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At least 397 records · Page 22

Emitted vibration measurement device and method

This invention is directed to a method and apparatus for measuring emitted vibrational forces produced by a reaction wheel assembly due to imbalances, misalignment, bearing defects and the like. The apparatus includes a low mass carriage supported on a large mass base. The carriage is in the form of an octagonal frame having an opening which is adapted for receiving the reaction wheel assembly supported thereon by means of a mounting ring. The carriage is supported on the base by means of air bearings which support the carriage in a generally frictionless manner when supplied with compressed air from a source. A plurality of carriage brackets and a plurality of base blocks provided for physical coupling of the base and carriage. The sensing axes of the load cells are arranged generally parallel to the base and connected between the base and carriage such that all of the vibrational forces emitted by the reaction wheel assembly are effectively transmitted through the sensing axes of the load cells. In this manner, a highly reliable and accurate measurment of the vibrational forces of the reaction wheel assembly can be had. The output signals from the load cells are subjected to a dynamical analyzer which analyzes and identifies the rotor and spin bearing components which are causing the vibrational forces.

Gisler, G. L.↗

The Boeing 747 fatigue integrity program

The fatigue integrity program which was established to insure economic operations and to provide foundation data for inspection and maintenance is discussed. Significant features of the 747 fatigue integrity program are: (1) fatigue analyses which are continually updated to reflect design changes, fatigue test results, and static and flight load survey measurements; (2) material selection and detail design by using initial fatigue analyses, service experience, and testing; and (3) fatigue testing to check detail design quality and to verify the analyses, culminated by the test of a structurally complete airframe. Fatigue stress analyses were performed with the aid of experimental as well as analytical procedures. Extensive application was made of the stress severity factor, developed at Boeing, for evaluating peak stresses in complex joints. A frame of reference was established by families of structural fatigue performance curves (S-N curves) encompassing the range of materials and fatigue qualities anticipated for the 747 airplane design.

Spencer, M. M.↗

Simulations of Evaporating Multicomponent Fuel Drops

A paper presents additional information on the subject matter of Model of Mixing Layer With Multicomponent Evaporating Drops (NPO-30505), NASA Tech Briefs, Vol. 28, No. 3 (March 2004), page 55. To recapitulate: A mathematical model of a three-dimensional mixing layer laden with evaporating fuel drops composed of many chemical species has been derived. The model is used to perform direct numerical simulations in continuing studies directed toward understanding the behaviors of sprays of liquid petroleum fuels in furnaces, industrial combustors, and engines. The model includes governing equations formulated in an Eulerian and a Lagrangian reference frame for the gas and drops, respectively, and incorporates a concept of continuous thermodynamics, according to which the chemical composition of a fuel is described by use of a distribution function. In this investigation, the distribution function depends solely on the species molar weight. The present paper reiterates the description of the model and discusses further in-depth analysis of the previous results as well as results of additional numerical simulations assessing the effect of the mass loading. The paper reiterates the conclusions reported in the cited previous article, and states some new conclusions. Some new conclusions are: 1. The slower evaporation and the evaporation/ condensation process for multicomponent-fuel drops resulted in a reduced drop-size polydispersity compared to their single-component counterpart. 2. The inhomogeneity in the spatial distribution of the species in the layer increases with the initial mass loading. 3. As evaporation becomes faster, the assumed invariant form of the molecular- weight distribution during evaporation becomes inaccurate.

Bellan, Josette↗

An overview of the NASA textile composites program

The NASA Langley Research Center is conducting and sponsoring research to explore the benefits of textile reinforced composites for civil transport aircraft primary structures. The objective of this program is to develop and demonstrate the potential of affordable textile reinforced composite materials to meet design properties and damage tolerance requirements of advanced aircraft structures. In addition to in-house research, the program includes major participation by the aircraft industry and aerospace textile companies. The major program elements include development of textile preforms, processing science, mechanics of materials, experimental characterization of materials, and development and evaluation of textile reinforced composite structural elements and subcomponents. The NASA Langley in-house research is focused on science-based understanding of resin transfer molding (RTM), development of powder-coated towpreg processes, analysis methodology, and development of a performance database on textile reinforced composites. The focus of the textile industry participation is on development of multidirectional, damage-tolerant preforms, and the aircraft industry participation is in the areas of innovative design concepts, cost-effective fabrication, and testing of textile reinforced composite structural elements and subcomponents. Textile processes such as 3-D weaving, 2-D and 3-D braiding, and knitting/stitching are being compared with conventional laminated tape processes for improved damage tolerance. Through-the-thickness reinforcements offer significant damage tolerance improvements. However, these gains must be weighed against potential loss in in-plane properties such as strength and stiffness. Analytical trade studies are underway to establish design guidelines for the application of textile material forms to meet specific loading requirements. Fabrication and testing of large structural components are required to establish the full potential of textile reinforced composite materials. The goals of the NASA Langley-sponsored research program are to demonstrate technology readiness with subscale composite components by 1995 and to verify the performance of full-scale composite primary aircraft structural components by 1997. The status of textile reinforced composite structural elements under development by Boeing, Douglas, Lockheed, and Grumman are presented. Included are braided frames and woven/stitched wing and fuselage panels.

Dexter, H. Benson↗

Progress on the Plasmoid Thruster Experiment (PTX)

A plasmoid is a compact plasma structure with an integral magnetic field, that may be categorized according to the relative strength of the poloidal and toroidal magnetic field (B(sub p) and B(sub t), respectively). An object with B(sub p)/B(sub t), much much more than 1 is called a Field Reverse Configuration (FRC); if B(sub p) approximately equal to B(sub t), it is called a Spheromak. The thruster operates by repetitively producing plasmoids that are accelerated and ejected at high velocity. As this process is inductive, there are no electrodes. Also, the magnetic structure of the plasmoid should suppress thermal and mass losses to the wall, and improve detachment of the plasma exhaust from the thruster. This concept should be capable of producing an Isp in the range of 5,000 - 10,000 s with thrust densities of order 10(exp 5) N per square meters. The current experiment is designed to produce jet powers in the range of 5-10 kW, although the concept should be scalable into the MW range. In PTX, the plasmoid is formed inside of a single turn conical theta-pinch coil (17.58 cone angle). The coil is driven by a 640 nF, 35 kV capacitor bank, which rings at a frequency of 500 kHz. Previous experiments on PTX were conducted with a static-fill of propellant gas (6% H2 in He), and demonstrated reliable ionization over a pressure range of 40 - 200 mTorr. We are now adding a fast gas-puff valve to load the propellant, and a ringing pre-ionization circuit (f = 5 Mhz) to better control the plasmoid formation. An alternate coil (8.58 cone angle) will also be used, so as to investigate the effect of coil shape on performance. In addition, a variety of propellants will be used, including hydrogen, nitrogen, and argon. The plasmoid mass and velocity will be measured with a variety of diagnostics, including external B-dot probes and flux loops, a high-speed framing camera, and a HeNe laser interferometer. Internal B-dot probes and a quadruple Langmuir probe will provide additional measurements of the plasmoid shape and structure, as well as density, and will be described in a companion paper. The experimental results will be compared to calculations made using a 0-D coil-gun model and also a 2-D time dependent MHD code.

Martin, Adam↗

Dynamics of plankton populations in upwelling areas

There are no author-identified significant results in this report. Repeated coverage over the test site along the northwest coast of Africa showed that the structure of chlorophyll distribution is much more complicated than expected from continuous recordings. ERTS-1 data showed a very fast change in the chlorophyll distribution and it seems that also the concentration changes quickly. ERTS-1 showed on some frames offshore transportation of dust from the Sahara. All frames from Channel 7 will be arranged as a montage to derive the transportation pattern of dust. This step is important in biological aspects of interpreting ERTS-1 data, because the dissolution kinetics of eolian dust particles may influence significantly the chemistry of the surface water. Since visibility and the biochemistry of the test site off Africa are influenced by the dust transport, dust collection will be included in the ground truth program. Besides chlorophyll and other hydrographical parameters, the dust load in the test area will be measured. The collection plan is discussed along with a description of the high volume air sampler and the Anderson particle sizing head sampler to be used for the dust measurements.

Szekielda, K.↗

Performance of a 14.9-kW laminated-frame dc series motor with chopper controller

Traction motor using two types of excitation: ripple free dc from a motor generator set for baseline data and chopped dc as supplied by a battery and chopper controller was tested. For the same average values of input voltage and current, the power output was independent of the type of excitation. At the same speeds, motor efficiency at low power output (corresponding to low duty cycle of the controller) was 5 to 10 percentage points less on chopped dc than on ripple-free dc. This illustrates that for chopped waveforms, it is incorrect to calculate input power as the product of average voltage and average current. Locked-rotor torque, no load losses, and magnetic saturation data were so determined.

Schwab, J. R.↗

Space Shuttle Crawler Transporter Vibration Analysis in Support of Rollout Fatigue Load Spectra Verification Program

The Crawler Transporter (CT), designed and built for the Apollo Program in the 1960's and surpassing its initial operational life, has become an integral part of the Space Shuttle Program (SSP). The CT transports the Space Shuttle Vehicle (SSV) stack, atop the Mobile Launch Platform (MLP), from the Vehicle Assembly Building (VAB) to the launch pad. This support structure provides hydraulic jacking, leveling and load equalization for the 12 million pound stack on its 3.5-5.0 mile rollout to the launch pad. Major elements of the SSV, consisting of the orbiter, solid rocket boosters (SRB) and external tank (ET) have required fatigue analyses as part of the mission life certification. Compared to rollout vibration, the SSV sees relatively high vibration loads during launch, ascent, descent and landing phases of the mission. Although preliminary measured SRB vibration levels during rollout were of low amplitude and frequency, the duration of the rollout phase is typically high, from 5-6 hours. As part of an expanded mission life assessment, additional certification effort was initiated to define fatigue load spectra for rollout. This study addresses the CT vibration analyses in support of the rollout fatigue study. Structural models developed for modal and vibration analyses were used to identify unique CT, CT/MLP and CT/MLP/SRB vibration characteristics for comparison to instrumented rollout tests. Whereas the main structural and vibration characteristics of the SSV are well defined, minimum analytical and vibration test data on the Crawler Transporter were available. Unique vibration characteristics of the CT are attributable to the drive mechanism, hydraulic jacking system, structural framing and the CT-to-MLP support pad restraints. Initial tests performed on the CT/MLP/SRB configuration showed reasonable correlation with predicted mode shapes and frequencies.

Margasahayam, Ravi N.↗

James Webb Space Telescope (JWST) Integrated Science Instruments Module (ISIM) Electronics Compartment (IEC) Conformal Shields Composite Bond Structure Qualification Test Method

The JWST IEC conformal shields are mounted onto a composite frame structure that must undergo qualification testing to satisfy mission assurance requirements. The composite frame segments are bonded together at the joints using epoxy, EA 9394. The development of a test method to verify the integrity of the bonded structure at its operating environment introduces challenges in terms of requirements definition and the attainment of success criteria. Even though protoflight thermal requirements were not achieved, the first attempt in exposing the structure to cryogenic operating conditions in a thermal vacuum environment resulted in approximately 1 bonded joints failure during mechanical pull tests performed at 1.25 times the flight loads. Failure analysis concluded that the failure mode was due to adhesive cracks that formed and propagated along stress concentrated fillets as a result of poor bond squeeze-out control during fabrication. Bond repairs were made and the structures successfully re-tested with an improved LN2 immersion test method to achieve protoflight thermal requirements.

Thermal Vacuum Testing Chamber↗

The Utilization Profiles of the CCSDS Unified Space Link Protocol (USLP)

The purpose of this paper is to identify the utilization profiles for interfacing the Data Protocol Sublayer using the Unified Space Link Protocols (USLP) (reference 1) with the space link coding procedures as specified in the CCSDS Coding & Synchronization Blue Books (references 2 through 5), used in both telecommand and telemetry applications. This paper describes how the USLP Protocol utilizes the coding and synchronization sublayer to support: a. Direct to Earth (DTE) telemetry links for engineering and science data b. Direct to Earth (DTE) telemetry links for very high rate science data c. Direct from Earth (DFE) command, sequencing and flight software loads d. Space to Space Links (Proximity) utilized by orbiters for data exchange to/from surface bound assets. The CCSDS has divided the functions of the Data Link Layer into two sublayers: the Data Link Protocol Sublayer (DLP-SL) and the Coding and Synchronization Sublayer (CS-SL). The Data Link Protocol Sublayer (DLP-SL) interfaces to the users, accepting the data that is to be transported, on the sending side of the link, and delivering that data on the receiving end. The Transfer Frame is the data unit that is transferred across the Data Link Protocol Sublayer and the Coding and Synchronization Sublayer boundary. The Coding and Synchronization Sublayer (CS-SL) provides the encoding, randomization, and frame synchronization functions that prepares the USLP Transfer Frame for transport across the space link. The CS-SL is divided into 2 processes: 1) The Frame Interface Processes (FIP) performs the interface functions required to prepare the data for delivery to the Coding/Decoding Process (CDP). This process includes prepending a Frame Start Marker to the provided frame, when management has designated that the frame is not to be aligned to the codeblock or when there is no block code used. 2) The Coding/Decoding Process (CDP) performs the forward error correction processes that are used to optimize the performance of the link and minimize the error rate. The CDP creates the symbol stream that is delivered to the Physical Layer. The transfer of the USLP transfer frames across different types of space links is the focus of this paper. The Protocol Data Unit (PDU) that is passed in both directions between the Data Link Protocol Sublayer (DLP-SL) and Coding and Synchronization Sublayer (CS-SL) is the transfer frame. The USLP frame structure provides flexibility that can be constrained by the functions utilized within the CS-SL that prepare the transfer frame for transit. For example, the USLP transfer frame contains a length field that enables the frame to be of variable length but CS-SL under certain conditions may constrain the frame to be fixed in length. This paper describes 5 operational modes available for use by the Data Link Layer to provide data exchange across the USLP space link. These modes are different because different operational requirements apply to vastly different types of space links and thus the communications implementation requirements differ. The environmental issues include the power or energy available, the distance between the end points of the link, the complexity of the equipment available at those end points, the atmospheric conditions and radiometric frequency selection. The CS-SL utilizes different forward error correcting codes supported by specific operational modes to configure the data for transit. This paper describes all of the operational modes in a series of data models which decompose the functionality between the Data Link Protocol Sublayer and the Coding and Synchronization sublayer. The operational modes described are: 1. Uncoded Mode: has been used for short links that contain significant available power to provide an acceptable frame error rate. The frames in this mode can be variable in length and typically use an error detection algorithm (i.e., CRC) to determine if there are errors in the received frame. 2. Convolutional Only Mode: is currently the prime forward error correction coding used for the proximity links. The frames in this mode can be variable in length and typically use an error detection algorithm (i.e., CRC) to determine if there are errors in the received frame. 3. Variable Length Frame Aligned to Variable Length Codeblock (TC): is used for Direct from Earth links were power levels are high and the simple, least complex code i.e., the BCH code is used. This mode has been in use since the early 1970s. The BCH code is a short code and the decoder is easy to implement. 4. Fixed Length Frame Aligned to Fixed Length Codeblock (AOS/TM): was introduced when the concatenated Convolutional and Reed-Solomon Code was formulated to provide significant reduction in link data error rate and the ability to determine if there was an error in the decoded codeblock. The frame is aligned to the codeblock so that there is a one to one relationship of frame errors to codeblock errors without additional error detection coding being added. This mode requires the protocol frames to be the exact size of the message portion of the codeblock. 5. Frames Unaligned to Fixed Length Codeblocks (Currently used for very high rates and space to space links): This mode is currently used for missions that have a very high data rate that can be controlled adaptively as the environment changes and as the next generation operating mode for the proximity link. This mode from a coded data stream point of view is exactly like that described in 4. above, except that the frame need not be aligned to the codeblock. There is no requirement on frame length when using this mode. Thus when using USLP it can be used to support links that require short or long frames. There is also no mandatory requirement that frames cannot be separated by idle data reducing the tight data rate connection requirements between the data link protocol sublayer and the coding & synchronization sublayer. In conclusion, how these operational modes can be put to use in mission operational scenarios is described for Direct from Earth links (DFE), Direct to Earth links (DTE), and Proximity links.

Greenberg, E.↗

A modified Newton-Raphson analysis of flight measurements of the trailing vortices of a heavy jet transport

A modified Newton-Raphson method has been used to determine the parameters in equations describing the vortex flow to obtain a best match with flight measurements of the flow behind the C-5A airplane. The flight measurements were made using a specially instrumented T-33 airplane which passed as closely as possible to the centers of the trailing vortices at several distances behind the C-5A airplane. The flight measurements were transformed to flow velocity relative to an inertial frame of reference. The assumed form of the flow consisted of the superposition of two counterrotating, finite core vortices. The positions of the vortex centers, their total circulation, the effective eddy viscosity and measurement bias were the parameters adjusted. The assumed form of vortex flow fit well the measured velocities for the numerous sets of data, both flaps up and down for the C-5A airplane. The resulting values of total circulation, however, were about two-thirds that expected of a wing with an elliptical loading. A partial explanation of the less than expected circulation is a dip in the spanwise lift distribution at the airplane's center line. The distance between the trailing vortices at the smallest times encountered is somewhat less than that expected for an elliptical wing loading.

Taylor, L. W., Jr.↗

Validation of bonded composite doubler technology through application oriented structural testing

One of the major thrusts established under the FAA's National Aging Aircraft Research Program is to foster new technologies associated with civil aircraft maintenance. Recent DOD and other government developments in the use of bonded composite patches on metal structures has supported the need for research and validation of such doubler applications on U.S. certificated airplanes. Composite patching is a rapidly maturing technology which shows promise of cost savings on aging aircraft. Sandia Labs is conducting a proof-of-concept project with Delta Air Lines, Lockheed Martin, Textron, and the FAA which seeks to remove any remaining obstacles to the approved use of composite doublers. By focusing on a specific commercial aircraft application - reinforcement of the L-1011 door frame - and encompassing all 'cradle-to-grave' tasks such as design, analysis, installation, and inspection, this program is designed to prove the capabilities of composite doublers. This paper reports on a series of structural tests which have been conducted on coupons and subsize test articles. Tension-tension fatigue and residual strength tests attempted to grow engineered flaws in coupons with composite doublers bonded to aluminum skin. Also, structures which modeled key aspects of the door corner installation were subjected to extreme tension, shear, and bending loads. In this manner it was possible to study strain fields in and around the Lockheed-designed composite doubler using realistic aircraft load scenarios and to assess the potential for interply delaminations and disbonds between the aluminum and the laminate. The data acquired was also used to validate finite element models (FEM) and associated Damage Tolerance Analyses.

Roach, Dennis↗

Rotation Rate of Saturn's Magnetosphere using CAPS Plasma Measurements

We present the present status of an investigation of the rotation rate of Saturn 's magnetosphere using a 3D velocity moment technique being developed at Goddard which is similar to the 2D version used by Sittler et al. (2005) [1] for SOI and similar to that used by Thomsen et al. (2010). This technique allows one to nearly cover the full energy range of the CAPS IMS from 1 V less than or equal to E/Q less than 50 kV. Since our technique maps the observations into a local inertial frame, it does work during roll manoeuvres. We have made comparisons with Wilson et al. (2008) [2] (2005-358 and 2005-284) who performs a bi-Maxwellian fit to the ion singles data and our results are nearly identical. We will also make comparisons with results by Thomsen et al. (2010) [3]. Our analysis uses ion composition data to weight the non-compositional data, referred to as singles data, to separate H+, H2+ and water group ions (W+) from each other. The ion data set is especially valuable for measuring flow velocities for protons, which are more difficult to derive using singles data within the inner magnetosphere, where the signal is dominated by heavy ions (i.e., proton peak merges with W+ peak as low energy shoulder). Our technique uses a flux function, which is zero in the proper plasma flow frame, to estimate fluid parameter uncertainties. The comparisons investigate the experimental errors and potential for systematic errors in the analyses, including ours. The rolls provide the best data set when it comes to getting 4PI coverage of the plasma but are more susceptible to time aliasing effects. Since our analysis is a velocity moments technique it will work within the inner magnetosphere where pickup ions are important and velocity distributions are non-Maxwellian. So, we will present results inside Enceladus' L shell and determine if mass loading is important. In the future we plan to make comparisons with magnetic field observations, use Saturn ionosphere conductivities as presently known and the field aligned currents necessary for the planet to enforce corotation of the rotating plasma.

Sittler, E.↗

Acoustic transmissibility of advanced turboprop aircraft windows

Advanced turboprop technology allows propeller aircraft to reach cruise speeds comparable to current jet aircraft yet with considerable fuel savings. Due to the higher blade loading and higher tip speed of these propellers, noise levels of up to 150 dB are expected on the outside of the fuselage in the propeller plane. In this study the transmissibility of triple pane windows, designed to provide 69 dB noise transmission loss at the blade propeller frequency of 164 Hz, was experimentally investigated using insertion loss and three-dimensional intensity techniques. A modal analysis on the outer window panes was conducted to determine pane modal frequencies. Coherence and phase relation of outer panes and window frame were established to obtain double/triple wall and lump mass resonance frequencies. Double/triple wall resonances were found to degrade the transmission loss of the two windows. It was shown that, at the blade passage frequency and the first two overtones, the combinations of window plus scratch shield provide less transmission loss than the average transmission loss of the treated fuselage. Strong disagreement was obtained between the experimental transmission loss of this investigation and the theoretical predictions from another study.

Grosveld, Ferdinand W.↗

Projection of distributed-collector solar-thermal electric power plant economics to years 1990-2000

A preliminary comparative evaluation of distributed-collector solar thermal power plants was undertaken by projecting power plant economics of selected systems to the 1990 to 2000 time frame. The selected systems include: (1) fixed orientation collectors with concentrating reflectors and vacuum tube absorbers, (2) one axis tracking linear concentrator including parabolic trough and variable slat designs, and (3) two axis tracking parabolic dish systems including concepts with small heat engine-electric generator assemblies at each focal point as well as approaches having steam generators at the focal point with pipeline collection to a central power conversion unit. Comparisons are presented primarily in terms of energy cost and capital cost over a wide range of operating load factors. Sensitvity of energy costs for a range of efficiency and cost of major subsystems/components is presented to delineate critical technological development needs.

Fujita, T.↗

Acoustically Tailored Composite Rotorcraft Fuselage Panels

A rotorcraft roof sandwich panel has been redesigned to optimize sound power transmission loss (TL) and minimize structure-borne sound for frequencies between 1 and 4 kHz where gear meshing noise from the transmission has the most impact on speech intelligibility. The roof section, framed by a grid of ribs, was originally constructed of a single honeycomb core/composite face sheet panel. The original panel has coincidence frequencies near 700 Hz, leading to poor TL across the frequency range of 1 to 4 kHz. To quiet the panel, the cross section was split into two thinner sandwich subpanels separated by an air gap. The air gap was sized to target the fundamental mass-spring-mass resonance of the double panel system to less than 500 Hz. The panels were designed to withstand structural loading from normal rotorcraft operation, as well as 'man-on-the-roof' static loads experienced during maintenance operations. Thin layers of VHB 9469 viscoelastomer from 3M were also included in the face sheet ply layups, increasing panel damping loss factors from about 0.01 to 0.05. Measurements in the NASA SALT facility show the optimized panel provides 6-11 dB of acoustic transmission loss improvement, and 6-15 dB of structure-borne sound reduction at critical rotorcraft transmission tonal frequencies. Analytic panel TL theory simulates the measured performance quite well. Detailed finite element/boundary element modeling of the baseline panel simulates TL slightly more accurately, and also simulates structure-borne sound well.

Hambric, Stephen↗

Preliminary evaluation of fiber composite reinforcement of truck frame rails

The use of graphite fiber/resin matrix composite to effectively reinforce a standard steel truck frame rail is studied. A preliminary design was made and it was determined that the reinforcement weight could be reduced by a factor of 10 when compared to a steel reinforcement. A section of a 1/3 scale reinforced rail was fabricated to demonstrate low cost manufacturing techniques. The scale rail section was then tested and increased stiffness was confirmed. No evidence of composite fatigue was found after 500,000 cycles to a fiber stress of 34,000 psi. The test specimen failed in bending in a static test at a load 50 percent greater than that predicted for a non-reinforced rail.

Faddoul, J. R.↗

Sensitivity analysis of limit state functions for probability-based plastic design

The evaluation of the total probability of a plastic collapse failure P sub f for a highly redundant structure of random interdependent plastic moments acted on by random interdepedent loads is a difficult and computationally very costly process. The evaluation of reasonable bounds to this probability requires the use of second moment algebra which involves man statistical parameters. A computer program which selects the best strategy for minimizing the interval between upper and lower bounds of P sub f is now in its final stage of development. The relative importance of various uncertainties involved in the computational process on the resulting bounds of P sub f, sensitivity is analyzed. Response sensitivities for both mode and system reliability of an ideal plastic portal frame are shown.

Frangopol, D. M.↗