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

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Solvent Impregnated Polymers Loaded with Liquid-Like Nanoparticle Organic Hybrid Materials for Enhanced Kinetics of Direct Air Capture and Point Source CO 2 Capture

Hybrid CO 2 capture materials, solvent impregnated polymers (SIPs), are developed based on a simple and scalable encapsulation technique to enhance CO 2 capture kinetics of water-lean solvents with high viscosity. Liquid-like nanoparticle organic hybrid materials functionalized with polyethylenimine (NOHM-I-PEI) are incorporated into a shell material and UV-cured to produce gas-permeable solid sorbents with uniform NOHMs loading (NPEI-SIPs). The CO 2 capture kinetics of NPEI-SIPs show a remarkable 50-fold increase compared to that of neat NOHM-I-PEI due to a large increase in the NOHMs-CO 2 interfacial surface area provided by the SIP design. The optimum NOHM-I-PEI loading and sorption temperature are found to be ≈49 wt% and 50 °C, respectively, and NPEI-SIPs exhibit great thermal stability over 20 CO 2 capture/sorbent regeneration temperature swing cycles. The pseudoequilibrium CO 2 loadings of NPEI-SIPs under humid conditions are as high as 3.1 mmol CO 2 g -1 NPEI - SIPs for 15 vol% CO 2 (postcombustion capture) and 1.7 mmol CO 2 g -1 NPEI - SIPs for 400 ppm (direct air capture). Overall, these findings suggest that NPEI-SIPs can effectively capture CO 2 from a wide range of CO 2 concentrations including direct air capture while allowing the flexible design of CO 2 capture reactors by combining the benefits of liquid solvents and solid sorbents.

36 MATERIALS SCIENCE↗
NASA NTRS1992

A probabilistic fracture mechanics approach for structural reliability assessment of space flight systems

A probabilistic fracture mechanics approach for predicting the failure life distribution due to subcritical crack growth is presented. A state-of-the-art crack propagation method is used in a Monte Carlo simulation to generate a distribution of failure lives. The crack growth failure model expresses failure life as a function of stochastic parameters including environment, loads, material properties, geometry, and model specification errors. A stochastic crack growth rate model that considers the uncertainties due to scatter in the data and mode misspecification is proposed. The rationale for choosing a particular type of probability distribution for each stochastic input parameter and for specifying the distribution parameters is presented. The approach is demonstrated through a probabilistic crack growth failure analysis of a welded tube in the Space Shuttle Main Engine. A discussion of the results from this application of the methodology is given.

Sutharshana, S.↗
DOE OSTI2025

Engineering PHL7 for Improved Poly(Ethylene Terephthalate) Depolymerization via Rational Design and Directed Evolution

Enzymatic depolymerization of poly(ethylene terephthalate) (PET) has emerged as a promising approach for polyester recycling, and, to date, many natural and engineered PET hydrolase enzymes have been reported. For industrial use, PET hydrolases must achieve high depolymerization extent and exhibit excellent thermostability. Here, we engineered a natural PET hydrolase, Polyester Hydrolase Leipzig #7 (PHL7), through rational design and directed evolution using a high-throughput screening platform. Four new enzymes were engineered with enhanced properties compared with the parent enzyme, wild-type PHL7 (PHL7-WT), and other benchmark PET hydrolases, under the tested conditions. In bioreactors, the exemplary engineered enzyme, PHL7-Jemez, exhibited improved ability to depolymerize amorphous PET film compared with PHL7-WT at 2.9% and 20% substrate loadings, with 37% and 270% higher hydrolysis, respectively, after 48 h. This study develops several state-of-the-art PET hydrolases and demonstrates a directed evolution platform to engineer high-performance enzymes, which can accelerate enzyme discovery toward improved biocatalytic recycling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

The Physical and Engineering Limits of Coupled In situ TEM Experiments

Almost all future energy systems (advanced nuclear reactors, fusion energy system, concentrating solar-thermal power (CSP), and wind technologies) are limited by degradation of key material systems exposed to multiple environmental stressors. The degradation during exposure to high temperatures, radiation, mechanical loading, and chemical attack is often dictated by mechanisms active at the microstructural level. The nature of these mechanisms and the associated variations between sequential and concurrent interplay can be explored if the transmission electron microscope (TEM) is utilized as a toolbox for exploration [1]. One such tool developed at Sandia National Laboratories to couple several of these environments is the In situ Ion Irradiation TEM (I3TEM) [2]. Several studies over the last decade utilizing this tool have shown that the scientific intuition developed over decades of sequential experiments is not always a good indicator of concurrent mechanisms or failure routes. This presentation will highlight the recent and planned additions into the I3TEM facility of a Waviks gas injection system and Raman system, respectively, as can be seen in Fig. 1, permitting environmental degradation from gas species leaked into the pole piece region during quantitative mechanical loading (indentation, monotonic loading, high temperature creep, irradiation induced creep, and high-cycle fatigue); multi-beam ion irradiation (energies ranging from 1 keV to 48 MeV and species from H to Au); laser exposure (20 W and 1064 nm), or various combinations thereof that are already possible [3]. This addition permits the facility to explore both sequential or concurrently the four axes of stressors: thermal, mechanical, radiation, and chemical. This information can be directly coupled to modeling, expediting the refinement and validation of both atomistic and mesoscale models.

degradation↗
DOE OSTI2021

Implementation and Verification of Cable Bending Stiffness in MoorDyn

The relatively large motions experienced by floating wind turbines and wave energy converters pose a challenge for power cables, whose internal components provide significant bending resistance and are sensitive to deformation. The behavior and associated design considerations of power cables in these highly dynamic applications make coupled analysis relevant for design. Bending stiffness capabilities have recently been added to the lumped-mass mooring dynamics model MoorDyn to enable simulation of dynamic power cables. MoorDyn is a common modeling choice for floating wind energy simulation (often coupled with OpenFAST) and floating wave energy converter simulation (often coupled with WEC-Sim) but the model’s previous line elasticity formulation only considered axial stiffness. To properly capture the dynamics of power cables, a bending stiffness model has been added that approximates cable curvature based on the difference in tangent vectors of adjacent elements. The resulting bending moment is realized by applying forces on adjacent nodes, enabling cable modeling while leaving the underlying lumped-mass formulation unchanged. In this paper, the new bending stiffness implementation is verified in static conditions against analytical solutions and then in a dynamic power cable scenario in comparison with the commercial simulator OrcaFlex. The dynamic scenario uses prescribed motions and includes wave loadings on the cable. Results indicate correct implementation of bending stiffness and show close agreement with OrcaFlex.

50 EE - Wind and Water Power Program - Water (EE-4↗
NASA NTRS2011

Verification and Validation of Requirements on the CEV Parachute Assembly System Using Design of Experiments

The Crew Exploration Vehicle Parachute Assembly System (CPAS) project conducts computer simulations to verify that flight performance requirements on parachute loads and terminal rate of descent are met. Design of Experiments (DoE) provides a systematic method for variation of simulation input parameters. When implemented and interpreted correctly, a DoE study of parachute simulation tools indicates values and combinations of parameters that may cause requirement limits to be violated. This paper describes one implementation of DoE that is currently being developed by CPAS, explains how DoE results can be interpreted, and presents the results of several preliminary studies. The potential uses of DoE to validate parachute simulation models and verify requirements are also explored.

Schulte, Peter Z.↗
NASA NTRSDate not supplied

Design, Instrumentation, and Data Analysis for the SLS Core Stage Green Run Test Series

The Space Launch System (SLS) Core Stage (CS) Thrust Vector Control (TVC) system is comprised of eight mechanical feedback Shuttle heritage Type III TVC actuators and four RS-25 engines, each attached to a Shuttle heritage gimbal block/bearing. The actuators are powered by a Shuttle-derived hydraulic Core Auxiliary Power Unit (CAPU), and integrated with an all-new Core Stage thrust structure. The actuators are interfaced to the SLS Vehicle Management (VM) software via an all-new TVC Actuator Control (TAC) avionics subsystem. Despite the significant test and flight experience of the Shuttle hardware, the SLS Green Run ambient and hot fire test activities revealed a number of new findings associated with the dynamic response of the TVC integrated system. Test responses suggested that the TVC system did not meet its performance specifications and its step and frequency responses exhibited unexpected departures from prior lab tests and modeled behavior. This paper is the fifth installment in a seven-paper series surveying the design, engineering, test validation, and flight performance of the Core Stage Thrust Vector Control system. In this paper, the design of the TVC analyses conducted during the Core Stage Green Run test series are discussed in detail. Throughout the course of the test activities, the SLS flight control team worked diligently with the Core Stage contractor to revise test command profiles and ensure sufficient instrumentation was available to collect data. Post-test analysis combined the Green Run modal, ambient, and hot fire test data, MSFC 2- axis Core Stage TVC Inertial Load Simulator (ILS) data, Hardware-In-the-Loop (HWIL) Systems Integration Lab (SIL) results, and actuator Acceptance Testing Procedure (ATP) responses. These data were used to characterize the response, validate critical math models of the TVC subsystem, and isolate the probable cause of the unexpected responses. Through comprehensive analysis of the available test data sources, the integrated team identified the dominant contributors to the observed response and developed test-correlated rationale for vehicle flight control system performance, ultimately leading to a confident posture for the Artemis I mission.

John H. Wall↗
DOE OSTI2024

High- and Mid-Fidelity Modeling Comparison for a Floating Marine Turbine System

There is a lack of suitable numerical tools, particularly open-source tools, that can be used for designing and optimizing marine turbine systems. The National Renewable Energy Laboratory has added features to their widely used mid-fidelity wind turbine modeling code, OpenFAST, to enable modeling of axial-flow marine turbines. This necessitated the addition of several physical effects relevant to marine turbines that are neglected for wind turbines. These include buoyancy, added mass and inertial loads, wave-current superposition, and changes to the coordinate systems. This updated version of OpenFAST allows for the modeling of both fixed and floating marine turbines at a speed comparable to real time. While efficient for large sets of load cases and design studies, mid-fidelity codes make simplifying assumptions that may impact their accuracy. High-fidelity computational fluid dynamics (CFD) simulations can capture more flow effects with fewer assumptions and provide detailed body pressure mapping and flow-field information. It is important to compare predictions between mid-fidelity and high-fidelity codes, both to verify the models and to understand the limitations. A floating marine turbine system was modeled both with OpenFAST and with the commercial CFD code STAR-CCM+. The CFD model used a three-dimensional unsteady Reynolds-averaged Navier-Stokes solver for a volume-of-fluid numerical wave and current tank. The blade-resolved simulations used the sliding-interface technique for the spinning rotor and an overset grid to accommodate the rigid-body motion of the floating system. The mooring system was modeled with a custom coupling of the CFD solver with the open-source code MoorDyn. This improves upon the existing quasi-static catenary solver in STAR-CCM+, which lacks seabed contact or line-to-line connections. Simulation results for a floating marine turbine are compared between OpenFAST and CFD, highlighting the capabilities of the mid-fidelity code and identifying the areas where a high-fidelity approach is needed.

CFD↗
DOE OSTI2024

High- and Mid-Fidelity Modeling Comparison for a Floating Marine Turbine System: Preprint

There is a lack of suitable numerical tools, particularly open-source tools, that can be used for designing and optimizing marine turbine systems. The National Renewable Energy Laboratory (NREL) has added features to their widely used mid-fidelity wind turbine modeling code, OpenFAST, to enable modeling of axial flow marine turbines. This necessitated the addition of several physical effects relevant to marine turbines that can be neglected for wind turbines. These include buoyant loads, added mass and inertia loads, wave-current superposition, and changes to the coordinate systems. This updated version of OpenFAST allows for the modeling of both fixed and floating marine turbine systems at a speed comparable to real time. While efficient for long simulations, large sets of load cases, and design studies, mid-fidelity codes cannot capture all of the potentially important physical phenomenon impacting marine turbine systems. High-fidelity computational fluid dynamics (CFD) simulations can capture more flow effects with fewer assumptions and provide detailed body pressure mapping and flow-field information. It is important to compare predictions between mid-fidelity and high-fidelity codes, both to verify the models and to understand the limitations. A floating marine turbine system designed by NREL was modeled both with OpenFAST and with the commercial CFD code, STARCCM+. The CFD model used a 3-D unsteady Reynolds-averaged Navier-Stokes solver for a volume-of-fluid numerical wave and current tank. The blade-resolved simulations used the sliding-interface technique for the spinning rotor and an overset grid to accommodate the rigid-body motion of the floating system. The mooring system was modelled with a custom coupling of the CFD solver with the open-source code, MoorDyn. This improves upon the existing quasi-static catenary solver in STARCCM+, which lacks seabed contact or line-to-line connections. Spatial and temporal convergence studies were conducted. The simulation results for a combined current and wave condition are compared between OpenFAST and CFD, highlighting the capabilities of the mid-fidelity code and identifying the areas where a high-fidelity approach is needed.

CFD↗
NASA NTRSDate not supplied

Impacts of Cold Ionospheric Ions in Magnetic Reconnection at the Earth’s Magnetopause and Magnetotail

The Earth’s magnetosphere is filled by particles from two sources: the solar wind and the ionosphere. Ionospheric ions are initially cold and contain He+ and O+, in addition to to H+. Depending on their initial magnetic latitude and local time, and the state of the magnetosphere, they may contribute to the plasmasphere, the plasma sheet, the ring current, the warm plasma cloak etc. Depending on which path they follow in the magnetosphere, some of these ionospheric ions remain cold when they reach the two key reconnection regions: the Earth’s magnetopause and the plasma sheet in the tail. In this presentation, we will first review previous statistical works that quantify the number of cold/ionospheric ions near these two regions. Several works have attempted to quantify these populations, but they are inherently difficult to characterize due to their low energy, often below the spacecraft potential. We will also discuss the impacts they have on the magnetic reconnection process. Ionospheric ions mass-load the regions where reconnection takes place and change the characteristic Alfven speed, resulting in a smaller reconnection electric field. They also take a portion of the energy that is imparted to particles, affecting the energy budget of magnetic reconnection. Finally, they introduce new length and time scales, associated to their gyroradius and gyroperiod. We will discuss what are the implications of these impacts for the evolution of the magnetosphere – solar wind interactions.

Sergio Toledo Redondo↗
DOE OSTI2025

Structure and mechanical properties of grain boundaries in molybdenum disulfide (MoS 2 )

Molybdenum disulfide (MoS 2 ) is a two-dimensional material widely used as a lubricant in many applications involving mechanical loading under a wide range of operating temperatures. Since many synthesis and processing techniques yield MoS 2 in its polycrystalline form, establishing grain boundary (GB) structure–property relations is key to designing MoS 2 microstructures with tailored properties. Here, we employ classical, reactive atomistic simulations to investigate the structure and mechanical behavior of a wide range of GBs in MoS 2 as a function of temperature. Using a bicrystal MoS 2 geometry, we characterize the atomic structure and calculate the energy of several low-angle GBs. Then, we simulate the tensile deformation behavior of MoS 2 bicrystals at several temperatures. Our results reveal that at temperatures above 100 K, the deformation of MoS 2 bicrystals is characterized by the nucleation of shear bands from GBs that grow, with subsequent loading, into the MoS 2 crystals. At low temperatures, the tensile deformation is characterized by the nucleation and propagation of deformation fronts, resulting in altered bond angles and bond lengths. Quantitative analysis reveals a decrease in the ultimate tensile stress and ultimate failure strain of MoS 2 bicrystals with the increase in temperature. Furthermore, our simulations of the mechanical behavior of metastable GBs reveal that the strength and ductility decrease with the increase in energy of these boundary structures. In broad terms, our work provides future avenues to employ GB engineering as a strategy to tailor the properties of MoS 2 microstructures.

Moore, Robert D. [Lehigh Univ., Bethlehem, PA (Uni↗
DOE OSTI2022

Understanding Phase and Interfacial Effects of Spall Fracture in Additively Manufactured Ti-5Al-5V-5Mo-3Cr

Additive manufactured Ti-5Al-5V-5Mo-3Cr (Ti-5553) is being considered as an AM repair material for engineering applications because of its superior strength properties compared to other titanium alloys. Here, we describe the failure mechanisms observed through computed tomography, electron backscatter diffraction (EBSD), and scanning electron microscopy (SEM) of spall damage as a result of tensile failure in as-built and annealed Ti-5553. We also investigate the phase stability in native powder, as-built and annealed Ti-5553 through diamond anvil cell (DAC) and ramp compression experiments. We then explore the effect of tensile loading on a sample containing an interface between a Ti-6Al-V4 (Ti-64) baseplate and additively manufactured Ti-5553 layer. Post-mortem materials characterization showed spallation occurred in regions of initial porosity and the interface provides a nucleation site for spall damage below the spall strength of Ti-5553. Preliminary peridynamics modeling of the dynamic experiments is described. Finally, we discuss further development of Stochastic Parallel PARticle Kinteic Simulator (SPPARKS) Monte Carlo (MC) capabilities to include the integration of alpha (α)-phase and microstructural simulations for this multiphase titanium alloy.

36 MATERIALS SCIENCE↗
NASA NTRS2013

Evaluating Global Emission Inventories of Biogenic Bromocarbons

Emissions of halogenated very short-lived substances (VSLS) are poorly constrained. However, their inclusion in global models is required to simulate a realistic inorganic bromine (Bry) loading in both the troposphere, where bromine chemistry perturbs global oxidizing capacity, and in the stratosphere, where it is a major sink for ozone (O3). We have performed simulations using a 3-D chemical transport model (CTM) including three top-down and a single bottom-up derived emission inventory of the major brominated VSLS bromoform (CHBr3) and dibromomethane (CH2Br2). We perform the first concerted evaluation of these inventories, comparing both the magnitude and spatial distribution of emissions. For a quantitative evaluation of each inventory, model output is compared with independent long-term observations at National Oceanic and Atmospheric Administration (NOAA) ground-based stations and with aircraft observations made during the NSF (National Science Foundation) HIAPER Pole-to-Pole Observations (HIPPO) project. For CHBr3, the mean absolute deviation between model and surface observation ranges from 0.22 (38 %) to 0.78 (115 %) parts per trillion (ppt) in the tropics, depending on emission inventory. For CH2Br2, the range is 0.17 (24 %) to 1.25 (167 %) ppt. We also use aircraft observations made during the 2011 Stratospheric Ozone: Halogen Impacts in a Varying Atmosphere (SHIVA) campaign, in the tropical western Pacific. Here, the performance of the various inventories also varies significantly, but overall the CTM is able to reproduce observed CHBr3 well in the free troposphere using an inventory based on observed sea-to-air fluxes. Finally, we identify the range of uncertainty associated with these VSLS emission inventories on stratospheric bromine loading due to VSLS (Br(VSLS/y)). Our simulations show Br(VSLS/y) ranges from approximately 4.0 to 8.0 ppt depending on the inventory. We report an optimized estimate at the lower end of this range (approximately 4 ppt) based on combining the CHBr3 and CH2Br2 inventories which give best agreement with the compilation of observations in the tropics.

bromocarbons↗
DOE OSTI2025

Materials Engineering for High Performance and Durability Proton Exchange Membrane Water Electrolyzers

Proton exchange membrane water electrolyzers (PEMWEs) are expected to play a crucial role in the global green energy transition during the 21st century. They provide a versatile and sustainable solution for generating hydrogen with very high purity in combination with renewable energies, such as solar and wind. Despite their promise, PEMWEs face several critical problems, including high costs, performance limitations, and durability challenges, particularly at low iridium (Ir) loading on the anode. Advancing next-generation PEMWEs requires extensive work on materials engineering of all cell components, including the catalyst layer (CL), membrane, porous transport layer (PTL), bipolar plate (BPP), and gasket. This task must be performed with the complementary contribution of different modeling and characterization techniques. This review presents a critical perspective from academia, research centers, and industry, mapping main developments, remaining gaps, and strategic pathways to advance PEMWE technology. A focus is devoted to key aspects, such as operation at low Ir loading, membrane durability, multiscale transport layers, porous and non-porous flow fields, multiphysics modeling, and multipurpose characterization techniques, which are thoroughly discussed. By unifying these topics, this review provides readers with the essential knowledge to grasp current developments and tackle tomorrow's challenges in PEMWE engineering.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Progress in Modeling the 2019 Extended Magnetically Insulated Transmission Line (MITL) and Courtyard Environment Trial at HERMES-III

This report documents the progress made in simulating the HERMES-III Magnetically Insulated Transmission Line (MITL) and courtyard with EMPIRE and ITS. This study focuses on the shots that were taken during the months of June and July of 2019 performed with the new MITL extension. There were a few shots where there was dose mapping of the courtyard, 11132, 11133, 11134, 11135, 11136, and 11146. This report focuses on these shots because there was full data return from the MITL electrical diagnostics and the radiation dose sensors in the courtyard. The comparison starts with improving the processing of the incoming voltage into the EMPIRE simulation from the experiment. The currents are then compared at several location along the MITL. The simulation results of the electrons impacting the anode are shown. The electron impact energy and angle is then handed off to ITS which calculates the dose on the faceplate and locations in the courtyard and they are compared to experimental measurements. ITS also calculates the photons and electrons that are injected into the courtyard, these quantities are then used by EMPIRE to calculated the photon and electron transport in the courtyard. The details for the algorithms used to perform the courtyard simulations are presented as well as qualitative comparisons of the electric field, magnetic field, and the conductivity in the courtyard. Because of the computational burden of these calculations the pressure was reduce in the courtyard to reduce the computational load. The computation performance is presented along with suggestion on how to improve both the computational performance as well as the algorithmic performance. Some of the algorithmic changed would reduce the accuracy of the models and detail comparison of these changes are left for a future study. As well as, list of code improvements there is also a list of suggested experimental improvements to improve the quality of the data return.

47 OTHER INSTRUMENTATION↗
NASA NTRS1997

High Temperature Brush Seal Tuft Testing of Selected Nickel-Chrome and Cobalt-Chrome Superalloys

The tribology of brush seals is of considerable interest to turbine engine designers because bristle wear continues to limit long term seal performance and life. To provide better materials characterization and foster the development of improved seals, NASA Lewis has developed a brush seal tuft tester. In this test, a 'paintbrush' sample tuft is loaded under constant contact pressure against the outside diameter of a rotating journal. With this configuration, load and friction are directly measured and accurate wear measurements are possible. Previously reported research using this facility showed excellent data repeatability and wear morphology similar to published seal data and dynamic rig tests. This paper is an update of the ongoing research into the tribology of brush seals. The effects of wire materials processing on seal wear and the tribological results for three journal coatings are discussed. Included in the materials processing were two nickel-chrome superalloys each processed to two different yield strengths. The results suggest that seal wear is dependent more on material composition than processing conditions.

Fellenstein, James A.↗
NASA NTRSDate not supplied

TPSAS-NF1676L-15304-DND

The Subsonic Fixed Wing Project conducts research to improve prediction methods and technologies that will produce lower noise, lower emissions, and higher performing subsonic aircraft for the Next Generation Air Transportation System. Subproject: FW Structural Efficiency: Lightweight, multi-objective and multifunctional structures (e.g., structures that can carry load and attenuate noise at the same time) are being developed to reduce the weight of both airframes and engines. Adaptive and flexible wing structures with aeroelastic tailoring offer significant weight reduction due to the elimination of a heavy actuation system. Extensive use of polymer matrix composites (PMCs) in airframe and engine structures (where applicable) will offer significant weight reduction opportunities. Research on composite technology is focused on developing alternate processes that will enable fabrication of large structures, increasing the temperature capability toward greater usage in engine and supersonic airframe structures, developing advanced structural concepts, and modeling damage initiation and progression in composite structures.

Jason P Moore↗
NASA NTRS1979

Design curves for non-linear analysis of simply-supported, uniformly-loaded rectangular plates

Design curves for the non-linear analysis of simply-supported rectangular plates subjected to uniform normal pressure loads have been developed. These curves yield the center deflection, center stress and corner stress in non-dimensionalized form plotted against a dimensionless parameter describing the load intensity. The results presented are based on extensive non-linear finite element analysis employing the ARGUS structural analysis program. Plates with length to width ratios of 1, 1.5, 2, 3 and 4 are included. The load range considered extends to 1000 times the load at which the behavior of the plate becomes significantly non-linear. Over the load range considered, the analysis shows that the ratio of center deflection to plate thickness for a square plate is less than 16 to 1, whereas linear theory would predict a center deflection 400 times the plate thickness. Likewise, the stress is markedly lower than would be predicted by linear theory. The present results are shown to be in excellent agreement with the classical linear theory up to a central deflection to plate thickness ratio of about one-half. In the non-linear regime the present results for deflection and stress are in very good agreement with the analytical and experimental work of other investigators.

Moore, D.↗