A mesh re-parameterization method using bilinear Möbius transformation for static, free vibration and buckling analyses of shells

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2025-10-02 DOI:10.1016/j.enganabound.2025.106491

Jiaqing Liang , Gang Wang , Chicheng Ma

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引用次数: 0

Abstract

Accurate analysis of shell structures is challenging due to their geometric complexity, mesh sensitivity and mechanical prediction reliability. To address this challenge, this work presents a mesh re-parameterization method for isogeometric analysis of shells using the bilinear Möbius transformation. Based on the Reissner-Mindlin theory, Non-Uniform Rational B-splines (NURBS) basis functions are employed as shape functions to accurately represent the shell geometry. Re-parameterization of the NURBS surface is achieved using the bilinear Möbius transformation, which introduces free parameters and applies linear interpolation to the basis functions. The values of the free parameters are determined by employing the Grey Wolf Optimizer algorithm. To evaluate the mesh quality before and after the bilinear Möbius transformation, the mesh shape quality coefficient is further constructed as the evaluation criterion. The re-parameterized NURBS basis functions are then used to discretize the shell structures, thereby enabling accurate isogeometric analysis. Finally, the present method is validated by examples of a free-form shell with large curvature, a simplified turbine blade and a square plate with a circular hole. The results demonstrate the present method possesses the following important advantages: (1) higher accuracy; (2) stronger adaptability; (3) faster convergence rate; (4) good stability.

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基于双线性Möbius变换的壳体静力、自由振动和屈曲分析网格再参数化方法

由于壳结构的几何复杂性、网格敏感性和力学预测的可靠性，对其进行精确分析具有挑战性。为了解决这一挑战，本工作提出了一种网格重新参数化方法，用于使用双线性Möbius变换进行壳的等几何分析。基于Reissner-Mindlin理论，采用非均匀有理b样条（NURBS）基函数作为形状函数，精确地表示壳体的几何形状。采用双线性Möbius变换实现NURBS曲面的重新参数化，该变换引入自由参数并对基函数进行线性插值。自由参数的取值采用灰狼优化算法确定。为了评价双线性Möbius变换前后的网格质量，进一步构造了网格形状质量系数作为评价标准。然后使用重新参数化的NURBS基函数对壳体结构进行离散化，从而实现精确的等几何分析。最后，通过大曲率自由壳体、简化涡轮叶片和带圆孔方形板的算例验证了该方法的有效性。结果表明，该方法具有以下重要优点：(1)精度较高；(2)适应性强；(3)收敛速度较快；(4)稳定性好。

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.