The improved interpolating element-free Galerkin method based on nonsingular weight functions for three-dimensional elastoplastic problems

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Engineering Analysis with Boundary Elements Pub Date : 2025-01-30 DOI:10.1016/j.enganabound.2025.106136

Y.F. Wang , Y. Lu , L. Chen , M.J. Peng , Y.M. Cheng

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Abstract

Because of the nonlinearity, three-dimensional (3D) elastoplastic problems are very important for any numerical method. In this study, the improved interpolating element-free Galerkin (IIEFG) method based on nonsingular weight functions for elastoplastic problems is presented. An improved interpolating moving least-squares (IIMLS) method with nonsingular weight functions is applied to construct the shape function. The elastoplastic control equations are formulated using the incremental Galerkin weak form with considering the nonlinear stress-strain relationship. Then the equations of IIEFG are presented. A key advantage of IIEFG is its ability to directly apply boundary conditions to improve computational efficiency because of the interpolating property of IIMLS. And using nonsingular weight functions can overcome the disadvantage of singular weight functions, and the computational accuracy is improved. Five numerical examples are presented to evaluate the impact of parameters such as node arrangement, the number of loading steps, and scaling parameters of the influence domain impact the calculation results of this method. Comparisons with other numerical methods demonstrate the superior computational efficiency and accuracy of IIEFG for solving 3D elastoplastic problems.

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基于非奇异权函数的三维弹塑性问题的改进无单元Galerkin插值方法

由于三维弹塑性问题的非线性特性，对任何数值方法来说都是非常重要的。针对弹塑性问题，提出了一种基于非奇异权函数的改进无单元伽辽金插值方法。采用改进的非奇异权函数插值移动最小二乘（IIMLS）方法构造形状函数。考虑非线性应力-应变关系，采用增量伽辽金弱形式建立弹塑性控制方程。然后给出了IIEFG的方程。由于IIMLS的插值特性，它的一个关键优点是能够直接应用边界条件来提高计算效率。采用非奇异权函数克服了奇异权函数的缺点，提高了计算精度。给出了5个算例，分析了节点布置、加载步骤数、影响域尺度参数等参数对该方法计算结果的影响。与其他数值方法的比较表明，IIEFG在求解三维弹塑性问题时具有较高的计算效率和精度。

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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.