radiation chemistry, was used to model damage on isolated and histone-bound DNA by various types of ions and photons. The changes made to the code to perform radiation-induced DNA damage, and simulation results on single nucleosomes are given in our recent paper. In this work, the DNA building capabilities of RITRACKS have been extended to simulate more complex DNA structures build on the coarse-grain simulation framework meso-WLCsim. This code can sample generic chromatin fiber conformation ensembles based on the geometry of nucleosomes and mechanical properties of DNA. Using RITRACKS, we simulated the fragment length distributions (FLD) of irradiated DNA structures built using the chromatin conformations of WLCsim and obtained results representative of those obtained with Radiation-Induced Correlated Cleavage with sequencing (RICC-Seq) experiments [6]. We have also performed Fe ion and photon irradiations of K562, IMR90, BJ and RPE-1 cells at NSRL to experimentally validate results. Sample processing and data analysis are in progress and any available preliminary results will be discussed. DISCUSSION The recent updates in the code RITRACKS allow the calculation of several quantities such as the DNA damage yield and the FLD. This approach can be used to model epigenetic state-specific chromatin structure parameters to leverage the epigenetic state data available for many human cell types to infer relative DNA damage sensitivity among genomic loci.

I Plante↗

Characterization of Composite Damage Using Passive Thermography

Passive thermography is used to monitor small increases in temperature on a composite structure during loading. A rise in temperature can be attributed to damage formation due to matrix cracking and fiber breaks. An infrared camera allows for imaging the damage location, size, and shape. Recently, a technique has been developed to estimate the depth of the damage in a composite hat-stiffened panel during quasi-static loading. This technique is based on two heat generation components. The first component is an instantaneous thermoelastic response due to a strain release. The second component is mechanical heating, at the interface of failure, due to fracture damage. This second component produces a transient rise in temperature that is a function of the damage depth and thermal diffusivity. The first component defines the thermal start time for the transient response. A one-dimensional thermal model is used to determine the damage depth for a known thermal diffusivity. The results are compared to ultrasonic and X-ray CT data and show good agreement for damage depth.

Thermal nondestructive evaluation↗

Damage tolerance research on composite compression panels

The damage tolerance of composites was investigated. Results show that severe degradation in material strength may occur due to impact damage and that reduced strain allowables should be considered to compensate for possible impact damage. The mechanisms of failure involved in impact so that local damage will be reduced and arrest of propagating fracture initiated at impact locations are examined. Compression strength reductions for damage due to impact by a 1.27 cm diameter spherical projectile in thick laminates representative of wing skin panels are presented. Also discussed are the results of concepts recently evaluated to improve damage tolerance. These concepts range from improvements at the materials level to advanced structural configurations designed to arrest or limit the growth of propagating fractures. The results indicate that substantial improvements in the damage tolerance of graphite-epoxy composite structures can be achieved through the proper combination of materials and structural design.

Rhodes, M. D.↗

Thermographic measurement of fatigue damage

The paper presents a thermographic technique developed to measure the extent of fatigue damage in composite materials during fatigue loading. It is noted that heat generated by cyclic loading of fatigue damaged material raises the surface temperature. These temperatures were measured with an infrared camera and were used as boundary conditions in a finite element heat transfer program, which has been developed especially to calculate the extent of the heat generation zone, and thereby to define the fatigue damage zone. It is reported that the finite element program was verified by comparing calculated heat generation with the actual heat generation for a simple heat transfer problem that had a closed form solution. Damage zones are calculated for several boron/epoxy fatigue specimens from thermograms of specimens. The calculated damage zones were compared with damage detected by C-scan, X-ray, and scanning electron microscope (SEM) examinations. It is concluded that the analysis was effective in locating the boundaries of the fatigue damage zones.

Whitcomb, J. D.↗

Preliminary design of composite wing-box structures for global damage tolerance

A procedure is presented that incorporates the influence of potential global damage conditions into the design process for minimum-mass wing-box structures. The procedure is based on mathematical-programming optimization techniques. Material-strength, minimum-gage, and panel-buckling constraints are introduced by penalty functions, and Newton's method with approximate second derivatives of the penalty terms is used as the search algorithm to obtain minimum-mass designs. A potential global damage condition is represented by a structural model with the damaged components removed. Example minimum-mass designs are obtained that simultaneously satisfy the constraints of the damaged and undamaged configurations of both graphite-epoxy and aluminum wing-box structural models. These examples are designed with and without the influence of potential damage conditions, and results indicate that for equal mass cases the residual strength of a damaged structure is higher when the influence of potential damage is properly included in the design from the outset. Results of these examples also identify the minimum structural mass increase required to increase residual strength levels.

Starnes, J. H., Jr.↗