Engineering Analysis with Boundary Elements最新文献

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Symplectic time-domain finite element method for solving dynamic impact and crack propagation problems in peridynamics 求解动力冲击与裂纹扩展问题的辛时域有限元法
IF 4.2 2区 工程技术
Engineering Analysis with Boundary Elements Pub Date : 2025-01-18 DOI: 10.1016/j.enganabound.2025.106119
Yajing Gong , Yong Peng , Shuguang Gong
{"title":"Symplectic time-domain finite element method for solving dynamic impact and crack propagation problems in peridynamics","authors":"Yajing Gong ,&nbsp;Yong Peng ,&nbsp;Shuguang Gong","doi":"10.1016/j.enganabound.2025.106119","DOIUrl":"10.1016/j.enganabound.2025.106119","url":null,"abstract":"<div><div>This paper proposes a novel algorithm, the symplectic time-domain finite element method (ST-FEM), for solving the equation of motion within the peridynamics (PD) framework, with a focus on dynamic impact problems and crack propagation prediction. An iterative scheme for the PD equation of motion is established using the time-domain finite element method (T-FEM), with symplectic conservation of the transfer matrix and algorithm stability verified. Three numerical examples demonstrate the feasibility and effectiveness of the ST-FEM algorithm, along with the analysis of the effects of time element size and material point spacing. The results indicate that, compared to the explicit forward difference method with the second-order convergence in both the time and spatial domains, the ST-FEM with a linear convergence in the time domain, achieves the same level of computational accuracy. This demonstrates that the proposed ST-FEM for solving PD equations of motion has the combined advantages of both the symplectic conservation algorithm and T-FEM. The algorithm's accuracy in predicting crack propagation paths is validated through the Kalthoff-Winkler experiment and dynamic fracture tests on an l-shaped beam. Furthermore, the time element size should match the impact process time step to achieve computational accuracy and efficiency.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106119"},"PeriodicalIF":4.2,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989685","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}
引用次数: 0
Oblique wave interaction with a floating dock in the presence of inverted trapezoidal pile-rock breakwaters 倒梯形桩岩防波堤存在时斜波与浮船坞的相互作用
IF 4.2 2区 工程技术
Engineering Analysis with Boundary Elements Pub Date : 2025-01-17 DOI: 10.1016/j.enganabound.2024.106111
M. Marshal Jins , K.G. Vijay , V. Venkateswarlu , H. Behera
{"title":"Oblique wave interaction with a floating dock in the presence of inverted trapezoidal pile-rock breakwaters","authors":"M. Marshal Jins ,&nbsp;K.G. Vijay ,&nbsp;V. Venkateswarlu ,&nbsp;H. Behera","doi":"10.1016/j.enganabound.2024.106111","DOIUrl":"10.1016/j.enganabound.2024.106111","url":null,"abstract":"<div><div>This study evaluates the performance of a pair of inverted trapezoidal pile-rock breakwaters (PRB) placed at a finite distance from the floating dock and connected to a partially reflecting seawall under the oblique wave incidence. The PRB consists of pile shields to protect the rock core from the displacements due to incident wave stroke. The porous boundary conditions, such as continuity of pressure and velocity, are incorporated between the breakwater and open water regions. The multi-domain boundary element method (MBEM) is used to evaluate the breakwater performance against the incident waves under the small amplitude wave theory assumption. Before analyzing the proposed breakwater system, the validation of study results is presented for specific structural configurations to strengthen the accuracy of the proposed results. The proposed non-identical inverted trapezoidal breakwaters of ascending heights, <em>D</em><sub>1</sub>/<em>h</em> = 0.6 (seaside) and <em>D</em><sub>2</sub>/<em>h</em> = 0.8 (shoreside) installed at a finite spacing with 40% porosity to minimize wave loads and to obtain well-balanced scattering and force coefficients. It shows peak energy damping of 92% for a porosity of 40%, which is 56% higher energy dissipation relative to the trapezoidal breakwater of comparable bulk with the same porosity, and it depicts the minimum moment on the floating dock for the extensive part of relative water depths. The harmonic peaks of higher magnitude are observed in the scattering and force coefficients against the relative spacing, with maximum (97%) wave energy dissipation and minimal (0.2) force coefficients for the escalated heights (<em>D</em><sub>1</sub> = <em>D</em><sub>2</sub> = 0.9<em>h</em>) of the inverted trapezoidal breakwaters.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106111"},"PeriodicalIF":4.2,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989687","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}
引用次数: 0
Reduced-order prediction model for the Cahn–Hilliard equation based on deep learning 基于深度学习的Cahn-Hilliard方程的降阶预测模型
IF 4.2 2区 工程技术
Engineering Analysis with Boundary Elements Pub Date : 2025-01-17 DOI: 10.1016/j.enganabound.2025.106118
Zhixian Lv , Xin Song , Jiachen Feng , Qing Xia , Binhu Xia , Yibao Li
{"title":"Reduced-order prediction model for the Cahn–Hilliard equation based on deep learning","authors":"Zhixian Lv ,&nbsp;Xin Song ,&nbsp;Jiachen Feng ,&nbsp;Qing Xia ,&nbsp;Binhu Xia ,&nbsp;Yibao Li","doi":"10.1016/j.enganabound.2025.106118","DOIUrl":"10.1016/j.enganabound.2025.106118","url":null,"abstract":"<div><div>This study presents an end-to-end deep learning framework for nonlinear reduced-order modeling and prediction, combining Variational Autoencoders (VAE) for feature extraction and Long Short-Term Memory (LSTM) networks for temporal prediction. The framework simplifies the modeling process by integrating multiple steps into a unified architecture, improving both design and training efficiency. The VAE compresses input data into a low-dimensional latent space while using a progressive channel reduction strategy to retain key features and minimize redundancy. The LSTM network captures temporal dependencies, ensuring accurate predictions based on historical data. The framework is validated through applications to the Cahn–Hilliard (CH) equation, demonstrating superior performance over traditional dimensionality reduction and prediction models. A comprehensive hyperparameter analysis identifies optimal configurations, and the model’s extrapolation capabilities and computational efficiency are thoroughly assessed. Results highlight the framework’s potential as an effective tool for modeling and predicting complex dynamic systems governed by partial differential equations.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106118"},"PeriodicalIF":4.2,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990205","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}
引用次数: 0
Isogeometric Reissner–Mindlin shell analysis for post-buckling of piezoelectric laminated shell panels 压电层合壳板后屈曲等几何Reissner-Mindlin壳分析
IF 4.2 2区 工程技术
Engineering Analysis with Boundary Elements Pub Date : 2025-01-17 DOI: 10.1016/j.enganabound.2025.106114
Tao Liu , Wenxiang Xu , Yuhang Wang , Shanshan Cai , Xiaolei Hu , Jiming Gu
{"title":"Isogeometric Reissner–Mindlin shell analysis for post-buckling of piezoelectric laminated shell panels","authors":"Tao Liu ,&nbsp;Wenxiang Xu ,&nbsp;Yuhang Wang ,&nbsp;Shanshan Cai ,&nbsp;Xiaolei Hu ,&nbsp;Jiming Gu","doi":"10.1016/j.enganabound.2025.106114","DOIUrl":"10.1016/j.enganabound.2025.106114","url":null,"abstract":"<div><div>Isogeometric analysis (IGA) employs NURBS basis functions as shape functions, possessing geometric accuracy, high precision and high-order continuity, thereby making it very suitable for analyzing complex curved surface structures. By taking advantage of these benefits, this paper presents a geometrically nonlinear electro-mechanical coupled IGA model for accurately predicting the post-buckling behavior of piezoelectric laminated shell panels. The geometrically nonlinear governing equations for piezoelectric laminated shell panels are derived in accordance with the Reissner–Mindlin shell theory, Hamilton’s principle and Total Lagrangian (TL) incremental scheme. The geometrically nonlinear static bending, dynamic and post-buckling equations are solved using the Newton–Raphson iterative method, Newmark-<span><math><mi>β</mi></math></span> direct integration method and Arc-length method. Several numerical examples involving geometrically nonlinear static bending, dynamic responses and post-buckling behaviors of piezoelectric laminated cylindrical and spherical shell panels subjected to electro-mechanical loads are performed, and then compared with the existing reference solutions and the results obtained by ABAQUS software to validate the accuracy and reliability of the proposed approach. The numerical results indicate that the present method exhibits high computational accuracy for piezoelectric laminated shell panels and can be applied to the analysis of arbitrary plate and shell structures.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106114"},"PeriodicalIF":4.2,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989745","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}
引用次数: 0
Numerical investigation of wave propagation across rock masses through a nodal-based 3D discontinuous deformation analysis method with contact potential 基于节点的三维接触势非连续变形分析方法在岩体中传播的数值研究
IF 4.2 2区 工程技术
Engineering Analysis with Boundary Elements Pub Date : 2025-01-16 DOI: 10.1016/j.enganabound.2025.106120
Yang Xia , Wenan Wu , Yuyong Jiao , Shanyong Wang
{"title":"Numerical investigation of wave propagation across rock masses through a nodal-based 3D discontinuous deformation analysis method with contact potential","authors":"Yang Xia ,&nbsp;Wenan Wu ,&nbsp;Yuyong Jiao ,&nbsp;Shanyong Wang","doi":"10.1016/j.enganabound.2025.106120","DOIUrl":"10.1016/j.enganabound.2025.106120","url":null,"abstract":"<div><div>The 3D-NDDACP method (nodal-based 3D discontinuous deformation analysis method with contact potential) shows its capability to simulate discontinuous deformation of rock block systems. Due to the adoption of contact potential for contact treatment and Newmark method for time integration, 3D-NDDACP method inherits attractive advantages from both FEM-DEM and discontinuous deformation analysis (DDA) method. Furthermore, tetrahedral meshes are adopted to discretize rock blocks to model their deformation. In this study, 3D-NDDACP method is enriched to simulate wave propagation in rock masses. The new enrichments to the 3D-NDDACP method include: 1) a viscous nonreflecting boundary is firstly adopted to absorb wave energy to minimize the negative effects from artificial boundaries; 2) on the basis of viscous nonreflecting boundary, a viscoelastic boundary is adopted to simulate the elastic recovery property of an infinite problem domain; and 3) to accurately input incident wave, the force input method is adopted. To validate the enriched 3D-NDDACP method, a series of typical numerical tests associated with P/S-wave propagation through jointed/homogeneous rock masses are conducted. Results from these numerical tests show that the enriched 3D-NDDACP method is able to correctly and reliably model the processes of P/S-wave propagation across homogeneous and jointed rock masses.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106120"},"PeriodicalIF":4.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989688","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}
引用次数: 0
Fatigue analysis of crack propagation in structures with bonded composite repairs 结合复合材料修复结构裂纹扩展的疲劳分析
IF 4.2 2区 工程技术
Engineering Analysis with Boundary Elements Pub Date : 2025-01-13 DOI: 10.1016/j.enganabound.2025.106116
Lucas S. Moura , Andres F. Galvis , Andres F. Ramirez , Eder L. Abuquerque , Paulo Sollero
{"title":"Fatigue analysis of crack propagation in structures with bonded composite repairs","authors":"Lucas S. Moura ,&nbsp;Andres F. Galvis ,&nbsp;Andres F. Ramirez ,&nbsp;Eder L. Abuquerque ,&nbsp;Paulo Sollero","doi":"10.1016/j.enganabound.2025.106116","DOIUrl":"10.1016/j.enganabound.2025.106116","url":null,"abstract":"<div><div>Recent growth in the aeronautical and oil industries has increased the demand for efficient repair techniques that offer shorter maintenance periods, greater durability, and reduced costs. Bonded composite repairs have emerged as an excellent solution, enabling the restoration of components without compromising structural integrity. By the first attempt, the coupling of the 3D boundary element method (BEM) coupled to the generalised energy failure criteria is used for analysing crack propagation and fatigue life in structures with bonded composite repairs. This criterion is based on strain energy density concept. Initially, crack propagation for bonded single lap joint (SLJ) and bonded double cantilever beam (DCB) served for experimental validation of the numerical approach. Experimentally, fatigue tests were performed to evaluate crack propagation using digital image correlation (DIC), and the repair debonding via an unidirectional laser vibrometer. Comparing numerical and experimental results revealed that incorporating the failure of the adhesive in the simulation setup improves the accuracy over those models in the literature that consider only the failure of the plate.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106116"},"PeriodicalIF":4.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989689","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}
引用次数: 0
Application of defined auxiliary system in the method of layer potentials for solving the stokes flow problem 层势法中定义辅助系统在求解斯托克斯流问题中的应用
IF 4.2 2区 工程技术
Engineering Analysis with Boundary Elements Pub Date : 2025-01-13 DOI: 10.1016/j.enganabound.2024.106102
Kue-Hong Chen , Yi-Kui Liu , Jeng-Tzong Chen
{"title":"Application of defined auxiliary system in the method of layer potentials for solving the stokes flow problem","authors":"Kue-Hong Chen ,&nbsp;Yi-Kui Liu ,&nbsp;Jeng-Tzong Chen","doi":"10.1016/j.enganabound.2024.106102","DOIUrl":"10.1016/j.enganabound.2024.106102","url":null,"abstract":"<div><div>In this article, we apply an error estimation technique to assess the numerical error of seven kinds of method of layer potentials for solving the Stokes flow problem governed by the biharmonic equation. The new error estimation technique allows us to estimate numerical errors in situations where analytical solutions are not available. Additionally, it enables us to determine the optimal solution for the seven methods, making them applicable in various engineering problems. We validate the developed algorithm through four numerical experiments on 2D flows: (1) a gear cavity, (2) a circular cavity, (3) a lid-driven square cavity, and (4) an amoeba-shaped cavity. The results demonstrate close agreement with previous research, affirming that the error estimation technique can guarantee the method of layer potentials an accurate and versatile approach to solving the Stokes flow problem.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106102"},"PeriodicalIF":4.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989748","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}
引用次数: 0
A deferred approach to include solid↔liquid phase change effects in the solution of advection–conduction heat transfer problems via the improved element-free Galerkin method 采用改进的无单元伽辽金法求解平流传导传热问题时,考虑固体[公式省略]液相变化效应的延迟方法
IF 4.2 2区 工程技术
Engineering Analysis with Boundary Elements Pub Date : 2025-01-13 DOI: 10.1016/j.enganabound.2024.106110
Juan C. Álvarez-Hostos , Benjamín A. Tourn , Alfonso D. Bencomo , Mauricio Mascotto , Javier A. Zambrano-Carrillo , Alirio J. Sarache-Piña
{"title":"A deferred approach to include solid↔liquid phase change effects in the solution of advection–conduction heat transfer problems via the improved element-free Galerkin method","authors":"Juan C. Álvarez-Hostos ,&nbsp;Benjamín A. Tourn ,&nbsp;Alfonso D. Bencomo ,&nbsp;Mauricio Mascotto ,&nbsp;Javier A. Zambrano-Carrillo ,&nbsp;Alirio J. Sarache-Piña","doi":"10.1016/j.enganabound.2024.106110","DOIUrl":"10.1016/j.enganabound.2024.106110","url":null,"abstract":"<div><div>In this communication, a novel strategy is presented for addressing advection–conduction problems with solid<span><math><mo>↔</mo></math></span>liquid phase change by using a modified implementation of the improved element-free Galerkin (IEFG) method. The approach involves a deferred inclusion of non-linear effects related to temperature-dependent material properties and the latent heat exchanged during phase change, incorporated within thermal load vectors. The temperature and solid phase fraction gradients needed to construct these thermal load vectors are computed iteratively within the non-linear solution process, delaying their assembly until required. This deferred approach eliminates the need for temperature derivatives of the solid or liquid fraction in the core problem formulation, a component that often complicates convergence when using conventional effective specific heat methods. A comprehensive description of the iterative process is given, along with the method for obtaining solid phase fraction gradients using a global reconstruction based on improved moving least squares (IMLS). The technique is rigorously validated through a 1-D advection–conduction phase change problem with an analytical solution and a 3-D application in direct chill casting of AA-1050 aluminium alloy. Outcomes demonstrate that this method not only enhances convergence over traditional effective specific heat techniques, but also achieves a substantial reduction in computational time.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106110"},"PeriodicalIF":4.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989749","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}
引用次数: 0
Solving electrostatic and electroelastic problems with the node's residual descent method 用节点残差下降法求解静电和电弹性问题
IF 4.2 2区 工程技术
Engineering Analysis with Boundary Elements Pub Date : 2025-01-01 DOI: 10.1016/j.enganabound.2024.106053
Tailang Dong, Shanju Wang, Yuhong Cui
{"title":"Solving electrostatic and electroelastic problems with the node's residual descent method","authors":"Tailang Dong,&nbsp;Shanju Wang,&nbsp;Yuhong Cui","doi":"10.1016/j.enganabound.2024.106053","DOIUrl":"10.1016/j.enganabound.2024.106053","url":null,"abstract":"<div><div>Piezoelectric materials are extensively used in engineering for the fabrication of sensors, transducers, and actuators. Due to the coupling characteristics, anisotropy, and arbitrariness of polarization directions, the tasks of mesh generation, numerical integration, and global equation formulation involved in numerical computations are complex and nontrivial. To solve electrostatic and electroelastic problems, an easily implementable node's residual descent method (NRDM) is established in this study. The capability and accuracy of NRDM are validated through the solution of three-dimensional electrostatic, linear elastic, and electroelastic problems, achieving relative errors of 0.17%–1.60% for stress and 0.02%–0.15% for other variables. Fundamental and higher-order variables exhibit second-order accuracy, with convergence rates ranging from 1.98 to 2.27 using a first-order generalized finite difference scheme. This comprehensively validates the double derivation technique. The electroelastic coupling problems can be addressed by explicitly calculating electric displacement and stress based on the stress–charge form of piezoelectric constitutive equations during the iteration process. Additionally, the local basis coordinate technique is seamlessly integrated, enabling the solution of anisotropic piezoelectric problems with arbitrary polarization directions through explicit tensor operations.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"170 ","pages":"Article 106053"},"PeriodicalIF":4.2,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142793491","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}
引用次数: 0
A meshless Runge-Kutta-based Physics-Informed Neural Network framework for structural vibration analysis 结构振动分析的无网格龙格-库塔神经网络框架
IF 4.2 2区 工程技术
Engineering Analysis with Boundary Elements Pub Date : 2025-01-01 DOI: 10.1016/j.enganabound.2024.106054
Shusheng Xiao , Jinshuai Bai , Hyogu Jeong , Laith Alzubaidi , YuanTong Gu
{"title":"A meshless Runge-Kutta-based Physics-Informed Neural Network framework for structural vibration analysis","authors":"Shusheng Xiao ,&nbsp;Jinshuai Bai ,&nbsp;Hyogu Jeong ,&nbsp;Laith Alzubaidi ,&nbsp;YuanTong Gu","doi":"10.1016/j.enganabound.2024.106054","DOIUrl":"10.1016/j.enganabound.2024.106054","url":null,"abstract":"<div><div>In recent years, Physics-Informed Neural Networks (PINN) have emerged as powerful meshless numerical methods for solving partial differential equations (PDEs) in engineering and science, including the field of structural vibration. However, PINN struggles due to the spectral bias when the target PDEs exhibit high-frequency features. In this work, a meshless Runge-Kutta-based PINN (R-KPINN) framework for structural vibration modelling is proposed for the first time. In the framework, the meshless features of traditional PINN are retained while applying Runge-Kutta (R-K) time integration to discretise the temporal domain, thereby reducing computational demands and enhancing temporal flexibility. Besides, the proposed R-KPINN allows for segmental training of PINN, reducing the dimensionality of the structural vibration problems and offering accurate solutions to relatively high-frequency functions. Through numerical examples including free, damped, and forced vibration of Euler-Bernoulli beams, the proposed framework provides effective and precise solutions for predicting the responses of structures. In summary, the proposed R-KPINN framework provides a flexible, efficient, and interpretable meshless method for solving structural vibration problems with state-of-the-art PINN techniques.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"170 ","pages":"Article 106054"},"PeriodicalIF":4.2,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142758687","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}
引用次数: 0
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