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Keywords = influence-domain discretization

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28 pages, 3975 KB  
Article
Melting Process of a Pure Material Confined Inside a Horizontal Rectangular Cavity in the Presence of Natural Convection: Numerical Investigation and Application to Thermal Energy Storage
by Larbi Mansouri, Ahmed Chellil, Salah Amroune, Amin Houari and Souad Benkherbache
Energies 2026, 19(14), 3398; https://doi.org/10.3390/en19143398 - 18 Jul 2026
Viewed by 215
Abstract
A two-dimensional dimensionless model is developed to investigate heat transfer during the melting of a pure phase change material (PCM) confined in a horizontal rectangular cavity. The model describes isothermal solid–liquid phase change in the presence of natural convection and is formulated using [...] Read more.
A two-dimensional dimensionless model is developed to investigate heat transfer during the melting of a pure phase change material (PCM) confined in a horizontal rectangular cavity. The model describes isothermal solid–liquid phase change in the presence of natural convection and is formulated using the momentum and energy conservation equations. To avoid explicit tracking of the moving solid–liquid interface, an enthalpy–porosity approach is employed, allowing the governing equations to be solved over the entire computational domain on a fixed grid. The finite volume method is used for spatial discretization, and a FORTRAN code based on the SIMPLER algorithm is implemented to simulate the melting process. Fluid motion in the solid region is suppressed through a porosity function linked to the local liquid fraction. After validation, a parametric analysis is performed to evaluate the effects of interpolation schemes, Fourier number, PCM subcooling, and liquid-phase superheating on melting dynamics and thermal energy storage. The results reveal that these parameters significantly influence melting behavior and storage performance. A predictive correlation for the dimensionless liquid volume during gallium melting is also proposed. Full article
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17 pages, 10797 KB  
Article
Nonlinear Dynamic Analysis of Drill-String System Coupling Rock Surface Morphology Evolution and Dry Friction Effect
by Pengfei Deng, Jinchao Zhang, Xiaofan Wang, Yiqiao Li, Luyuan Gong and Shengqiang Shen
Coatings 2026, 16(7), 774; https://doi.org/10.3390/coatings16070774 - 29 Jun 2026
Viewed by 269
Abstract
Stick–slip vibration, reversal, axial impact, and dynamic instability are major challenges in deep drilling operations and are closely associated with nonlinear bit–rock interaction. To investigate these phenomena, this study develops a nonlinear axial–torsional coupled dynamic model of a drill-string system by integrating rock [...] Read more.
Stick–slip vibration, reversal, axial impact, and dynamic instability are major challenges in deep drilling operations and are closely associated with nonlinear bit–rock interaction. To investigate these phenomena, this study develops a nonlinear axial–torsional coupled dynamic model of a drill-string system by integrating rock surface morphology evolution with a Stribeck dry friction model. The drill string is discretized into a distributed lumped-parameter model with coupled axial and torsional degrees of freedom. A surface morphology matrix is introduced to simulate the rock-cutting process, while the Stribeck friction model is employed to characterise the nonlinear frictional behaviour at the bit–rock interface. Time-domain simulations, bifurcation analysis, and frequency spectrum analysis are performed to investigate the dynamic responses of the system. The results indicate that rock surface morphology evolution significantly influences the contact conditions and frictional behaviour at the bit–rock interface, and together with dry friction induces transitions among steady-state, multi-periodic, and chaotic motions. Stick–slip vibration is accompanied by axial impact, bit bounce, and a reduction in the dominant torsional vibration frequency. In addition, variations in both driving and frictional parameters can trigger dynamic instability and state transitions. The proposed model provides an effective framework for analysing nonlinear drilling dynamics and offers theoretical guidance for drill-string vibration suppression, drilling parameter optimisation, and efficient drilling in complex formations. Full article
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28 pages, 2838 KB  
Article
Investigation of Thermally Induced Stiffness Variation and Its Aeroelastic Implications in Supersonic Flight
by Farhad Guliyev and Ali Öztürk
Appl. Sci. 2026, 16(12), 6027; https://doi.org/10.3390/app16126027 - 14 Jun 2026
Viewed by 274
Abstract
In this study, the influence of thermal loading in a supersonic flight environment on the mechanical stiffness of elastic structures and the corresponding aeroelastic stability limits is investigated analytically. Recognizing that elevated temperatures inherently alter constituent elastic properties, a temperature-dependent continuous elasticity framework [...] Read more.
In this study, the influence of thermal loading in a supersonic flight environment on the mechanical stiffness of elastic structures and the corresponding aeroelastic stability limits is investigated analytically. Recognizing that elevated temperatures inherently alter constituent elastic properties, a temperature-dependent continuous elasticity framework is incorporated directly into the governing differential operators of the structural domain. The macro-mechanical behavior of representative panel- and wing-type elements is modeled utilizing the Euler–Bernoulli beam formulation, while high-speed supersonic aerodynamic effects are represented through linearized first-order piston theory. The continuous spatial displacement fields are discretized by means of a modal expansion, and the coupled aeroelastic system is subsequently transformed into a finite set of dynamic state-space equations using the Ritz–Galerkin truncation method. The numerical and analytical outputs demonstrate that aerothermal softening not only induces continuous erosion in the material stiffness but also directly modulates the aeroelastic pole trajectories, thereby prematurely contracting the safe supersonic flight envelope. The primary novelty of the proposed framework lies in the derivation of explicit analytical expressions that directly map temperature-dependent stiffness variations onto supersonic aeroelastic instability boundaries. Because this approach is formulated in a generalized analytical form, it can be applied across diverse material systems, geometric profiles, and thermal conditions with reduced computational overhead compared to full fluid–structure interaction solvers, thereby providing a theoretical basis for preliminary stability assessment of supersonic aerospace configurations operating under high-temperature conditions. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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20 pages, 6571 KB  
Article
High-Resolution Site Characterization (HRSC) for Pollution Investigation of Petrochemical Enterprises: Integrated Technology Application and Validation
by Shuai Yang, Shucai Zhang, Jiahui Wu, Shici Ma and Xinzhe Wang
Sustainability 2026, 18(12), 5836; https://doi.org/10.3390/su18125836 - 8 Jun 2026
Viewed by 292
Abstract
High-Resolution Site Characterization (HRSC) offers a promising approach to delineate spatially heterogeneous contamination in complex petrochemical sites, overcoming limitations of conventional discrete sampling. This study implemented an integrated HRSC framework combining surface soil microbial metabolic gas/functional gene detection, geophysical surveys (time-domain electromagnetics and [...] Read more.
High-Resolution Site Characterization (HRSC) offers a promising approach to delineate spatially heterogeneous contamination in complex petrochemical sites, overcoming limitations of conventional discrete sampling. This study implemented an integrated HRSC framework combining surface soil microbial metabolic gas/functional gene detection, geophysical surveys (time-domain electromagnetics and ground-penetrating radar), and Membrane Interface Probe (MIP) sensing at a petrochemical facility in southern China. Results identified composite contamination (aromatic hydrocarbons, short-chain petroleum hydrocarbons, alkanes) primarily concentrated at 5–9 m depth, with a heavily contaminated zone of 1163 m2 and a total influence area of 17,724 m2. The contamination plume showed high spatial correlation with an underground wastewater storage pond, confirmed as the primary leakage source. Post-remediation monitoring indicated restoration of natural groundwater flow and reduced contaminant concentrations. Compared to traditional drilling, the HRSC approach improved resolution from meter to centimeter scale, reduced investigation time by 75%, and lowered overall costs by >30% through targeted sampling and real-time data acquisition. This study validates HRSC as an efficient, accurate, and cost-effective strategy for contamination delineation and source identification in operational industrial sites, supporting precise remediation and site redevelopment. Full article
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28 pages, 925 KB  
Article
Space–Time Discretization of a Wave Equation with Fractional Kelvin–Voigt Damping
by Yong Wang, Muhammad Zainul Abidin and Anwarud Din
Fractal Fract. 2026, 10(6), 381; https://doi.org/10.3390/fractalfract10060381 - 31 May 2026
Viewed by 465
Abstract
This work is concerned with the numerical treatment of a wave equation with fractional Kelvin–Voigt damping, where the viscoelastic contribution is described by a Caputo derivative in time acting on the elliptic part of the model. Such models are of interest because memory [...] Read more.
This work is concerned with the numerical treatment of a wave equation with fractional Kelvin–Voigt damping, where the viscoelastic contribution is described by a Caputo derivative in time acting on the elliptic part of the model. Such models are of interest because memory effects produce hereditary damping and reduced regularity near the initial time, which makes both the analysis and the numerical discretization more delicate than in the classical wave equation. We study the problem on a bounded convex domain under homogeneous Dirichlet boundary conditions and derive a solution representation that is suitable for regularity analysis. Based on this representation, we establish stability and smoothing estimates for both homogeneous data and forcing terms, with particular attention to the influence of nonsmooth initial data. For the spatial discretization, we employ a continuous Galerkin finite element method with piecewise linear elements and prove error estimates that are explicit in the regularity of the initial displacement, initial velocity, and source term. We show that the fully discrete approximation inherits the regularity-dependent behavior of the continuous problem and achieves optimal convergence in space together with second-order accuracy in time under appropriate assumptions on the data. Several numerical experiments are presented to illustrate the theoretical findings and to confirm the predicted convergence rates, thereby supporting the effectiveness of the proposed space–time discretization. Full article
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22 pages, 3625 KB  
Article
Topics and Insights on 1-D Tension Stiffening of an RC Member
by David Z. Yankelevsky, Yuri S. Karinski, Dina Tsemakh and Vladimir R. Feldgun
Materials 2026, 19(11), 2303; https://doi.org/10.3390/ma19112303 - 29 May 2026
Viewed by 342
Abstract
One-dimensional (1-D) tension stiffening is a fundamental behavior of structural concrete. It refers to the composite uniaxial behavior of a slender, symmetric concrete member of constant cross-section, bonded to a single reinforcing bar (rebar) along its axis. The rebar is subjected to tension [...] Read more.
One-dimensional (1-D) tension stiffening is a fundamental behavior of structural concrete. It refers to the composite uniaxial behavior of a slender, symmetric concrete member of constant cross-section, bonded to a single reinforcing bar (rebar) along its axis. The rebar is subjected to tension by a pair of axial tensile forces applied at its ends. Despite the apparent simplicity of this configuration, the problem represents a cornerstone in RC mechanics. During the loading process, cracks are formed at different cross-sections along the structural member at stages where the tensile stress in the concrete at these cross-sections reaches the concrete tensile strength level. Each crack formation reduces the overall axial stiffness of the RC member, while inducing stress and strain redistributions in both the concrete and the rebar. The interaction between the concrete and the rebar is governed by the bond–slip relationship along their interface, which plays a critical role in controlling the transfer of stresses, the development of strains and the evolution of cracking. Most existing analytical and numerical models addressing this problem are based on simplifying assumptions assuming constant (deterministic) material properties and are denoted herein as “deterministic models”. Comparisons between analysis results of such models and experimental observations reveal substantial discrepancies in terms of the number of cracks, their spatial distribution, crack spacing, and the order of crack formation. Considering these inconsistencies, the present study postulates that the inherent variability of concrete properties, particularly its tensile strength, has a decisive influence on the structural response. To address this issue, the tensile strength of concrete is treated as a random variable characterized by the prescribed mean tensile strength and the coefficient of variation (CoV). The “stochastic analyses” with the variable tensile strength are conducted using an exact one-dimensional finite element formulation that explicitly accounts for discrete crack formation within the structural domain. These analyses yield results that differ markedly from those predicted by the deterministic approaches and exhibit characteristics that are in closer agreement with experimental evidence. These analyses indicate a more complex behavior of real structural members. It demonstrates that the CoV significantly influences the magnitude of cracking loads, crack locations, crack spacing, and the order of crack formation. The findings highlight the critical role of even slight material variability in tension stiffening behavior and justify the incorporation of concrete strength variability in tension stiffening modeling. Full article
(This article belongs to the Section Construction and Building Materials)
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30 pages, 9985 KB  
Article
3D Response Characteristics Analysis of Vertical Electric Dipole Transient Electromagnetic Fields Under Complex Geological Conditions
by Xianxiang Wang, Zefan Hu, Shanmei Li and Qing Sun
Geosciences 2026, 16(5), 206; https://doi.org/10.3390/geosciences16050206 - 21 May 2026
Viewed by 316
Abstract
Vertical electric sources serve as an effective method for identifying deep hydrocarbon reservoirs. This involves the ability to generate transverse magnetic fields, concentrate currents at reservoir interfaces, and effectively emphasize resistivity anomalies in late-time domains. Marine geological conditions are often complex, marked by [...] Read more.
Vertical electric sources serve as an effective method for identifying deep hydrocarbon reservoirs. This involves the ability to generate transverse magnetic fields, concentrate currents at reservoir interfaces, and effectively emphasize resistivity anomalies in late-time domains. Marine geological conditions are often complex, marked by rugged topography and intricate structures. This complexity results in highly complicated electromagnetic response features, presenting significant challenges for data interpretation. This research employs the Time-Domain Finite Element Method (TDFEM) using unstructured meshes to accurately discretize complex geological models. Through the formulation of TDFEM equations, we successfully performed three-dimensional forward modeling of VED transient electromagnetic (VSTEM) responses in intricate geological environments. An analysis was conducted on the diffusion mechanisms and spatial distribution characteristics of VSTEM fields located beneath the seabed. A comparative analysis was conducted on the resolution capabilities of different fields stimulated by horizontal and VED sources. The findings show that the Ex provides enhanced boundary identification for the lateral extent of targets, whereas the Ez displays the greatest anomaly contrast, highlighting its exceptional results in anomaly detection. We investigated how complex seabed topography and geological structures affect the resolution of hydrocarbon targets. The research indicates that complex topography significantly influences electromagnetic fields; however, the proposed method can still effectively identify resistive hydrocarbon reservoirs, even in intricate model scenarios, thus confirming its reliability in challenging marine environments. Full article
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31 pages, 9062 KB  
Article
Periodicity of FEM Discrete Models and Its Influence on Solutions to the 1-D Wave Equation
by Wiktor Waszkowiak, Łukasz Doliński, Paweł Kowalski and Arkadiusz Żak
Appl. Sci. 2026, 16(10), 5150; https://doi.org/10.3390/app16105150 - 21 May 2026
Cited by 1 | Viewed by 377
Abstract
This paper discusses the influence of the periodicity of finite-element (FE) discrete models and its influence on solutions to the one-dimensional (1-D) wave equation. Numerical solutions to wave-propagation problems obtained via the displacement-based formulations of the finite-element method (FEM) often exhibit high-frequency behavior, [...] Read more.
This paper discusses the influence of the periodicity of finite-element (FE) discrete models and its influence on solutions to the one-dimensional (1-D) wave equation. Numerical solutions to wave-propagation problems obtained via the displacement-based formulations of the finite-element method (FEM) often exhibit high-frequency behavior, which is frequently dismissed in the literature as undesired, spurious, and/or having no physical meaning. In this paper, we verify this notion by demonstrating that this behavior is not merely a computational anomaly but is due to the inherent periodic properties of discrete numerical models. Using Bloch’s theorem, we reveal and demonstrate how, at high frequencies, the discrete nature of FEM numerical models leads to the prevailing behavior governed by the periodic nature of the computational models. In order to illustrate this phenomenon, we investigate 1-D wave propagation in rods, leveraging the non-dispersive nature of the governing equation as a benchmark. In addition to the classical and specialized FEM, we analyze two alternative formulations: the time-domain spectral finite-element method (TD-SFEM) and a novel spline-based finite-element method (spFEM) proposed by the authors. The results obtained and presented explain qualitatively the origins of these numerical anomalies and suggest strategies to mitigate their effects, effectively shifting the periodicity-induced behavior beyond the range of physically relevant frequencies by appropriate selection of approximation polynomials. The authors demonstrate that this can be fully achieved only in the case of spFEM, for which the usable percentage of the available spectra of eigenfrequencies reaches 67%, while in the case of other FEM approaches discussed is significantly smaller as determined by numerical dispersion and the presence of frequency band gaps. Full article
(This article belongs to the Section Mechanical Engineering)
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22 pages, 872 KB  
Review
The “Are You OK?” Paradox: A Scoping Review of Nocebo and Negative Suggestion in Healthcare Communication
by Orion K. O’Brien and Christopher C. Donnell
Dent. J. 2026, 14(5), 274; https://doi.org/10.3390/dj14050274 - 6 May 2026
Viewed by 1091
Abstract
Background: Nocebo effects are described as adverse symptoms arising from negative expectations rather than direct physiological harm, and are increasingly recognised across healthcare. While traditionally examined within pharmacological trials, emerging literature suggests that nocebo effects are shaped by broader interactional, situational, and communicative [...] Read more.
Background: Nocebo effects are described as adverse symptoms arising from negative expectations rather than direct physiological harm, and are increasingly recognised across healthcare. While traditionally examined within pharmacological trials, emerging literature suggests that nocebo effects are shaped by broader interactional, situational, and communicative processes. In dentistry and paediatric care, where behaviour support and reassurance are central to practice, these mechanisms remain under-synthesised. Objectives: This scoping review aimed to map how nocebo effects are conceptualised across healthcare literature, with particular attention to the role of communication, reassurance, and behaviour support, and to explore how these mechanisms are discussed in paediatric, procedural, and dental contexts. Methods: An interpretive scoping review was conducted in line with JBI guidance and PRISMA-ScR reporting standards. Multidisciplinary literature spanning experimental, clinical, ethical, and applied domains was systematically identified and charted. Studies were grouped using a conceptual framework encompassing expectancy, learning, communication-mediated, ethical, and contextual mechanisms, allowing overlap between categories. Results: A large and heterogeneous body of literature was identified, with most studies conceptualising nocebo effects through overlapping mechanisms rather than discrete pathways. Expectancy and learning processes formed a foundational substrate across contexts, while communication, including framing, tone, reassurance, and checking-in, emerged as an active mechanism shaping symptom perception and vigilance. Ethical discussions highlighted tensions between transparency and potential harm, particularly in consent and risk communication. Paediatric and procedural settings, including dental sedation, were comparatively underrepresented despite features likely to amplify nocebo effects, such as reduced agency and heightened attentional focus. Conclusions: Nocebo effects are best understood as interactional phenomena that emerge within everyday clinical encounters. This review highlights the need to critically examine behaviour support practices, including reassurance, that are typically assumed to be benign. Greater conceptual clarity and reflexivity in communication may support future research and training aimed at minimising unintended distress within dental and paediatric care. These findings suggest that routine communication practices, including reassurance and expectation-setting, should be understood as active components of care that can influence patient experience, rather than as neutral or purely supportive interactions. Full article
(This article belongs to the Special Issue Feature Review Papers in Dentistry: 2nd Edition)
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36 pages, 23663 KB  
Article
Neuro-Prismatic Video Models for Causality-Aware Action Recognition in Neural Rehabilitation Systems
by Hend Alshaya
Mathematics 2026, 14(8), 1341; https://doi.org/10.3390/math14081341 - 16 Apr 2026
Viewed by 588
Abstract
Video-based action recognition for neural rehabilitation—spanning stroke recovery, Parkinsonian gait assessment, and cerebral palsy monitoring—faces critical challenges, including temporal ambiguity, non-causal motion correlations, and the absence of causally grounded dynamics modeling. While transformer-based architectures achieve strong performance, they often exploit spurious temporal and [...] Read more.
Video-based action recognition for neural rehabilitation—spanning stroke recovery, Parkinsonian gait assessment, and cerebral palsy monitoring—faces critical challenges, including temporal ambiguity, non-causal motion correlations, and the absence of causally grounded dynamics modeling. While transformer-based architectures achieve strong performance, they often exploit spurious temporal and environmental cues, limiting reliability in safety-critical clinical settings. We propose NeuroPrisma, a neuro-prismatic video framework that integrates frequency-domain spectral decomposition with causal intervention under Structural Causal Models (SCMs) via the backdoor criterion. NeuroPrisma introduces (i) a Prismatic Spectral Attention (PSA) module, which applies discrete Fourier transforms to decompose temporal features into multi-scale frequency bands, disentangling slow postural dynamics from rapid corrective movements, and (ii) a Causal Intervention Layer (CIL), which performs do-calculus-based backdoor adjustment to remove confounding influences and produce causally invariant representations. PSA preconditions representations prior to intervention, improving confounder estimation and causal robustness. Extensive evaluation against seven state-of-the-art models (I3D, SlowFast, TimeSformer, ViViT, Video Swin Transformer, UniFormerV2, and VideoMAE) demonstrates that NeuroPrisma achieves 98.7% Top-1 accuracy on UCF101, 82.4% on HMDB51, 71.2% on Something-Something V2, and 91.5%/95.8% on NTU RGB+D (Cross-Subject/Cross-View), consistently outperforming prior methods. It further reduces the Causal Confusion Score (CCS) by 42.3%, indicating substantially lower reliance on spurious correlations, while maintaining real-time performance with 23.4 ms latency per 16-frame clip on an NVIDIA A100 GPU. All improvements are statistically significant (p < 0.001, Cohen’s d = 0.72–1.24). Evaluation was conducted exclusively on benchmark datasets (UCF101, HMDB51, Something-Something V2, and NTU RGB+D) under controlled conditions, without direct clinical validation on neurological patient cohorts. Overfitting was mitigated using three random seeds (42, 123, 456), RandAugment, Mixup (α = 0.8), weight decay (0.05), and early stopping. Cross-dataset generalization from UCF101 to HMDB51 without fine-tuning achieved 76.2% Top-1 accuracy. Future work will focus on prospective clinical validation across stroke, Parkinson’s disease, and cerebral palsy populations, including correlation with standardized clinical assessment scales such as Fugl–Meyer, UPDRS, and GMFCS. These results establish NeuroPrisma as a causally grounded and computationally efficient framework for reliable, real-time movement assessment in clinical rehabilitation systems. Full article
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25 pages, 4082 KB  
Article
Time-Domain Hydroelastic Analysis of Floating Structures Under Nonlinear Shallow-Water Waves over Variable Bathymetry
by Xu Duan, Xiaoyu Chen, Yujin Dong and Yuwang Xu
J. Mar. Sci. Eng. 2026, 14(8), 729; https://doi.org/10.3390/jmse14080729 - 15 Apr 2026
Viewed by 631
Abstract
Photovoltaic systems deployed on large floating platforms in nearshore waters are strongly influenced by hydroelastic effects, nonlinear shallow-water waves, and variable bathymetry. This study develops a time-domain hydroelastic framework that couples the fully nonlinear non-hydrostatic wave model NHWAVE with a Rankine-source potential-flow solver [...] Read more.
Photovoltaic systems deployed on large floating platforms in nearshore waters are strongly influenced by hydroelastic effects, nonlinear shallow-water waves, and variable bathymetry. This study develops a time-domain hydroelastic framework that couples the fully nonlinear non-hydrostatic wave model NHWAVE with a Rankine-source potential-flow solver and a discrete-module Cummins formulation. The wave model provides incident pressures and kinematics over uneven seabeds, while the potential-flow solver evaluates radiation and diffraction effects and transfers the resulting hydrodynamic coefficients into the time domain. Numerical simulations are carried out for a 600 m modular floating structure under regular waves over flat and sloped bathymetries with tanα=0.0133, wave periods of 4–6 s, and wave heights of 0.3–1.0 m. The results show that bathymetric variation intensifies shoaling-induced excitation, modifies added-mass and damping distributions, increases the spatial non-uniformity of hydroelastic motions, and amplifies bending-moment RMS responses relative to the flat-bottom case. Additional comparisons between rigid-body and hydroelastic models show clear period-dependent redistribution of motions and bending demand. These results demonstrate that both local bathymetry and structural elasticity must be considered for the reliable analysis and design of nearshore floating photovoltaic systems and other large floating structures. Full article
(This article belongs to the Special Issue Advanced Analysis of Ship and Offshore Structures)
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22 pages, 2681 KB  
Article
Fracture and Fatigue Assessment of Bonded Composite Patch Repairs in Notched and Cracked Plates
by Bertan Beylergil, Hasan Ulus, Mehmet Emin Çetin, Halil Burak Kaybal, Sefa Yildirim, Abdulrahman Al-Nadhari and Mehmet Yildiz
Polymers 2026, 18(8), 912; https://doi.org/10.3390/polym18080912 - 8 Apr 2026
Cited by 7 | Viewed by 783
Abstract
This study presents a unified mechanics-based framework for evaluating bonded composite patch repairs. Discrete fracture, fatigue, and adhesive responses are transformed into continuous master equations over the design space. Low-order polynomial surfaces model stress intensity and concentration responses, enabling continuous prediction of repair [...] Read more.
This study presents a unified mechanics-based framework for evaluating bonded composite patch repairs. Discrete fracture, fatigue, and adhesive responses are transformed into continuous master equations over the design space. Low-order polynomial surfaces model stress intensity and concentration responses, enabling continuous prediction of repair performance without repeated finite-element analyses. A fracture-based repair efficiency index is derived from the analytical master surface. This index quantifies the average reduction in crack-driving force across the domain. Combined with adhesive stiffness and strength, it defines an adhesive-based repair efficiency index (A-REI), providing a direct link between structural response and material properties. The results show that repair effectiveness is strongly influenced by both geometric severity and adhesive properties. Fatigue performance decreases significantly with increasing notch ratio in single-sided repairs. Double-sided configurations maintain consistently higher efficiency. Symmetric reinforcement more effectively reduces stress concentration, with improvements exceeding 40% at intermediate notch ratios. Adhesive selection is governed by stiffness and strength. Structural adhesives achieve significantly higher A-REI values, whereas compliant adhesives contribute negligibly. Overall, repair symmetry controls the magnitude of improvement, while adhesive properties determine performance ranking. This framework provides a clear, practical basis for design and material selection. Full article
(This article belongs to the Special Issue Advanced Polymer Composites with High Mechanical Properties)
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18 pages, 1685 KB  
Article
Symmetric Element Stiffness and Symplectic Integration for Eringen’s Integral Nonlocal Rods: Static Response and Higher-Order Vibrations
by Zheng Yao, Changliang Zheng and Lulu Wen
Symmetry 2026, 18(4), 571; https://doi.org/10.3390/sym18040571 - 27 Mar 2026
Viewed by 491
Abstract
Integral-form nonlocal elasticity provides a mechanically meaningful approach to describing size effects, yet it leads to Volterra-type integro-differential equations that are difficult to solve analytically and numerically challenging for boundary layers and high-order modes. In this work, we developed a symplectic numerical integration [...] Read more.
Integral-form nonlocal elasticity provides a mechanically meaningful approach to describing size effects, yet it leads to Volterra-type integro-differential equations that are difficult to solve analytically and numerically challenging for boundary layers and high-order modes. In this work, we developed a symplectic numerical integration framework for Eringen’s two-phase (local/nonlocal mixture) integral model by embedding the constitutive operator into a Hamiltonian formulation and discretizing the influence domain in a belt-wise manner. A step-increase strategy was incorporated to allow flexible spatial marching while preserving the geometric (symplectic) structure of the transfer operation. In addition, a symmetry-explicit, element-level stiffness representation was derived for the discretized integral operator; it exposes a mirrored long-range coupling pattern and enables symmetric, energy-consistent assembly. The resulting kernel-agnostic algorithm accommodates both smooth and finite-range kernels. Static benchmarks and longitudinal vibrations are investigated for exponential, Gaussian, and triangular kernels over representative length ratios and mixture parameters. Comparisons with available analytical and asymptotic solutions show good agreement within their validity ranges, and the method yields stable higher-order eigenfrequencies when asymptotic expansions may be unreliable. The current study is limited to a linear one-dimensional rod setting, and validation is restricted to published analytical/asymptotic solutions rather than experimental calibration. Full article
(This article belongs to the Section F: Engineering and Materials)
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33 pages, 5405 KB  
Article
Design and Implementation of Finite-Time Convergent Adaptive ADRC for the Resilient Control of Power Converters
by Ghulam Shabbir, Ali Hasan, Muhammad Yaqoob Javed, Aamer Bilal Asghar and Thomas Mussenbrock
Energies 2026, 19(7), 1653; https://doi.org/10.3390/en19071653 - 27 Mar 2026
Viewed by 674
Abstract
The dynamics of power converters are highly influenced by uncertainties, nonlinearities, and external disturbances. Thus, high-performance, extremely resilient, and robust control strategies are necessary for their control. For the robust operation of power converters, this article presents an adaptive and finite-time convergent active [...] Read more.
The dynamics of power converters are highly influenced by uncertainties, nonlinearities, and external disturbances. Thus, high-performance, extremely resilient, and robust control strategies are necessary for their control. For the robust operation of power converters, this article presents an adaptive and finite-time convergent active disturbance rejection control (ADRC) framework inspired by Professor Han’s seminal paper. Based on ADRC’s philosophy, this article proposes a control scheme that integrates adaptiveness and finite-time convergence in both the extended state observer and the control law. The proposed framework ensures quick disturbance estimation and its rejection, thus ensuring that the required response is tracked successfully. The controllers for different power converters, such as buck converters, boost converters, and single-phase inverters, are designed to ensure the desired dynamics, including low settling times and zero-percent overshoots. The controllers are implemented in the discrete-time domain using forward differences. Simscape simulation experiments on buck converters, boost converters, and single-phase inverters demonstrate that the responses are achieved with finite settling time with no overshoots. Thus, such control strategies are highly crucial for mission-critical power applications. Full article
(This article belongs to the Section F1: Electrical Power System)
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23 pages, 4699 KB  
Article
A Symplectic Method for Analyzing the Nonlocal Modal Behavior of Kirchhoff Plates and Numerical Validation
by Zehan Zhang and Zheng Yao
Appl. Sci. 2026, 16(6), 3033; https://doi.org/10.3390/app16063033 - 20 Mar 2026
Viewed by 1049
Abstract
Eringen’s integral constitutive relation is more general than its differential counterpart for modeling small-scale effects in micro- and nanostructures; however, it leads to integro-differential governing equations that are difficult to solve, which has limited the practical use of integral formulations. To directly address [...] Read more.
Eringen’s integral constitutive relation is more general than its differential counterpart for modeling small-scale effects in micro- and nanostructures; however, it leads to integro-differential governing equations that are difficult to solve, which has limited the practical use of integral formulations. To directly address this gap, this paper introduces a novel symplectic-based numerical method that efficiently and accurately analyzes the free vibration of small-scale Kirchhoff plates governed by Eringen’s integral nonlocal model. The method discretizes the nonlocal integral operator by introducing inter-belt elements for long-range interactions and adopting a truncated influence domain, while balancing computational efficiency and accuracy. The effects of the nonlocal parameter, two-phase mixture parameter, mode numbers, kernel types, and geometric parameters on the natural frequencies are systematically investigated. The results indicate stiffness softening. For a simply supported square nanoplate with side length a=10 nm, the first-order frequency parameter decreases by approximately 25% as the nonlocal parameter increases from 0 to 4 nm, and higher-order modes exhibit substantially greater sensitivity to nonlocal effects. Convergence and accuracy are validated against published continuum-level solutions and molecular dynamics simulations; relative deviations are below 2% in most cases, and the local limit (la=0) yields errors on the order of 103. Full article
(This article belongs to the Section Mechanical Engineering)
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