A NURBS-enhanced semi-analytical method for nonlinear liquid sloshing analysis in liquid storage structures with various baffles

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2025-02-14 DOI:10.1016/j.enganabound.2025.106155

Quansheng Zang , Yanhui Zhong , Wenbin Ye , Jun Liu , Bin Li , Fan Yang , Songtao Li

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引用次数: 0

Abstract

Within the framework of scaled boundary finite element method (SBFEM) and inspired by isogeometric analysis (IGA), the NURBS-enhanced semi-analytical method, referred to as the scaled boundary isogeometric analysis (SBIGA), is extended for solving nonlinear liquid sloshing analysis in storage structures. This method leverages the advantages of Non-Uniform Rational B-Splines (NURBS), offering a highly efficient and accurate solution. NURBS provides high-order continuity, making it particularly suitable for capturing the smoothness of free liquid surfaces in sloshing phenomena. Compared to traditional Lagrangian elements, the proposed approach efficiently utilizes control points, enabling accurate geometric representation with fewer degrees of freedom. A semi-Lagrangian algorithm establishes a global fixed coordinate system and a local system moving with the structure, enabling flexible mesh updating and efficient computation. Based on potential flow theory, the SBIGA equations for nonlinear liquid sloshing are derived using the weighted residual method, with dual variables introduced. The eigenfunction expansion method solves the equations, and the fourth-order Runge–Kutta method is applied for time integration. This approach combines the strengths of SBFEM and IGA, featuring boundary-only discretization, radial analytical solutions, and precise geometric boundary representation. Meanwhile, the present SBIGA does not require fundamental solutions as in traditional methods, nor does it require handling corner singularities or singular integrals as in boundary element methods. Numerical examples validate the accuracy of the present model, followed by analyses of the sloshing reduction effects of horizontal and vertical baffles in rectangular liquid storage structures. Finally, a U-shaped aqueduct under seismic loading is examined to evaluate the effectiveness of baffles in reducing sloshing responses in complex structures under seismic conditions.

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具有不同挡板的储液结构中非线性晃动分析的nurbs增强半解析方法

在尺度边界有限元法（SBFEM）的框架下，受等几何分析（IGA）的启发，将nurbs增强的半解析方法扩展为尺度边界等几何分析（SBIGA），用于求解存储结构中的非线性液体晃动分析。该方法利用了非均匀有理b样条（NURBS）的优点，提供了一个高效、准确的解决方案。NURBS提供高阶连续性，使其特别适合捕获晃动现象中自由液体表面的平滑度。与传统的拉格朗日单元相比，该方法有效地利用了控制点，以较少的自由度实现了精确的几何表示。半拉格朗日算法建立全局固定坐标系和随结构运动的局部坐标系，使网格更新灵活，计算效率高。基于势流理论，采用加权残差法，引入对偶变量，推导了非线性液体晃动的SBIGA方程。采用特征函数展开法求解方程，采用四阶龙格-库塔法进行时间积分。该方法结合了SBFEM和IGA的优点，具有仅边界离散化、径向解析解和精确的几何边界表示。同时，本文的SBIGA不像传统方法那样需要基本解，也不像边界元方法那样需要处理角点奇点或奇异积分。数值算例验证了模型的准确性，并分析了矩形储液结构中水平挡板和垂直挡板的减振效果。最后，对地震荷载作用下的u型渡槽进行了试验，以评估在地震条件下挡板减少复杂结构晃动响应的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.