Quansheng Zang , Hao Hong , Jun Liu , Yanhui Zhong , Bei Zhang , Bin Li , Lei Gan
{"title":"俯仰振荡下容器内非线性液体晃动等几何边界元分析","authors":"Quansheng Zang , Hao Hong , Jun Liu , Yanhui Zhong , Bei Zhang , Bin Li , Lei Gan","doi":"10.1016/j.ijengsci.2025.104371","DOIUrl":null,"url":null,"abstract":"<div><div>This paper proposes an isogeometric boundary element method (IGABEM) to solve the nonlinear liquid sloshing problem in a rectangular container subjected to oscillatory excitation. Based on the semi-Lagrange approach, a fixed global coordinate system and a local Cartesian coordinate system that moves synchronously with the container are defined. Starting from the Laplace equation, the boundary integral equations for the liquid sloshing problem are derived using Gauss’s divergence theorem and the integration by parts technique, while incorporating nonlinear kinematic and dynamic boundary conditions of the free surface. The corresponding boundary element solution system is then formulated. Non-Uniform Rational B-Splines (NURBS) are employed as shape functions to accurately describe the geometric boundaries and approximate the unknown physical fields. This method ultimately produces the discrete equations governing nonlinear liquid sloshing problem in an oscillating container. Compared with traditional polynomial interpolation shape functions, NURBS provide improved continuity both within elements and across element interfaces as well as local support. These properties make them particularly suitable for satisfying the continuity requirements of the liquid surface. For time integration, a second-order Runge–Kutta algorithm is employed for time-stepping to solve the IGABEM system equations, compute variable gradients at each time step, and update the computational grid in real-time. A series of numerical examples are presented, the results are compared with analytical solutions, experimental data, and alternative numerical methods for free and forced liquid sloshing, free surface fluctuations and internal pressures. These comparisons validate the accuracy and robustness of the proposed method. The numerical examples further investigate the effects of external excitation frequency, excitation amplitude, rotation center position, and bottom obstacle height on liquid sloshing responses in the rectangular container. The results indicate that changes in excitation frequency, vertical eccentricity of the rotation center, and obstacle height significantly influence the liquid sloshing behavior.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"217 ","pages":"Article 104371"},"PeriodicalIF":5.7000,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Isogeometric boundary element analysis of nonlinear liquid sloshing in containers under pitching oscillation\",\"authors\":\"Quansheng Zang , Hao Hong , Jun Liu , Yanhui Zhong , Bei Zhang , Bin Li , Lei Gan\",\"doi\":\"10.1016/j.ijengsci.2025.104371\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper proposes an isogeometric boundary element method (IGABEM) to solve the nonlinear liquid sloshing problem in a rectangular container subjected to oscillatory excitation. Based on the semi-Lagrange approach, a fixed global coordinate system and a local Cartesian coordinate system that moves synchronously with the container are defined. Starting from the Laplace equation, the boundary integral equations for the liquid sloshing problem are derived using Gauss’s divergence theorem and the integration by parts technique, while incorporating nonlinear kinematic and dynamic boundary conditions of the free surface. The corresponding boundary element solution system is then formulated. Non-Uniform Rational B-Splines (NURBS) are employed as shape functions to accurately describe the geometric boundaries and approximate the unknown physical fields. This method ultimately produces the discrete equations governing nonlinear liquid sloshing problem in an oscillating container. Compared with traditional polynomial interpolation shape functions, NURBS provide improved continuity both within elements and across element interfaces as well as local support. These properties make them particularly suitable for satisfying the continuity requirements of the liquid surface. For time integration, a second-order Runge–Kutta algorithm is employed for time-stepping to solve the IGABEM system equations, compute variable gradients at each time step, and update the computational grid in real-time. A series of numerical examples are presented, the results are compared with analytical solutions, experimental data, and alternative numerical methods for free and forced liquid sloshing, free surface fluctuations and internal pressures. These comparisons validate the accuracy and robustness of the proposed method. The numerical examples further investigate the effects of external excitation frequency, excitation amplitude, rotation center position, and bottom obstacle height on liquid sloshing responses in the rectangular container. The results indicate that changes in excitation frequency, vertical eccentricity of the rotation center, and obstacle height significantly influence the liquid sloshing behavior.</div></div>\",\"PeriodicalId\":14053,\"journal\":{\"name\":\"International Journal of Engineering Science\",\"volume\":\"217 \",\"pages\":\"Article 104371\"},\"PeriodicalIF\":5.7000,\"publicationDate\":\"2025-08-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Engineering Science\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0020722525001582\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Engineering Science","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020722525001582","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
Isogeometric boundary element analysis of nonlinear liquid sloshing in containers under pitching oscillation
This paper proposes an isogeometric boundary element method (IGABEM) to solve the nonlinear liquid sloshing problem in a rectangular container subjected to oscillatory excitation. Based on the semi-Lagrange approach, a fixed global coordinate system and a local Cartesian coordinate system that moves synchronously with the container are defined. Starting from the Laplace equation, the boundary integral equations for the liquid sloshing problem are derived using Gauss’s divergence theorem and the integration by parts technique, while incorporating nonlinear kinematic and dynamic boundary conditions of the free surface. The corresponding boundary element solution system is then formulated. Non-Uniform Rational B-Splines (NURBS) are employed as shape functions to accurately describe the geometric boundaries and approximate the unknown physical fields. This method ultimately produces the discrete equations governing nonlinear liquid sloshing problem in an oscillating container. Compared with traditional polynomial interpolation shape functions, NURBS provide improved continuity both within elements and across element interfaces as well as local support. These properties make them particularly suitable for satisfying the continuity requirements of the liquid surface. For time integration, a second-order Runge–Kutta algorithm is employed for time-stepping to solve the IGABEM system equations, compute variable gradients at each time step, and update the computational grid in real-time. A series of numerical examples are presented, the results are compared with analytical solutions, experimental data, and alternative numerical methods for free and forced liquid sloshing, free surface fluctuations and internal pressures. These comparisons validate the accuracy and robustness of the proposed method. The numerical examples further investigate the effects of external excitation frequency, excitation amplitude, rotation center position, and bottom obstacle height on liquid sloshing responses in the rectangular container. The results indicate that changes in excitation frequency, vertical eccentricity of the rotation center, and obstacle height significantly influence the liquid sloshing behavior.
期刊介绍:
The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome.
The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process.
Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.