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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Streamlined Loads Analysis of Floating Wind Turbines With Fiber Rope Mooring Lines

This paper presents an approach for more accurate yet relatively streamlined accounting for the nonlinear characteristics of synthetic fiber rope mooring lines for floating wind turbines. First, we select a minimal set of parameters that can efficiently approximate a mooring line material's quasi-static and dynamic stiffness characteristics. We also develop a set of baseline coefficients for different rope materials based on published product information and research papers. We then expand a quasi-static mooring model to include dynamic mooring line stiffness terms in a way that allows the nonlinear stiffness behavior of fiber ropes to be considered even in quasi-static analyses. For dynamic analysis, we have updated the model MoorDyn, coupled with OpenFAST, to work with the new dynamic mooring line stiffness terms. This includes the implementation of a new viscoelastic approach that allows the tension-strain relation of each mooring line segment to vary between two stiffness values, depending on the strain rate. After presenting the formulation of the approaches for modeling synthetic ropes, they are demonstrated on a floating wind turbine mooring system with taut polyester rope mooring lines. The results are compared with those of other approaches of similar fidelity, including the static-dynamic method and separate simulations with static and dynamic stiffness values. Comparing the results shows the ability of the new method to match the results of the previous methods in a more streamlined manner.

elasticity↗
DOE OSTI2026

Additively Reinforced Thermoformable PETG Composite Sheets for Improved Structural Efficiency

Thermoforming of short-fiber reinforced thermoplastic sheets offers a viable pathway for producing lightweight composite components; however, inherent anisotropy in fiber-reinforced sheets can limit structural performance under multidirectional loading. In this work, short carbon fiber, glass fiber, and hybrid fiber–reinforced PETG sheets were evaluated as candidate feedstock materials for thermoforming, with flexural and tensile testing performed both along the primary fiber direction and in the off-axis orientation to establish baseline stiffness, strength, and anisotropy. As expected, short carbon fiber PETG exhibited the highest stiffness and strength in the primary fiber direction, while all systems showed reduced performance in the off-axis direction. This off-axis performance reduction provides clear justification for the use of additive reinforcement when such thermoformed sheets are intended for structural applications. The intended manufacturing sequence involves thermoforming the reinforced sheet first, followed by the application of additively manufactured lattice reinforcement; therefore, the reinforcement strategy does not impose limitations on sheet formability during thermoforming. Post-forming lattice reinforcement significantly reduced load-normalized displacement by approximately 95–99% relative to non-reinforced sheets and improved weight-normalized stiffness by ~70%. These findings demonstrate that geometry-driven additive reinforcement can effectively compensate for off-axis property reductions in thermoformed PETG composites, enabling enhanced multidirectional structural performance without compromising manufacturability.

Talabi, Isaac [ORNL] (ORCID:0000000340215594)↗
DOE OSTI2024

Monotonic testing of single shear-plane CLT-to-CLT joint with hardwood dowels

Reducing embodied carbon emissions in buildings and striving for carbon neutrality through sustainable design has become a primary goal in the construction industry. The industry is expanding its use of wood-engineered products, such as cross-laminated timber (CLT) to achieve those sustainability goals. Furthermore, replacing steel fasteners with lower embodied carbon alternatives is gaining increased attention in timber engineering. This paper aims to quantify the mechanical behavior of single shear-plane CLT-to-CLT joints using hardwood dowels. The study includes 154 single shear-plane experimental tests with four different CLT species, two hardwood dowel species, and two dowel diameters. Further, the test specimens were subjected to cyclic and monotonic loading until failure, and mechanical properties such as yielding and ultimate strength, serviceability and yielding stiffness, and ductility were quantified. The hardwood dowel CLT-to-CLT joints demonstrated high strength with up to 10.3 kN (2.3 kips) capacity per dowel and lateral stiffness of up to 5.2 kN/mm (30.8 k/in) per dowel. This strength and stiffness are roughly equivalent to or exceed values for mass timber wood screws, making hardwood dowels a good alternative. In addition, the observed mean ductility of joints ranged from 2.4 to 4.5. Finally, analytical equations for the joints' yielding strength, lateral serviceability stiffness, and yielding stiffness were derived with non-linear regression analysis and validated using the experimental test results.

42 ENGINEERING↗
DOE OSTI2021

Recent advances in the mechanical characterization of shales at nano-to micro-scales: A review

Understanding geomechanical properties of shales, such as stiffness properties and fracture toughness, is important in different areas of petroleum industry-related activities. Nanoscale to microscale experiments on shale samples require a much smaller sample compared to macroscale experiments. This is a major advantage because irregularly-shaped drill cuttings from shales can be used for experimental analyses, such as nanoindentation or atomic force microscopy (AFM). However, characterization of mechanical properties at the nano- to micro-scale is a relatively new addition to classical geomechanical experiments on shales, and there is still a lack of both fundamental knowledge and standard procedures for conducting experiments at this scale. The theoretical principles of nanoindentation-based (Gridded Nanoindentation and Modulus Mapping) and AFM-based experimental methods (PeakForce QNMTM and AFM-IR), a review of the literature results and the major findings are explained in Sections 2 and 3, respectively. These experimental techniques are compared in Section 4. Overall, nanoindentation experiments reveal the anisotropy of organic matter (OM)-rich shales at the nanoscale, and it is shown that gridded nanoindentation is capable of characterizing different minerals with respect to their stiffness properties. The capability of AFM (PeakForce QNMTM) to differentiate between different minerals within OM-rich shales with distinct mechanical properties, in particular stiffness, is also demonstrated. It is shown that AFM-based methods are more straightforward than gridded-nanoindentation to characterize OM-rich shales based on the stiffness of different constituent minerals of OM-rich shales, but nanoindentation can apply higher loads than AFM-based methods. Therefore, they can measure creep properties and fracture toughness of OM-rich shales. Here, it is shown that the OM is the most compliant part of the OM-rich shales, but it is still unclear if thermal maturation has an impact on the stiffness of OM. It is necessary to investigate if there is a relationship between the OM type (kerogen, bitumen, etc.) and mechanical properties such as Young’s modulus and Creep rate.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Regulating hydrogel mechanical properties with an electric field

Stimuli-responsive polymeric materials have attracted significant attention due to their ability to change properties in response to various external stimuli. Using an electric field as the stimulus is of particular interest as it possesses the potential for seamless integration of materials with electronic systems. While many materials with electric field responsive actuation have an associated mechanical property change, it is beneficial to develop materials that exhibit mechanical property changes without accompanying significant shape deformation. To address this challenge, here we designed a semi-interpenetrating polymer network (semi-IPN) hydrogel system containing both polyelectrolytes and salt ions, which enables electric field induced changes in mechanical properties while minimizing actuation. We first successfully verified the viability of our design by removing salt ions through a diffusion-only method where we witnessed the stiffness increased to 4.5 times the initial value while still being highly deformable. After this, we applied an electric field to transport the salt ions out of the hydrogel, as shown by both Raman spectroscopy and scanning electron microscopy. We were able to show a time-dependent stiffness increase, the maximum of which was 5 times the original stiffness. We quantified ion transport and water-splitting in the hydrogel by both experiments and simulations. Following this, we showed functional system reversibility by reversing the direction of the current to reinject salt ions into the semi-IPN hydrogel and reducing its stiffness to below the initial value. It's worth noting that our simulations enable us to understand the governing mechanisms behind ion generation and salt transport that leads to mechanical property changes. Finally, we were able to fabricate a spatially variable stiffness haptic interface with our hydrogel, with demonstrated reversibility and cyclability. This research can possibly find applications in soft robotics and haptics and also inspire the development of bio-compatible electronics related devices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Effect of inversion asymmetry on the superconducting and exciton condensates of bilayer graphene

Inversion asymmetry in bilayer graphene can be tuned by the displacement field. As a result, the band dispersion in biased bilayer graphene acquires flatband regions near the Dirac points along with a nontrivial band geometry. We analyze the effect of inversion asymmetry on the critical temperature and superfluid stiffness of the superconducting state of AB-stacked graphene bilayer and the exciton condensate in double layers formed by two AB-stacked graphene bilayers. We find that the geometric superfluid stiffness in bilayer graphene superconductors is negligible due to the small superconducting gap. Furthermore, since the geometric superfluid stiffness is maximized for a constant order parameter, it can be neglected in biased bilayer graphene superconductors with any pairing symmetry. In contrast, the displacement field enhances the geometric superfluid stiffness in exciton condensates. It is most prominent at low densities and high displacement fields. Here, a consequence of the geometric superfluid stiffness is a modest enhancement of the Berezinskii-Kosterlitz-Thouless transition temperature in bilayer graphene’s exciton condensate.

BKT transition↗
DOE OSTI2022

Effective design of vibro-impact energy harvesting absorbers with asymmetric stoppers

We report that an investigation is carried out for the purpose of simultaneously controlling a base-excited dynamical system and enhancing the effectiveness of a piezoelectric energy harvesting absorber. Amplitude absorbers are included to improve the energy harvested by the absorber with the possibility of activating broadband resonant regions to increase the operable range of the absorber. This study optimizes the stoppers’ ability for the energy harvesting absorber to generate energy by investigating asymmetric gap and stiffness configurations. Medium stiffnesses of 5 x 10 4 N/m and 1 x 10 5 N/m show significant impact on the primary system’s dynamics and improvement in the level of the harvested power for the absorber. A solo stopper configuration when the gap distance is 0.02m improves 29% in peak power and 9% in average power over the symmetrical case. Additionally, an asymmetric stiffness configuration when one of the stiffnesses is 1 x 10 5 N/m and a gap size of 0.02m indicates an improvement of 25% and 8% for peak and average harvested power, respectively, and the second stopper’s stiffness is 5 x 10 3 N/m. Hard stopper configurations shows improvements with both asymmetric cases, but not enough improvements to outperform the system without amplitude stoppers.

42 ENGINEERING↗
DOE OSTI2026

Mechanically graded granular scaffolds for osteochondral tissue engineering

Engineered scaffolds designed to approximate the mechanical microenvironment of the osteochondral unit often address this complexity using discrete, two-phase architectures that introduce mechanical discontinuities and interfacial stress concentrations rather than a contiguous stiffness transition. To address this challenge, we created a photoannealed polyethylene glycol (PEG) granular scaffold with a spatially controlled stiffness gradient within a cell-permissive, macroporous architecture. Stiffness was dictated by photoannealing microgels using a photomask. We tuned void volume and available surface area by varying microgel diameter and tested how mesenchymal stromal cells (MSCs) interpret local mechanical environments. MSCs exhibited position-dependent differences in morphology, cytoskeletal structure, matrix deposition, and lineage-specific gene expression within the gradient scaffolds. Softer regions supported rounded cell morphology and deposition of a glycosaminoglycan-rich matrix, whereas stiffer regions promoted cell elongation, increased cytoskeletal tension, and expression of mineral-associated markers. Gradients formed from smaller microgels magnified these spatial responses by increasing cellular confinement and adhesion site availability. Disruption of actomyosin contractility eliminated these regional differences, demonstrating that MSCs rely on tension-dependent mechanotransduction to interpret the gradient. These findings reveal that coupling microgel architecture with continuous stiffness transitions provides a tractable platform to study multiscale mechanobiologic regulation and spatially guide osteochondral tissue formation.

Biological and medical sciences↗
DOE OSTI2024

Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation

Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat multiscale equations that contain a stiff part and a non-stiff part, where the stiff part is characterized by a small parameter. Here, in this work, we prove rigorously the uniform stability and uniform accuracy of a class of IMEX-RK schemes for a linear hyperbolic system with stiff relaxation. The result we obtain is optimal in the sense that it holds regardless of the value of and the order of accuracy is the same as the design order of the original scheme, i.e., there is no order reduction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Intermittent supplementation with fisetin improves arterial function in old mice by decreasing cellular senescence

Cellular senescence and the senescence-associated secretory phenotype (SASP) contribute to age-related arterial dysfunction, in part, by promoting oxidative stress and inflammation, which reduce the bioavailability of the vasodilatory molecule nitric oxide (NO). In the present study, we assessed the efficacy of fisetin, a natural compound, as a senolytic to reduce vascular cell senescence and SASP factors and improve arterial function in old mice. We found that fisetin decreased cellular senescence in human endothelial cell culture. In old mice, vascular cell senescence and SASP-related inflammation were lower 1 week after the final dose of oral intermittent (1 week on—2 weeks off—1 weeks on dosing) fisetin supplementation. Old fisetin-supplemented mice had higher endothelial function. Leveraging old p16-3MR mice, a transgenic model allowing genetic clearance of p16 INK4A -positive senescent cells, we found that ex vivo removal of senescent cells from arteries isolated from vehicle- but not fisetin-treated mice increased endothelium-dependent dilation, demonstrating that fisetin improved endothelial function through senolysis. Enhanced endothelial function with fisetin was mediated by increased NO bioavailability and reduced cellular- and mitochondrial-related oxidative stress. Arterial stiffness was lower in fisetin-treated mice. Ex vivo genetic senolysis in aorta rings from p16-3MR mice did not further reduce mechanical wall stiffness in fisetin-treated mice, demonstrating lower arterial stiffness after fisetin was due to senolysis. Lower arterial stiffness with fisetin was accompanied by favorable arterial wall remodeling. The findings from this study identify fisetin as promising therapy for clinical translation to target excess cell senescence to treat age-related arterial dysfunction.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Hydrokinetic Power Conversion Using Vortex-Induced Oscillation with Cubic Restoring Force

A cubic-spring restoring function with high-deformation stiffening is introduced to passively improve the harnessed marine hydrokinetic power by using flow-induced oscillations/vibrations (FIO/V) of a cylinder. In these FIO/V experiments, a smooth, rigid, single-cylinder on elastic end-supports is tested at Reynolds numbers ranging from 24,000 < Re < 120,000. The parameters of the tested current energy converter (CEC) are cubic stiffness and linear damping. Using the second generation of digital virtual spring-damping (Vck) controller developed by the Marine Renewable Energy Laboratory (MRELab), the cubic modeling of the oscillator stiffness is tested. Experimental results show the influence of the parameter variation on the amplitude, frequency, energy conversion, energy efficiency, and power of the converter. All experiments are conducted in the low turbulence-free surface water (LTFSW) channel of the MRELab of the University of Michigan. The main conclusions are: (1) The nonlinearity in the cubic oscillator is an effective way to extend the vortex-induced vibration (VIV) upper branch, which results in higher harnessing power and efficiency compared to the linear stiffness cylinder converter. (2) Compared to the linear converter, the overall power increase is substantial. The nonlinear power optimum, occurring at the end of the VIV upper branch, is 63% higher than its linear counterpart. (3) The cubic stiffness converter with low harnessing damping achieves consistently good performance in all the VIV regions because of the hardening restoring force, especially at higher flow velocity.

13 HYDRO ENERGY↗
DOE OSTI2025

Toward engineering lattice structures with the material point method (MPM)

This study examines the potential of two variants of the material point method—the generalized interpolation material point (GIMP) and dual domain material point (DDMP) methods—in developing a robust computational framework for engineering lattice structures under different loading conditions. The study begins with assessing the ability of the two methods in predicting elastic buckling phenomena using column geometries with and without initial geometric imperfections. The results indicate that both methods effectively capture buckling phenomena when initial geometric imperfections are introduced. After this verification step, we create several models of tetrahedral lattice structures with varying strut diameter and orientation and subject them to quasi-static loading. We then validate the numerical results using laboratory test results. The results show that, while both methods accurately predict load–displacement curves in the pre-buckling regime, their predictive capabilities diminish in the post-buckling regime. Through visual comparison between the numerical and experimental deformed shapes, it appears that the discrepancies between model and experimental results are attributed to initial geometric imperfections in the lattices that occurred during 3D printing. We then establish a second set of lattice models where different types of initial geometric imperfections are considered. The results from these models show that imperfections have a negligible influence in the pre-buckling regime but affect the behavior considerably in the post-buckling regime. As a final step in this work, we subject the lattice models to impact loading and employ hypothetical soft and stiff materials. These results show that the lattice stiffness, which depends on material stiffness, strut diameter, and orientation, significantly influences the ability of a lattice structure to resist impact. In particular, we find that a stiffer lattice (i.e., one made with a stiff material and thicker struts) is capable of absorbing more energy than a softer one during impact. Although material nonlinearities, inelasticity, and detailed contact formulations are not considered in this study, the findings obtained herein lay the groundwork for engineering lattice structures under extreme loading conditions through a simulation-driven framework based on particle-based methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Nonlinear viscoelastic response of silicone additively manufactured direct ink write (DIW) foams under repetitive compression

To investigate dynamic fatigue behavior of foam in military protective applications, such as helmets, additively manufactured (AM) foams were compressively strained into the plateau region using a reduced design of experiments. A simple power law was found to govern the decline in dynamic stiffness (complex modulus) as the foams underwent the purchase order requirement of 10,000 cycles of small deformation in the plateau region. This rate of decline was newly found to correlate with the degree of nonlinearity in the material’s deformation, quantified using total harmonic distortion. Materials with low nonlinearity exhibited relatively stable stiffness across cycles, while those with high nonlinearity experienced greater losses. The observed nonlinearity depended on both applied stress and strain rate. A strong linear correlation (R 2 = 0.78) was identified between second-order nonlinearity and the time-dependent stiffness response. Two lattice structures were examined: face-centered tetragonal (FCT) and simple cubic (SC). The SC material exhibited higher total harmonic distortion (5%) and lower stiffness retention than the FCT (2%). In conclusion, these results suggest that for cyclic compression applications in a wide variety of industries such as packaging, personal protective equipment, or aerospace, selecting materials with lower stress and greater structural uniformity can enhance the stability of dynamic performance.

42 ENGINEERING↗
DOE OSTI2023

Nonlinear analysis and vibro-impact characteristics of a shaft-bearing assembly

Here this study investigates the nonlinear frequency response of a shaft-bearing assembly with vibro-impacts occurring at the bearing clearances. The formation of nonlinear behavior as system parameters change is examined, along with the effects of asymmetries in the nominal, inherently symmetric system. The primary effect of increasing the forcing magnitude or decreasing the contact gap sizes is the formation of grazing-induced chaotic solution branches occurring over a wide frequency range near each system resonance. The system's nominal setup has very hard contact stiffness and shows no evidence of isolas or superharmonic resonances over the frequency ranges of interest. Moderate contact stiffnesses cause symmetry breaking and introduce superharmonic resonance branches of primary resonances. Even if some primary resonances are not present due to the system's inherent symmetry, their superharmonic resonances still manifest. Branches of quasiperiodic isolas (isolated resonance branches) are also discovered, along with a cloud of isolas near a high-frequency resonance. Parameter asymmetries are found to produce a few significant changes in behavior: asymmetric linear stiffness, contact stiffness, and gap size could affect the behavior of primary resonant frequencies and isolas.

42 ENGINEERING↗
DOE OSTI2023

Efficacy of vibro-impact energy harvesting absorbers on controlling dynamical systems under vortex-induced vibrations and base excitation

Here this study investigates improving the efficacy of an energy harvesting absorber's ability to control a structure under vortex-induced vibrations, base excitation, and a combination of the two by including mechanical amplitude stoppers. The nonlinear reduced-order model is developed through modifying trilinear spring models to represent the impact forces, a modified van der Pol oscillator to represent the forcing due to the vortex-induced vibrations and using the Euler-Lagrange principle to express the equations of motion. It is seen that a soft stopper stiffness and a 5mm gap performs the most effectively of increasing the power generated from the absorber while still greatly reducing the primary structure's amplitude. By changing the stopper's location towards the middle of the energy harvesting absorber, the large effects of the impact forces are reduced and improves the efficacy of medium and hard stopper stiffnesses to generate near the amount of power the soft stopper does, while greatly improving the control of the primary structure. When the system is under combined loadings, the large oscillations of the synchronization region cause the effective configuration to be that of a 27.5 mm gap with soft stiffnesses. The results shows that medium stiffness stoppers with small gaps generate large aperiodic regions due to the high impact force. When the oscillations are close to the stoppers, the beating phenomenon is observed and is not overpowered by the vibro-impact force.

16 TIDAL AND WAVE POWER↗
DOE OSTI2021

Organotypic platform for studying cancer cell metastasis

Highlights: • Liver and brain slices can be stable, realistic in vitro 3D models. • Cell stiffness and adhesion to the tissue play determinant roles in cellular invasion in 3D. • MEK inhibitors can lead to increased cell stiffness and adhesion forces, and consequently reduced cancer cell invasion. • MDA-MB-231 breast cancer cells migrate faster and deeper into brain tissue compared to liver tissue. Metastasis is the leading cause of mortality in cancer patients. To migrate to distant sites, cancer cells would need to adapt their behaviour in response to different tissue environments. Thus, it is essential to study this process in models that can closely replicate the tumour microenvironment. Here, we evaluate the use of organotypic liver and brain slices to study cancer metastasis. Morphological and viability parameters of the slices were monitored daily over 3 days in culture to assess their stability as a realistic 3D tissue platform for in vitro metastatic assays. Using these slices, we evaluated the invasion of MDA-MB-231 breast cancer cells and of a subpopulation that was selected for increased motility. We show that the more aggressive invasion of the selected cells likely resulted not only from their lower stiffness, but also from their lower adhesion to the surrounding tissue. Different invasion patterns in the brain and liver slices were observed for both subpopulations. Cells migrated faster in the brain slices (with an amoeboid-like mode) compared to in the liver slices (where they migrated with mesenchymal or collective migration-like modes). Inhibition of the Ras/MAPK/ERK pathway increased cell stiffness and adhesion forces, which resulted in reduced invasiveness. These results illustrate the potential for organotypic tissue slices to more closely mimic in vivo conditions during cancer cell metastasis than most in vitro models.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Highly stretchable ionically crosslinked acrylate elastomers inspired by polyelectrolyte complexes

Dynamic bonds are a powerful approach to tailor the mechanical properties of elastomers and introduce shape-memory, self-healing, and recyclability. Among the library of dynamic crosslinks, electrostatic interactions among oppositely charged ions have been shown to enable tough and resilient elastomers and hydrogels. In this work, we investigate the mechanical properties of ionically crosslinked ethyl acrylate-based elastomers assembled from oppositely charged copolymers. Using both infrared and Raman spectroscopy, we confirm that ionic interactions are established among polymer chains. We find that the glass transition temperature of the complex is in between the two individual copolymers, while the complex demonstrates higher stiffness and more recovery, indicating that ionic bonds can strengthen and enhance recovery of these elastomers. We compare cycles to increasing strain levels at different strain rates, and hypothesize that at fast strain rates ionic bonds dynamically break and reform while entanglements do not have time to slip, and at slow strain rates ionic interactions are disrupted and these entanglements slip significantly. Further, we show that a higher ionic to neutral monomer ratio can increase the stiffness, but its effect on recovery is minimal. Lastly, taking advantage of the versatility of acrylates, ethyl acrylate is replaced with the more hydrophilic 2-hydroxyethyl acrylate, and the latter is shown to exhibit better recovery and self-healing at a cost of stiffness and strength. The design principles uncovered for these easy-to-manufacture polyelectrolyte complex-inspired bulk materials can be broadly applied to tailor elastomer stiffness, strength, inelastic recovery, and self-healing for various applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Reinforcement Learning-Based Approach for EMT Automation of Large-Scale PV Plants

In the pursuit of efficient and precise modeling of large-scale power systems, particularly utility-scale photovoltaic (PV) plants, Electromagnetic Transient (EMT) simulations play a crucial role. As utility-scale PV plants increase in size and complexity, traditional computational methods become inadequate, necessitating more advanced techniques. This paper highlights the progressive efforts made to accelerate EMT simulations. A novel continuous reinforcement learning (RL) strategy is explored to automate the differentiation and categorization of stiff and non-stiff differential algebraic equations (DAEs). The use of stiff and non-stiff integration methods applied to relevant parts of the DAEs assists with the speed-up of the simulations. The paper details the data acquisition, development and offline training of the RL model, leading to its validation that demonstrates a high precision in optimizing simulation methods. The proposed RL promises to significantly enhance the efficacy of EMT simulations, offering a robust framework for the future of power system analysis.

Xia, Qianxue↗