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Keywords = finite-element calculation

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17 pages, 3124 KB  
Article
Reliability Analysis and Optimization of Power Terminal Solder Joints in PPS-Packaged IPMs
by Jun Xu and Bin Zhang
Micromachines 2026, 17(6), 749; https://doi.org/10.3390/mi17060749 (registering DOI) - 21 Jun 2026
Abstract
Thisstudy investigates the reliability of power-terminal solder joints in intelligent power modules (IPMs) subjected to thermal cycling, random vibration, and packaging/assembly-induced deformation. Fifty IPMs were tested under temperature cycling from −55 °C to 125 °C and random vibration from 20 to 2000 Hz, [...] Read more.
Thisstudy investigates the reliability of power-terminal solder joints in intelligent power modules (IPMs) subjected to thermal cycling, random vibration, and packaging/assembly-induced deformation. Fifty IPMs were tested under temperature cycling from −55 °C to 125 °C and random vibration from 20 to 2000 Hz, and the experimental observations were combined with finite element simulations of thermal, vibration, and deformation loads. The modules survived 200 temperature cycles in the free state, whereas functional abnormalities occurred after board-level assembly and subsequent environmental loading. Simulation results showed that random vibration produced limited solder-layer stress because the first structural mode was above the excitation range, while packaging and PCB deformation markedly increased the initial stress of the power-terminal solder joints. When local deformation reached approximately 0.5 mm, the calculated solder-pad stress reached or exceeded the shear-strength risk range, consistent with the failure tendency observed in highly deformed modules. Weibull analysis further indicated a fatigue-dominated failure process with an increasing failure rate. These findings suggest that deformation control, package stiffness improvement, and assembly flatness management are critical for improving the reliability of IPM power-terminal solder joints. Full article
(This article belongs to the Special Issue Reliability and Degradation in Power Transistors)
39 pages, 16877 KB  
Article
Stress Evolution and Integrity Evaluation of Cement Sheath Under Alternating Temperature–Pressure Coupled Loads During Multi-Stage Fracturing in Shale Gas Wells
by Mingxin Jiang, Yumei Li, Shengzhe Huo, Hailong Jiang and Yan Xi
Appl. Sci. 2026, 16(12), 6181; https://doi.org/10.3390/app16126181 - 18 Jun 2026
Viewed by 195
Abstract
Based on measured data from a shale gas well, this study develops a wellbore temperature cycle model and a temperature–pressure coupled finite element model to evaluate cement sheath stress during multi-stage fracturing. Dynamic temperature and pressure boundaries are applied to calculate radial and [...] Read more.
Based on measured data from a shale gas well, this study develops a wellbore temperature cycle model and a temperature–pressure coupled finite element model to evaluate cement sheath stress during multi-stage fracturing. Dynamic temperature and pressure boundaries are applied to calculate radial and tangential stresses, while cumulative mechanical degradation and failure modes are assessed using the modified Mohr–Coulomb criterion. The results show that cement sheath temperature changes significantly, and stresses vary periodically with fracturing stages. The injection period is the most critical stage for cement sheath failure. Lower casing pressure and reduced fracturing fluid displacement can improve stress distribution and reduce damage. Higher initial fluid temperature increases radial stress but decreases tangential stress, while shallower horizontal well depth weakens temperature–pressure coupling. Optimizing these parameters can mitigate cement sheath damage, enhance structural integrity, and ensure safe fracturing operations. Full article
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18 pages, 3052 KB  
Article
Rehabilitation of the Severely Atrophic Maxilla with Subperiosteal Implants: A Biomechanical and Decision Analysis of Material and Configuration Choices
by Barış Erkut Türk, Bersu Bedirhandede, Dilan Gizem Doğan and Beyza Güney
Biomimetics 2026, 11(6), 433; https://doi.org/10.3390/biomimetics11060433 - 18 Jun 2026
Viewed by 179
Abstract
Background/Objectives: Patient-specific subperiosteal implants are increasingly used to treat severely atrophic ridges due to advances in digital planning and additive manufacturing. This study aimed to evaluate the effects of material type and implant configuration on stress distribution in subperiosteal implant systems and [...] Read more.
Background/Objectives: Patient-specific subperiosteal implants are increasingly used to treat severely atrophic ridges due to advances in digital planning and additive manufacturing. This study aimed to evaluate the effects of material type and implant configuration on stress distribution in subperiosteal implant systems and to compare their overall biomechanical performance using a multi-criteria decision framework. Methods: A three-dimensional model of a severely atrophic maxilla was reconstructed to simulate four clinical scenarios combining two configurations (one-piece and two-piece) and two materials (titanium and 60% carbon fiber-reinforced polyetheretherketone). Finite element analysis was conducted to assess stress distribution within the implant body, fixation screws, prosthetic framework, and surrounding bone under vertical and oblique loading conditions. Maximum and minimum principal stresses were evaluated in bone, whereas von Mises stresses were calculated for implant components. The resulting biomechanical indicators were subsequently integrated using an entropy weight–TOPSIS multi-criteria decision analysis. Results: Principal stresses in the surrounding bone showed minimal variation between titanium and 60% carbon fiber-reinforced polyetheretherketone across all configurations. Implant configuration had a more pronounced effect on implant body stress. Under oblique loading, the two-piece configuration demonstrated substantially higher implant stresses than the one-piece design, whereas under vertical loading, lower implant stresses were observed in the two-piece configuration. The multi-criteria analysis ranked the one-piece titanium model highest under oblique loading and the two-piece titanium model highest under vertical loading. Conclusions: Implant configuration and loading direction influenced biomechanical behavior more than material selection in patient-specific subperiosteal implants. Full article
(This article belongs to the Special Issue Dentistry and Craniofacial District: The Role of Biomimetics 2026)
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41 pages, 10080 KB  
Article
Research on Design Methodology and Finite Element Analysis of Inner Cores for Multi-Level Energy Dissipation and Self-Centering BRBs—Part II: Self-Centering Circular Frustum Device
by Lixiang Cai, Jie Chen, Weibing Xu, Xiaomin Huang, Qingchuang Guo, Chunjuan Zhou and Dingqing Feng
Buildings 2026, 16(12), 2418; https://doi.org/10.3390/buildings16122418 - 17 Jun 2026
Viewed by 226
Abstract
This paper introduces an innovative inner core for buckling-restrained braces, referred to as the Aluminum-Engineered Cementitious Composite-Circular Frustum Composite (ALECCYT) inner core, which incorporates multi-stage energy dissipation mechanisms and self-centering capabilities. The initial stiffness calculation formula for the self-centering circular frustum (YT) device [...] Read more.
This paper introduces an innovative inner core for buckling-restrained braces, referred to as the Aluminum-Engineered Cementitious Composite-Circular Frustum Composite (ALECCYT) inner core, which incorporates multi-stage energy dissipation mechanisms and self-centering capabilities. The initial stiffness calculation formula for the self-centering circular frustum (YT) device is derived theoretically, and a sizing design methodology for its critical components is proposed, specifically tailored to achieve a preset failure mode. Based on this, seven YT device specimens with varying tonnages, both conforming and non-conforming to the design methodology, were designed and analyzed through finite element simulations. The results demonstrate that the hysteretic curve of the appropriately designed YT device exhibits a flag-like shape, with minimal residual displacement after unloading, effective hysteretic energy dissipation, and robust self-centering capabilities, while adhering to the intended failure mode. Conversely, specimens that fail to meet the buckling constraints may encounter failures such as Shape Memory Alloy (SMA) buckling, steel ring buckling, and Carbon Fiber Reinforced Polymer (CFRP) ring buckling during loading, leading to the inefficient utilization of material strengths. The findings from the finite element analyses provide preliminary validation of the effectiveness of the proposed design methodology. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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29 pages, 50460 KB  
Article
Analysis of Winding Losses in Permanent Magnet Synchronous Motors with Multilayer Thin Flat-Wire Windings
by Simeng Zhong, Xiaoting Zhang, Aimin Liu, Bingyi Zhang, Yongpeng Cao and Decai Liu
Electronics 2026, 15(12), 2665; https://doi.org/10.3390/electronics15122665 - 16 Jun 2026
Viewed by 106
Abstract
Flat-wire windings have been widely used in high-power-density electric vehicle motors because of their high slot fill factor and high efficiency. However, conventional flat-wire conductors usually have relatively large cross-sectional dimensions, which may lead to significant AC winding losses under high-frequency operation due [...] Read more.
Flat-wire windings have been widely used in high-power-density electric vehicle motors because of their high slot fill factor and high efficiency. However, conventional flat-wire conductors usually have relatively large cross-sectional dimensions, which may lead to significant AC winding losses under high-frequency operation due to the combined effects of the rotor magnetic field and the armature-reaction field. To address this issue, this paper proposes a multilayer thin flat-wire continuous-wave winding and its end-winding transposition method. The parallel multilayer thin flat-wire structure effectively suppresses AC losses by reducing the characteristic dimension of each conductor, while the end-winding transposition method reduces or even eliminates circulating-current losses among parallel strands without compromising slot utilization. An analytical calculation method is established to investigate the AC loss characteristics of the multilayer thin flat-wire winding, and the main influencing factors of winding losses are analyzed. To address the circulating-current loss issue, the loss suppression effect of the transposition method is quantitatively evaluated, and an intermittent transposition method with both effective circulating-current suppression and fewer end-winding crossovers is proposed. Finally, the proposed method is validated by finite-element analysis (FEA) and prototype experiments. The results show that the proposed winding can significantly reduce AC losses over a wide speed range, providing a low loss and manufacturable winding design solution for high-power-density electric vehicle traction motors. Full article
(This article belongs to the Special Issue Modeling and Control of Power Converters for Power Systems)
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17 pages, 481 KB  
Entry
Digital Tools in Aluminum Alloy Processing
by Mihail Kolev and Tatiana Simeonova
Encyclopedia 2026, 6(6), 134; https://doi.org/10.3390/encyclopedia6060134 - 15 Jun 2026
Viewed by 244
Definition
Digital tools in aluminum alloy processing are computational, sensing-based, and data-driven methods used to understand, predict, monitor, optimize, and control how aluminum alloys are transformed into components. They support decisions across casting, deformation processing, heat treatment, welding, surface engineering, and additive manufacturing by [...] Read more.
Digital tools in aluminum alloy processing are computational, sensing-based, and data-driven methods used to understand, predict, monitor, optimize, and control how aluminum alloys are transformed into components. They support decisions across casting, deformation processing, heat treatment, welding, surface engineering, and additive manufacturing by linking processing conditions with geometry, microstructure, defects, properties, and service performance. In technical use, the term includes finite element method (FEM), computational fluid dynamics (CFD), CALculation of PHAse Diagrams (CALPHAD), microstructure models, machine-learning regressors, surrogate models, nondestructive digital inspection, image-analysis tools, and digital twins. These tools are most effective when they establish links among controllable processing variables, underlying metallurgical mechanisms, measurable quality indicators, and service-relevant performance outcomes. Full article
(This article belongs to the Section Material Sciences)
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12 pages, 17370 KB  
Article
Design and Research of a High-Pressure-Resistant Constant Volume Combustion Device
by Qingmiao Ma, Weige Liang, Qizheng Zhou, Peiyi Zhou, Xupeng Huo, Yang Zhao and Xiangyu Zeng
Appl. Sci. 2026, 16(12), 6031; https://doi.org/10.3390/app16126031 - 15 Jun 2026
Viewed by 106
Abstract
In response to the current limitation where conventional constant volume combustion apparatuses are generally confined to pressure ratings of 5–20 MPa, insufficient for the demands of ultra-high-pressure combustion fundamental research, this study designs and verifies a high-pressure-resistant constant volume combustion apparatus with a [...] Read more.
In response to the current limitation where conventional constant volume combustion apparatuses are generally confined to pressure ratings of 5–20 MPa, insufficient for the demands of ultra-high-pressure combustion fundamental research, this study designs and verifies a high-pressure-resistant constant volume combustion apparatus with a rated working pressure of 250 MPa. The strength design and safety factor calculation for the combustion chamber main body were conducted based on the Lame thick-walled cylinder elastic theory. A finite element numerical simulation method was systematically employed to perform static analysis, transient impact response analysis, and high-cycle fatigue-life assessment of the key components of the apparatus. The results indicate that under a 250 MPa design internal pressure load, the maximum circumferential stress at the inner wall of the combustion chamber main body is 328.0 MPa, with a safety factor greater than 1.5, complying with relevant safety codes for high-pressure vessels. Under transient loading simulating combustion impact, the maximum equivalent stress of all structural components is below the material yield strength, with a maximum elastic deformation of less than 0.06 mm, demonstrating excellent structural stiffness and impact resistance. Fatigue assessment with a design-life target of 1.0 × 106 pressure cycles shows that the cumulative damage values for all components are significantly less than 1.0, meeting the reliability requirements for long-term cyclic service. This apparatus integrates functional modules such as high-pressure precision gas mixing, high-energy reliable ignition, high-speed transient parameter acquisition, and safe product collection, providing a stable, controllable, and safe experimental platform for in-depth research on the combustion mechanisms of gaseous fuels under ultra-high-pressure conditions. Full article
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26 pages, 9383 KB  
Article
Multi-Objective Optimization Method for Marine Propulsion Shaft Alignment Under Multiple Operating Conditions
by Shuzhe Wang, Zhongxu Tian and Shouqi Cao
J. Mar. Sci. Eng. 2026, 14(12), 1101; https://doi.org/10.3390/jmse14121101 - 15 Jun 2026
Viewed by 160
Abstract
Marine propulsion shaft alignment is affected by bearing offsets, hull deformation, thermal growth, and condition-dependent propeller and gear loads. An alignment scheme optimized for a single condition may therefore lead to unbalanced bearing reactions or excessive shaft-line deformation in service. To improve multi-condition [...] Read more.
Marine propulsion shaft alignment is affected by bearing offsets, hull deformation, thermal growth, and condition-dependent propeller and gear loads. An alignment scheme optimized for a single condition may therefore lead to unbalanced bearing reactions or excessive shaft-line deformation in service. To improve multi-condition alignment performance while reducing the reliance on repeated direct finite element evaluations during optimization, this study proposes a hybrid surrogate-assisted multi-objective optimization framework for a container-ship propulsion shafting system. A beam finite element model based on Euler–Bernoulli theory is established and numerically checked using jack-up calculations. Cold static, hot operating, and zero-pitch conditions are considered. Bearing-load uniformity, maximum coupling vertical offset, and maximum shaft slope are selected as objectives. According to response characteristics, an extremely randomized trees model is used for the nonlinear load-uniformity response, whereas response surface models are used for the smoother coupling-offset and shaft-slope responses. The Pareto front is obtained using multi-objective particle swarm optimization, and a compromise scheme is selected using entropy-weighted TOPSIS. For the investigated case, the preferred scheme reduces the three objectives by 44.36%, 38.62%, and 8.65%, respectively, relative to the pre-optimization scheme, and finite element recalculation gives prediction deviations below 5%. The proposed framework provides a practical reference for propulsion shaft alignment optimization under operating conditions. Full article
(This article belongs to the Special Issue Advances in High-Efficiency Marine Propulsion Systems)
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28 pages, 23403 KB  
Article
Ground Control Interpretation of Open-Pit Slope Deformation Using Integrated Radar, InSAR, and Stability Analyses: A Monitoring-Based Framework
by Murat Tolunay Bulgurcu and Cuneyt Atilla Ozturk
Mining 2026, 6(2), 40; https://doi.org/10.3390/mining6020040 - 14 Jun 2026
Viewed by 223
Abstract
Slope stability in open-pit mining is not a static condition but evolves continuously as excavation progresses and geomechanical conditions change. In this study, an integrated approach combining ground-based radar monitoring, satellite-based InSAR time-series analysis, and numerical stability modeling was applied to evaluate slope [...] Read more.
Slope stability in open-pit mining is not a static condition but evolves continuously as excavation progresses and geomechanical conditions change. In this study, an integrated approach combining ground-based radar monitoring, satellite-based InSAR time-series analysis, and numerical stability modeling was applied to evaluate slope behavior in a large-scale open-pit copper mine with complex geological and structural characteristics. Radar data revealed progressive and episodic deformation concentrated in specific slope sectors, while InSAR observations showed that deformation continued at lower rates after the main movement phase, providing a longer-term perspective of slope response. Stability analyses using limit equilibrium and finite element methods indicate that the slope operates close to a limit equilibrium condition, particularly under saturated scenarios where factors of safety approach critical levels and strain localization becomes more pronounced. The results show a clear link between observed deformation patterns and calculated stability conditions, with structural discontinuities and groundwater playing a dominant role in controlling slope behavior. Based on these findings, an integrated workflow is proposed that links monitoring data with stability assessment, enabling the identification of critical zones and supporting the evaluation of slope conditions during ongoing mining operations. This approach contributes to more reliable decision-making and supports safer and more sustainable open-pit mining practices. Full article
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22 pages, 3318 KB  
Article
Research on Global Seismic Reliability Analysis of Steel Frames Based on Machine Learning
by Ziyang Wu, Dewei Kong, Mingming Jia and Xianbao Li
Buildings 2026, 16(12), 2379; https://doi.org/10.3390/buildings16122379 - 14 Jun 2026
Viewed by 238
Abstract
Seismic reliability assessment of steel frame structures using nonlinear finite element analysis is often hindered by implicit limit state functions and high computational cost. To address these challenges, this study proposes a machine learning-based framework for global seismic reliability analysis. A nine-story steel [...] Read more.
Seismic reliability assessment of steel frame structures using nonlinear finite element analysis is often hindered by implicit limit state functions and high computational cost. To address these challenges, this study proposes a machine learning-based framework for global seismic reliability analysis. A nine-story steel frame model is established and validated through modal and pushover analysis. Global sensitivity analysis using the Sobol’ method is performed to identify key parameters governing the maximum inter-story drift ratio. Three machine learning models—PSO-SVR, PSO-XGBoost, and PSO-BPNN—are trained with the selected features and integrated into Monte Carlo simulation (MCS) for reliability calculation. The results show that the PSO-BPNN model achieves the highest accuracy with the maximum error of 1.0259% relative to direct MCS, outperforming the conventional MLE-based approach, which yields errors up to 11.9383% due to the non-standard distribution of the structural response. The impact of training sample size on model performance is also examined, with 1000 samples identified as a practical threshold for acceptable prediction accuracy. Existing code design methods require modifications based on the total probability approach for global reliability analysis. This study offers an efficient and precise methodology for seismic reliability design of steel frame structures, particularly when structural responses deviate from standard parametric distributions. Full article
(This article belongs to the Special Issue Resilience Analysis and Intelligent Simulation in Civil Engineering)
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18 pages, 5110 KB  
Article
A Novel Metal Forming Process Based on Upsetting with Two Movable Deformation Zones Demonstrated on Railway Axle Forming
by Grzegorz Winiarski
Materials 2026, 19(12), 2570; https://doi.org/10.3390/ma19122570 - 14 Jun 2026
Viewed by 186
Abstract
This paper presents a new process for forming stepped shafts by upsetting with two movable deformation zones. The developed technology enables several shaft steps to be formed at the same time, thereby increasing process efficiency and reducing material consumption. A distinctive feature of [...] Read more.
This paper presents a new process for forming stepped shafts by upsetting with two movable deformation zones. The developed technology enables several shaft steps to be formed at the same time, thereby increasing process efficiency and reducing material consumption. A distinctive feature of the process is that it uses two forming sleeves, each with a variable cross-section of the impression, which move in an opposite direction to that of the punches during operation. This results in a simultaneous occurrence of upsetting and extrusion, thus leading to intensified plastic deformation and stabilized metal flow. The practical applicability of the process is demonstrated on the example of a forged railway axle. An analysis is carried out by the finite element method (FEM) using specimens of hot-formed C35 steel. The obtained results reveal proper material flow and the correct filling of the tool impressions. The examination of strain and stress distributions confirms favorable forming conditions. The calculated values of the Cockcroft–Latham integral indicate favorable forming conditions and a low risk of fracture initiation during the analyzed process. The results demonstrate the potential of the proposed technology and provide a basis for future experimental verification and industrial assessment. Full article
(This article belongs to the Special Issue Progress in Plastic Deformation of Metals and Alloys (Third Edition))
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28 pages, 5029 KB  
Review
Beyond SINS: A Critical Review of Biomechanical, Microstructural, and Radiomic Biomarkers for Predicting Fracture Risk in Spinal Metastases
by An Sen Tan, Calvin Kai En Tjio, Jonathan Jiong Hao Tan, Naresh Kumar, Wilson Ong, Shuliang Ge, Yi Liang Tan, Eric Fang, Balamurugan A. Vellayappan and James Thomas Patrick Decourcy Hallinan
Diagnostics 2026, 16(12), 1835; https://doi.org/10.3390/diagnostics16121835 - 13 Jun 2026
Viewed by 133
Abstract
Background/Objectives: Although the Spinal Instability Neoplastic Score (SINS) is widely used to estimate spinal metastases fracture risk and guide decisions on stabilisation procedures, prior studies have demonstrated mixed results. Patients with the same score exhibit clinically heterogeneous outcomes, with some SINS criteria correlating [...] Read more.
Background/Objectives: Although the Spinal Instability Neoplastic Score (SINS) is widely used to estimate spinal metastases fracture risk and guide decisions on stabilisation procedures, prior studies have demonstrated mixed results. Patients with the same score exhibit clinically heterogeneous outcomes, with some SINS criteria correlating less well with the estimated fracture risk than others. There are also barriers to implementation such as the time burden required for manual calculation and interobserver variability associated with qualitative morphological criteria. SINS also lacks sensitivity for detecting latent structural compromise in treatment-naive patients and those susceptible to the iatrogenic effects of stereotactic body radiation therapy. This review aims to evaluate emerging imaging, biomechanical, and microstructural markers with the potential to improve fracture risk stratification and prognostication for spinal oncology patients. Methods: We synthesise evidence across three innovative frontiers: (1) biomechanical modelling, including CT-derived finite element analysis and failure-load pattern models; (2) radiomics, utilizing radiomics features from radiological imaging to develop a predictive model; and (3) microstructural MRI biomarkers, exploring the translatability of the Vertebral Bone Quality score, fat fraction, and paraspinal muscle atrophy from osteoporosis to the metastatic spine. Results: Emerging biomechanical, radiomic and microstructural imaging markers show potential in addressing some limitations of traditional SINS criteria for fracture risk stratification across the spinal oncology treatment continuum, from initial diagnosis to post-radiation surveillance, thereby facilitating more precise risk assessment. However, current evidence remains largely retrospective and heterogeneous, and further validation is required before clinical adoption. Conclusions: We propose a framework that shifts the paradigm from conventional morphological scoring toward a multiparametric assessment of spinal stability. Full article
(This article belongs to the Special Issue Contemporary Spine Diagnostics and Management)
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22 pages, 5125 KB  
Article
Mixed-Mode Dynamic Stress Intensity Factors and Fracture Analysis Using Ordinary State-Based Peridynamics
by Yanyun Ru, Fei Li, Xingyu Li, Caidan Wang, Qianlong Yang, Shuqin Zheng, Lei Zhou and Xu Wang
Materials 2026, 19(12), 2560; https://doi.org/10.3390/ma19122560 - 12 Jun 2026
Viewed by 148
Abstract
An ordinary state-based peridynamic (OSPD) approach combined with an interaction integral method is proposed to calculate dynamic stress intensity factors (DSIFs) and simulate crack propagation in two-dimensional cracked brittle solids. Numerical investigations are carried out for mode I and mixed-mode cracked plates under [...] Read more.
An ordinary state-based peridynamic (OSPD) approach combined with an interaction integral method is proposed to calculate dynamic stress intensity factors (DSIFs) and simulate crack propagation in two-dimensional cracked brittle solids. Numerical investigations are carried out for mode I and mixed-mode cracked plates under static, quasi-static, and dynamic loading conditions. A local damping scheme is incorporated into the peridynamic equations of motion to achieve convergence in static and quasi-static analyses. The influence of circular holes on DSIFs and crack propagation paths is systematically examined. Quantitative analyses of elastic deformation and quasi-static fracture behavior for mode I and mixed-mode cracks are verified through the uniaxial tension of a slab. The peak values of DSIFs exceed their static counterparts under dynamic loading. Complex dynamic fracture phenomena, including crack branching in both straight and inclined edge cracks, are successfully captured. The results obtained by the OSPD approach are validated through comparisons with theoretical benchmarks and finite element results, demonstrating high accuracy and effectiveness in calculating elastic deformation and stress intensity factors (SIFs), as well as accurately predicting crack propagation paths in quasi-static and dynamic fracture problems in brittle solids. Beyond the benchmark problems, the proposed OSPD approach is particularly well-suited for investigating more complex fracture systems. Full article
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35 pages, 1713 KB  
Article
Iterative Form-Finding Method for Overhead Transmission Conductors Based on a Geometric Update Strategy
by Huaichao Wang, Dongsheng Xia, Anqi Zhou, Xiaoyu Xiong, Xin Feng and Qing Sun
Appl. Sci. 2026, 16(12), 5976; https://doi.org/10.3390/app16125976 - 12 Jun 2026
Viewed by 112
Abstract
Overhead transmission conductors are flexible cable structures. Their initial equilibrium configuration is affected by self-weight, tension, boundary constraints, and material deformation, and is required for force analysis, sag calculation, and safety assessment. Existing studies use catenary theory or numerical iterative methods. The direct [...] Read more.
Overhead transmission conductors are flexible cable structures. Their initial equilibrium configuration is affected by self-weight, tension, boundary constraints, and material deformation, and is required for force analysis, sag calculation, and safety assessment. Existing studies use catenary theory or numerical iterative methods. The direct iterative method is used in conductor form-finding. However, its geometric update ratio is assigned in segments based on empirical thresholds. This may cause unsmooth updates, low efficiency, and numerical instability in sensitive cases. This study investigates a single-span conductor within a nonlinear finite element form-finding framework. The direct iterative method is analyzed in terms of control variables, implementation process, and update-ratio control mode. A continuous error-driven adaptive geometric update strategy is proposed and an adaptive direct iterative method is developed. The two methods are compared under the same finite element model, parameters, loads, constraints, convergence threshold, and maximum iterations. Three factors are selected: element number, nonlinear substep number, and initial strain coefficient. A total of 27 full-factorial cases are calculated. Convergence efficiency, final error, and abnormal case distribution are evaluated. The results show that the proposed method reduces iterations, improves computational efficiency, and enhances numerical stability in sensitive cases without changing the finite element solution framework. Full article
(This article belongs to the Section Civil Engineering)
25 pages, 14083 KB  
Article
Vertical Bearing Behavior and Capacity Calculation Method of Rock-Socketed Self-Drilling Hollow Bar Micropiles
by Fengjun Liu, Xiao Yang and Yiyao Sun
Appl. Sci. 2026, 16(12), 5898; https://doi.org/10.3390/app16125898 - 11 Jun 2026
Viewed by 110
Abstract
Self-drilling hollow bar micropiles (HBMPs), which integrate drilling, grouting, and reinforcement into a single process, have broad application prospects in mountainous transmission lines and offshore wind power projects. However, existing research has focused mainly on friction piles in soil layers, and there is [...] Read more.
Self-drilling hollow bar micropiles (HBMPs), which integrate drilling, grouting, and reinforcement into a single process, have broad application prospects in mountainous transmission lines and offshore wind power projects. However, existing research has focused mainly on friction piles in soil layers, and there is a lack of systematic understanding of the load-transfer mechanism and bearing capacity calculation method for rock-socketed HBMPs. Based on field static load tests of rock-socketed HBMPs, this study systematically investigates the vertical bearing behavior and capacity calculation method of single rock-socketed HBMPs through a combination of test data analysis, finite element numerical simulation, and theoretical analysis. The field test results show that the load-settlement curves of rock-socketed HBMPs are of a slowly varying type, exhibiting mixed friction-end-bearing characteristics. After data screening, the average Q-s curve of Pile No. 1 and Pile No. 5 was taken as the benchmark, and the representative ultimate bearing capacity of a single pile determined by the 40 mm settlement criterion is 5860 kN. The test data of Pile No. 3 and Pile No. 4 were retained as independent validation data. A three-dimensional finite element model considering the cohesive contact behavior at the pile–rock/soil interface was established using ABAQUS. After calibration with the test results, the error between the simulated and measured bearing capacity is −3.4%, demonstrating good model reliability. Parametric analysis indicates that the bearing capacity increases linearly with the grouting volume increase rate Vinc, with the expansion effect being the main enhancement mechanism; the improvement amplitude under hard rock conditions is significantly smaller than that in cohesive soils. The effect of uniaxial compressive strength qu of hard rock on bearing capacity is negligible because the capacity is controlled by the pile–rock interface shear strength. The bearing capacity increases approximately linearly with the rock-socketed depth Lr, and a minimum rock-socketed depth of 1.0 m is recommended. Analysis of the load-transfer mechanism shows that rock-socketed HBMPs rely mainly on shaft resistance (accounting for 90.6%), and the axial force decays significantly along the pile length. Elastic compression of the pile accounts for 78% of the pile head settlement, and the limited displacement at the pile tip leads to insufficient mobilization of end bearing. A modified bearing capacity formula considering the grouting expansion effect is established with shaft resistance as the core. A hierarchical validation strategy is adopted to test its predictive ability: for the finite element cases not participating in parameter calibration, the prediction error is within ±2%; for the field test piles, the prediction error is +7.9%; and for Pile No. 3 and Pile No. 4, the errors are +1.7% and −2.1%, respectively. These values are significantly better than those of existing methods (errors ranging from −72.1% to +54.5%). The research results can provide a theoretical basis for the design of single HBMP bearing capacity under rock-socketed conditions. Full article
(This article belongs to the Special Issue Advanced Technology in Geotechnical Engineering)
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