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In this paper, the feasibility of orthogonal polynomials in the meshless local Petrov Galerkin method (MLPG) method is studied. The orthogonal polynomials, Chebyshev and Legendre polynomials, are used in this MLPG method as trial functions. The test functions used were power functions with smooth derivatives at their ends. The performance of these methods is studied by applying these methods to Euler-Bernoulli beam problems. The MLPG-Galerkin and Legendre methods passed all the patch tests for simple beam problems. Next the formulations are tested on complex beam problems such as beams with partial loadings and continuous beam problems. Problems with load discontinuities and additional supports require special attention. Near discontinuities, judicious choice of number of nodes and nodal placements are needed to obtain accurate deflections, slopes, moments and shear forces. As polynomial functions are used, the large number of nodes can create a transformation matrix that is ill-conditioned, resulting in problems with the inversion of the matrix. The conditioning worsens as the number of nodes are increased beyond 20. Quadruple precision was needed for models to obtain accurate solutions. Even with quadruple precision the accuracy of the method suffers as the number of nodes is increased beyond 20. This appears to be a drawback of the MLPG-Chebyshev and MLPG-Legendre methods.

Characterization of the near crack-tip stress/strain fields is the foundation of fracture mechanics. The description of the near tip stress field and the prediction of when fracture occurs is well established for brittle materials that exhibit linear elastic behavior. However, in ductile materials or conditions that violate linear elastic assumptions (Aluminum alloys, Al 2024-T3, Al 2024- T351 etc.), the elastic-plastic crack-tip stress fields are characterized by the Hutchison-Rice-Rosengren (HRR) field. The J-integral is commonly used to characterize amplitude of the HRR field under elastic-plastic conditions. The J-integral has been demonstrated for crack-tip fields that are under high constraint conditions (i.e., small-scale plasticity where the J-dominance is maintained). However, as the external load increases, yielding changes from small- to largescale plasticity and usually a loss of constraint (i.e., reduction in the triaxial stress field along the crack front). The loss of constraint leads to the deviation of the crack-tip stress fields from that given by the HRR field. Hence, the J-dominance will be gradually lost and additional parameter(s) are required to quantify the crack-tip stress fields and predict fracture behavior. The assessment objectives were to: 1) implement a two-parameter (i.e., J-A) fracture criterion into an elastic-plastic three-dimensional (3D) finite element analysis (FEA), 2) validate the implementation by comparison with the A parameter from literature data, 3) conduct material characterization tests to quantify the material behavior and provide fracture data for validation of the J-A fracture criteria, and (4) perform evaluations to establish if the J-A criteria can be used to predict fracture in a ductile metallic material (e.g., aluminum alloys). The A parameter in these criteria is the second parameter in a three-term elastic-plastic asymptotic expansion of the neartip stress behavior. A series of extensive FEAs were performed using WARP3D software package to obtain solutions for the A parameter for different specimen configurations. The methodology needed for the estimation of the A parameter in the asymptotic expansion was developed and implemented using Matlab®. A user material (UMAT) routine was used to model the material stress-strain response using a Ramberg-Osgood power law with a hardening exponent (n) and a material coefficient (alpha). This UMAT routine was successfully implemented in WARP3D software and validated through comparison with the experimental data. Three configurations were extracted from published results: 1) center cracked plate (CCP), 2) single edge-cracked plate (SECP), and 3) double edge-cracked plate (DECP). These configurations and four other configurations (three-hole tension (THT)), three-point bend (3PTB), three-hole compact tension (3PCT), and compact tension (CT)) were analyzed to verify the methodology that was developed and implemented into WARP3D. Solutions of the A parameter were obtained for remote tension loading conditions that started with small-scale yielding and continued into the large-scale plasticity regime. The results indicate that the methodology developed can be used to calculate the elastic-plastic J-A parameters for test specimens with a range of crack geometries, material strain hardening behaviors, and loading conditions. The J-A parameters were implemented as fracture criteria and used to predict the test results. For comparison, other fracture criteria were used to predict the same test results. Major findings include: The A constraint parameter A varies with specimen type and applied load thus accurate determination is crucial in predicting the failure load, and the A parameter is asymptotic as the failure load is approached, making an accurate determination difficult (i.e., small differences in the A parameter can cause large variations in failure load) for materials exhibiting elastic-plastic behavior. The failure predictions from J-A methodology were more accurate than the traditionally used KC and J methods, and have comparable scatter to that observed when using the crack-tip opening angle (CTOA) method. However, the J-A methodology requires considerable effort (expertise level and labor) to implement and to evaluate the A parameter for different specimen types and materials, or to apply this methodology to part-through crack (e.g., 3D problems) structural applications.

The performance of the finite element alternating (FEAM) method for two-dimensional crack problems is studied with respect to a polynomial pressure distribution fitted to the crack face stresses. The FEAM alternates between the analytical solution of crack in an infinite plate subjected to arbitrary polynomial distribution and a finite element solution of an uncracked body to satisfy the required boundary conditions in the crack problem. In this paper, the FEAM is applied to embedded crack and edge crack problems. For embedded crack problems, all of the constant, linear, and quadratic ( N=0,1, or 2, respectively) pressure distributions yield very accurate results with this algorithm with 4 to 5 iterations. The edge crack problems, on the other hand, require much higher order polynomials distributions (N=5 to 6) to yield accurate solutions. For slant edge crack problems, the mode-I stress-intensity factors have better accuracy than the mode-II stress-intensity factors for the same convergence tolerance.

AIAA standards S080 and S081 are applicable for certification of metallic pressure vessels (PV) and composite overwrap pressure vessels (COPV), respectively. These standards require damage tolerance analyses with a minimum reliable detectible flaw/crack and demonstration of safe life four times the service life with these cracks at the worst-case location in the PVs and oriented perpendicular to the maximum principal tensile stress. The standards require consideration of semi-elliptical surface cracks in the range of aspect ratios (crack depth a to half of the surface length c, i.e., (a/c) of 0.2 to 1). NASA-STD-5009 provides the minimum reliably detectible standard crack sizes (90/95 probability of detection (POD) for several non-destructive evaluation (NDE) methods (eddy current (ET), penetrant (PT), radiography (RT) and ultrasonic (UT)) for the two limits of the aspect ratio range required by the AIAA standards. This paper tries to answer the questions: can the safe life analysis consider only the life for the crack sizes at the two required limits, or endpoints, of the (a/c) range for the NDE method used or does the analysis need to consider values within that range? What would be an appropriate method to interpolate 90/95 POD crack sizes at intermediate (a/c) values? Several procedures to develop combinations of a and c within the specified range are explored. A simple linear relationship between a and c is chosen to compare the effects of seven different approaches to determine combinations of aj and cj that are between the (a/c) endpoints. Two of the seven are selected for evaluation: Approach I, the simple linear relationship, and a more conservative option, Approach III. For each of these two Approaches, the lives are computed for initial semi-elliptic crack configurations in a plate subjected to remote tensile fatigue loading with an R-ratio of 0.1, for an assumed material evaluated using NASGRO (registered 4) version 8.1. These calculations demonstrate that for this loading, using Approach I and the initial detectable crack sizes at the (a/c) endpoints in 5009 specified for the ET and UT NDE methods, the smallest life is not at the two required limits of the (a/c) range, but rather is at an intermediate configuration in the range (a/c) of 0.4 to 0.6. Similar analyses using both Approach I and III with the initial detectable crack size at the (a/c) endpoints in 5009 for PT NDE showed the smallest life may be at an (a/c) endpoint or an intermediate (a/c), depending upon which Approach is used. As such, analyses that interrogate only the two (a/c) values of 0.2 and 1 may result in unconservative life predictions. The standard practice may need to be revised based on these results.

Aerospace structures are traditionally designed using the factor of safety (FOS) approach. The limit load on the structure is determined and the structure is then designed for FOS times the limit load - the ultimate load. Probabilistic approaches utilize distributions for loads and strengths. Failures are predicted to occur in the region of intersection of the two distributions. The load and resistance factor design (LRFD) approach judiciously combines these two approaches by intensive calibration studies on loads and strength to result in structures that are efficient and reliable. This paper discusses these three approaches.

Two meshless local Petrov-Galerkin (MLPG) methods based on two different trial functions but that use a simple linear test function were developed for beam and column problems. These methods used generalized moving least squares (GMLS) and radial basis (RB) interpolation functions as trial functions. These two methods were tested on various patch test problems. Both methods passed the patch tests successfully. Then the methods were applied to various beam vibration problems and problems involving Euler and Beck's columns. Both methods yielded accurate solutions for all problems studied. The simple linear test function offers considerable savings in computing efforts as the domain integrals involved in the weak form are avoided. The two methods based on this simple linear test function method produced accurate results for frequencies and buckling loads. Of the two methods studied, the method with radial basis trial functions is very attractive as the method is simple, accurate, and robust.

Aerospace structures are complex high-performance structures. Advances in reliable and efficient computing and modeling tools are enabling analysts to consider complex configurations, build complex finite element models, and perform analysis rapidly. Many of the early career engineers of today are very proficient in the usage of modern computers, computing engines, complex software systems, and visualization tools. These young engineers are becoming increasingly efficient in building complex 3D models of complicated aerospace components. However, the current trends demonstrate blind acceptance of the results of the finite element analysis results. This paper is aimed at raising an awareness of this situation. Examples of the common encounters are presented. To overcome the current trends, some guidelines and suggestions for analysts, senior engineers, and educators are offered.

Recent developments in fracture mechanics analyses of the interfacial crack problem are reviewed. The intent of the review is to renew the awareness of the oscillatory singularity at the crack tip of a bimaterial interface and the problems that occur when calculating mode mixity using numerical methods such as the finite element method in conjunction with the virtual crack closure technique. Established approaches to overcome the nonconvergence issue of the individual mode strain energy release rates are reviewed. In the recent literature many attempts to overcome the nonconvergence issue have been developed. Among the many approaches found only a few methods hold the promise of providing practical solutions. These are the resin interlayer method, the method that chooses the crack tip element size greater than the oscillation zone, the crack tip element method that is based on plate theory and the crack surface displacement extrapolation method. Each of the methods is validated on a very limited set of simple interface crack problems. However, their utility for a wide range of interfacial crack problems is yet to be established.

Elastic-plastic, large-deflection nonlinear stress analyses are performed for the external hat-shaped stringers (or stiffeners) on the intertank portion of the Space Shuttle s external tank. These stringers are subjected to assembly strains when the stringers are initially installed on an intertank panel. Four different stringer-feet configurations including the baseline flat-feet, the heels-up, the diving-board, and the toes-up configurations are considered. The assembly procedure is analytically simulated for each of these stringer configurations. The location, size, and amplitude of the strain field associated with the stringer assembly are sensitive to the assumed geometry and assembly procedure. The von Mises stress distributions from these simulations indicate that localized plasticity will develop around the first eight fasteners for each stringer-feet configuration examined. However, only the toes-up configuration resulted in high assembly hoop strains.

Coating spallation events have been observed along the slip-side joggle region of the Space Shuttle Orbiter wing-leading-edge panels. One potential contributor to the spallation event is a pressure build up within subsurface voids or defects due to volatiles or water vapor entrapped during fabrication, refurbishment, or normal operational use. The influence of entrapped pressure on the thermo-mechanical fracture-mechanics response of reinforced carbon-carbon with subsurface defects is studied. Plane-strain simulations with embedded subsurface defects are performed to characterize the fracture mechanics response for a given defect length when subjected to combined elevated-temperature and subsurface-defect pressure loadings to simulate the unvented defect condition. Various subsurface defect locations of a fixed-length substrate defect are examined for elevated temperature conditions. Fracture mechanics results suggest that entrapped pressure combined with local elevated temperatures have the potential to cause subsurface defect growth and possibly contribute to further material separation or even spallation. For this anomaly to occur, several unusual circumstances would be required making such an outcome unlikely but plausible.

The Space Shuttle wing-leading edge consists of panels that are made of reinforced carbon-carbon. Coating spallation was observed near the slip-side region of the panels that experience extreme heating. To understand this phenomenon, a root-cause investigation was conducted. As part of that investigation, fracture mechanics analyses of the slip-side joggle regions of the hot panels were conducted. This paper presents an overview of the fracture mechanics analyses.

In this report, the aircraft and space vehicle requirements for composite structures are compared. It is a valuable exercise to study composite structural design approaches used in the airframe industry and to adopt methodology that is applicable for space vehicles. The missions, environments, analysis methods, analysis validation approaches, testing programs, build quantities, inspection, and maintenance procedures used by the airframe industry, in general, are not transferable to spaceflight hardware. Therefore, while the application of composite design approaches from aircraft and other industries is appealing, many aspects cannot be directly utilized. Nevertheless, experiences and research for composite aircraft structures may be of use in unexpected arenas as space exploration technology develops, and so continued technology exchanges are encouraged.

Glenn Research Center Chief Engineer's Office requested an independent review of the structural analysis and modeling of the Communications, Navigation, and Networking re-Configurable Testbed (CoNNeCT) Project Antenna Pointing Subsystem (APS) Integrated Gimbal Assembly (IGA) to be conducted by the NASA Engineering and Safety Center (NESC). At this time, the IGA had completed its critical design review (CDR). The assessment was to be a peer review of the NEi-NASTRAN1 model of the APS Antenna, and not a peer review of the design and the analysis that had been completed by the GRC team for CDR. Thus, only a limited amount of information was provided on the structural analysis. However, the NESC team had difficulty separating analysis concerns from modeling issues. The team studied the NASTRAN model, but did not fully investigate how the model was used by the CoNNeCT Project and how the Project was interpreting the results. The team's findings, observations, and NESC recommendations are contained in this report.

The Space Shuttle Orbiter wing comprises of 22 leading edge panels on each side of the wing. These panels are part of the thermal protection system that protects the Orbiter wings from extreme heating that take place on the reentry in to the earth atmosphere. On some panels that experience extreme heating, liberation of silicon carbon (SiC) coating was observed on the slip side regions of the panels. Global structural and local fracture mechanics analyses were performed on these panels as a part of the root cause investigation of this coating liberation anomaly. The wing-leading-edge reinforced carbon-carbon (RCC) panels, Panel 9, T-seal 10, and Panel 10, are shown in Figure 1 and the progression of the stress analysis models is presented in Figure 2. The global structural analyses showed minimal interaction between adjacent panels and the T-seal that bridges the gap between the panels. A bounding uniform temperature is applied to a representative panel and the resulting stress distribution is examined. For this loading condition, the interlaminar normal stresses showed negligible variation in the chord direction and increased values in the vicinity of the slip-side joggle shoulder. As such, a representative span wise slice on the panel can be taken and the cross section can be analyzed using plane strain analysis.

Fracture mechanics analyses of subsurface defects within the joggle regions of the Space Shuttle wing-leading-edge RCC panels are performed. A 2D plane strain idealized joggle finite element model is developed to study the fracture behavior of the panels for three distinct loading conditions - lift-off and ascent, on-orbit, and entry. For lift-off and ascent, an estimated bounding aerodynamic pressure load is used for the analyses, while for on-orbit and entry, thermo-mechanical analyses are performed using the extreme cold and hot temperatures experienced by the panels. In addition, a best estimate for the material stress-free temperature is used in the thermo-mechanical analyses. In the finite element models, the substrate and coating are modeled separately as two distinct materials. Subsurface defects are introduced at the coating-substrate interface and within the substrate. The objective of the fracture mechanics analyses is to evaluate the defect driving forces, which are characterized by the strain energy release rates, and determine if defects can become unstable for each of the loading conditions.

Linear elastic, thermo-mechanical stress analyses of the Space Shuttle Orbiter wing-leading-edge panels is presented for entry heating conditions. The wing-leading-edge panels are made from reinforced carbon-carbon and serve as a part of the overall thermal protection system. Three-dimensional finite element models are described for three configurations: integrated configuration, an independent single-panel configuration, and a local lower-apex joggle segment. Entry temperature conditions are imposed and the through-the-thickness response is examined. From the integrated model, it was concluded that individual panels can be analyzed independently since minimal interaction between adjacent components occurred. From the independent single-panel model, it was concluded that increased through-the-thickness stress levels developed all along the chord of a panel s slip-side joggle region, and hence isolated local joggle sections will exhibit the same trend. From the local joggle models, it was concluded that two-dimensional plane-strain models can be used to study the influence of subsurface defects along the slip-side joggle region of these panels.

The NASA Engineering and Safety Center (NESC) was tasked with assessing the validity of an alternate opinion that surfaced during the investigation of recurrent failures at the Space Shuttle T-0 umbilical interface. The most visible problem occurred during the Space Transportation System (STS)-112 launch when pyrotechnics used to separate Solid Rocket Booster (SRB) Hold-Down Post (HDP) frangible nuts failed to fire. Subsequent investigations recommended several improvements to the Ground Support Equipment (GSE) and processing changes were implemented, including replacement of ground-half cables and connectors between flights, along with wiring modifications to make critical circuits quad-redundant across the interface. The alternate opinions maintained that insufficient data existed to exonerate the design, that additional data needed to be gathered under launch conditions, and that the interface should be further modified to ensure additional margin existed to preclude failure. The results of the assessment are contained in this report.

Bolted, segmented cylindrical shells are a common structural component in many engineering systems especially for aerospace launch vehicles. Segmented shells are often needed due to limitations of manufacturing capabilities or transportation issues related to very long, large-diameter cylindrical shells. These cylindrical shells typically have a flange or ring welded to opposite ends so that shell segments can be mated together and bolted to form a larger structural system. As the diameter of these shells increases, maintaining strict fabrication tolerances for the flanges to be flat and parallel on a welded structure is an extreme challenge. Local fit-up stresses develop in the structure due to flange mating-surface mismatch (flange waviness). These local stresses need to be considered when predicting a critical initial flaw size. Flange waviness is one contributor to the fit-up stress state. The present paper describes the modeling and analysis effort to simulate fit-up stresses due to flange waviness in a typical bolted, segmented cylindrical shell. Results from parametric studies are presented for various flange mating-surface waviness distributions and amplitudes.

An independent assessment was conducted to determine the critical initial flaw size (CIFS) for the flange-to-skin weld in the Ares I-X Upper Stage Simulator (USS). A series of weld analyses are performed to determine the residual stresses in a critical region of the USS. Weld residual stresses both increase constraint and mean stress thereby having an important effect on the fatigue life. The purpose of the weld analyses was to model the weld process using a variety of sequences to determine the 'best' sequence in terms of weld residual stresses and distortions. The many factors examined in this study include weld design (single-V, double-V groove), weld sequence, boundary conditions, and material properties, among others. The results of this weld analysis are included with service loads to perform a fatigue and critical initial flaw size evaluation.

An independent assessment was conducted to determine the critical initial flaw size (CIFS) for the flange-to-skin weld in the Ares I-X Upper Stage Simulator (USS). Material characterization tests were conducted to quantify the material behavior for use in the CIFS analyses. Fatigue crack growth rate, Charpy impact, and fracture tests were conducted on the parent and welded A516 Grade 70 steel. The crack growth rate tests confirmed that the material behaved in agreement with literature data and that a salt water environment would not significantly degrade the fatigue resistance. The Charpy impact tests confirmed that the fracture resistance of the material did not have a significant reduction for the expected operational temperatures of the vehicle.

An independent assessment was conducted to determine the critical initial flaw size (CIFS) for the flange-to-skin weld in the Ares I-X Upper Stage Simulator (USS). The USS consists of several "tuna can" segments that are approximately 216 inches in diameter, 115 inches tall, and 0.5 inches thick. A 6 inch wide by 1 inch thick flange is welded to the skin and is used to fasten adjacent tuna cans. A schematic of a "tuna can" and the location of the flange-to-skin weld are shown in Figure 1. Gussets (shown in yellow in Figure 1) are welded to the skin and flange every 10 degrees around the circumference of the "tuna can". The flange-to-skin weld is a flux core butt weld with a fillet weld on the inside surface, as illustrated in Figure 2. The welding process may create loss of fusion defects in the weld that could develop into fatigue cracks and jeopardize the structural integrity of the Ares I-X vehicle. The CIFS analysis was conducted to determine the largest crack in the weld region that will not grow to failure within 4 lifetimes, as specified by NASA standard 5001 & 5019 [1].

The structural analyses described in the present report were performed in support of the NASA Engineering and Safety Center (NESC) Critical Initial Flaw Size (CIFS) assessment for the ARES I-X Upper Stage Simulator (USS) common shell segment. The structural analysis effort for the NESC assessment had three thrusts: shell buckling analyses, detailed stress analyses of the single-bolt joint test; and stress analyses of two-segment 10 degree-wedge models for the peak axial tensile running load. Elasto-plastic, large-deformation simulations were performed. Stress analysis results indicated that the stress levels were well below the material yield stress for the bounding axial tensile design load. This report also summarizes the analyses and results from parametric studies on modeling the shell-to-gusset weld, flange-surface mismatch, bolt preload, and washer-bearing-surface modeling. These analyses models were used to generate the stress levels specified for the fatigue crack growth assessment using the design load with a factor of safety.

The structural analyses described in the present report were performed in support of the NASA Engineering and Safety Center (NESC) Critical Initial Flaw Size (CIFS) assessment for the Ares I-X Upper Stage Simulator (USS) common shell segment. An independent assessment was conducted to determine the critical initial flaw size (CIFS) for the flange-to-skin weld in the Ares I-X Upper Stage Simulator (USS). The Ares system of space launch vehicles is the US National Aeronautics and Space Administration s plan for replacement of the aging space shuttle. The new Ares space launch system is somewhat of a combination of the space shuttle system and the Saturn launch vehicles used prior to the shuttle. Here, a series of weld analyses are performed to determine the residual stresses in a critical region of the USS. Weld residual stresses both increase constraint and mean stress thereby having an important effect on fatigue and fracture life. The results of this effort served as one of the critical load inputs required to perform a CIFS assessment of the same segment.

The present paper describes the structural analyses performed on a preloaded bolted-joint configuration. The joint modeled was comprised of two L-shaped structures connected together using a single bolt. Each L-shaped structure involved a vertical flat segment (or shell wall) welded to a horizontal segment (or flange). Parametric studies were performed using elasto-plastic, large-deformation nonlinear finite element analyses to determine the influence of several factors on the bolted-joint response. The factors considered included bolt preload, washer-surface-bearing size, edge boundary conditions, joint segment length, and loading history. Joint response is reported in terms of displacements, gap opening, and surface strains. Most of the factors studied were determined to have minimal effect on the bolted-joint response; however, the washer-bearing-surface size affected the response significantly.

Following STS-107, the External Tank (ET) Project implemented corrective actions and configuration changes at the ET bipod fitting. Among the corrective actions, the existing bolt lock wire which provided resistance to potential bolt rotation was removed. The lock wire removal was because of concerns with creating voids during foam application and potential for lock wire to become debris. The bolts had been previously lubricated to facilitate assembly but, because of elimination of the lock wire, the ET Project wanted to enable the locking feature of the insert. Thus, the lubrication was removed from bolt threads and instead applied to the washer under the bolt head. Lubrication is necessary to maximize joint pre-load while remaining within the bolt torque specification. The locking feature is implemented by thread crimping in at four places in the insert. As the bolt is torqued into the insert the bolt threads its way past the crimped parts of the insert. This provides the locking of the bolt, as torque is required to loosen the joint after clamping.

In Spring of 2005, the NASA Engineering Safety Center (NESC) was engaged by the Space Shuttle Program (SSP) to peer review the suite of analytical tools being developed to support the determination of impact and damage tolerance of the Orbiter Thermal Protection Systems (TPS). The NESC formed an independent review team with the core disciplines of materials, flight sciences, structures, mechanical analysis and thermal analysis. The Math Model Tools reviewed included damage prediction and stress analysis, aeroheating analysis, and thermal analysis tools. Some tools are physics-based and other tools are empirically-derived. Each tool was created for a specific use and timeframe, including certification, real-time pre-launch assessments. In addition, the tools are used together in an integrated strategy for assessing the ramifications of impact damage to tile and RCC. The NESC teams conducted a peer review of the engineering data package for each Math Model Tool. This report contains the summary of the team observations and recommendations from these reviews.

A study was undertaken to capture the best practices for the development of reliable and robust spacecraft structures for NASA s next generation cargo and crewed launch vehicles. In this study, the NASA heritage programs such as Mercury, Gemini, Apollo, and the Space Shuttle program were examined. A series of lessons learned during the NASA and DoD heritage programs are captured. The processes that "make the right structural system" are examined along with the processes to "make the structural system right". The impact of technology advancements in materials and analysis and testing methods on reliability and robustness of spacecraft structures is studied. The best practices and lessons learned are extracted from these studies. Since the first human space flight, the best practices for reliable and robust spacecraft structures appear to be well established, understood, and articulated by each generation of designers and engineers. However, these best practices apparently have not always been followed. When the best practices are ignored or short cuts are taken, risks accumulate, and reliability suffers. Thus program managers need to be vigilant of circumstances and situations that tend to violate best practices. Adherence to the best practices may help develop spacecraft systems with high reliability and robustness against certain anomalies and unforeseen events.

A detailed finite element analysis of the right rear lug of the American Airlines Flight 587 - Airbus A300-600R was performed as part of the National Transportation Safety Board s failure investigation of the accident that occurred on November 12, 2001. The loads experienced by the right rear lug are evaluated using global models of the vertical tail, local models near the right rear lug, and a global-local analysis procedure. The right rear lug was analyzed using two modeling approaches. In the first approach, solid-shell type modeling is used, and in the second approach, layered-shell type modeling is used. The solid-shell and the layered-shell modeling approaches were used in progressive failure analyses (PFA) to determine the load, mode, and location of failure in the right rear lug under loading representative of an Airbus certification test conducted in 1985 (the 1985-certification test). Both analyses were in excellent agreement with each other on the predicted failure loads, failure mode, and location of failure. The solid-shell type modeling was then used to analyze both a subcomponent test conducted by Airbus in 2003 (the 2003-subcomponent test) and the accident condition. Excellent agreement was observed between the analyses and the observed failures in both cases. The moment, Mx (moment about the fuselage longitudinal axis), has significant effect on the failure load of the lugs. Higher absolute values of Mx give lower failure loads. The predicted load, mode, and location of the failure of the 1985- certification test, 2003-subcomponent test, and the accident condition are in very good agreement. This agreement suggests that the 1985-certification and 2003-subcomponent tests represent the accident condition accurately. The failure mode of the right rear lug for the 1985-certification test, 2003-subcomponent test, and the accident load case is identified as a cleavage-type failure. For the accident case, the predicted failure load for the right rear lug from the PFA is greater than 1.98 times the limit load of the lugs.

Inspections of the Space Shuttle Main Engine revealed fatigue cracks growing from slots in the flow liner of the liquid hydrogen (LH2) feed lines. During flight, the flow liners experience complex loading induced by flow of LH2 and the resonance characteristics of the structure. The flow liners are made of Inconel 718 and had previously not been considered a fracture critical component. However, fatigue failure of a flow liner could have catastrophic effect on the Shuttle engines. A fracture mechanics study was performed to determine if a damage tolerance approach to life management was possible and to determine the sensitivity to the load spectra, material properties, and crack size. The load spectra were derived separately from ground tests and material properties were obtained from coupon tests. The stress-intensity factors for the fatigue cracks were determined from a shell-dynamics approach that simulated the dominant resonant frequencies. Life predictions were obtained using the NASGRO life prediction code. The results indicated that adequate life could not be demonstrated for initial crack lengths of the size that could be detected by traditional NDE techniques.

In Spring of 2005, the NASA Engineering Safety Center (NESC) was engaged by the Space Shuttle Program (SSP) to peer review the suite of analytical tools being developed to support the determination of impact and damage tolerance of the Orbiter Thermal Protection Systems (TPS). The NESC formed an independent review team with the core disciplines of materials, flight sciences, structures, mechanical analysis and thermal analysis. The Math Model Tools reviewed included damage prediction and stress analysis, aeroheating analysis, and thermal analysis tools. Some tools are physics-based and other tools are empirically-derived. Each tool was created for a specific use and timeframe, including certification, real-time pre-launch assessments, and real-time on-orbit assessments. The tools are used together in an integrated strategy for assessing the ramifications of impact damage to tile and RCC. The NESC teams conducted a peer review of the engineering data package for each Math Model Tool. This report contains the summary of the team observations and recommendations from these reviews.

Since the loss of Columbia on February 1, 2003, the Space Shuttle Program (SSP) has significantly improved the understanding of launch and ascent debris, implemented hardware modifications to reduce debris, and conducted tests and analyses to understand the risks associated with expected debris. The STS-114 flight rationale for expected debris relies on a combination of all three of these factors. A number of design improvements have been implemented to reduce debris at the source. The External Tank (ET) thermal protection system (TPS) foam has been redesigned and/or process improvements have been implemented in the following locations: the bipod closeout, the first ten feet of the liquid hydrogen (LH2) tank protuberance air load (PAL) ramp, and the LH2 tank-to-intertank flange closeout. In addition, the forward bipod ramp has been eliminated and heaters have been installed on the bipod fittings and the liquid oxygen (LO2) feedline forward bellows to prevent ice formation. The Solid Rocket Booster (SRB) bolt catcher has been redesigned. The Orbiter reaction control system (RCS) thruster cover "butcher paper" has been replaced with a material that sheds at a low velocity. Finally, the pad area has been cleaned to reduce debris during lift-off.

In May of 2002, three cracks were found in the downstream flowliner at the gimbal joint in the LH2 feedline at the interface with the Low Pressure Fuel Turbopump (LPFP) of Space Shuttle Main Engine (SSME) #1 of Orbiter OV-104. Subsequent inspections of the feedline flowliners in the other orbiters revealed the existence of 8 additional cracks. No cracks were found in the LO2 feedline flowliners. A solution to the cracking problem was developed and implemented on all orbiters. The solution included weld repair of all detectable cracks and the polishing of all slot edges to remove manufacturing discrepancies that could initiate new cracks. Using the results of a fracture mechanics analysis with a scatter factor of 4 on the predicted fatigue life, the orbiters were cleared for return to flight with a one-flight rationale requiring inspections after each flight. OV-104 flew mission STS-112 and OV-105 flew mission STS-113. The post-flight inspections did not find any cracks in the repaired flowliners. At the request of the Orbiter Program, the NESC conducted an assessment of the Orbiter LH2 Feedline Flowliner cracking problem with a team of subject matter experts from throughout NASA.

A detailed finite element analysis of the right rear lug of the American Airlines Flight 587 - Airbus A300-600R was performed as part of the National Transportation Safety Board s failure investigation of the accident that occurred on November 12, 2001. The loads experienced by the right rear lug are evaluated using global models of the vertical tail, local models near the right rear lug, and a global-local analysis procedure. The right rear lug was analyzed using two modeling approaches. In the first approach, solid-shell type modeling is used, and in the second approach, layered-shell type modeling is used. The solid-shell and the layered-shell modeling approaches were used in progressive failure analyses (PFA) to determine the load, mode, and location of failure in the right rear lug under loading representative of an Airbus certification test conducted in 1985 (the 1985-certification test). Both analyses were in excellent agreement with each other on the predicted failure loads, failure mode, and location of failure. The solid-shell type modeling was then used to analyze both a subcomponent test conducted by Airbus in 2003 (the 2003-subcomponent test) and the accident condition. Excellent agreement was observed between the analyses and the observed failures in both cases. From the analyses conducted and presented in this paper, the following conclusions were drawn. The moment, Mx (moment about the fuselage longitudinal axis), has significant effect on the failure load of the lugs. Higher absolute values of Mx give lower failure loads. The predicted load, mode, and location of the failure of the 1985-certification test, 2003-subcomponent test, and the accident condition are in very good agreement. This agreement suggests that the 1985-certification and 2003- subcomponent tests represent the accident condition accurately. The failure mode of the right rear lug for the 1985-certification test, 2003-subcomponent test, and the accident load case is identified as a cleavage-type failure. For the accident case, the predicted failure load for the right rear lug from the PFA is greater than 1.98 times the limit load of the lugs. I.

Recent literature shows extensive research work on meshless or element-free methods as alternatives to the versatile Finite Element Method. One such meshless method is the Meshless Local Petrov-Galerkin (MLPG) method. In this report, the method is developed for bending of beams - C1 problems. A generalized moving least squares (GMLS) interpolation is used to construct the trial functions, and spline and power weight functions are used as the test functions. The method is applied to problems for which exact solutions are available to evaluate its effectiveness. The accuracy of the method is demonstrated for problems with load discontinuities and continuous beam problems. A Petrov-Galerkin implementation of the method is shown to greatly reduce computational time and effort and is thus preferable over the previously developed Galerkin approach. The MLPG method for beam problems yields very accurate deflections and slopes and continuous moment and shear forces without the need for elaborate post-processing techniques.

System matrices for Euler-Bernoulli beam problems for the meshless local Petrov-Galerkin (MLPG) method deteriorate as the number of nodes in the beam models are consistently increased. The reason for this behavior is explained. To overcome this difficulty and improve the accuracy of the solutions, a local coordinate approach for the evaluation of the generalized moving least squares shape functions and their derivatives is proposed. The proposed approach retains the accuracy of the MLPG methods.

The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The sub-domains for the shape functions in the MLS approximation are defined only from the primary nodes, and the secondary nodes use the same sub-domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and/or moved without an additional mesh. The essential boundary conditions can be imposed exactly, and non-convex boundaries can be treated without special techniques. Several numerical examples are presented to illustrate the performance of the present method.

Flaws resulting from improper welding and forging are usually modeled as cracks in flat plates, hollow cylinders or spheres. The stress intensity factor solutions for these crack cases are of great practical interest. This report describes some recent efforts at improving the stress intensity factor solutions for cracks in such geometries with emphasis on hollow cylinders. Specifically, two crack configurations for cylinders are documented. One is that of a surface crack in an axial plane and the other is a part-through thumb-nail crack in a circumferential plane. The case of a part-through surface crack in flat plates is used as a limiting case for very thin cylinders. A combination of the two cases for cylinders is used to derive a relation for the case of a surface crack in a sphere. Solutions were sought which cover the entire range of the geometrical parameters such as cylinder thickness, crack aspect ratio and crack depth. Both the internal and external position of the cracks are considered for cylinders and spheres. The finite element method was employed to obtain the basic solutions. Power-law form of loading was applied in the case of flat plates and axial cracks in cylinders and uniform tension and bending loads were applied in the case of circumferential (thumb-nail) cracks in cylinders. In the case of axial cracks, the results for tensile and bending loads were used as reference solutions in a weight function scheme so that the stress intensity factors could be computed for arbitrary stress gradients in the thickness direction. For circumferential cracks, since the crack front is not straight, the above technique could not be used. Hence for this case, only the tension and bending solutions are available at this time. The stress intensity factors from the finite element method were tabulated so that results for various geometric parameters such as crack depth-to-thickness ratio (a/t), crack aspect ratio (a/c) and internal radius-to-thickness ratio (R/t) or the crack length-to-width ratio (2c/W) could be obtained by interpolation and extrapolation. Such complete tables were then incorporated into the NASA/FLAGRO computer program which is widely used by the aerospace community for fracture mechanics analysis.

Current research on fracture mechanics is reviewed, focusing on ductile fracture; high-temperature and time-dependent fracture; 3D problems; interface fracture; microstructural aspects of fatigue and fracture; and fracture predictions and applications. Particular attention is given to the determination and comparison of crack resistance curves from wide plates and fracture mechanics specimens; a relationship between R-curves in contained and uncontained yield; the creep crack growth behavior of titanium alloy Ti-6242; a crack growth response in three heat resistant materials at elevated temperature; a crack-surface-contact model for determining effective-stress-intensity factors; interfacial dislocations in anisotropic bimaterials; an effect of intergranular crack branching on fracture toughness evaluation; the fracture toughness behavior of exservice chromium-molybdenum steels; the application of fracture mechanics to assess the significance of proof loading; and a load ratio method for estimating crack extension.

The exact analytical solution for an embedded elliptical crack in an infinite body subjected to arbitrary loading was used in conjunction with the finite element alternating method to obtain crack-mouth-opening displacements (CMOD) for surface cracks in finite plates subjected to remote tension. Identical surface-crack configurations were also analyzed with the finite element method using 20-noded element for plates subjected to both remote tension and bending. The CMODs from these two methods generally agreed within a few percent of each other. Comparisons made with experimental results obtained from surface cracks in welded aluminum alloy specimens subjected to tension also showed good agreement. Empirical equations were developed for CMOD for a wide range of surface-crack shapes and sizes subjected to tension and bending loads. These equations were obtained by modifying the Green-Sneddon exact solution for an elliptical crack in an infinite body to account for finite boundary effects. These equations should be useful in monitoring surface-crack growth in tests and in developing complete crack-face-displacement equations for use in three-dimensional weight-function methods.