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This report gives formulas for analyzing the critical shear load of a simply supported square, isotropic (simple flat plate), or orthogonal anisotropic plate (a plate in which the rigidity in two directions perpendicular to each other is different, i.e. plywood or corrugated sheet), these formulas, although arrived at by approximation method, seem to agree fairly well with experimental results.
As renewable energy technologies are increasingly adopted, they pose an opportunity to improve the sustainability and resilience of distributed grids, especially when their design and operation is coordinated as a hybrid power plant. When included in hybrid power plants, distributed wind turbines in particular have the potential to enhance the resilience of distributed grids in areas with good wind resource, due to their ability to provide more consistent generation and ancillary services as compared to photo-voltaic (PV) solar panels. Despite this benefit, U.S. distributed wind adoption is lower than other comparable renewable energy technologies. In this study, we seek to demonstrate how hybrid power plants that include distributed wind turbines can contribute to distribution grid resilience by meeting loads (especially critical loads) more consistently, increasing reserve capacity, and providing value to customers during outages. To demonstrate these contributions, we integrate three separate frameworks and apply them to a case study in a rural electric cooperative in Iowa. Through this case study, we simulate and compare hybrid power plant design and operation during two hazard events: a tornado that causes a 48-hour distribution outage and a winter weather event that causes a 6-hour generation outage. The inclusion of a hybrid power plant that leverages 1) increased battery duration and 2) advanced forecasting and dispatch strategies that reserve capacity leading up to a hazard event best reduce lost loads as well as diesel consumption that would otherwise be used to meet those loads during short- and long-duration hazard events. Depending on the hybrid power plant capacity and operation, we find that the outage mitigation value of a hybrid power plant (measured in value to customers to avoid an outage and avoided lost revenues for the utility) is significant in both hazard events; adding wind, solar, and battery assets to the existing system adds about $50-$100M in avoided lost load and at least $4-$8k in utility value in the tornado hazard event, and $570k-$2.2M in avoided lost load and at least $220-$650 in utility value in the winter hazard scenario. In both the tornado and winter hazard scenarios, optimizing the operation of the hybrid system for resilience can lend similar value as increasing battery duration by 5 MWh for the lower capacity systems considered.
Critical high-pressure sealing joints on the Space Shuttle reusable solid rocket motor require precise control of bolt preload to ensure proper joint function. As the reusable solid rocket motor experiences rapid internal pressurization, correct bolt preloads maintain the sealing capability and structural integrity of the hardware. The angle-of-twist process provides the right combination of preload accuracy, reliability, process control, and assembly-friendly design. It improves significantly over previous methods. The sophisticated angle-of-twist process controls have yielded answers to all discrepancies encountered while the simplicity of the root process has assured joint preload reliability.
Computer program aids in reduction and analysis of data. It determines critical loading conditions for critical values of reactions, applied loads, deflections, stresses, internal loads, etc. Input to program must be in one of specified three-part format.
The NASA Advanced Composites Project is a multi-year consortium of government, industry and academia to develop and validate technology that will reduce development and certification of advanced composite materials for aircraft structures. One of its tasks is to simulate and predict composite damage progression accurately through high fidelity finite element models. It included a subtask to verify an approach based on the Virtual Crack Closure Technology (VCCT) as well as Floating Node Method (FNM). This paper discusses predicted damage onset and growth in a thin-ply buckling problem. Sensitivity of the simulations to various initial crack length is studied. The compressive load-displacement curves are plotted and the crack growth critical load is predicted. Overall, the crack progression follows simulation benchmarks well. However, the critical-load overshoot phenomenon is observed in both VCCT and FNM, suggesting further investigation may be worth pursuing.
Critical loading conditions determined from analysis of each structural element. Automated Thrust Structures Loads and Stresses (ATLAS) system is series of programs developed to analyze elements of complex structure under static-loading conditions. ATLAS calculates internal loads, beam-bending loads, column- and web-buckling loads, beam and panel stresses, and beam-corner stresses. Programs written in FORTRAN IV and Assembler for batch execution.
Results from the testing of cylinder test article SBKF-P2-CYLTA01 (referred to herein as TA01) are presented. The testing was conducted at the Marshall Space Flight Center (MSFC), November 19‒21, 2008, in support of the Shell Buckling Knockdown Factor (SBKF) Project.i The test was used to verify the performance of a newly constructed buckling test facility at MSFC and to verify the test article design and analysis approach used by the SBKF project researchers. TA01 is an 8-foot-diameter (96-inches), 78.0-inch long, aluminum-lithium (Al-Li), orthogrid-stiffened cylindrical shell similar to those used in current state-of-the-art launch vehicle structures and was designed to exhibit global buckling when subjected to compression loads. Five different load sequences were applied to TA01 during testing and included four sub-critical load sequences, i.e., loading conditions that did not cause buckling or material failure, and one final load sequence to buckling and collapse. The sub-critical load sequences consisted of either uniform axial compression loading or combined axial compression and bending and the final load sequence subjected TA01 to uniform axial compression. Traditional displacement transducers and strain gages were used to monitor the test article response at nearly 300 locations and an advanced digital image correlation system was used to obtain low-speed and high-speed full-field displacement measurements of the outer surface of the test article. Overall, the test facility and test article performed as designed. In particular, the test facility successfully applied all desired load combinations to the test article and was able to test safely into the postbuckling range of loading, and the test article failed by global buckling. In addition, the test results correlated well with initial pretest predictions.
Shaftwhirling critical speeds and bearing loads for model I and model II fuel turbopumps
A change of variables that stabilizes numerical computations for periodic solutions of autonomous systems is derived. Computation of the period is decoupled from the rest of the problem for conservative systems of any order and for any second-order system. Numerical results are included for a second-order conservative system under a suddenly applied constant load. Near the critical load for the system, a small increment in load amplitude results in a large increase in amplitude of the response.
The various wear mechanisms involved with single-crystal ceramic materials in indentation and in sliding contacts. Experiments simulating interfacial events have been conducted with hemispherical, conical and pyramidal indenters (riders). With spherical riders, under either abrasive or adhesive conditions, two types of fracture pits have been observed. First, spherical-shaped fracture pits and wear particles are found as a result of either indenting or sliding. These are shown to be due to a spherical-shaped fracture along the circular or spherical stress trajectories. Second, polyhedral fracture pits and debris, produced by anisotropic fracture, and also found both during indenting and sliding. These are primarily controlled by surface and subsurface cracking along cleavage planes. Several quantitative results have also been obtained from this work. For example, using a pyramidal diamond, crack length of Mn-Zn ferrite in the indentation process grows linearly with increasing normal load. Moreover, the critical load to fracture both in indentation and sliding is essentially isotropic and is found to be directly proportional to the indenter radius.
The various wear mechanisms involved with single-crystal ceramic materials in indentation and in sliding contacts. Experiments simulating interfacial events have been conducted with hemispherical, conical and pyramidal indenters (riders). With spherical riders, under either abrasive or adhesive conditions, two types of fracture pits have been observed. First, spherical-shaped fracture pits and wear particles are found as a result of either indenting or sliding. These are shown to be due to a spherical-shaped fracture along the circular or spherical stress trajectories. Second, polyhedral fracture pits and debris, produced by anisotropic fracture, and also found both during indenting and sliding. These are primarily controlled by surface and subsurface cracking along cleavage planes. Several quantitative results have also been obtained from this work. For example, using a pyramidal diamond, crack length of Mn-Zn ferrite in the indentation process grows linearly with increasing normal load. Moreover, the critical load to fracture both in indentation and sliding is essentially isotropic and is found to be directly proportional to the indenter radius.
The 8-Foot High Temperature Tunnel (HTT) at NASA Langley Research Center is a combustion-driven blow-down wind tunnel. A major potential failure mode that was considered during the combustor redesign was the possibility of a deflagration and/or detonation in the combustor. If a main burner flame-out were to occur, then unburned fuel gases could accumulate and, if reignited, an explosion could occur. An analysis has been performed to determine the safe operating limits of the combustor under transient explosive loads. The failure criteria was defined and the failure mechanisms were determined for both peak pressures and differential pressure loadings. An overview of the gas dynamics analysis was given. A finite element model was constructed to evaluate 13 transient load cases. The sensitivity of the structure to the frequency content of the transient loading was assessed. In addition, two closed form dynamic analyses were conducted to verify the finite element analysis. It was determined that the differential pressure load or thrust load was the critical load mechanism and that the nozzle is the weak link in the combustor system.
A generalized method of analyzing experimental observations in problems of elastic stability is presented in which the initial readings of load and deflection may be taken at any load less the critical load. The analysis is an extension of a method published by Southwell in 1932, in which it was assumed that the initial readings are taken at zero load.
In this work, ultrasonic techniques to nondestructively evaluate adhesive bond degradation have been studied. The key to the present approach is the introduction of an external factor which pulls the adhesive bond in the nonlinear range, simultaneously with the application of an ultrasonic technique. With the aid of an external static tensile loading, a superimposed longitudinal wave has.been used to obtain the slopes of the stress-strain curve of an adhesive bond at a series of load levels. The critical load, at which a reduction of the slope is detected by the superimposed longitudinal wave, is an indication of the onset of nonlinear behavior of the adhesive bond, and therefore of bond degradation. This approach has been applied to the detection of adhesive bond degradation induced by cyclic fatigue loading. Analogously to the longitudinal wave case, a superimposed shear wave has been used to obtain the effective shear modulus of adhesive layers at different shear load levels. The onset of the nonlinear behavior of an adhesive bond under shear loading has been detected by the use of a superimposed shear wave. Experiments show that a longitudinal wave can also detect the nonlinear behavior when an adhesive bond is subjected to shear loading. An optimal combination of ultrasonic testing and mechanical loading methods for the detection of degradation related nonlinear behavior of adhesive bonds has been discussed. For the purpose of a practical application, an ultrasonic technique that uses a temperature increase as an alternative to static loading has also been investigated. A general strain-temperature correspondence principle that relates a mechanical strain to a temperature has been presented. Explicit strain-temperature correspondence relations for both the tension and shear cases have been derived. An important parameter which quantifies the relation between the wave velocity and temperature has been defined. This parameter, which is indicative of adhesive bond nonlinearity and which can be conveniently obtained by an ultrasonic measurement, has been used as an indication of adhesive bond degradation. Experimental results have shown that the temperature increase method is a convenient and productive alternative to static loading. A technique which uses the reflected waveform data to obtain the fundamental ultrasonic parameters (transit time, reflection coefficient and attenuation coefficient) of an adhesive bond has also been presented.
The resilience of safety-critical systems is gaining importance due to the rise in cyber and physical threats, especially within critical infrastructure. Traditional static resilience metrics may not capture dynamic system states, leading to inaccurate assessments and ineffective responses to cyber threats. This work aims to develop a data-driven, adaptive method for resilience metric learning. We propose a data-driven approach using inverse reinforcement learning (IRL) to learn a single, adaptive resilience metric. The method infers a reward function from expert control actions. Unlike previous approaches using static weights or fuzzy logic, this work applies adversarial inverse reinforcement learning (AIRL), training a generator and discriminator in parallel to learn the reward structure and derive an optimal policy. The proposed approach is evaluated on multiple scenarios: optimal communication network rerouting, power distribution network reconfiguration, and cyber–physical restoration of critical loads using the IEEE 123-bus system. The adaptive, learned resilience metric enables faster critical load restoration in comparison to conventional RL approaches.
The effect of a type of magnetic damping on the stability of equilibrium of some circulatory elastic systems is examined. A simple system with two degrees of freedom is considered first, and a destabilization is found to be caused by the magnetic field. The nature of the destabilization, however, is not identical to that caused by internal viscous damping. The differences and similarities between the two effects are discussed, and the results are also compared with those of linear external viscous damping. A continuous cantilever bar subjected to a follower force at its free end is then examined. It is found that the critical load is independent of the strength of the magnetic field, and is considerably lower than the corresponding critical load in the absence of a magnetic field. Finally, the continuous cantilever is treated approximately by Galerkin's procedure and also by using a two-degree-of-freedom model of the cantilever; the results obtained are qualitatively the same.
This report presents the findings of an energy system planning study for the towns of Aquinnah and Chilmark, MA, on the island of Martha’s Vineyard, conducted under the U.S. Department of Energy ETIPP program. The study used the DER-CAM model to optimize the deployment of PV and battery microgrids to enhance energy resilience against power outages, particularly winter storms. Key findings show that PV is highly cost-effective and delivers net annual savings. However, due to limited rooftop space and low winter solar output, PV and battery storage alone cannot support the full critical load during outages. Solutions incorporating conventional backup generators were found to be more economically viable for achieving 100% critical load support.
The effect of loading for antennas over an imperfect ground is analyzed. The Fresnel reflection coefficient technique is used to derive an E-integral equation for the antenna current. An optimization method is employed to determine the critical loading parameter which enforces a traveling wave current on the antenna. Results are given for the critical loading parameters, antenna currents, input impedances, and radiation patterns for various antenna dimensions and ground parameters. Calculations of the time-domain behavior of the current are presented to show the effect of loading on antenna transient response.