Pub Date : 2025-01-23DOI: 10.1016/j.apm.2025.115971
M. Lei , T. Li , H. Meng
In this paper, the performance of the proposed improved boundary knot method and the method of fundamental solutions in solving Helmholtz-type equations within multi-connected domains is investigated. The method of fundamental solutions typically requires multiple layers of source points, resulting in a tedious and time-consuming process of optimizing their distribution. Although the traditional boundary knot method circumvents this challenge by using non-singular general solutions, it often struggles to deliver satisfactory accuracy for complex problems. To address these limitations, the improved boundary knot method that incorporates a ghost points technique is proposed. These ghost points can be positioned flexibly in various configurations, such as circular or cloud-like patterns, located either inside or outside the problem domain. To further optimize the ghost points' position, we study the influence of the free parameter ghost radius R, where two strategies, namely the effective condition number and economic effective condition number, are employed and analyzed. Finally, various examples demonstrate that the improved boundary knot method outperforms the conventional version. Compared to the method of fundamental solutions, it simplifies the placement of source/ghost nodes while maintaining accuracy. Code is available at https://github.com/LT306/one/tree/main/IBKM
{"title":"Comparative analysis of the improved boundary knot and fundamental solutions methods for complex multi-connected Helmholtz-type equations","authors":"M. Lei , T. Li , H. Meng","doi":"10.1016/j.apm.2025.115971","DOIUrl":"10.1016/j.apm.2025.115971","url":null,"abstract":"<div><div>In this paper, the performance of the proposed improved boundary knot method and the method of fundamental solutions in solving Helmholtz-type equations within multi-connected domains is investigated. The method of fundamental solutions typically requires multiple layers of source points, resulting in a tedious and time-consuming process of optimizing their distribution. Although the traditional boundary knot method circumvents this challenge by using non-singular general solutions, it often struggles to deliver satisfactory accuracy for complex problems. To address these limitations, the improved boundary knot method that incorporates a ghost points technique is proposed. These ghost points can be positioned flexibly in various configurations, such as circular or cloud-like patterns, located either inside or outside the problem domain. To further optimize the ghost points' position, we study the influence of the free parameter ghost radius <em>R</em>, where two strategies, namely the effective condition number and economic effective condition number, are employed and analyzed. Finally, various examples demonstrate that the improved boundary knot method outperforms the conventional version. Compared to the method of fundamental solutions, it simplifies the placement of source/ghost nodes while maintaining accuracy. Code is available at <span><span>https://github.com/LT306/one/tree/main/IBKM</span><svg><path></path></svg></span></div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115971"},"PeriodicalIF":4.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-22DOI: 10.1016/j.apm.2025.115967
Sayandip Ganguly, Koushik Roy
Localization of damage using modal parameter changes has been the focus of research in many recent studies. Efforts have also been made to establish an analytical correlation between changes in modal response from the healthy state and the eventual reduction in stiffness. Prevailing methodologies predominantly integrate baseline responses to attain these objectives. However, non-availability of pre-recorded data practically complicates the application of reference state-based damage investigations. In the present study, a novel formulation is proposed for evaluation of existing crack with spectral responses of only damaged state. Efficiency of derived mathematical formulation is numerically verified on a shear building with several damage cases. Robustness of the method is then examined through noise sensitivity analysis. Further, an experimental investigation is conducted on a reduced scale in-house steel building model. Two cases of damage severity are examined by introducing reduced cross-sectional member at the damage location. Finally, practical applicability of the method is explored with a case study using real post-damage data of a 7-story building. Significant accuracy evolved from these exhaustive analyses, highlights the potential of present baseline-free damage quantification technique. This instantaneous data-based methodology can further be extended in future to assess residual useful life of a structure.
{"title":"Baseline-free localization and quantification of structural damage using spectral response","authors":"Sayandip Ganguly, Koushik Roy","doi":"10.1016/j.apm.2025.115967","DOIUrl":"10.1016/j.apm.2025.115967","url":null,"abstract":"<div><div>Localization of damage using modal parameter changes has been the focus of research in many recent studies. Efforts have also been made to establish an analytical correlation between changes in modal response from the healthy state and the eventual reduction in stiffness. Prevailing methodologies predominantly integrate baseline responses to attain these objectives. However, non-availability of pre-recorded data practically complicates the application of reference state-based damage investigations. In the present study, a novel formulation is proposed for evaluation of existing crack with spectral responses of only damaged state. Efficiency of derived mathematical formulation is numerically verified on a shear building with several damage cases. Robustness of the method is then examined through noise sensitivity analysis. Further, an experimental investigation is conducted on a reduced scale in-house steel building model. Two cases of damage severity are examined by introducing reduced cross-sectional member at the damage location. Finally, practical applicability of the method is explored with a case study using real post-damage data of a 7-story building. Significant accuracy evolved from these exhaustive analyses, highlights the potential of present baseline-free damage quantification technique. This instantaneous data-based methodology can further be extended in future to assess residual useful life of a structure.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115967"},"PeriodicalIF":4.4,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-22DOI: 10.1016/j.apm.2025.115975
Ji Li , Aiwen Liu , Yan Wang
Cardiovascular disease has become a major cause of global mortality. Clinically, quantitative assessment of cardiac MR image is usually used to determine the type and severity of cardiovascular disease, in which segmentation of cardiac MR image is a fundamental but important step. However, due to the inhomogeneity and special anatomical structures, accurate segmentation of cardiac MR images is still a challenging task. This paper proposes a double nonzero level set model for the segmentation of cardiac MR images, incorporating an adaptive convexity preserving mechanism and an improved distance regularization term. The double nonzero level set is capable of simultaneously and rapidly segmenting the left ventricle (LV) and right ventricle (RV). The adaptive convexity preserving mechanism guarantees that the segmentation of LV encompasses the cavity, papillary muscles and trabeculae while preserving convexity to meet clinical criteria. In addition, it ensures that RV retains its inherent physiological form, i.e. crescent-like shape. The improved distance regularization term effectively eliminates the need for reinitialization of double level set functions. The proposed model is evaluated on the data of ACDC MICCAI 2017. Experimental results show that in the end-diastolic (ED) and end-systolic (ES) phases, the mean Dice coefficients of LV segmentation are 0.961 (ED) and 0.936 (ES), with mean Hausdorff distances of 4.89 (ED) and 5.79 (ES), while the mean Dice coefficients of RV segmentation are 0.952 (ED) and 0.914 (ES), with mean Hausdorff distances of 8.52 (ED) and 9.60 (ES). The prominent advantage of our model is that, without the requirement of manual annotation and tedious training, it exhibits segmentation accuracy and robustness comparable to deep learning-based cardiac segmentation models. Especially, the segmentation accuracy of RV surpasses that of current state-of-the-art models.
{"title":"ACPDNLS: Adaptive convexity preserving double nonzero level set for cardiac MR image segmentation","authors":"Ji Li , Aiwen Liu , Yan Wang","doi":"10.1016/j.apm.2025.115975","DOIUrl":"10.1016/j.apm.2025.115975","url":null,"abstract":"<div><div>Cardiovascular disease has become a major cause of global mortality. Clinically, quantitative assessment of cardiac MR image is usually used to determine the type and severity of cardiovascular disease, in which segmentation of cardiac MR image is a fundamental but important step. However, due to the inhomogeneity and special anatomical structures, accurate segmentation of cardiac MR images is still a challenging task. This paper proposes a double nonzero level set model for the segmentation of cardiac MR images, incorporating an adaptive convexity preserving mechanism and an improved distance regularization term. The double nonzero level set is capable of simultaneously and rapidly segmenting the left ventricle (LV) and right ventricle (RV). The adaptive convexity preserving mechanism guarantees that the segmentation of LV encompasses the cavity, papillary muscles and trabeculae while preserving convexity to meet clinical criteria. In addition, it ensures that RV retains its inherent physiological form, i.e. crescent-like shape. The improved distance regularization term effectively eliminates the need for reinitialization of double level set functions. The proposed model is evaluated on the data of ACDC MICCAI 2017. Experimental results show that in the end-diastolic (ED) and end-systolic (ES) phases, the mean Dice coefficients of LV segmentation are 0.961 (ED) and 0.936 (ES), with mean Hausdorff distances of 4.89 (ED) and 5.79 (ES), while the mean Dice coefficients of RV segmentation are 0.952 (ED) and 0.914 (ES), with mean Hausdorff distances of 8.52 (ED) and 9.60 (ES). The prominent advantage of our model is that, without the requirement of manual annotation and tedious training, it exhibits segmentation accuracy and robustness comparable to deep learning-based cardiac segmentation models. Especially, the segmentation accuracy of RV surpasses that of current state-of-the-art models.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115975"},"PeriodicalIF":4.4,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-22DOI: 10.1016/j.apm.2025.115968
Haojie Hou , Youguo Wang , Qiqing Zhai , Xianli Sun
Activity-driven networks have become a key paradigm for studying the time evolution of stochastic networked systems. Consider the fact that individuals in activity-driven networks have some degree of memory, and they assess the credibility of current information based on their prior knowledge. In addition, the number of potential participants in rumor propagation dynamically changes, and the actual network topology driven by activity is affected by environmental noise. Previous studies have overlooked the stochastic nature of activities and instead generalized the system dynamics with constant parameters. To fill this gap, we propose a stochastic fractional-order rumor propagation model that takes into account the variation of node activity rates and conduct an optimal control study. We utilize Caputo fractional-order derivatives to depict memorability, model stochasticity using standard Wiener processes, and formulate fractional-order stochastic differential equations to describe the dynamics of rumor propagation on activity-driven networks. Firstly, stochastic fractional-order equations with consistent unit dimensions are derived. Secondly, the existence and uniqueness of the solution to the stochastic fractional-order model are proven using Picard's iterative method, and the issue of rumor extinction is investigated. Then, Pontryagin's minimum principle and optimal control theory are applied to derive the necessary conditions for fractional-order optimal control. Finally, the theoretical results are validated using two real datasets, and the optimal fractional order is determined through a real-world case. The simulation results show that the smaller the fractional order, the more significant the suppression effect on rumor outbreaks, but the extinction time of the rumor is prolonged accordingly. In addition, the appropriate level of noise intensity can effectively suppress rumor outbreaks, suggesting the presence of stochastic resonance. Furthermore, the implementation of optimal control can effectively curb rumor outbreaks and shorten the life cycle of rumors.
{"title":"Optimal control of stochastic fractional rumor propagation model in activity-driven networks","authors":"Haojie Hou , Youguo Wang , Qiqing Zhai , Xianli Sun","doi":"10.1016/j.apm.2025.115968","DOIUrl":"10.1016/j.apm.2025.115968","url":null,"abstract":"<div><div>Activity-driven networks have become a key paradigm for studying the time evolution of stochastic networked systems. Consider the fact that individuals in activity-driven networks have some degree of memory, and they assess the credibility of current information based on their prior knowledge. In addition, the number of potential participants in rumor propagation dynamically changes, and the actual network topology driven by activity is affected by environmental noise. Previous studies have overlooked the stochastic nature of activities and instead generalized the system dynamics with constant parameters. To fill this gap, we propose a stochastic fractional-order rumor propagation model that takes into account the variation of node activity rates and conduct an optimal control study. We utilize Caputo fractional-order derivatives to depict memorability, model stochasticity using standard Wiener processes, and formulate fractional-order stochastic differential equations to describe the dynamics of rumor propagation on activity-driven networks. Firstly, stochastic fractional-order equations with consistent unit dimensions are derived. Secondly, the existence and uniqueness of the solution to the stochastic fractional-order model are proven using Picard's iterative method, and the issue of rumor extinction is investigated. Then, Pontryagin's minimum principle and optimal control theory are applied to derive the necessary conditions for fractional-order optimal control. Finally, the theoretical results are validated using two real datasets, and the optimal fractional order is determined through a real-world case. The simulation results show that the smaller the fractional order, the more significant the suppression effect on rumor outbreaks, but the extinction time of the rumor is prolonged accordingly. In addition, the appropriate level of noise intensity can effectively suppress rumor outbreaks, suggesting the presence of stochastic resonance. Furthermore, the implementation of optimal control can effectively curb rumor outbreaks and shorten the life cycle of rumors.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115968"},"PeriodicalIF":4.4,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143072090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sediment-laden flow is a common phenomenon in nature and the deposition of sediments can make a great difference in landscape formation or marine systems. The complexity of this issue can be further increased with temporal variations in the free surface elevation. This paper aims to present a two-phase flow model that effectively integrates the non-hydrostatic free surface model with the Lagrangian point-particle model. The free surface elevation is conceptualized as a height function and is tracked using a Lagrangian-Eulerian method. This new model is validated by five test cases, showing a good agreement with analytical or experimental results. This demonstrates the model's proficiency in handling sediment-laden flow under various free surface flow conditions, particularly with surface waves. Consequently, the proposed model holds promise for investigating sediment-laden flow issues in coastal regions.
{"title":"Coupling of non-hydrostatic model with unresolved point-particle model for simulating particle-laden free surface flows","authors":"Yuhang Chen , Yongping Chen , Zhenshan Xu , Pengzhi Lin , Zhihua Xie","doi":"10.1016/j.apm.2025.115962","DOIUrl":"10.1016/j.apm.2025.115962","url":null,"abstract":"<div><div>Sediment-laden flow is a common phenomenon in nature and the deposition of sediments can make a great difference in landscape formation or marine systems. The complexity of this issue can be further increased with temporal variations in the free surface elevation. This paper aims to present a two-phase flow model that effectively integrates the non-hydrostatic free surface model with the Lagrangian point-particle model. The free surface elevation is conceptualized as a height function and is tracked using a Lagrangian-Eulerian method. This new model is validated by five test cases, showing a good agreement with analytical or experimental results. This demonstrates the model's proficiency in handling sediment-laden flow under various free surface flow conditions, particularly with surface waves. Consequently, the proposed model holds promise for investigating sediment-laden flow issues in coastal regions.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115962"},"PeriodicalIF":4.4,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-22DOI: 10.1016/j.apm.2025.115974
Xiaoyan Li, Zhimin Zhang
In this paper, we introduce an efficient surrogate loss method for large-scale expectile regression in non-randomly distributed scenarios. Specifically, a Poisson subsampling-based distributed asymmetric least squares estimator is proposed. Our theoretical analysis establishes the consistency and asymptotic normality as the dimensionality tends to infinity, demonstrating that the proposed estimator achieves statistical efficiency comparable to that of the global estimator. A practical three-step algorithm is presented, offering an efficient implementation in practical applications. The proposed estimator exhibits two notable advantages: (i) it is communication-efficient, utilising all the data but only requiring the transmission of a small subsample and the local gradient from each local site; and (ii) it can effectively adapt to unevenly distributed data and non-randomly stored data. Within the Newton-Raphson algorithm, the initial value and the Hessian matrix are computed with enhanced robustness using the Poisson subsampling-derived subsample than using one local dataset or uniform subsampling-derived subsample. Both simulation studies and empirical results confirm that the proposed estimator enhanced estimation efficiency relative to existing methods.
{"title":"Efficient distributed estimation for expectile regression in increasing dimensions","authors":"Xiaoyan Li, Zhimin Zhang","doi":"10.1016/j.apm.2025.115974","DOIUrl":"10.1016/j.apm.2025.115974","url":null,"abstract":"<div><div>In this paper, we introduce an efficient surrogate loss method for large-scale expectile regression in non-randomly distributed scenarios. Specifically, a Poisson subsampling-based distributed asymmetric least squares estimator is proposed. Our theoretical analysis establishes the consistency and asymptotic normality as the dimensionality tends to infinity, demonstrating that the proposed estimator achieves statistical efficiency comparable to that of the global estimator. A practical three-step algorithm is presented, offering an efficient implementation in practical applications. The proposed estimator exhibits two notable advantages: (i) it is communication-efficient, utilising all the data but only requiring the transmission of a small subsample and the local gradient from each local site; and (ii) it can effectively adapt to unevenly distributed data and non-randomly stored data. Within the Newton-Raphson algorithm, the initial value and the Hessian matrix are computed with enhanced robustness using the Poisson subsampling-derived subsample than using one local dataset or uniform subsampling-derived subsample. Both simulation studies and empirical results confirm that the proposed estimator enhanced estimation efficiency relative to existing methods.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115974"},"PeriodicalIF":4.4,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-21DOI: 10.1016/j.apm.2025.115959
Shuya Onodera , Takayuki Yamada
In this study, a topology optimization method for coupled thermomechanical problems is proposed by incorporating approximated thermal radiation boundary conditions that depend on design variables. The challenge of designing mechanical structures influenced by thermal radiation is briefly discussed. Partial Differential Equations are introduced to represent the geometric features influenced by thermal radiation. The boundary under thermal radiation conditions is expressed using the solution. In addition, a mathematical model is developed to approximate the view factor, which is related to the contribution of thermal radiation. To address this, the historical temperature data calculated during the optimization iterations are employed to create a linear approximation of the sensitivity analysis. The objective functional for temperature and displacement are evaluated using the weighted sum method. Furthermore, a specific optimization algorithm using the finite element method is proposed. The proposed method is applied to two- and three-dimensional problems to confirm the effectiveness and applicability of the proposed method.
{"title":"Topology optimization for coupled thermomechanical problems with approximated thermal radiation boundary conditions depending on design variables","authors":"Shuya Onodera , Takayuki Yamada","doi":"10.1016/j.apm.2025.115959","DOIUrl":"10.1016/j.apm.2025.115959","url":null,"abstract":"<div><div>In this study, a topology optimization method for coupled thermomechanical problems is proposed by incorporating approximated thermal radiation boundary conditions that depend on design variables. The challenge of designing mechanical structures influenced by thermal radiation is briefly discussed. Partial Differential Equations are introduced to represent the geometric features influenced by thermal radiation. The boundary under thermal radiation conditions is expressed using the solution. In addition, a mathematical model is developed to approximate the view factor, which is related to the contribution of thermal radiation. To address this, the historical temperature data calculated during the optimization iterations are employed to create a linear approximation of the sensitivity analysis. The objective functional for temperature and displacement are evaluated using the weighted sum method. Furthermore, a specific optimization algorithm using the finite element method is proposed. The proposed method is applied to two- and three-dimensional problems to confirm the effectiveness and applicability of the proposed method.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115959"},"PeriodicalIF":4.4,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-21DOI: 10.1016/j.apm.2025.115955
Yutao Guo, Manjur Alam
Beams resting on elastic foundation are widely employed as smart nanostructures, which commonly consists of intelligent materials to offer multifunctional capabilities. Molecular interactions, in these cases, are incorporated into the mechanics of nanostructures through the Nonlocal (NL) and Strain Gradient (SG) continuum model. Surface elasticity theory integrates the influence of surface molecules resulting from high surface-to-bulk ratio of nanostructures. This study explores the nonlinear bending and thermal postbuckling of magneto-electro-elastic (MEE), NLSG beam including the impact of surface molecules. The governing equations for laminated MEE beam supported on Pasternak foundation are derived using variational principles, involving higher-order shear deformation theory and von-Kármán nonlinearity. The electric and magnetic potential are given by a thickness-wise cosine distribution. A closed-form analytical solution is obtained by solving the resulting nonlinear partial differential equations using asymptotic expansions of the field variables. The numerical illustration of the solution highlights the importance of molecular interaction in bending compared to the postbuckling scenario. The prevailing impact of foundation stiffness is demonstrated. Surface molecules are observed to show a comparable effect as the electric or magnetic fields. The solution can be used to develop basic design concepts for MEE nanobeams at different temperatures and to validate numerical solutions.
{"title":"Nonlinear bending and thermal postbuckling of magneto-electro-elastic nonlocal strain-gradient beam including surface effects","authors":"Yutao Guo, Manjur Alam","doi":"10.1016/j.apm.2025.115955","DOIUrl":"10.1016/j.apm.2025.115955","url":null,"abstract":"<div><div>Beams resting on elastic foundation are widely employed as smart nanostructures, which commonly consists of intelligent materials to offer multifunctional capabilities. Molecular interactions, in these cases, are incorporated into the mechanics of nanostructures through the Nonlocal (NL) and Strain Gradient (SG) continuum model. Surface elasticity theory integrates the influence of surface molecules resulting from high surface-to-bulk ratio of nanostructures. This study explores the nonlinear bending and thermal postbuckling of magneto-electro-elastic (MEE), NLSG beam including the impact of surface molecules. The governing equations for laminated MEE beam supported on Pasternak foundation are derived using variational principles, involving higher-order shear deformation theory and von-Kármán nonlinearity. The electric and magnetic potential are given by a thickness-wise cosine distribution. A closed-form analytical solution is obtained by solving the resulting nonlinear partial differential equations using asymptotic expansions of the field variables. The numerical illustration of the solution highlights the importance of molecular interaction in bending compared to the postbuckling scenario. The prevailing impact of foundation stiffness is demonstrated. Surface molecules are observed to show a comparable effect as the electric or magnetic fields. The solution can be used to develop basic design concepts for MEE nanobeams at different temperatures and to validate numerical solutions.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115955"},"PeriodicalIF":4.4,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-21DOI: 10.1016/j.apm.2025.115960
Alia Al-Ghosoun , Mohammed Seaid , Ashraf S. Osman
Sediment transport in shallow waters occurs when the water flows over the bed for which the amount of generated sediments can be determined from the transport mechanism caused by the consequent flow. Recently, investigating the bedload and sediment transport using numerical models has been rapidly increased and various techniques have been developed to quantify both the hydrodynamics and morphodynamics in these systems but not the stress distributions in the deformed beds. In the present study, we propose a novel class of coupled finite element/finite volume methods to resolve the effect of sedimentary shallow water flows on the internal stresses in bed topographies. The coupled model employs the linear elasticity for the bed and the nonlinear shallow water equations for the water flow. Suspended sediments are also taken into consideration in this study, and impacts of the erosion and deposition are modelled using well-established empirical equations. The linear equations of elasticity are solved numerically using a finite element approach on unstructured meshes, while the nonlinear shallow water equations are numerically solved using a well-balanced finite volume method. We also introduce an accurate algorithm to sample forces on the interface between the water flow and bed topography to be implemented as coupling conditions between finite volume cells and finite element nodes. Distributions of stress fields in the bed topography due to erosion and sediment transport by shallow water flows are presented for several test examples. The novel coupled model is stable, efficient, accurate, well-balanced and it can be used for solving complex geometries. In addition, the proposed approach offers significant advancements in understanding sedimentary processes in shallow water environments and the induced underground stresses as a result of these processes.
{"title":"A novel approach for modelling stress fields induced by shallow water flows on movable beds","authors":"Alia Al-Ghosoun , Mohammed Seaid , Ashraf S. Osman","doi":"10.1016/j.apm.2025.115960","DOIUrl":"10.1016/j.apm.2025.115960","url":null,"abstract":"<div><div>Sediment transport in shallow waters occurs when the water flows over the bed for which the amount of generated sediments can be determined from the transport mechanism caused by the consequent flow. Recently, investigating the bedload and sediment transport using numerical models has been rapidly increased and various techniques have been developed to quantify both the hydrodynamics and morphodynamics in these systems but not the stress distributions in the deformed beds. In the present study, we propose a novel class of coupled finite element/finite volume methods to resolve the effect of sedimentary shallow water flows on the internal stresses in bed topographies. The coupled model employs the linear elasticity for the bed and the nonlinear shallow water equations for the water flow. Suspended sediments are also taken into consideration in this study, and impacts of the erosion and deposition are modelled using well-established empirical equations. The linear equations of elasticity are solved numerically using a finite element approach on unstructured meshes, while the nonlinear shallow water equations are numerically solved using a well-balanced finite volume method. We also introduce an accurate algorithm to sample forces on the interface between the water flow and bed topography to be implemented as coupling conditions between finite volume cells and finite element nodes. Distributions of stress fields in the bed topography due to erosion and sediment transport by shallow water flows are presented for several test examples. The novel coupled model is stable, efficient, accurate, well-balanced and it can be used for solving complex geometries. In addition, the proposed approach offers significant advancements in understanding sedimentary processes in shallow water environments and the induced underground stresses as a result of these processes.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115960"},"PeriodicalIF":4.4,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-20DOI: 10.1016/j.apm.2025.115957
Yuhang Tian , Qingya Li , Yuan Feng , Wei Gao
This study presents a semi-analytical method to investigate the nonlinear dynamic responses of a geometrically imperfect multi-direction functionally graded graphene platelets reinforced composite plate with magneto-electro-elastic coupling (MDFG GPLRC-MEE) under blast loads. The mechanical properties of the plate structure are tailored by adjusting the spatial distribution of graphene platelets (GPL) content in the core layer. The localised geometrical imperfections of the structure are introduced and modelled as an initial deflection of the plate in the form of products of hyperbolic and trigonometric functions. Three boundary conditions are considered for the plate with different combinations of the simply supported and clamped edges. Based on the third-order shear deformation theory (TSDT) and von Kármán nonlinearity, the equations of motion are derived according to Hamilton's principle. The Galerkin method is then used to reduce the system to a set of ordinary differential equations. The fourth-order Runge-Kutta approach is subsequently employed to address the dynamic behaviours of the structure subjected to blast load. After verification, parametric experiments are conducted to explore the influences of some key factors, including boundary conditions, damping ratios, the Winkler-Pasternak foundation moduli, geometrical imperfection configurations, GPL content and distribution, blast load parameters, and external electromagnetic potentials. The numerical results indicate that for MDFG GPLRC-MEE plates, incorporating more GPL in the middle portion of the plate provides superior blast impact resistance compared to structures with more GPL at the margins.
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