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Keywords = simplification rule

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17 pages, 3898 KB  
Article
Zone-Based Simplification of Fuzzy Logic Controllers for Switched Reluctance Motor Drives
by Abbas Uğurenver and Ahmed Ibrahim Khudhur Khudhur
Electronics 2025, 14(21), 4248; https://doi.org/10.3390/electronics14214248 - 30 Oct 2025
Cited by 1 | Viewed by 594 | Correction
Abstract
In the context of fuzzy logic speed control for switching reluctance motor (SRM) applications, the objective of this work is to propose a unique zone-based simplification technique. Using the procedure that has been outlined, it is made easier to reduce membership functions as [...] Read more.
In the context of fuzzy logic speed control for switching reluctance motor (SRM) applications, the objective of this work is to propose a unique zone-based simplification technique. Using the procedure that has been outlined, it is made easier to reduce membership functions as well as rule sets in a logical manner. This is accomplished by splitting the error–change-of-error plane into discrete decision zones. This method is separate from heuristic or adaptive reduction strategies since it employs a systematic framework that reduces the number of rules from 49 in the standard design to 9 and 5 without compromising the accuracy of the control. This is accomplished without adversely affecting the performance of the control. The simplified controller that was produced as a consequence of this study decreases the amount of overshoot, enhances the speed at which a dynamic response happens, and makes it simpler to use on digital platforms that are affordable. All of these capabilities were achieved by the controller. Based on simulations and testing carried out in the real world, it has been determined that the zone-based simplified fuzzy controller that was proposed has a superior performance to traditional PID and full-rule fuzzy systems in terms of reaction time, stability, and energy efficiency. Taking all of this into consideration, it is evident that it has the potential to be useful in real-world applications for SRM drives that demand a high level of speed while maintaining a low cost factor. Full article
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21 pages, 13284 KB  
Article
Closed-Loop Control Strategies for a Modular Under-Actuated Smart Surface: From Threshold-Based Logic to Decentralized PID Regulation
by Edoardo Bianchi, Francisco Javier Brosed Dueso and José A. Yagüe-Fabra
Appl. Sci. 2025, 15(14), 7628; https://doi.org/10.3390/app15147628 - 8 Jul 2025
Viewed by 687
Abstract
In the field of intralogistics, new systems are continuously being studied to increase flexibility and adaptability while striving to maintain high handling capabilities and performance. Among these new systems, this article focuses on a novel under-actuated intelligent surface capable of performing various handling [...] Read more.
In the field of intralogistics, new systems are continuously being studied to increase flexibility and adaptability while striving to maintain high handling capabilities and performance. Among these new systems, this article focuses on a novel under-actuated intelligent surface capable of performing various handling tasks with a simplified design and without employing motors. The technology behind the device involves idle rotors, i.e., without motor-driven spinning, whose axis of rotation can be controlled in a few discrete positions. The system’s operation and digital model have already been tested and validated; however, a control system that makes the surface “smart” has not yet been developed. In this context, the following work analyzes control methodologies for the concept. Specifically, in a first phase, a threshold-based method is introduced and tested on a prototype of the surface for sorting and orientation operations. This basic technique involves actuating the surface modules according to pre-assigned rules once a chosen threshold condition is reached. In a second phase, instead, a decentralizd PID control is described and simulated based on real and potential industrial applications. Unlike the first method, in this case, it is the control law that defines the actuation and, through the dynamic description of the device, determines the best combination to achieve the goal. Additionally, the article illustrates how the difficulties introduced by the numerous nonlinearities, due to the under-actuation and the simplifications of the physical system, were overcome. For both control methods, promising results were obtained in terms of handling capability and errors in achieving the desired movement. Full article
(This article belongs to the Section Mechanical Engineering)
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18 pages, 332 KB  
Article
Hydrogenic Matrix Elements with Different Effective Charges: Non-Relativistic and Relativistic Cases
by Héctor O. Di Rocco and Julio C. Aguiar
Atoms 2025, 13(7), 60; https://doi.org/10.3390/atoms13070060 - 20 Jun 2025
Viewed by 910
Abstract
This work explores the evaluation of hydrogenic matrix elements for non-relativistic and relativistic cases under the Screened Hydrogenic Model (SHM). It focuses on scenarios where the initial and final states have different effective charges Z1Z2, deriving closed-form solutions [...] Read more.
This work explores the evaluation of hydrogenic matrix elements for non-relativistic and relativistic cases under the Screened Hydrogenic Model (SHM). It focuses on scenarios where the initial and final states have different effective charges Z1Z2, deriving closed-form solutions for particular cases n1=n2 and Z1=Z2. In addition, analytical expressions for radial matrix elements nl|rβ|nl and their relativistic counterparts are presented. These are applicable for discrete–discrete transitions and allow simplifications for specific configurations using Laplace transforms. The study discusses generalizations of SHM for calculating cross-sections in hot and dense plasmas, employing the Plane Wave Born Approximation (PWBA). It also addresses the transition from LS to jj coupling for matrix elements, providing rules for such transformations. Full article
(This article belongs to the Special Issue Atom and Plasma Spectroscopy)
23 pages, 3258 KB  
Article
Singular Configuration Analysis of Modular-Driven 4- and 6-DoF Parallel Topology Robots
by Zoltán Forgó, Ferenc Tolvaly-Roșca and Attila Csobán
Robotics 2025, 14(5), 61; https://doi.org/10.3390/robotics14050061 - 2 May 2025
Cited by 1 | Viewed by 1350
Abstract
The number of applications of parallel topology robots in industry is growing, and the interest of academics in finding new solutions and applications to implement such mechanisms is present all over the world. Industrywide, the most commonly used motion types need four- and [...] Read more.
The number of applications of parallel topology robots in industry is growing, and the interest of academics in finding new solutions and applications to implement such mechanisms is present all over the world. Industrywide, the most commonly used motion types need four- and six-degrees-of-freedom (DoF) robots. While there are commercial variants from different robot vendors, this study offers new alternatives to these. Based on Lie algebra synthesis, symmetrical parallel structures are identified, according to certain rules. Implementing 2-DoF actuation modules, the number of robot limbs is reduced compared to existing commercial robot structures. In terms of the applicability of a parallel mechanism (also concerning the control algorithm), it is important to determine singular configurations. Therefore, in addition to the kinematic schematics of the newly proposed mechanisms, their singular configurations are also discussed. Based on some dimensional simplifications (without a loss of generality), the conditions for the singular configurations are enumerated for the presented parallel topology robots with symmetrical kinematic chains. Finally, a comparison of the proposed mechanism is presented, considering its singular configurations. Full article
(This article belongs to the Section Intelligent Robots and Mechatronics)
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17 pages, 3036 KB  
Article
Auto-Derivation of Simplified Contracted Graphs with Quaternary Links and Re-Construction Contracted Graphs for Topology Synthesis of Parallel Manipulators
by Nijia Ye and Zhengwei Geng
Mathematics 2025, 13(7), 1076; https://doi.org/10.3390/math13071076 - 25 Mar 2025
Viewed by 539
Abstract
To address the complexity of constructing traditional topological contracted graphs due to the significant increase in the types and quantities of basic links during the synthesis of complex parallel mechanisms, this paper introduces a novel concept termed “Simplified Contraction Graph (SCG)”. The SCG [...] Read more.
To address the complexity of constructing traditional topological contracted graphs due to the significant increase in the types and quantities of basic links during the synthesis of complex parallel mechanisms, this paper introduces a novel concept termed “Simplified Contraction Graph (SCG)”. The SCG achieves a deeper level of simplification by omitting the consideration of ternary links on the basis of traditional contracted graphs. Firstly, this paper defines the application of characteristic strings to express the construction rules of SCG, thereby transforming the construction process into an automated generation problem of characteristic strings. Building on this, to mitigate the interference of link arrangement in the construction of conventional SCGs, this paper further proposes the concept of a simplified SCG and investigates its isomorphism properties. A program is designed based on the criteria for generating characteristic strings and isomorphism judgment, successfully generating several special SCGs. Finally, this paper introduces the edge-adding method, which enables the reconstruction of special SCGs into ordinary SCGs and contracted graphs, providing an effective tool for the topological synthesis of parallel mechanisms. Full article
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29 pages, 10229 KB  
Article
End-to-End Vector Simplification for Building Contours via a Sequence Generation Model
by Longfei Cui, Junkui Xu, Lin Jiang and Haizhong Qian
ISPRS Int. J. Geo-Inf. 2025, 14(3), 124; https://doi.org/10.3390/ijgi14030124 - 9 Mar 2025
Viewed by 1597
Abstract
Simplifying building contours involves reducing data volume while preserving the continuity, accuracy, and essential characteristics of building shapes. This presents significant challenges for sequence representation and generation. Traditional methods often rely on complex rule design, feature engineering, and iterative optimization. To overcome these [...] Read more.
Simplifying building contours involves reducing data volume while preserving the continuity, accuracy, and essential characteristics of building shapes. This presents significant challenges for sequence representation and generation. Traditional methods often rely on complex rule design, feature engineering, and iterative optimization. To overcome these limitations, this study proposes a Transformer-based Polygon Simplification Model (TPSM) for the end-to-end vector simplification of building contours. TPSM processes ordered vertex coordinate sequences of building contours, leveraging the inherent sequence modeling capabilities of the Transformer architecture to directly generate simplified coordinate sequences. To enhance spatial understanding, positional encoding is embedded within the multihead self-attention mechanism, allowing the TPSM to effectively capture relative vertex positions. Additionally, a self-supervised reconstruction mechanism is introduced, where random perturbations are applied to input sequences, and the model learns to reconstruct the original contours. This mechanism enables TPSM to better understand underlying geometric relationships and implicit simplification rules. Experiments were conducted using a 1:10,000 building dataset from Shenzhen, China, targeting a simplification scale of 1:25,000. The results demonstrate that TPSM outperforms five established simplification algorithms in controlling changes to building area, orientation, and shape fidelity, achieving an average intersection over union (IoU) of 0.901 and a complexity-aware IoU (C-IoU) of 0.735. Full article
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23 pages, 454 KB  
Article
New Simplification Rules for Databases with Positive and Negative Attributes
by Domingo López-Rodríguez, Manuel Ojeda-Hernández and Carlos Bejines
Mathematics 2025, 13(2), 309; https://doi.org/10.3390/math13020309 - 18 Jan 2025
Viewed by 960
Abstract
In this paper, new logical equivalences are presented within the simplification logic with mixed attributes paradigm, which allow the obtention of bases of shorter, easier-to-read attribute implications. In addition to the theoretical results which show that the proposed equivalences indeed hold in simplification [...] Read more.
In this paper, new logical equivalences are presented within the simplification logic with mixed attributes paradigm, which allow the obtention of bases of shorter, easier-to-read attribute implications. In addition to the theoretical results which show that the proposed equivalences indeed hold in simplification logic with mixed attributes, experimental results which showcase the effectiveness of this method are also provided. Furthermore, the simplification method presented is iterative and gives sufficiently good results in only one or two iterations, therefore presenting itself as a reasonable procedure in time-sensitive experiments. Full article
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14 pages, 1246 KB  
Perspective
The Evidence-Based Medicine Management of Endometriosis Should Be Updated for the Limitations of Trial Evidence, the Multivariability of Decisions, Collective Experience, Heuristics, and Bayesian Thinking
by Philippe R. Koninckx, Anastasia Ussia, Assia Stepanian, Ertan Saridogan, Mario Malzoni, Charles E. Miller, Jörg Keckstein, Arnaud Wattiez, Geert Page, Jan Bosteels, Emmanuel Lesaffre and Leila Adamyan
J. Clin. Med. 2025, 14(1), 248; https://doi.org/10.3390/jcm14010248 - 3 Jan 2025
Cited by 2 | Viewed by 4601
Abstract
Background/Objectives: The diagnosis and treatment of endometriosis should be based on the best available evidence. Emphasising the risk of bias, the pyramid of evidence has the double-blind, randomised controlled trial and its meta-analyses on top. After the grading of all evidence by [...] Read more.
Background/Objectives: The diagnosis and treatment of endometriosis should be based on the best available evidence. Emphasising the risk of bias, the pyramid of evidence has the double-blind, randomised controlled trial and its meta-analyses on top. After the grading of all evidence by a group of experts, clinical guidelines are formulated using well-defined rules. Unfortunately, the impact of evidence-based medicine (EBM) on the management of endometriosis has been limited and, possibly, occasionally harmful. Methods: For this research, the inherent problems of diagnosis and treatment were discussed by a working group of endometriosis and EBM specialists, and the relevant literature was reviewed. Results: Most clinical decisions are multivariable, but randomized controlled trials (RCTs) cannot handle multivariability because adopting a factorial design would require prohibitively large cohorts and create randomization problems. Single-factor RCTs represent a simplification of the clinical reality. Heuristics and intuition are both important for training and decision-making in surgery; experience, Bayesian thinking, and learning from the past are seldom considered. Black swan events or severe complications and accidents are marginally discussed in EBM since trial evidence is limited for rare medical events. Conclusions: The limitations of EBM for managing endometriosis and the complementarity of multivariability, heuristics, Bayesian thinking, and experience should be recognized. Especially in surgery, the value of training and heuristics, as well as the importance of documenting the collective experience and of the prevention of complications, are fundamental. These additions to EBM and guidelines will be useful in changing the Wild West mentality of surgery resulting from the limited scope of EBM data because of the inherent multivariability, combined with the low number of similar interventions. Full article
(This article belongs to the Section Obstetrics & Gynecology)
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37 pages, 1179 KB  
Article
A Rule-Based Parser in Comparison with Statistical Neuronal Approaches in Terms of Grammar Competence
by Simon M. Strübbe, Alexander T. D. Grünwald, Irina Sidorenko and Renée Lampe
Appl. Sci. 2025, 15(1), 87; https://doi.org/10.3390/app15010087 - 26 Dec 2024
Cited by 2 | Viewed by 2707
Abstract
The “Easy Language” standard was created to help individuals with cognitive disabilities understand texts more easily. Typically, text simplification is performed by language experts and is available for limited materials. We introduce a new software tool designed to analyze and simplify any text [...] Read more.
The “Easy Language” standard was created to help individuals with cognitive disabilities understand texts more easily. Typically, text simplification is performed by language experts and is available for limited materials. We introduce a new software tool designed to analyze and simplify any text according to the “Easy Language” rules. This tool uses a rule-based system, conducting a full grammatical analysis of each sentence and then simplifying it into a grammatically correct form. Unlike neuronal approaches, which are based on statistics and are very popular today, our rule-based approach explicitly addresses language ambiguities by examining all possible interpretations and eliminating the incorrect ones. The purpose of the present study is to compare the performance of our rule-base parser with two state-of-the-art statistical parsers, one based on dependencies between words (SpaCy parser) and the other based on linguistic constituents (Stanford parser). Although large language models (LLMs), which are the technical basis of the software ChatGPT, were not designed specifically for grammatical parsing, because of their popularity, users, especially language learners, often ask them grammatical questions as well. Therefore, we use LLMs as supplementary models for comparison. LMMs produce grammatically correct text on any topic; however, their grammar knowledge is implicit within the trained weights. To evaluate how well state-of-the-art methods can perform a grammatical analysis, we parse ten sentences with our tool, the statistical parsers from SpaCy and Stanford, and ask two LLMs equivalent grammar questions. The results show that our rule-based method provides a more informative and reliable grammatical analysis compared to these two parsers and outperforms LLMs in that specific task. Full article
(This article belongs to the Special Issue Natural Language Processing (NLP) and Applications—2nd Edition)
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25 pages, 6176 KB  
Article
Numerical Permeation Models to Predict the Annulus Composition of Flexible Pipes
by João Marcos B. Vieira and José Renato M. de Sousa
J. Mar. Sci. Eng. 2024, 12(12), 2294; https://doi.org/10.3390/jmse12122294 - 13 Dec 2024
Cited by 1 | Viewed by 1388
Abstract
The migration of acid gases through the pressure sheath of flexible pipes may induce a corrosive environment that can lead to steel armors’ failure by SCC (stress corrosion cracking). This permeation process depends on temperature, partial pressures, materials, and the pipe’s geometry. However, [...] Read more.
The migration of acid gases through the pressure sheath of flexible pipes may induce a corrosive environment that can lead to steel armors’ failure by SCC (stress corrosion cracking). This permeation process depends on temperature, partial pressures, materials, and the pipe’s geometry. However, there are few works related to permeation modeling in flexible pipes, and these works usually contain significant simplification in pipes’ geometry. Hence, this work proposes two finite element (FE) permeation models and discusses the effects of the pipe’s characteristics. The models were developed in Ansys®, considering two- (2DFE) and three-dimensional (3DFE) approaches, and rely on gas fugacities instead of concentrations to describe the mass transport phenomenon. A radial temperature gradient is also considered, and the heat transfer is uncoupled from the mass transfer. Dry and flooded annulus analyses were conducted with the proposed models. In dry conditions, the results obtained with the 2DFE and the 3DFE approaches showed no significant differences, demonstrating that 3D effects are irrelevant. Hence, the permeation phenomenon is ruled by the permeation properties of the polymeric layers (pressure and outer sheaths) and possible shield effects promoted by the metallic armors. In contrast, the flooded annulus analyses resulted in a non-uniform fugacity distribution in the annulus with significant differences between the 2DFE and the 3DFE approaches, showing the importance of modeling the helical geometries of the metallic armors in this condition. Finally, a conservative 2DFE approach, which neglects the contribution of the pressure sheath, is proposed to analyze the flooded annulus condition, aiming to overcome the high computational cost demanded by the 3DFE approach. Full article
(This article belongs to the Special Issue Advanced Research in Flexible Risers and Pipelines)
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21 pages, 59527 KB  
Article
Recognition and Classification of Typical Building Shapes Based on YOLO Object Detection Models
by Xiao Wang, Haizhong Qian, Limin Xie, Xu Wang and Bohao Li
ISPRS Int. J. Geo-Inf. 2024, 13(12), 433; https://doi.org/10.3390/ijgi13120433 - 2 Dec 2024
Cited by 6 | Viewed by 2399
Abstract
The recognition and classification of building shapes are the prerequisites and foundation for building simplification, matching, and change detection, which have always been important research problems in the field of cartographic generalization. Due to the ambiguity and uncertainty of building shape outlines, it [...] Read more.
The recognition and classification of building shapes are the prerequisites and foundation for building simplification, matching, and change detection, which have always been important research problems in the field of cartographic generalization. Due to the ambiguity and uncertainty of building shape outlines, it is difficult to describe them using unified rules, which has always limited the quality and automation level of building shape recognition. In response to the above issues, by introducing object detection technology in computer vision, this article proposes a building shape recognition and classification method based on the YOLO object detection model. Firstly, for different types of buildings, four levels of building training data samples are constructed, and YOLOv5, YOLOv8, YOLOv9, and YOLOv9 integrating attention modules are selected for training. The trained models are used to test the shape judgment of buildings in the dataset and verify the learning effectiveness of the models. The experimental results show that the YOLO model can accurately classify and locate the shape of buildings, and its recognition and detection effect have the ability to simulate advanced human visual cognition, which provides a new solution for the fuzzy shape recognition of buildings with complex outlines and local deformation. Full article
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19 pages, 1117 KB  
Article
Automatic Simplification of Lithuanian Administrative Texts
by Justina Mandravickaitė, Eglė Rimkienė, Danguolė Kotryna Kapkan, Danguolė Kalinauskaitė and Tomas Krilavičius
Algorithms 2024, 17(11), 533; https://doi.org/10.3390/a17110533 - 20 Nov 2024
Viewed by 1673
Abstract
Text simplification reduces the complexity of text while preserving essential information, thus making it more accessible to a broad range of readers, including individuals with cognitive disorders, non-native speakers, children, and the general public. In this paper, we present experiments on text simplification [...] Read more.
Text simplification reduces the complexity of text while preserving essential information, thus making it more accessible to a broad range of readers, including individuals with cognitive disorders, non-native speakers, children, and the general public. In this paper, we present experiments on text simplification for the Lithuanian language, aiming to simplify administrative texts to a Plain Language level. We fine-tuned mT5 and mBART models for this task and evaluated the effectiveness of ChatGPT as well. We assessed simplification results via both quantitative metrics and qualitative evaluation. Our findings indicated that mBART performed the best as it achieved the best scores across all evaluation metrics. The qualitative analysis further supported these findings. ChatGPT experiments showed that it responded quite well to a short and simple prompt to simplify the given text; however, it ignored most of the rules given in a more elaborate prompt. Finally, our analysis revealed that BERTScore and ROUGE aligned moderately well with human evaluations, while BLEU and readability scores indicated lower or even negative correlations Full article
(This article belongs to the Section Evolutionary Algorithms and Machine Learning)
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11 pages, 1517 KB  
Article
Modified Use of the Component Method to Get More Realistic Force Distribution in Joints of Steel Structures
by László Radnay and Imre Kovács
Buildings 2024, 14(11), 3553; https://doi.org/10.3390/buildings14113553 - 7 Nov 2024
Cited by 1 | Viewed by 1431
Abstract
According to the EN 1993-1-8 Standard, the moment resistance of end-plated connections can be calculated with the use of the component method. In this, a pair-of-force defines the moment resistance. The magnitude and the location of the compression force can be accurately identified. [...] Read more.
According to the EN 1993-1-8 Standard, the moment resistance of end-plated connections can be calculated with the use of the component method. In this, a pair-of-force defines the moment resistance. The magnitude and the location of the compression force can be accurately identified. The tension force part is usually the resultant of parallel forces appearing in line with the bolt rows. Following the rules of manual calculation and using a mechanical finite element model, where each component is modelled with spring elements, in some—easily identifiable—cases, leads to different force distribution. The simplifications defined in the Standard provide a longer arm for the same force, and because of this, larger moment resistance at the expense of safety. In this work, an alternative calculation method will be presented that provides the same force values in each bolt row, as the mechanical model of the connection, without constructing the finite element model. Full article
(This article belongs to the Section Building Structures)
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22 pages, 1138 KB  
Systematic Review
A Systematic Review of the Twelve Most Popular Bean Varieties, Highlighting Their Potential as Functional Foods Based on the Health Benefits Derived from Their Nutritional Profiles, Focused on Non-Communicable Diseases
by Maria Dimopoulou, Patroklos Vareltzis and Olga Gortzi
Appl. Sci. 2024, 14(22), 10215; https://doi.org/10.3390/app142210215 - 7 Nov 2024
Cited by 12 | Viewed by 10340
Abstract
According to the US Department of Agriculture, more than 4000 types of beans are cultivated in the United States and worldwide; nevertheless, the demand for beans continues to rise. To some extent, diet can treat inflammation and consequently reduce the chances of developing [...] Read more.
According to the US Department of Agriculture, more than 4000 types of beans are cultivated in the United States and worldwide; nevertheless, the demand for beans continues to rise. To some extent, diet can treat inflammation and consequently reduce the chances of developing comorbidities, such as diabetes. A diet based on alternative plant protein sources, such as beans, is a sustainable solution for overall health due to the overconsumption of meat that characterizes Western societies and is even more important for regions that suffer from malnutrition, such as Africa. Reviewing the nutritional profile of the different varieties of beans produced in various locations would help enhance their quality, strengthen the role of producer groups, and protecting Geographical Indications (GI), thereby increasing simplification, sustainability, and transparency towards consumers. PubMed-Medline, Web of Science, Scopus, and Cochrane Library databases were searched for relevant articles published by 30 March 2024. The results have given the green light to the reform of EFSA rules, strengthening the health claims of beans, protecting the GI for each variety, and also highlighting the public demands for functional foods based on the nutritional aspects of this product and its impact on disease management or prevention. Full article
(This article belongs to the Special Issue Enrichment of Foods with Phytonutrients)
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18 pages, 9623 KB  
Article
Study on Multi-Crack Damage Evolution and Fatigue Life of Corroded Steel Wires Inside In-Service Bridge Suspenders
by Luming Deng and Yulin Deng
Appl. Sci. 2024, 14(20), 9596; https://doi.org/10.3390/app14209596 - 21 Oct 2024
Cited by 3 | Viewed by 2045
Abstract
The parallel steel wires used in arch bridge suspenders experience random corrosion damage on their surfaces during service. Corrosion damage, including micro-cracks, pitting, and a combination of both, leads to significant stress concentration under axial loading, which affects the performance of the steel [...] Read more.
The parallel steel wires used in arch bridge suspenders experience random corrosion damage on their surfaces during service. Corrosion damage, including micro-cracks, pitting, and a combination of both, leads to significant stress concentration under axial loading, which affects the performance of the steel wires. The change in the stress field caused by surface damage alters the stress intensity factor at the crack tip, and the presence of adjacent crack tips significantly amplifies the stress intensity factor, thereby accelerating crack propagation. The development of small surface damages in the steel wires is difficult to control and observe through experiments. By utilizing finite element methods for simulation, it is possible to intuitively analyze the crack propagation process, the trend of stress changes at the crack tip, and the interaction between damages. Numerical simulation results based on Paris’ law indicate that corrosion pits have a certain impact on the stress intensity factor at the crack tip. The propagation process of coplanar double cracks is highly sensitive to the initial crack size and the distance between adjacent crack tips. When the crack spacing is less than the crack depth, the stress intensity factor at the adjacent crack tips exhibits significant amplification. Based on this phenomenon, the coplanar double-crack system can be simplified to a complete single crack for analysis. By comparing the fatigue life of the double-crack system with that of the equivalent single crack, the effectiveness of the simplification rule has been validated. Full article
(This article belongs to the Special Issue Construction Materials: Characterization, Structure and Durability)
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