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At least 955 records · Page 53

Mechanisms of proton transport in aqueous acid solutions

The fundamental understanding of proton transport, specifically the Grotthuss-like mechanism, is critical for many technological applications. The present study presents a comprehensive analysis of proton transport in aqueous solutions of sulfuric and phosphoric acids using quasielastic neutron and light scattering, broadband dielectric spectroscopy, rheology, pulsed-field gradient-NMR measurements, and ab initio molecular dynamic simulations. Results show that in all systems, proton transport occurs through short “jumps” of ~0.5 Å that are faster than structural relaxation. However, proton hopping appears to be coupled to structural relaxation in aqueous solutions of sulfuric acid, while these processes are decoupled in phosphoric acid. Neutron scattering indicates that all protons have the same fast mobility in phosphoric acid systems, while at least one proton per sulfuric molecule remains slower than other protons. Analysis reveals correlated proton jumps, but these correlations suppress conductivity, suggesting that expected Grotthuss-like enhancement of conductivity is unlikely in bulk liquids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Temperature Homogeneity under Selective and Localized Microwave Heating in Structured Flow Reactors

Selective heating of different phases of multiphase systems via microwaves can result in energy savings and suppression of side reactions. However, materials properties and operating conditions that maximize temperature gradients are poorly understood. Here we utilize computational fluid dynamics (CFD) computations and temperature measurements in structured flow reactors (monoliths) in a monomodal microwave cavity to assess the temperature difference between the walls and the fluid and develop a simple lumped model to estimate when temperature gradients exist. We also explore the material’s thermal and electrical properties of structured reactors for isothermal catalyst conditions. We propose that CFD simulations can be used as a nonintrusive, predictive tool of temperature homogeneity. Importantly, we demonstrate that localized heating in the bed under several conditions rather than selective heating is responsible for the selectivity enhancement. Furthermore, our results indicate that structured beds made of high thermal conductivity materials avoid arcing and enable temperature homogeneity and low electrical conductivity materials allow microwaves to penetrate the domain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Characterization of the Heat Extraction Capability of a Compliant, Sliding, Thermal Interface for Use in a High Temperature, Vacuum Microgravity Furnace

Much of the material science gained in microgravity research requires processing a sample in a high performance furnace. One such furnace currently being designed is the Quench Module Insert (QMI). The Principle Investigators, for whom the furnace is proposed, require high temperature gradients in their cylindrical samples to achieve the science objectives. One of the components critical to achieving high sample axial temperature gradients in the Quench Module Insert is a high performance cold zone to extract the heat from the sample. This cold zone employs a compliant, sliding thermal interface based on a Vel-Therm felt. This felt provides a conductive path between the Sample Cartridge Assembly (SCA) exterior surface and the interior surface of the water cooled chill block while allowing movement of the sample relative to the chill block. The Vel-Therm felt is composed of long polymer-based fibers affixed to a thin flexible substrate layer. The fibers are oriented perpendicular to this substrate giving the felt the appearance of a velvet fabric. The Vel-Therm felt heat extraction capability was quantified in earlier tests performed in an inert gas environment. The current activity, described in this paper, is intended to characterize the extraction capability of Vel-Therm felt in a vacuum environment similar to the QMI environment. This testing is necessary to quantify the thermal performance of the Vel-Therm felt and the sensitivity of that performance to key variables. The data derived from these tests will be incorporated into the current thermal models to improve the quality of the models and reduce uncertainty of the analytical results. In addition, the data will be used to help select the appropriate Vel-Therm felt and set proper operating limits as well as assess the performance range of the furnace. The objective of this test is to measure the heat extraction rate of the Vel-Therm felt as specified by the effective heat transfer coefficient. Therefore, the test setup was designed to force the bulk of the heat transfer through the area where the Vel-Therm felt was applied. A heat source, consisting of a ceramic heating element encased in a Copper (Cu) housing is mounted on four isolated support rods. A 6-layer molybdenum radiation shield is used to insulate against heat loss from the heater and prevent heat exchange between the hot and cold sides of the test apparatus. The Vel-Therm felt is affixed to the surface of the cold sink, a water-cooled Cu chill block. An adjustable plate supports and isolates the cold sink from above and is used to control the amount of the deflection of the Vel- Therm when in contact with the Cu heating element housing. The primary means of establishing the power being conducted through the felt is to measure the energy being transferred to the water passing through the chill block. Analysis was performed to support the assumption that the source and sink surfaces were approximately isothermal under the specific test conditions. As a check on the amount of power passing through the felt, the power supplied to the heater was also measured. Thermocouples were strategically located throughout the test apparatus for measurement purposes. A bell jar was lowered over the assembly to impose vacuum conditions. Currently, variables tested have been fiber compression and fiber type and surface temperatures (both the hot and cold side temperatures are hypothesized to be important to the performance of the Vel-Therm.) Selected runs were repeated to ensure consistency and repeatability. Results obtained thus far reveal that Vel-Therm performance is significantly degraded by fibers being exposed to high compression. It also shows that performance is somewhat negatively impacted by previous compression, thereby, raising the question of repeatability. In addition, early results show a significant dependence on temperature. A computer aided mathematical analysis of the test setup is ongoing. The results will be correlated to actual results. The correlation will examine such details as parasitic loses, conduction down the power leads and many other concerns.

Bellomy-Ezell, Jenny↗

Mapping Competitive Reduction upon Charging in LiNi 0.8 Co 0.15 Al 0.05 O 2 Primary Particles

Side reactions involving surface reduction play a critical role in the failure of LiNi 0.8 Co 0.15 Al 0.05 O 2 to reach its theoretical capacity as a cathode material for Li-ion batteries. While macroscopic consequences are known, the underlying nanoscopic mechanisms are not fully elucidated. By coupling X-ray spectroscopy with several X-ray microscopy modalities, we have spatially resolved the extent of Ni oxidation at several states of charge and uncovered heterogeneity that is hidden when considering ensemble measurements alone. The use of morphologically controlled particles enabled high-resolution imaging of these materials, uncovering gradients of Ni oxidation states within individual primary particles. At high states of charge, these gradients revealed regions of possible oxygen deficiency extending deeper into the particle than previously observed. Surface-sensitive X-ray coupled scanning tunneling microscopy allows oxidation states to be measured at the material's surface, showing predominantly Ni II in the first atomic layer and mixtures of Ni II with Ni III /Ni IV already appearing 1.5 nm into the particle. These results reveal the subtle interplay between irreversible surface transformations and the bulk reactions that ultimately define function, which will refine strategies of surface passivation that are key to overcoming current performance limitations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Stimulated Nucleation of Skyrmions in a Centrosymmetric Magnet

Understanding the dynamics of skyrmion nucleation and manipulation is important for applications in spintronic devices. In this contribution, the spin textures at magnetic domain-boundaries stimulated by application of in-plane magnetic fields in a centrosymmetric kagome ferromagnet, Fe 3 Sn 2 , with thickness gradient are investigated using Lorentz transmission electron microscopy. Switching of the in-plane magnetic field is shown to induce a reversible transformation from magnetic stripes to skyrmions, or vice versa, at the interface between differently oriented domains. Micromagnetic simulations combined with experiments reveal that the rotatable anisotropy and thickness dependence of the response to the external in-plane field are the critical factors for the skyrmion formation. In addition, it is shown that the helicity of skyrmions can also be controlled using this dynamic process. Finally, the results suggest that magnetic materials with rotatable anisotropy are potential skyrmionic systems and provides a different approach for nucleation and manipulation of skyrmions in spintronic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Shuttle Damage/Repair from the Perspective of Hypersonic Boundary Layer Transition - Experimental Results

An overview is provided of the experimental wind tunnel program conducted at the NASA Langley Research Center Aerothermodynamics Laboratory in support of an agency-wide effort to prepare the Shuttle Orbiter for Return-to-Flight. The effect of an isolated protuberance and an isolated rectangular cavity on hypersonic boundary layer transition onset on the windward surface of the Shuttle Orbiter has been experimentally characterized. These experimental studies were initiated to provide a protuberance and cavity effects database for developing hypersonic transition criteria to support on-orbit disposition of thermal protection system damage or repair. In addition, a synergistic experimental investigation was undertaken to assess the impact of an isolated mass-flow entrainment source (simulating pyrolysis/outgassing from a proposed tile repair material) on boundary layer transition. A brief review of the relevant literature regarding hypersonic boundary layer transition induced from cavities and localized mass addition from ablation is presented. Boundary layer transition results were obtained using 0.0075-scale Orbiter models with simulated tile damage (rectangular cavities) of varying length, width, and depth and simulated tile damage or repair (protuberances) of varying height. Cavity and mass addition effects were assessed at a fixed location (x/L = 0.3) along the model centerline in a region of near zero pressure gradient. Cavity length-to-depth ratio was systematically varied from 2.5 to 17.7 and length-to-width ratio of 1 to 8.5. Cavity depth-to-local boundary layer thickness ranged from 0.5 to 4.8. Protuberances were located at several sites along the centerline and port/starboard attachment lines along the chine and wing leading edge. Protuberance height-to-boundary layer thickness was varied from approximately 0.2 to 1.1. Global heat transfer images and heating distributions of the Orbiter windward surface using phosphor thermography were used to infer the state of the boundary layer (laminar, transitional, or turbulent). Test parametrics include angles-of-attack of 30 deg and 40 deg, sideslip angle of 0 deg, freestream Reynolds numbers from 0.02x106 to 7.3x106 per foot, edge-to-wall temperature ratio from 0.4 to 0.8, and normal shock density ratios of approximately 5.3, 6.0, and 12 in Mach 6 air, Mach 10 air, and Mach 6 CF4, respectively. Testing to simulate the effects of ablation from a proposed tile repair concept indicated that transition was not a concern. The experimental protuberance and cavity databases highlighted in this report were used to formulate boundary layer transition correlations that were an integral part of an analytical process to disposition observed Orbiter TPS damage during STS- 114.

Horvath, Thomas J.↗

Spatially varying colloidal phase behavior on multi-dimensional energy landscapes

A method is reported to determine equilibrium concentration profiles and local phase behavior for colloids on multi-dimensional energy landscapes. A general expression is derived based on local particle concentration and osmotic pressure differences that are balanced by forces on colloids due to energy landscape gradients. This analysis is applied to colloidal particles in high frequency AC electric fields within octupolar electrodes, where the energy landscape can be shaped in two dimensions. These results are also directly applicable to any particles having induced dipoles in spatially non-uniform electromagnetic fields. Predictions based on modelling colloids with an effective hard disk equation of state indicate inhomogeneous solid and fluid states coexisting on different shaped energy landscapes including multiple minima. Model predictions show excellent agreement with time-averaged Brownian Dynamic simulations at equilibrium. Findings demonstrate a general approach to understand colloidal phase behavior on energy landscapes due to external fields, which could enable control of colloidal microstructure on morphing energy landscapes and the inverse design of fields to assemble hierarchically structured colloidal materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Along the Channel Gradients Impact on the Spatioactivity of Gas Diffusion Electrodes at High Conversions during CO 2 Electroreduction

Results of a 2-D transport model for a gas diffusion electrode performing CO 2 reduction to CO with a flowing catholyte are presented, including the concentration gradients along the flow cell, spatial distribution of the current density and local pH in the catalyst layer. The model predicts that both the concentration of CO 2 and the buffer electrolyte gradually diminish along the channels for a parallel flow of gas and electrolyte as a result of electrochemical conversion and nonelectrochemical consumption. At high single-pass conversions, significant concentration gradients exist along the flow channels leading to large local variations in the current density (>150 mA/cm 2 ), which becomes prominent when compared to ohmic losses. In addition, concentration overpotentials change dramatically with CO 2 flow rate, which results in significant differences in outlet concentrations at high conversions. The outlet concentration of CO attains a maximum of 80% along with 5% CO 2 and 15% H 2 , although the maximum single-pass conversion is limited to below 60% due to homogeneous consumption by the electrolyte. Fundamental and practical implications of our findings on electrochemical CO 2 reduction are discussed with a focus on the trade-off between high current density operation and high single-pass conversion efficiency.

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Suspended Membrane Evaporators Integrating Environmental and Solar Evaporation for Oily Wastewater Purification

Solar-driven evaporation is promising in oily wastewater treatment, in particular for emulsions, but conventional evaporators suffer from pore blocking by residual oil or contamination by volatile oil compounds in the condensed water. In the current research, we develop a suspended membrane evaporator integrating solar evaporation with oil-in-water emulsion separation. The heating and evaporating interface is separated from the rejecting interface to avoid oil escape and improve heat management. A temperature gradient forms on the membrane surface that can promote evaporation performance by combining both solar and environmental evaporation. Such an evaporator achieves a maximum evaporation rate of 1.645 kg/(m 2 ·h) as well as an apparent evaporation efficiency of 111.9%. Moreover, the superhydrophilic and superoleophobic membrane shows excellent oil repellence and emulsion rejection, which can achieve an oil removal efficiency above 98.8% in oil-in-water emulsion separation, and high evaporation rate recovery in cycling tests. Furthermore, a scaled-up membrane evaporator array produces ~8 kg/(m 2 ·d) of clean water from oily wastewater in outdoor experiments, further demonstrating the strong purification performance of this evaporator in oily wastewater treatment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enabling complete multichannel nonadiabatic dynamics: A global representation of the two-channel coupled, 1,2 1 A and 1 3 A states of NH 3 using neural networks

Global coupled three-state two-channel potential energy and property/interaction (dipole and spin–orbit coupling) surfaces for the dissociation of NH 3 (Ã) into NH + H 2 and NH 2 + H are reported. The permutational invariant polynomial-neural network approach is used to simultaneously fit and diabatize the electronic Hamiltonian by fitting the energies, energy gradients, and derivative couplings of the two coupled lowest-lying singlet states as well as fitting the energy and energy gradients of the lowest-lying triplet state. The key issue in fitting property matrix elements in the diabatic basis is that the diabatic surfaces must be smooth, that is, the diabatization must remove spikes in the original adiabatic property surfaces attributable to the switch of electronic wavefunctions at the conical intersection seam. Here, we employ the fit potential energy matrix to transform properties in the adiabatic representation to a quasi-diabatic representation and remove the discontinuity near the conical intersection seam. The property matrix elements can then be fit with smooth neural network functions. The coupled potential energy surfaces along with the dipole and spin–orbit coupling surfaces will enable more accurate and complete treatment of optical transitions, as well as nonadiabatic internal conversion and intersystem crossing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evaluating proxies for the drivers of natural gas productivity using machine-learning models

We report the extensive development of unconventional reservoirs using horizontal drilling and multistage hydraulic fracturing has generated large volumes of reservoir characterization and production data. The analysis of this abundant data using statistical methods and advanced machine-learning (ML) techniques can provide data-driven insights into well performance. Most predictive modeling studies have focused on the impact that different well completion and stimulation strategies have on well production but have not fully exploited the available in situ rock property data to determine its role in reservoir productivity. We have used machine-learning techniques to rank rock mechanical properties, microseismic attributes, and stimulation parameters in the order of their significance for predicting natural gas production from an unconventional reservoir. The data for this study came from a hydraulically fractured well in the Marcellus Shale in Monongalia County, West Virginia. The data classes included measurements aggregated by well completion stage that included (1) gas production, (2) well-log-derived measurements including bulk density, elastic moduli, shear impedance, compressional impedance, brittleness, and gamma measurements, (3) microseismic attributes, (4) long-period long-duration (LPLD) event counts, (5) fracture counts, and (6) stimulation parameters that included the fluid injection volume and average pumping pressure. To identify observable proxies for the drivers of gas production, we evaluated five commonly used ML approaches including multivariate adaptive regression spline, Gaussian mixture model, random forest, gradient boosting, and neural network. We selected five variables including LPLD event count, seismogenic b-value, hydraulic diffusivity, cumulative moment, and fluid volume as the features most likely to impact gas productivity at the stage level in the study area. The data-driven selection of these parameters for their importance in determining gas production can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs. Plain language summary: We use machine-learning methods and data-driven selection of reservoir parameters to rank and better understand their importance in determining gas production, which can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs.

58 GEOSCIENCES↗

Evaluating the Role of Metastable Surfaces in Mechanochemical Reduction of Molybdenum Oxide

Mechanochemistry and mechanocatalysis are gaining increasing attention as environmentally friendly chemical processes because of their solvent-free nature and scalability. Significant effort has been devoted for studying continuum-scale phenomena in mechanochemistry, such as temperature and pressure gradients, but the atomic-scale mechanisms remain relatively unexplored. In this work, we focus on the mechanochemical reduction of MoO3 as a case study. We use experimental techniques to determine the mechanochemical reduction conditions and density functional theory (DFT) simulations to establish an atomistic framework for identifying the metastable surfaces that are most likely to enable this process. Our results show that metastable surfaces can significantly lower or remove thermodynamic barriers for surface reduction and that kinetic energy from milling can facilitate the formation of metastable surfaces that have high surface fracture energies and are not thermally accessible. These findings indicate that metastable surfaces are an important aspect of mechanochemistry along with hot spots and other continuum-scale phenomena.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Assessing density functionals for describing methane dissociative chemisorption on Pt(110)-(2×1) surface

In this work, we explore the suitability of several density functionals with the generalized gradient approximation (GGA) and beyond for describing the dissociative chemisorption of methane on the reconstructed Pt(110)-(2×1) surface. The bulk and surface structures of the metal, methane adsorption energy, and dissociation barrier are used to assess the functionals. A van der Waals corrected GGA functional (optPBE-vdW) and a metaGGA functional with van der Waals correction (MS PBEl-rVV10) are selected for ab initio molecular dynamics calculations of the sticking probability. Our results suggest that the use of these two functionals may lead to a better agreement with existing experimental results, thus serving as a good starting point for future development of reliable machine-learned potential energy surfaces for the dissociation of methane on the Pt(110)-(2×1) surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fermi–Löwdin orbital self-interaction correction of adsorption energies on transition metal ions

Density functional theory (DFT)-based descriptions of the adsorption of small molecules on transition metal ions are prone to self-interaction errors. Here, we show that such errors lead to a large over-estimation of adsorption energies of small molecules on Cu + , Zn + , Zn 2+ , and Mn + in local spin density approximation (LSDA) and Perdew, Burke, Ernzerhof (PBE) generalized gradient approximation calculations compared to reference values computed using the coupled-cluster with single, doubles, and perturbative triple excitations method. These errors are significantly reduced by removing self-interaction using the Perdew–Zunger self-interaction correction (PZ-SIC) in the Fermi–Löwdin Orbital (FLO) SIC framework. In the case of FLO-PBE, typical errors are reduced to less than 0.1 eV. Furthermore, analysis of the results using DFT energies evaluated on self-interaction-corrected densities [DFT(@FLO)] indicates that the density-driven contributions to the FLO-DFT adsorption energy corrections are roughly the same size in DFT = LSDA and PBE, but the total corrections due to removing self-interaction are larger in LSDA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mixing by barotropic instability in a nonlinear model

A global, nonlinear, equivalent barotropic model is used to study the isentropic mixing of passive tracers by barotropic instability. Basic states are analytical zonal-mean jets representative of the zonal-mean flow in the upper stratosphere, where the observed 4-day wave is thought to be a result of barotropic, and possibly baroclinic, instability. As is known from previous studies, the phase speed and growth rate of the unstable waves is fairly sensitive to the shape of the zonal-mean jet; and the dominant wave mode at saturation is not necessarily the fastest growing mode; but the unstable modes share many features of the observed 4-day wave. Lagrangian trajectories computed from model winds are used to characterize the mixing by the flow. For profiles with both midlatitude and polar modes, mixing is stronger in midlatitude than inside the vortex; but there is little exchange of air across the vortex boundary. There is a minimum in the Lyapunov exponents of the flow and the particle dispersion at the jet maximum. For profiles with only polar unstable modes, there is weak mixing inside the vortex, no mixing outside the vortex, and no exchange of air across the vortex boundary. These results support the theoretical arguments that, whether wave disturbances are generated by local instability or propagate from other regions, the mixing properties of the total flow are determined by the locations of the wave critical lines and that strong gradients of potential vorticity are very resistant to mixing.

Bowman, Kenneth P.↗

Spatially Resolved, In Situ Carbon Isotope Analysis of Archean Organic Matter

Spatiotemporal variability in the carbon isotope composition of sedimentary organic matter (OM) preserves information about the evolution of the biosphere and of the exogenic carbon cycle as a whole. Primary compositions, and imprints of the post-depositional processes that obscure them, exist at the scale of individual sedimentary grains (mm to micron). Secondary ion mass spectrometry (SIMS) (1) enables analysis at these scales and in petrographic context, (2) permits morphological and compositional characterization of the analyte and associated minerals prior to isotopic analysis, and (3) reveals patterns of variability homogenized by bulk techniques. Here we present new methods for in situ organic carbon isotope analysis with sub-permil precision and spatial resolution to 1 micron using SIMS, as well as new data acquired from a suite of Archean rocks. Three analytical protocols were developed for the CAMECA ims1280 at WiscSIMS to analyze domains of varying size and carbon concentration. Average reproducibility (at 2SD) using a 6 micron spot size with two Faraday cup detectors was 0.4 %, and 0.8 % for analyses using 1 micron and 3 micron spot sizes with a Faraday cup (for C-12) and an electron multiplier (for C-13). Eight coals, two ambers, a shungite, and a graphite were evaluated for micron-scale isotopic heterogeneity, and LCNN anthracite (delta C-13 = -23.56 +/- 0.1 %, 2SD) was chosen as the working standard. Correlation between instrumental bias and H/C was observed and calibrated for each analytical session using organic materials with H/C between 0.1 and 1.5 (atomic), allowing a correction based upon a C-13H/C-13 measurement included in every analysis. Matrix effects of variable C/SiO2 were evaluated by measuring mm to sub-micron graphite domains in quartzite from Bogala mine, Sri Lanka. Apparent instrumental bias and C-12 count rate are correlated in this case, but this may be related to a crystal orientation effect in graphite. Analyses of amorphous Archean OM suggest that instrumental bias is consistent for 12C count rates as low as 10% relative to anthracite. Samples from the ABDP-9 (n=3; Mount McRae Shale, approximately 2.5 Ga), RHDH2a (n=2; Carrawine Dolomite and Jeerinah Fm, approximately 2.6 Ga), WRL1 (n=3; Wittenoom Fm, Marra Mamba Iron Formation, and Jeerinah Fm, approximately 2.6 Ga), and SV1 (n=1; Tumbiana Fm, approximately 2.7 Ga) drill cores, each previously analyzed for bulk organic carbon isotope composition, yielded 100 new, in situ data from Neoarchean sedimentary OM. In these samples, delta C-13 varies between -53.1 and -28.3 % and offsets between in situ and bulk compositions range from -8.3 to 18.8%. In some cases, isotopic composition and mode of occurrence (e.g. morphology and mineral associations) are statistically correlated, enabling the identification of distinct reservoirs of OM. Our results support previous evidence for gradients of oxidation with depth in Neoarchean environments driven by photosynthesis and methane metabolism. The relevance of these findings to questions of bio- and syngenicity as well as the alteration history of previously reported Archean OM will be discussed.

Williford, Kenneth H.↗

Mode interaction in stiffened composite shells under combined mechanical and thermal loadings

Stiffened shells of various configurations fabricated out of composite materials find extensive applications in aircraft structures. Two distinctive modes of buckling dominate structural response of stiffened panels, viz. the short-wave local mode in which the shell skin buckles essentially between the stiffeners and the long-wave overall mode in which the shell skin buckles carrying the stiffeners with it. In optimized designs, the critical stresses corresponding to these modes of buckling would be close to each other. This leads to a nonlinear mode interaction which is recognized to be the principal cause of the failure of stiffened structures. If the structure is subjected to through-the-thickness thermal gradients, then large-wave bending effects would begin to occur well below the overall critical load and these would play the role of overall imperfections. The load carrying capacity would be significantly diminished as a result of interaction of local buckling with overall thermal distortions. The analysis of this problem using standard finite element techniques can be shown to be prohibitively expensive for design iterations. A concept which would greatly facilitate the analysis of mode interaction is advanced. We note that the local buckling occurs in a more or less periodic pattern in a structure having regular spacings of stiffeners. Thus it is a relatively simple matter to analyze the local buckling and the second order effects (which are essential for modeling postbuckling phenomena) using a unit cell of the structure. Once analyzed, these dormations are embedded in a shell element. Thus, a shell element could span several half-waves of local buckling and still be able to depict local buckling effects with requisite accuracy. A major consequence of the interaction of overall buckling/bending is the slow variation of the local buckling amplitude across the structure - the phenomenon of 'amplitude modulation' - and this is accounted for in the present model by letting the scaling parameter of the local mode vary according to a 'slowly varying' function. The construction of the analytical model involves essentially two stages and these are described briefly.

Sridharan, Srinivasan↗