Pub Date : 2025-03-07DOI: 10.1016/j.enganabound.2025.106178
Chang-Yeol Jung , Junghwa Kim , Eaint Phoo Ngon
We introduce a novel semi-analytic method for solving singularly perturbed reaction–diffusion problems in a smooth domain using neural network architectures. To manage steep solution transitions near the boundary, we utilize the boundary-fitted coordinates and perform boundary layer analysis to construct a corrector function which describes the singular behavior of the solution near the boundary. By integrating the boundary layer corrector into the conventional PINN structure, we propose our new sl-PINNs (singular-layer Physics-Informed Neural Networks). The sl-PINN framework is specifically designed to capture sharp transitions inside boundary layers, significantly improving the approximation accuracy for solutions under small perturbation parameters. The computational results of various simulations in this article demonstrate the superior performance of sl-PINNs over conventional PINNs in handling such problems.
{"title":"Singular layer PINN methods for steep reaction–diffusion equations in a smooth convex domain","authors":"Chang-Yeol Jung , Junghwa Kim , Eaint Phoo Ngon","doi":"10.1016/j.enganabound.2025.106178","DOIUrl":"10.1016/j.enganabound.2025.106178","url":null,"abstract":"<div><div>We introduce a novel semi-analytic method for solving singularly perturbed reaction–diffusion problems in a smooth domain using neural network architectures. To manage steep solution transitions near the boundary, we utilize the boundary-fitted coordinates and perform boundary layer analysis to construct a corrector function which describes the singular behavior of the solution near the boundary. By integrating the boundary layer corrector into the conventional PINN structure, we propose our new sl-PINNs (singular-layer Physics-Informed Neural Networks). The sl-PINN framework is specifically designed to capture sharp transitions inside boundary layers, significantly improving the approximation accuracy for solutions under small perturbation parameters. The computational results of various simulations in this article demonstrate the superior performance of sl-PINNs over conventional PINNs in handling such problems.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"175 ","pages":"Article 106178"},"PeriodicalIF":4.2,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563736","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 : 2025-03-07DOI: 10.1016/j.enganabound.2025.106199
Ali Cheraghback , M. Botshekanan Dehkordi , Y. Kiani
Due to the many applications of shape memory alloys (SMAs) to make the structures more intelligent, these materials are getting great attention of researchers. Meanwhile, the nonlinear dynamic analysis of curved beams made of SMAs has not been investigated so far. Therefore, this work focuses on a nonlinear dynamic analysis of SMA curved beams under transverse impulse loading taking into account the pseudo-elastic behavior of SMAs. It is worth noting that both material and geometrical nonlinearities of the SMA curved beam are considered in this study. In order to model the nonlinear behavior of SMAs, the Lagoudas model is employed and for the mathematical modeling of the curved beam the Timoshenko beam theory under the assumption of von Karman nonlinear strains is used. Then, by employing the Hamilton principle, the governing equations of the structure are extracted, while the nonlinear kinematic equations of SMAs are coupled with the governing equations of the curved beam. To solve these coupled nonlinear equations, the numerical technique of differential quadrature method (DQM) along with Newmark's time integration scheme is employed. In this regard, the return mapping algorithm in conjunction with the Newton–Raphson method is employed to solve the nonlinear terms of equations. The quick convergence and high accuracy of the proposed formulation are achieved by the analysis of different examples. After that, some novel results are presented by investigating the influence of different types of boundary conditions, radius of curvature, angle of curvature and thickness of beam on the transient damped response, hysteresis loops and also martensite phase transformation of the SMA curved beams.
{"title":"Nonlinear numerical assessment of damped oscillation of SMA Timoshenko curved beams under impulsive loading","authors":"Ali Cheraghback , M. Botshekanan Dehkordi , Y. Kiani","doi":"10.1016/j.enganabound.2025.106199","DOIUrl":"10.1016/j.enganabound.2025.106199","url":null,"abstract":"<div><div>Due to the many applications of shape memory alloys (SMAs) to make the structures more intelligent, these materials are getting great attention of researchers. Meanwhile, the nonlinear dynamic analysis of curved beams made of SMAs has not been investigated so far. Therefore, this work focuses on a nonlinear dynamic analysis of SMA curved beams under transverse impulse loading taking into account the pseudo-elastic behavior of SMAs. It is worth noting that both material and geometrical nonlinearities of the SMA curved beam are considered in this study. In order to model the nonlinear behavior of SMAs, the Lagoudas model is employed and for the mathematical modeling of the curved beam the Timoshenko beam theory under the assumption of von Karman nonlinear strains is used. Then, by employing the Hamilton principle, the governing equations of the structure are extracted, while the nonlinear kinematic equations of SMAs are coupled with the governing equations of the curved beam. To solve these coupled nonlinear equations, the numerical technique of differential quadrature method (DQM) along with Newmark's time integration scheme is employed. In this regard, the return mapping algorithm in conjunction with the Newton–Raphson method is employed to solve the nonlinear terms of equations. The quick convergence and high accuracy of the proposed formulation are achieved by the analysis of different examples. After that, some novel results are presented by investigating the influence of different types of boundary conditions, radius of curvature, angle of curvature and thickness of beam on the transient damped response, hysteresis loops and also martensite phase transformation of the SMA curved beams.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"175 ","pages":"Article 106199"},"PeriodicalIF":4.2,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563735","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}
A novel computational framework based on modified bond-based peridynamics is proposed for viscoelastic laminas. The framework accurately captures deformations, damage initiation, and propagation under mechanical and thermal loads. It reduces numerical complexity by directly assessing viscoelastic strains each time step, eliminating real-time increment constraints. Constitutive component models, including viscoelastic Prony series and lamina stiffness matrices, are integrated into a 2D formulation. To address the limitations of the adaptive dynamic relaxation (ADR) method in modeling high-rate phenomena, an innovative ADR variant with an infinitesimal steady time step is introduced, enabling accurate capture of thermoviscoelastic creep-recovery responses above glass transition temperatures. Model validation against literature data, analytical solutions, and finite element models demonstrates accurate predictions of thermoviscoelastic responses, lamina deformations, damage initiation, and propagation patterns. Stress-strain diagrams reveal an inverse relationship between fiber orientation and stress peaks. The framework's efficiency makes it suitable for modeling complex viscoelastic composites and delamination damage. Its capabilities enable high-fidelity virtual testing and design of advanced composites under multi-axial viscoelastic conditions.
{"title":"A computationally efficient peridynamic framework for modeling damage in viscoelastic fiber-reinforced lamina","authors":"Alireza Masoumi , Amirreza Moradi , Mohammad Ravandi , Manouchehr Salehi","doi":"10.1016/j.enganabound.2025.106196","DOIUrl":"10.1016/j.enganabound.2025.106196","url":null,"abstract":"<div><div>A novel computational framework based on modified bond-based peridynamics is proposed for viscoelastic laminas. The framework accurately captures deformations, damage initiation, and propagation under mechanical and thermal loads. It reduces numerical complexity by directly assessing viscoelastic strains each time step, eliminating real-time increment constraints. Constitutive component models, including viscoelastic Prony series and lamina stiffness matrices, are integrated into a 2D formulation. To address the limitations of the adaptive dynamic relaxation (ADR) method in modeling high-rate phenomena, an innovative ADR variant with an infinitesimal steady time step is introduced, enabling accurate capture of thermoviscoelastic creep-recovery responses above glass transition temperatures. Model validation against literature data, analytical solutions, and finite element models demonstrates accurate predictions of thermoviscoelastic responses, lamina deformations, damage initiation, and propagation patterns. Stress-strain diagrams reveal an inverse relationship between fiber orientation and stress peaks. The framework's efficiency makes it suitable for modeling complex viscoelastic composites and delamination damage. Its capabilities enable high-fidelity virtual testing and design of advanced composites under multi-axial viscoelastic conditions.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"175 ","pages":"Article 106196"},"PeriodicalIF":4.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563150","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 : 2025-03-06DOI: 10.1016/j.enganabound.2025.106180
Csaba Gáspár , Andreas Karageorghis
We consider various method of fundamental solution (MFS) formulations for the numerical solution of two-dimensional boundary value problems (BVPs) governed by the homogeneous biharmonic equation. The motivation for employing the proposed techniques comes from the corresponding boundary integral representations. These are carefully analyzed in the case the domain of the BVP under consideration is a disk. The results of this analysis detect a potentially troublesome case in one of the proposed MFS approaches. Numerical results confirm the analytical findings for more general domains.
{"title":"Method of fundamental solutions formulations for biharmonic problems","authors":"Csaba Gáspár , Andreas Karageorghis","doi":"10.1016/j.enganabound.2025.106180","DOIUrl":"10.1016/j.enganabound.2025.106180","url":null,"abstract":"<div><div>We consider various method of fundamental solution (MFS) formulations for the numerical solution of two-dimensional boundary value problems (BVPs) governed by the homogeneous biharmonic equation. The motivation for employing the proposed techniques comes from the corresponding boundary integral representations. These are carefully analyzed in the case the domain of the BVP under consideration is a disk. The results of this analysis detect a potentially troublesome case in one of the proposed MFS approaches. Numerical results confirm the analytical findings for more general domains.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"175 ","pages":"Article 106180"},"PeriodicalIF":4.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143548112","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 : 2025-03-01DOI: 10.1016/j.enganabound.2025.106192
Youjun Ning , Xuanhao Lin , Dayong Chen , Haofeng Chen , Mangong Zhang
Numerical manifold method (NMM) is a powerful unified continuous-discontinuous method due to its dual cover systems and the flexibility of the cover types. In this work, to better solve problems with various discontinuity geometry characteristics by NMM, the finite element method (FEM) mesh and the NMM traditional regular mathematical mesh are employed to construct finite covers for NMM, respectively. Moreover, an independent cover method by which a single physical domain is represented as one manifold element is also introduced. Different types of covers are coupled to simulate the uniaxial loading of mesoscopic concrete models, as well as a rock slope slumping model. The corresponding deformation, fracturing and failure processes are numerically reproduced satisfactorily and consistently by NMM with different combinations of the cover methods. Simulations are also carried out to investigate the important problem of dynamic sliding for discontinua by employing different cover methods in NMM simulations. The results in this work indicate that an appropriate application of the cover methods benefits the reasonable construction of NMM simulation models by avoiding unfavorable extremely small or elongated manifold elements. Meanwhile, the simulation efficiency could be improved due to the reduction of the manifold element number and the contact number at discontinuities.
{"title":"Study on the applications of different cover methods in numerical manifold method (NMM)","authors":"Youjun Ning , Xuanhao Lin , Dayong Chen , Haofeng Chen , Mangong Zhang","doi":"10.1016/j.enganabound.2025.106192","DOIUrl":"10.1016/j.enganabound.2025.106192","url":null,"abstract":"<div><div>Numerical manifold method (NMM) is a powerful unified continuous-discontinuous method due to its dual cover systems and the flexibility of the cover types. In this work, to better solve problems with various discontinuity geometry characteristics by NMM, the finite element method (FEM) mesh and the NMM traditional regular mathematical mesh are employed to construct finite covers for NMM, respectively. Moreover, an independent cover method by which a single physical domain is represented as one manifold element is also introduced. Different types of covers are coupled to simulate the uniaxial loading of mesoscopic concrete models, as well as a rock slope slumping model. The corresponding deformation, fracturing and failure processes are numerically reproduced satisfactorily and consistently by NMM with different combinations of the cover methods. Simulations are also carried out to investigate the important problem of dynamic sliding for discontinua by employing different cover methods in NMM simulations. The results in this work indicate that an appropriate application of the cover methods benefits the reasonable construction of NMM simulation models by avoiding unfavorable extremely small or elongated manifold elements. Meanwhile, the simulation efficiency could be improved due to the reduction of the manifold element number and the contact number at discontinuities.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"174 ","pages":"Article 106192"},"PeriodicalIF":4.2,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143520862","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 : 2025-02-27DOI: 10.1016/j.enganabound.2025.106179
Y.L. Li , X.P. Zhou
Modeling the structural failures induced by fluid-structure interaction (FSI) are crucial because it dominates many engineering problems. In this paper, a nonlocal general particle dynamic (NGPD) method is proposed to solve the FSI problems considering the structural failure. In this framework, the governing equations for fluid and solid are reformulated by introducing nonlocal theories. The tensile strength criterion is introduced to simulate crack initiation and propagation. A coupled strategy is proposed to calculate the interaction forces in the fluid-structure interface. The different particle spacings are utilized to discretize the fluid and solid computational domains to enhance the accuracy of modeling structural failure. A series of benchmark examples involving fluid and solid, and FSI models, are studied to demonstrate the accuracy, robustness, and stability of the proposed method. Subsequently, the failure of a tank floor under hydrostatic pressure and the Koyna Dam are illustrated to demonstrate the efficacy and versatility of the method in modeling structural failure induced by FSI. The numerical results demonstrate that the proposed NGPD framework is suitable for simulating fluid-structure interaction problems considering the structural failure.
{"title":"Nonlocal general particle dynamics for fluid-structure interaction problems considering the structural failure","authors":"Y.L. Li , X.P. Zhou","doi":"10.1016/j.enganabound.2025.106179","DOIUrl":"10.1016/j.enganabound.2025.106179","url":null,"abstract":"<div><div>Modeling the structural failures induced by fluid-structure interaction (FSI) are crucial because it dominates many engineering problems. In this paper, a nonlocal general particle dynamic (NGPD) method is proposed to solve the FSI problems considering the structural failure. In this framework, the governing equations for fluid and solid are reformulated by introducing nonlocal theories. The tensile strength criterion is introduced to simulate crack initiation and propagation. A coupled strategy is proposed to calculate the interaction forces in the fluid-structure interface. The different particle spacings are utilized to discretize the fluid and solid computational domains to enhance the accuracy of modeling structural failure. A series of benchmark examples involving fluid and solid, and FSI models, are studied to demonstrate the accuracy, robustness, and stability of the proposed method. Subsequently, the failure of a tank floor under hydrostatic pressure and the Koyna Dam are illustrated to demonstrate the efficacy and versatility of the method in modeling structural failure induced by FSI. The numerical results demonstrate that the proposed NGPD framework is suitable for simulating fluid-structure interaction problems considering the structural failure.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"174 ","pages":"Article 106179"},"PeriodicalIF":4.2,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509021","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 : 2025-02-26DOI: 10.1016/j.enganabound.2025.106157
Kim Q. Tran , Thoi V. Duong , Tien-Dat Hoang , Magd Abdel Wahab , Klaus Hackl , H. Nguyen-Xuan
A new thermoelastic model is introduced to reveal equivalent mechanical and thermal properties of randomly oriented (RO), agglomerated carbon nanotube (CNT) inclusions within a matrix material. Thereafter, a bio-inspired FG-CNTR-TPMS material model is established through three typical triply periodic minimal surfaces (TPMS) microstructures reinforced with CNTs and functionally graded (FG) schemes. The free vibration behavior of macro-scale plates made from FG-CNTR-TPMS materials under thermal effects and material temperature dependencies is then devised. A new higher-order shear deformation (HSDT) five-variable plate theory incorporated with isogeometric analysis (IGA) is proposed to show its reliability and efficiency. Various material conditions have been thoroughly studied, emphasizing the influence of CNT reinforcement states and environment temperatures. While increasing the CNT volume fraction () greatly improves the plate frequencies, the temperature rise () leads to an opposite influence. These properties can amplify or weaken the effects of porosity distributions on the plate’s natural frequencies both beneficial and unfavorable aspects. Notably, the outstanding elastic modulus of IWP-type TPMS enlarges the initial thermal stress and ratio between mechanical and thermal stiffness, causing greater impacts on plate behaviors in the thermal environment. In some exceptional cases, FG-CNTR-TPMS plates with P-type can exceed isotropic plates in stiffness-to-weight ratios, which is an extraordinary characteristic of porous structures. In various scenarios of CNT agglomeration, this natural phenomenon shows noticeable reductions in plate frequencies up to 40% when considering temperature changes. Bridging the gap between TPMS-based lattice structures and CNT-reinforced composites, this study contributes to advancing the knowledge of advanced bio-inspired materials. The findings from this work can revolutionize their potential applications in various engineering areas, particularly biomedical devices, energy storage, flexible electronics, advanced textiles, and soft robotics, where lightweight, high-strength, and temperature-resistant structural components are critical.
{"title":"A new thermoelastic model for agglomerated and randomly-oriented CNT-reinforced bio-inspired materials: Temperature-dependent free vibration analysis of FG-CNTR-TPMS plates","authors":"Kim Q. Tran , Thoi V. Duong , Tien-Dat Hoang , Magd Abdel Wahab , Klaus Hackl , H. Nguyen-Xuan","doi":"10.1016/j.enganabound.2025.106157","DOIUrl":"10.1016/j.enganabound.2025.106157","url":null,"abstract":"<div><div>A new thermoelastic model is introduced to reveal equivalent mechanical and thermal properties of randomly oriented (RO), agglomerated carbon nanotube (CNT) inclusions within a matrix material. Thereafter, a bio-inspired FG-CNTR-TPMS material model is established through three typical triply periodic minimal surfaces (TPMS) microstructures reinforced with CNTs and functionally graded (FG) schemes. The free vibration behavior of macro-scale plates made from FG-CNTR-TPMS materials under thermal effects and material temperature dependencies is then devised. A new higher-order shear deformation (HSDT) five-variable plate theory incorporated with isogeometric analysis (IGA) is proposed to show its reliability and efficiency. Various material conditions have been thoroughly studied, emphasizing the influence of CNT reinforcement states and environment temperatures. While increasing the CNT volume fraction (<span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span>) greatly improves the plate frequencies, the temperature rise (<span><math><mrow><mi>Δ</mi><mi>T</mi></mrow></math></span>) leads to an opposite influence. These properties can amplify or weaken the effects of porosity distributions on the plate’s natural frequencies both beneficial and unfavorable aspects. Notably, the outstanding elastic modulus of IWP-type TPMS enlarges the initial thermal stress and ratio between mechanical and thermal stiffness, causing greater impacts on plate behaviors in the thermal environment. In some exceptional cases, FG-CNTR-TPMS plates with P-type can exceed isotropic plates in stiffness-to-weight ratios, which is an extraordinary characteristic of porous structures. In various scenarios of CNT agglomeration, this natural phenomenon shows noticeable reductions in plate frequencies up to 40% when considering temperature changes. Bridging the gap between TPMS-based lattice structures and CNT-reinforced composites, this study contributes to advancing the knowledge of advanced bio-inspired materials. The findings from this work can revolutionize their potential applications in various engineering areas, particularly biomedical devices, energy storage, flexible electronics, advanced textiles, and soft robotics, where lightweight, high-strength, and temperature-resistant structural components are critical.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"174 ","pages":"Article 106157"},"PeriodicalIF":4.2,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487565","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}
Slag accumulation is one of the key and most difficult problems in solid rocket motor (SRM) having submerged nozzles, which may cause severe ablation of insulation and even has a great influence on the interior ballistic performance. This study aims to establish a computational framework mainly based on a Lagrangian-Euler coupled particle model, which consider granular flow as a combination of smoke particle continuum phase and large particle discrete phase, to simulate two-phase flow and explore the characteristics of slag accumulation. The computational framework integrated particle injection model, Al particle combustion model and multiphase coupling model as well, and was verified by the Jet Propulsion Laboratory (JPL) nozzle numerical example. The result of the slag accumulation simulation are in good agreement with experiment data. It shows that, the slag starts to be produced after the motor is ignited, and the accumulation rate is larger at the initial time and gradually decreases. The influences of inject particle diameter in slag accumulation are explored. Discrete particles with larger peak diameter cause lower total combustion efficiency, lower conversion rate of Al, and higher slag rate. The particle size of Al2O3 smoke have the smallest contribution to the slag rate in the range of 1.5μm-2.5μm.
{"title":"Numerical study on slag accumulation in solid rocket motor with a new Lagrangian-Euler coupled particle computational framework","authors":"Dudou Wang, Yuxiang Liu, Zhensheng Sun, Xueren Wang, Hongfu Qiang","doi":"10.1016/j.enganabound.2025.106187","DOIUrl":"10.1016/j.enganabound.2025.106187","url":null,"abstract":"<div><div>Slag accumulation is one of the key and most difficult problems in solid rocket motor (SRM) having submerged nozzles, which may cause severe ablation of insulation and even has a great influence on the interior ballistic performance. This study aims to establish a computational framework mainly based on a Lagrangian-Euler coupled particle model, which consider granular flow as a combination of smoke particle continuum phase and large particle discrete phase, to simulate two-phase flow and explore the characteristics of slag accumulation. The computational framework integrated particle injection model, <em>Al</em> particle combustion model and multiphase coupling model as well, and was verified by the Jet Propulsion Laboratory (JPL) nozzle numerical example. The result of the slag accumulation simulation are in good agreement with experiment data. It shows that, the slag starts to be produced after the motor is ignited, and the accumulation rate is larger at the initial time and gradually decreases. The influences of inject particle diameter in slag accumulation are explored. Discrete particles with larger peak diameter cause lower total combustion efficiency, lower conversion rate of <em>Al</em>, and higher slag rate. The particle size of <em>Al<sub>2</sub>O<sub>3</sub></em> smoke have the smallest contribution to the slag rate in the range of 1.5μm-2.5μm.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"174 ","pages":"Article 106187"},"PeriodicalIF":4.2,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509022","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 : 2025-02-25DOI: 10.1016/j.enganabound.2025.106171
Shaojie Zeng, Yijie Liang, Qinghui Zhang
Neural network (NN) methods have been developed to solve interface problems recently. In comparison with conventional techniques (e.g., finite element method), the NN method enjoys the merits of meshless features, powerful ability to approximate complex interface geometries, and high accuracy. The current NN studies are mostly focused on elliptic interface problems. The methodology will cause difficulties for evolving (time-dependent) and moving interface problems. (a) The accuracy is also characterized by time discretization strategies; if the time step is small, the training time is unbearable. (b) At each time step, it is difficult to design the high-precision NNs because of involvement of complex interfaces, especially for the moving interfaces. This study is devoted to proposing the high-precision NN methods for the evolving and moving interface problems. The first method is based on the time stepping scheme. In every time step we develop piecewise extreme learning machine (ELM) to improve the accuracy of space discretization and reduce the training time. As a consequence, the optimal overall error with respect to the time, , is achieved (for the backward Euler method). Evidently, the accuracy is still limited by . To improve the accuracy further, the second method is to treat the time dimension as an additional space dimension to formulate the equation in an extended time–space domain . A time–space piecewise ELM in is designed. The new method avoids the time stepping so that the training time is saved essentially, and the approximation errors are also reduced significantly. We note that the increase of dimension in does not yield additional computational complexities because of the dimensionless feature of NN techniques. A great many numerical experiments are executed to verify the accuracy and efficiency of the proposed methods, including two- and three-dimensional evolving and moving interface problems with the complex interface geometries. The comparisons with other NN methods, such as PINN, fully-connected NN, are also made.
{"title":"High-precision physics-informed extreme learning machines for evolving interface problems","authors":"Shaojie Zeng, Yijie Liang, Qinghui Zhang","doi":"10.1016/j.enganabound.2025.106171","DOIUrl":"10.1016/j.enganabound.2025.106171","url":null,"abstract":"<div><div>Neural network (NN) methods have been developed to solve interface problems recently. In comparison with conventional techniques (e.g., finite element method), the NN method enjoys the merits of meshless features, powerful ability to approximate complex interface geometries, and high accuracy. The current NN studies are mostly focused on elliptic interface problems. The methodology will cause difficulties for evolving (time-dependent) and moving interface problems. (a) The accuracy is also characterized by time discretization strategies; if the time step <span><math><mi>τ</mi></math></span> is small, the training time is unbearable. (b) At each time step, it is difficult to design the high-precision NNs because of involvement of complex interfaces, especially for the moving interfaces. This study is devoted to proposing the high-precision NN methods for the evolving and moving interface problems. The first method is based on the time stepping scheme. In every time step we develop piecewise extreme learning machine (ELM) to improve the accuracy of space discretization and reduce the training time. As a consequence, the optimal overall error with respect to the time, <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>τ</mi><mo>)</mo></mrow></mrow></math></span>, is achieved (for the backward Euler method). Evidently, the accuracy is still limited by <span><math><mi>τ</mi></math></span>. To improve the accuracy further, the second method is to treat the time dimension as an additional space dimension to formulate the equation in an extended time–space domain <span><math><mover><mrow><mi>Ω</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span>. A time–space piecewise ELM in <span><math><mover><mrow><mi>Ω</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span> is designed. The new method avoids the time stepping so that the training time is saved essentially, and the approximation errors are also reduced significantly. We note that the increase of dimension in <span><math><mover><mrow><mi>Ω</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span> does not yield additional computational complexities because of the dimensionless feature of NN techniques. A great many numerical experiments are executed to verify the accuracy and efficiency of the proposed methods, including two- and three-dimensional evolving and moving interface problems with the complex interface geometries. The comparisons with other NN methods, such as PINN, fully-connected NN, are also made.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"174 ","pages":"Article 106171"},"PeriodicalIF":4.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479648","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}
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