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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 271 records · Page 15

Expeditious Coordination-Driven Construction of Hierarchically Nanoporous Barium Salts

Organic moieties-derived salts with permanent porosity and polarized channels have shown unique features and attractive performance in the field of adsorption, separation, and conduction. However, state-of-the-art organic salts generally rely on ionic interaction and hydrogen bonding formation to maintain the porous channels. The synthesis of organic moiety-derived salts with permanent accessible pores even after removal of the trapped guest molecules, and without the constraint of hydrogen bonding formation still remains a great challenge. Herein, we present an expeditious construction pathway to generate hierarchically nanoporous barium salts without hydrogen bonding formation. The strong ionic interaction of the barium cation and sulfonate anions led to rapid reaction equilibrium (~2 min), affording diverse barium-derived ionic polymer (Ba-IP) with permanent porosity and highly polarized channels. The produced Ba-IP materials with abundant cations and anions displayed high CO 2 /N 2 and CO 2 /CH 4 separation performance, with the selectivities reaching up to 89.5 and 280, respectively, at 273 K, surpassing most of the organic polymers functionalized by ionic moieties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Incorporation of Failure Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased use in the aerospace and automotive communities. The aerospace community has identified several key capabilities which are currently lacking in the available material models in commercial transient dynamic finite element codes. To attempt to improve the predictive capability of composite impact simulations, a next generation material model is being developed for incorporation within the commercial transient dynamic finite element code LS-DYNA. The material model, which incorporates plasticity, damage and failure, utilizes experimentally based tabulated input to define the evolution of plasticity and damage and the initiation of failure as opposed to specifying discrete input parameters such as modulus and strength. The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. For the damage model, a strain equivalent formulation is used to allow for the uncoupling of the deformation and damage analyses. In the damage model, a semi-coupled approach is employed where the overall damage in a particular coordinate direction is assumed to be a multiplicative combination of the damage in that direction resulting from the applied loads in various coordinate directions. For the failure model, a tabulated approach is utilized in which a stress or strain based invariant is defined as a function of the location of the current stress state in stress space to define the initiation of failure. Failure surfaces can be defined with any arbitrary shape, unlike traditional failure models where the mathematical functions used to define the failure surface impose a specific shape on the failure surface. In the current paper, the complete development of the failure model is described and the generation of a tabulated failure surface for a representative composite material is discussed.

Impact↗

Experimental Calibration of Flow Rule Coefficients for LS-Dyna Mat_213

Composite materials have become a popular choice in aerospace engineering applications due to their low weight, high specific stiffness, high specific energy absorption, and economic synthesis. As use of composite materials has proliferated, the need for accurate simulation under extreme loading conditions is of increasing importance. *MAT_213 is a tabulated plasticity and damage material model in LS-DYNA designed for such use cases. To account for the nonlinear material response, a plasticity algorithm is used, which employs a non-associative flow rule with coefficients requiring experimental calibration. This work outlines an experimental methodology for calibrating these coefficients using the macroscopic stress-strain response and microscopic in-plane strain measurements from coupon scale experiments. The model material used for the development and demonstration of this methodology is a plain weave woven fabric with T300 carbon fiber tows in the warp direction and Kevlar© 49 fiber tows in the weft direction, and an Epon© 828/Epikure© 3223 thermoset epoxy matrix. Coupon-scale tensile testing performed at multiple fiber angles (carbon fibers oriented 0º, 22.5º, 45º, 67.5º, and 90º relative to the loading axis) provides data for multiple calibration processes. The measured plastic strain increments in the principal material coordinate are used to set limits for ratios between flow rule coefficients. The identified ranges are used to bound the search for a set of coefficients, leading to convergence of different coupon responses in the effective stress – effective plastic strain space. Flow rule coefficients found by this methodology are then used as (i) input for LS-DYNA simulations of uniaxial tension coupon tests at varying fiber angles, and (ii) comparison of predicted values for the plastic Poisson’s ratio in global coordinates with the experimentally measured one for all off-axis orientations. These results are quantitatively and qualitatively compared to macroscopic stress-strain curves and experimental strain components. The conformity of the experimentally measured quantities with those derived from the simulations provide a means for assessing the quality of calibrated coefficients.

Polymer Matrix Composites↗

Nonvanishing quadrature derivatives in the analytical gradients of density functional energies in crystals and helices

It is shown that the quadrature derivatives in some analytical gradients of energies evaluated with a multi-centre radial-angular grid do not vanish even in the limit of an infinitely dense grid, causing severe errors when neglected. The gradients in question are those with respect to a lattice constant of a crystal or to the helical angle of a chain with screw axis symmetry. Furthermore, this is in contrast with the quadrature derivatives in atomic gradients, which can be made arbitrarily small by grid extension. The disparate behaviour is traced to whether the grid points depend on the coordinate with respect to which the derivative of energy is taken. Whereas the nonvanishing quadrature derivative in the lattice-constant gradient is identified as the surface integral arising from an expanding integration domain, the analytical origin of the nonvanishing quadrature derivative in the helical-angle gradient remains unknown.

74 ATOMIC AND MOLECULAR PHYSICS↗

Multiscale Computer Simulation of Failure in Aerogels

Aerogels have been of interest to the aerospace community primarily for their thermal properties, notably their low thermal conductivities. While such gels are typically fragile, recent advances in the application of conformal polymer layers to these gels has made them potentially useful as lightweight structural materials as well. We have previously performed computer simulations of aerogel thermal conductivity and tensile and compressive failure, with results that are in qualitative, and sometimes quantitative, agreement with experiment. However, recent experiments in our laboratory suggest that gels having similar densities may exhibit substantially different properties. In this work, we extend our original diffusion limited cluster aggregation (DLCA) model for gel structure to incorporate additional variation in DLCA simulation parameters, with the aim of producing DLCA clusters of similar densities that nevertheless have different fractal dimension and secondary particle coordination. We perform particle statics simulations of gel strain on these clusters, and consider the effects of differing DLCA simulation conditions, and the resultant differences in fractal dimension and coordination, on gel strain properties.

Good, Brian S.↗

Co(salen)-Catalyzed Oxidation of Lignin Models to Form Benzoquinones and Benzaldehydes: A Computational and Experimental Study

Lignin is a highly abundant polyphenolic polymer that imparts mechanical strength to plant biomass. Transition-metal complexes can catalyze lignin oxidation to produce value-added products, but low catalytic efficiency has hampered their use in industry. Identifying the chemical and structural factors that govern catalytic activity is a prerequisite to rational design of catalysts with improved activity. In this study, we combine computational and experimental approaches to investigate the mechanism of Co(salen)-catalyzed oxidation of the monomeric lignin models syringyl (S), vanillyl (G), and 4-hydroxybenzyl alcohol (H) to produce benzoquinone and benzaldehyde products. Experimentally, S oxidation to form dimethoxybenzoquinone proceeded efficiently with a Co(salen) catalyst coordinated by a pyridine ligand, but G and H did not undergo oxidation. Density functional theory calculations reveal that catalyst regeneration is energetically unfavorable in the presence of H, which prevents oxidation. In contrast, S readily facilitates catalyst regeneration. Formation of methoxybenzoquinone from G was achieved experimentally by adding bulky, noncoordinating bases. These findings provide a fundamental baseline for enhancing the activity of Co-Schiff base catalysts toward lignin-like molecules by adding sterically hindered nitrogenous bases or potentially by including a cocatalyst that promotes catalyst regeneration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Composite Nozzle/Thrust Chambers Analyzed for Low-Cost Boosters

The Low Cost Booster Technology Program is an initiative to minimize the cost of future liquid engines by using advanced materials and innovative designs, and by reducing engine complexity. NASA Marshall Space Flight Center s 60K FASTRAC Engine is one example where these design philosophies have been put into practice. This engine burns a liquid kerosene/oxygen mixture. It uses a one-piece, polymer composite thrust chamber/nozzle that is constructed of a tape-wrapped silica phenolic liner, a metallic injector interface ring, and a filament-wound epoxy overwrap. A cooperative effort between NASA Lewis Research Center s Structures Division and Marshall is underway to perform a finite element analysis of the FASTRAC chamber/nozzle under all the loading and environmental conditions that it will experience during its lifetime. The chamber/nozzle is a complex composite structure. Of its three different materials, the two composite components have distinctly different fiber architectures and, consequently, require separate material model descriptions. Since the liner is tape wrapped, it is orthotropic in the nozzle global coordinates; and since the overwrap is filament wound, it is treated as a monoclinic material. Furthermore, the wind angle on the overwrap varies continuously along the length of the chamber/nozzle.

Sullivan, Roy M.↗

Control of Excitonic Energy Transfer in RGB Quantum Dot:Polymer Composites for Tunable White Emission

Tint-controlled white light is crucial for both illumination systems and display applications. Here, in this study, we demonstrate solution-processed quantum-dot light-emitting diodes (QD-LEDs) featuring a red–green–blue (RGB) QD–poly(methyl methacrylate) (PMMA) composite emissive layer (EML) for tunable white electroluminescence (EL). In this composite EML, PMMA functions as a dispersion matrix that modulates the interdot spacing (d), thereby controlling Förster resonance energy transfer (FRET) between QDs. By adjustment of the PMMA content, the balance of R, G, and B emissions is controlled, enabling systematic and continuous tuning of the EL color from greenish to reddish white at a fixed RGB ratio and constant driving bias. Time-resolved photoluminescence measurements confirm that the variation in the exciton lifetime with the PMMA fraction is the primary factor for tuning the EL color. Notably, nearly pure white EL with CIE coordinates close to (0.33, 0.33) is achieved using a diluted PMMA matrix without significant degradation of the electrical properties. Our results demonstrate d as an independent design parameter for decoupling color tuning from RGB composition and electrical operation, providing a versatile design framework for high-quality white- or tint-controlled QD-LEDs toward advanced solid-state lighting and display technologies.

36 MATERIALS SCIENCE↗

Underlying Roles of Polyol Additives in Promoting CO2 Capture in PEI/Silica Adsorbents

Solid-supported amines having low molecular weight branched poly(ethylenimine) (PEI) physically impregnated into porous solid supports are promising adsorbents for CO2 capture. Co-impregnating short-chain poly(ethylene glycol) (PEG) together with PEI alters the performance of the adsorbent, delivering improved amine efficiency (AE, mol CO2 sorbed / mol N) and faster CO2 uptake rates. To uncover the physical basis for this improved gas capture performance, we probed the distribution and mobility of the polymers in the pores via small angle neutron scattering (SANS), solid-state NMR, and molecular dynamic (MD) simulation studies. SANS and MD simulations reveal that PEG displaces wall-bound PEI, making amines more accessible for CO2 sorption. Solid-state NMR and MD simulation suggest intercalation of PEG into PEI domains, separating PEI domains and reducing amine-amine interactions, providing potential PEG-rich and amine-poor interfacial domains that bind CO2 weakly via physisorption while providing facile pathways for CO2 diffusion. Contrary to a prior literature hypothesis, no evidence is obtained for PEG facilitating PEI mobility in solid supports. Instead, the data suggest that PEG chains coordinate to PEI, form larger bodies with reduced mobility compared to PEI alone. We also demonstrate promising CO2 uptake and desorption kinetics at varied temperatures, given by favorable amine distribution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Visualizing and analyzing 3D biomolecular structures using Mol* at RCSB.org: Influenza A H5N1 virus proteome case study

The easiest and often most useful way to work with experimentally determined or computationally predicted structures of biomolecules is by viewing their three-dimensional (3D) shapes using a molecular visualization tool. Mol* was collaboratively developed by RCSB Protein Data Bank (RCSB PDB, RCSB.org) and Protein Data Bank in Europe (PDBe, PDBe.org) as an open-source, web-based, 3D visualization software suite for examination and analyses of biostructures. It is capable of displaying atomic coordinates and related experimental data of biomolecular structures together with a variety of annotations, facilitating basic and applied research, training, education, and information dissemination. Across RCSB.org, the RCSB PDB research-focused web portal, Mol* has been implemented to support single-mouse-click atomic-level visualization of biomolecules (e.g., proteins, nucleic acids, carbohydrates) with bound cofactors, small-molecule ligands, ions, water molecules, or other macromolecules. RCSB.org Mol* can seamlessly display 3D structures from various sources, allowing structure interrogation, superimposition, and comparison. Using influenza A H5N1 virus as a topical case study of an important pathogen, we exemplify how Mol* has been embedded within various RCSB.org tools—allowing users to view polymer sequence and structure-based annotations integrated from trusted bioinformatics data resources, assess patterns and trends in groups of structures, and view structures of any size and compositional complexity. In addition to being linked to every experimentally determined biostructure and Computed Structure Model made available at RCSB.org, Standalone Mol* is freely available for visualizing any atomic-level or multi-scale biostructure at rcsb.org/3d-view.

3D biostructure↗

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

Here, we analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call “complexity reduction”. In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature T g of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2–6 nm at T g . Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

cancer↗

Amino‐Functionalised Hybrid Ultramicroporous Materials that Enable Single‐Step Ethylene Purification from a Ternary Mixture

Abstract Pyrazine‐linked hybrid ultramicroporous (pore size <7 Å) materials (HUMs) offer benchmark performance for trace carbon capture thanks to strong selectivity for CO 2 over small gas molecules, including light hydrocarbons. That the prototypal pyrazine‐linked HUMs are amenable to crystal engineering has enabled second generation HUMs to supersede the performance of the parent HUM, SIFSIX‐3‐Zn , mainly through substitution of the metal and/or the inorganic pillar. Herein, we report that two isostructural aminopyrazine‐linked HUMs, MFSIX‐17‐Ni (17=aminopyrazine; M=Si, Ti), which we had anticipated would offer even stronger affinity for CO 2 than their pyrazine analogs, unexpectedly exhibit reduced CO 2 affinity but enhanced C 2 H 2 affinity. MFSIX‐17‐Ni are consequently the first physisorbents that enable single‐step production of polymer‐grade ethylene (>99.95 % for SIFSIX‐17‐Ni ) from a ternary equimolar mixture of ethylene, acetylene and CO 2 thanks to coadsorption of the latter two gases. We attribute this performance to the very different binding sites in MFSIX‐17‐Ni versus SIFSIX‐3‐Zn .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Long Duration Exposure Facility (LDEF) experiment M0003 meteoroid and debris survey

A survey of the meteoroid and space debris impacts on LDEF experiment M0003 was performed. The purpose of this survey was to document significant impact phenomenology and to obtain impact crater data for comparison to current space debris and micrometeoroid models. The survey consists of the following: photomicrographs of significant impacts in a variety of material types; accurate measurements of impact crater coordinates and dimensions for selected experiment surfaces; and databasing of the crater data for reduction, manipulation, and comparison to models. Large area surfaces that were studied include the experiment power and data system (EPDS) sunshields, environment exposure control canister (EECC) sunshields, and the M0003 signal conditioning unit (SCU) covers. Crater diameters down to 25 microns were measured and cataloged. Both leading (D8) and trailing (D4) edge surfaces were studied and compared. The EPDS sunshields are aluminum panels painted with Chemglaze A-276 white thermal control paint, the EECC sunshields are chromic acid-anodized aluminum, and the SCU covers are aluminum painted with S13GLO white thermal control paint. Typical materials that have documented impacts are metals, glasses and ceramics, composites, polymers, electronic materials, and paints. The results of this survey demonstrate the different response of materials to hypervelocity impacts. Comparison of the survey data to curves derived from the Kessler debris model and the Cour-Palais micrometeoroid model indicates that these models overpredict small impacts (less than 100 micron) and may underpredict large impacts (greater than 1000 micron) while having fair to good agreement for the intermediate impacts. Comparison of the impact distributions among the various surfaces indicates significant variations, which may be a function of material response effects, or in some cases surface roughness. Representative photographs and summary graphs of the impact data are presented.

Meshishnek, M. J.↗

Mechanistic studies of polymeric samples exposed aboard STS 8

The early Shuttle flights and the attendant opportunity to deploy material samples to the near-Earth space environment, along well-defined trajectories and accompanied by detailed characterization of these samples prior to and following the flight exposure, have brought to light several novel phenomena associated with interaction of these materials with the space environment. JPL, in coordination with other NASA Centers, has carried out a research program to study the degradation and oxidation processes caused by interaction of these materials with atomic oxygen at an energy of 5 eV. In addition, energetic atomic oxygen is believed to be responsible for the shuttle glow first observed during the flight of STS-3. The shuttle glow phenomenon has been extensively studied and modeled because of its long-range potential impact on optical communication schemes and its more immediate impact on the Space Telescope. This report summarizes the results of certian material degradation and erosion experiments carried out aboard STS-8 between August 30, 1983 and September 5, 1983. Based on these data, a generic degradation model has been developed for common structural polymers.

Liang, Ranty H.↗

Unraveling Reactivity Differences: Room-Temperature Ring-Opening Metathesis Polymerization (ROMP) versus Frontal ROMP

Here, in this study, we explore the distinct reactivity patterns between frontal ring-opening metathesis polymerization (FROMP) and room-temperature solventless ring-opening metathesis polymerization (ROMP). Despite their shared mechanism, we find that FROMP is less sensitive to inhibitor concentration than room-temperature ROMP. By increasing the initiator-to-monomer ratio for a fixed inhibitor/initiator quantity, we find reduction in the ROMP background reactivity at room temperature (i.e., increased resin pot life). At elevated temperatures where inhibitor dissociation prevails, accelerated frontal polymerization rates are observed because of the concentrated presence of the initiator. Surprisingly, the strategy of employing higher initiator loading enhances both pot life and front speeds, which leads to FROMP rates exceeding prior reported values by over 5 times. This counterintuitive behavior is attributed to an increase in the proximity of the inhibitor to the initiator within the bulk resin and to whether the temperature favors coordination or dissociation of the inhibitor. A rapid method was developed for assessing resin pot life, and a straightforward model for active initiator behavior was established. Modified resin systems enabled direct ink writing of robust thermoset structures at rates much faster than previously possible.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

New Anti-Corrosive Coatings with Resin-Bonded Polyaniline and Related Electroactive Groups

It is already known that polyaniline (an electroactive polymer) functions as a corrosion inhibitor for steel and in view of the fact that it is known to perform in the presence of hydrochloric acid, it has been considered likely that it may be useful to NASA for protecting launch structures at KSC which are exposed to not only continual ocean-side salt spray but also to hydrochloric acid at the times that solid-fuel boosters are fired. The currently used zinc-rich silicate-bonded coating is not wholly protective against the hydrochloric acid. Water pollution from zinc salts is another concern. Other earlier and concurrent NASA sponsored projects have been focussed on polyaniline specifically. Our project, administered for NASA by Dr. K. Thompson of KSC and these more-specifically polyaniline-related projects are included in a CRADA coordinated by Dr. F. Via of Akzo Nobel. A parallel project at Polytechnic under Prof K. Levon concentrated more specifically on polyaniline with various dopants. Our exploratory project reported herein was aimed at broadening the range of such corrosion inhibitors, to give protective paint compounders a wider latitude for adding corrosion inhibitors having polyaniline-like performance, and thus we diverged in several probing directions from polyaniline. Our working hypothesis was that physical variants of polyaniline, such as supported formulations on pigments or carriers, and chemical variants of polyaniline, including those having no electroconductive character, may have enhanced anticorrosion activity. We also hypothesized that small (non-polymeric) molecules having structures related to those occurring in polyaniline, may be active as corrosion inhibitors. We did preliminary testing, using an ASTM salt spray method at a nearby commercial paint testing laboratory. Our most interesting findings were that a non-electroconductive meta-isomer of polyaniline showed some corrosion activity, suggesting that the features of the polyaniline molecule associated with conductivity are not necessary for the anticorrosion action. Also, signtficantly, small molecular weight aromatic diamines and diimines resembling the reduced and the oxidized repeating unit in polyaniline showed an interesting degree of anticorrosive activity, suggesting that the polymeric feature of polyaniline is not necessary for anticorrosion action.

Weil, Edward D.↗

Developing Procedures to Implement Geometric Imperfections Beyond Right Circular Cylindrical Shells in Finite Element Method Models

Analysis of aerospace structures is frequently conducted using nominal dimensions and frequently assumes ideal conditions in loading, contact, constraints, et cetera. Off-nominal dimensions and nonideal conditions, however, are present in all structures. These are the result of widely ranging causes from coefficient of thermal expansion mismatches, manufacturing tooling anomalies, to assembly procedures that inadvertently alter the structure. Specifically, geometric imperfections can have potentially significant influence on the response of a structural test article observed in an experiment versus the response given by a numerical simulation. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS) was previously presented as a set of Python scripts to calculate and implement as-manufactured geometric midsurface and thickness imperfections into finite element method (FEM) shell models of nominally right circular cylinders. By taking advantage of the simple shape of a right circular cylinder, interpolations of the measured data points were able to be performed along directions that aligned to the cylindrical coordinate system axes of the entire structure. By taking advantage of the shell representation of the real structure as opposed to modeling using a continuum representation, the thickness variation was able to be implemented by shell section definitions instead of having to modify the position of multiple nodes in the thickness direction. Py_TIGIRS is a useful tool that established a procedural example on how to implement geometric imperfections in right circular cylindrical shell structures. Three new procedures, each expanded from concepts established in Py_TIGIRS, are proposed for various test-article designs and are intended to broaden the range of structures that can be modeled with measured geometric imperfections in the structural analysis community. Each test-article design introduces new challenges to successfully implement geometric imperfections into a FEM model. The first test-article design consists of a carbon fiber reinforced polymer square plate with a hat-shaped stiffener co-cured on one side. This test-article design was for a novel seven-point bend test that was also previously presented. Manufacturing and cure-cycle imperfections are observed using digital image correlation (DIC) techniques. As thermal expansion coefficient mismatches between the plate and stiffener materials were anticipated, a thermal analysis study with continuum shell and solid elements was conducted to capture the global shape observed prior to testing. The second test-article design is of a similar hat-stiffened plate configuration, but with a side length ratio near 3:1 with elongation in the stiffener direction. The test article was used to characterize the response to uniaxial compressive loading in the direction of the stiffener. Due to differing manufacturing steps, a thermal analysis like the one developed for the seven-point bend configuration was unable to mimic the observed geometric imperfections. Instead, a strategy based on applying deformations directly to the structure during analysis was developed for continuum shell and solid element representation of a stiffened panel.

Geometric imperfections↗