RIM-IGABEM and DRM-IGABEM in three-dimensional general anisotropic elastic problems with complex-shape cavities

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Engineering Analysis with Boundary Elements Pub Date : 2024-10-22 DOI:10.1016/j.enganabound.2024.106000

Fangling Sun , Chunying Dong

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Abstract

The paper establishes the pure boundary integral equations of the isogeometric boundary element method (IGABEM) based on isotropic fundamental solutions to solve three-dimensional (3D) general anisotropic elastic problems including various complex cavities. The residual method is employed which introduces the fictitious body force causing the domain integral. Subsequently, the radial integration method (RIM) and the dual reciprocity method (DRM) are utilized to transform the domain integral to the boundary integral, respectively. Moreover, the Bézier extraction technique are used to facilitate the incorporation of NURBS into boundary element codes. Based on this, a novel scheme to determine the location of the collocation points in NURBS elements is proposed. Finally, the theoretical frameworks of the RIM-IGABEM and the DRM-IGABEM are developed, which retain the advantages of BEM and IGA, i.e. only boundary is discretized and complex geometry is described exactly, and the schemes are adaptable that only require to change pre-processing of a considered anisotropic problems, including the material properties and the geometry. Several numerical examples are used to demonstrate effectiveness of the schemes, and the effects of the material properties and the geometric shape on the distribution of displacements are discussed in detail.

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带有复杂形状空腔的三维一般各向异性弹性问题中的 RIM-IGABEM 和 DRM-IGABEM

本文建立了基于各向同性基本解的等几何边界元法（IGABEM）纯边界积分方程，用于求解包括各种复杂空腔在内的三维（3D）一般各向异性弹性问题。残差法引入了引起域积分的虚体力。随后，利用径向积分法（RIM）和二元互易法（DRM）分别将域积分转换为边界积分。此外，贝塞尔抽取技术也有助于将 NURBS 纳入边界元代码。在此基础上，提出了一种确定 NURBS 元素中配位点位置的新方案。最后，提出了 RIM-IGABEM 和 DRM-IGABEM 的理论框架，它们保留了 BEM 和 IGA 的优点，即只对边界进行离散化，并精确描述复杂的几何形状，而且方案适应性强，只需改变对所考虑的各向异性问题的预处理，包括材料属性和几何形状。我们使用了几个数值示例来证明这些方案的有效性，并详细讨论了材料属性和几何形状对位移分布的影响。

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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.