Engineering Analysis with Boundary Elements最新文献_第9页

A reproducing kernel gradient smoothing meshfree method with least squares stabilization for nearly incompressible elasticity 近乎不可压缩弹性的最小二乘稳定再现核梯度平滑无网格方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-04 DOI: 10.1016/j.enganabound.2025.106571

Yingjie Chu , Junchao Wu , Penglin Chen , Canhui Zhang , Dongdong Wang

A reproducing kernel gradient smoothing meshfree method with least squares stabilization is developed for the nearly incompressible elasticity problems. This meshfree scheme is formulated in the context of the Hellinger-Reissner (HR) variational principle, where the displacement and stress fields are independently approximated and the incompressibility constraint is implicitly embedded in the formulation. It is noteworthy that the total stress field is directly approximated herein, as does not need the conventional tedious decomposition of the stress field into deviatoric stress and pressure components. The variational integration consistency is naturally fulfilled by the reproducing kernel gradient smoothing framework, which ensures the optimal convergence of meshfree solutions. Meanwhile, the least squares stabilization is introduced to suppress the pressure oscillation. A thorough theoretical analysis evinces that the proposed reproducing kernel gradient smoothing meshfree method with least squares stabilization displays the desirable stability through satisfying both Ladyzhenskaya-Babuška-Brezzi (LBB) and kernel-coercivity conditions, which is thus conveniently termed as the stabilized variationally consistent meshfree method. The accuracy and stability of the proposed method for nearly incompressible elasticity problems are systematically validated by numerical results.

针对几乎不可压缩弹性问题，提出了一种具有最小二乘稳定性的再现核梯度平滑无网格方法。这种无网格格式是在Hellinger-Reissner （HR）变分原理的背景下制定的，其中位移和应力场是独立近似的，不可压缩性约束隐式嵌入在公式中。值得注意的是，本文直接逼近了总应力场，而不需要将应力场分解为偏应力和压力分量。再现核梯度平滑框架自然地满足了变分积分一致性，保证了无网格解的最优收敛性。同时，引入最小二乘镇定来抑制压力振荡。理论分析表明，该方法在满足Ladyzhenskaya-Babuška-Brezzi （LBB）条件和核矫顽力条件的前提下，具有较好的稳定性，可方便地称为稳定变分一致无网格方法。数值结果系统地验证了所提方法对近不可压缩弹性问题的准确性和稳定性。

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引用次数: 0

An adaptive cell-based smoothed finite element method with arbitrary polygonal elements for coupled thermo-mechanical analysis 基于自适应单元的任意多边形单元光滑有限元法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-03 DOI: 10.1016/j.enganabound.2025.106553

Ruiping Niu , Shijie Zhao , Xinglong Lu , Qiuxia Fan , Lei han Wang

This paper proposes, for the first time, an adaptive cell-based smoothed finite element method (A-CS-FEM) based on arbitrary polygonal elements for thermo-mechanical coupling problems. By utilizing mean value coordinates, the proposed model accommodates non-convex polygons without self-intersection, enabling robust handling of diverse polygonal elements. The approach integrates constrained Delaunay triangulation with adaptive techniques to partition triangulation-cell-based smoothing domains, naturally ensuring the positivity condition for a normed

G_{h}^{1}

space without additional stabilization, while maintaining the high-quality meshes. The gradient smoothing technique in CS-FEM eliminates the coordinate mapping inherent in traditional polygonal finite element methods, because it requires only the shape function values along the segments of cell smoothing domains instead of the shape function derivatives. Numerical results demonstrate that A-CS-FEM significantly improves the quality of smoothing domains for complex geometries with arbitrary convex and concave polygonal discretization, thereby achieving high-precision solutions for both displacement and temperature.

本文首次提出了一种基于任意多边形单元的自适应单元光滑有限元法（A-CS-FEM）。该模型采用均值坐标，可容纳无自交的非凸多边形，实现对多种多边形元素的鲁棒处理。该方法将约束Delaunay三角剖分与自适应技术相结合，对基于三角剖分单元的平滑域进行划分，自然地保证了归一化Gh1空间的正性条件，而无需额外的稳定化，同时保持了高质量的网格。CS-FEM中的梯度平滑技术消除了传统多边形有限元方法固有的坐标映射问题，因为它只需要沿单元平滑域段的形状函数值，而不需要形状函数导数。数值结果表明，A-CS-FEM显著提高了具有任意凸、凹多边形离散化的复杂几何图形的光滑域质量，从而获得了位移和温度的高精度解。

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引用次数: 0

Point Jacobi-type preconditioning and parameter tuning for Calderon-preconditioned Burton–Miller method in transmission problems 传输问题中Calderon-preconditioned Burton-Miller方法的点jacobi型预处理和参数整定

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-03 DOI: 10.1016/j.enganabound.2025.106572

Keigo Tomoyasu, Hiroshi Isakari

It was recently demonstrated that the boundary element method based on the Burton–Miller formulation (BM-BEM), widely used for solving exterior problems, can be adapted to solve transmission problems efficiently. This adaptation utilises Calderon’s identities to improve the spectral properties of the underlying integral operator. Consequently, most eigenvalues of the squared BEM coefficient matrix, i.e., the collocation-discretised version of the operator, cluster at a few points in the complex plane. When these clustering points are closely packed, the resulting linear system is well-conditioned and can be solved efficiently using the generalised minimal residual (GMRES) method with only a few iterations. However, when multiple materials with significantly different material constants are involved, some eigenvalues become separated, deteriorating the conditioning. To address this, we propose an enhanced Calderon-preconditioned BM-BEM with two strategies. First, we apply a preconditioning scheme inspired by the point Jacobi method. Second, we tune the BM parameters to improve the conditioning of the coefficient matrix. Both strategies leverage a newly derived analytical expression for the eigenvalue clustering points of the relevant operator. Numerical experiments demonstrate that the proposed method, combining both strategies, is particularly efficient for solving scattering problems involving composite penetrable materials with high contrast in material properties.

近年来的研究表明，基于Burton-Miller公式的边界元法（BM-BEM）可以有效地适用于求解外部问题。这种自适应利用卡尔德隆恒等式来改善底层积分算子的谱性质。因此，平方的BEM系数矩阵的大多数特征值，即算子的配位离散版本，聚集在复平面上的几个点上。当这些聚类点紧密聚集时，得到的线性系统是条件良好的，并且可以使用广义最小残差（GMRES）方法，只需少量迭代即可有效地求解。然而，当涉及多个材料且材料常数显著不同时，一些特征值会分离，使条件恶化。为了解决这个问题，我们提出了一个具有两种策略的增强型卡尔德龙预置BM-BEM。首先，我们采用了一种受点Jacobi法启发的预处理方案。其次，我们调整了BM参数，以改善系数矩阵的条件。这两种策略都利用了相关算子的特征值聚类点的新导出的解析表达式。数值实验表明，本文提出的方法结合了这两种策略，特别有效地解决了材料性能具有高对比度的复合可穿透材料的散射问题。

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引用次数: 0

Physics-informed neural network based on layerwise theory for bending analysis of laminated plates 基于分层理论的层合板弯曲分析的物理信息神经网络

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-02 DOI: 10.1016/j.enganabound.2025.106569

Zefeng Liu , Jinshuai Bai , Yuantong Gu , Ping Xiang

This paper introduces a novel computational framework that integrates physics-informed neural network (PINN) with generalized layerwise theory (LW) for the bending analysis of laminated composite plates. The framework leverages the approximation capability of deep neural networks while incorporating the physical constraints from LW theory to accurately capture the displacement fields of laminated composite plates as well as the shear stresses variations along the thickness direction. The framework is validated using various laminated plate configurations and loading conditions, with results showing excellent agreement with the meshless radial point interpolation method (RPIM), as well as other published solutions. These results highlight the potential of the PINN framework to enhance the predictive bending analysis of laminated composite plates, positioning it as a promising alternative for laminated composite structures.

介绍了一种将物理信息神经网络（PINN）与广义分层理论（LW）相结合的新型计算框架，用于层合复合材料板的弯曲分析。该框架利用深度神经网络的近似能力，同时结合LW理论的物理约束，准确捕获层合复合材料板的位移场以及沿厚度方向的剪切应力变化。该框架在各种层合板结构和加载条件下进行了验证，结果与无网格径向点插值方法（RPIM）以及其他已发表的解决方案非常吻合。这些结果突出了PINN框架在增强层压复合材料板的预测弯曲分析方面的潜力，将其定位为层压复合材料结构的有前途的替代品。

引用次数: 0

A modified finite particle method with adaptive strategy for solving bilateral obstacle problems 基于自适应策略的修正有限粒子法求解双边障碍问题

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-02 DOI: 10.1016/j.enganabound.2025.106561

Dianjian Ruan , Zhanheng Chen , Daming Yuan

Bilateral obstacle problems are fundamental in the study of partial differential equations (PDEs) and variational inequalities, with significant applications in optimal control, elasticity, and material deformation under constraints. However, numerically solving these problems is challenging due to the inherent nonlinearities and the presence of free boundaries that evolve with complex contact dynamics. Conventional discretization methods, including finite element and finite difference approaches, often struggle to balance accuracy with computational efficiency, especially when dealing with irregular geometries or the need for adaptive resolution. In the present work we introduce a meshless method that overcomes these challenges by combining the modified finite-particle method (MFPM) for discretization with the Picard iteration technique for solving the result piecewise linear system. The proposed technique employs adaptive stencil selection to guarantee a result linear system with a moderate condition number. An adaptive meshless refinement method enhances the free boundary resolution, particularly in capturing the unknown free boundary a priori. Numerical experiments confirm the method’s flexibility and robustness across a range of node layouts – including Cartesian grids, PNP nodes, and Halton points – demonstrating its potential as an effective tool for solving bilateral obstacle problems and broadening the applicability of PDE and variational inequality models.

双边障碍问题是研究偏微分方程（PDEs）和变分不等式的基础，在最优控制、弹性和约束下的材料变形方面有着重要的应用。然而，由于固有的非线性和自由边界的存在，随着复杂接触动力学的发展，数值解决这些问题是具有挑战性的。传统的离散化方法，包括有限元和有限差分方法，常常难以平衡精度和计算效率，特别是在处理不规则几何形状或需要自适应分辨率时。在目前的工作中，我们介绍了一种无网格方法，该方法通过将用于离散化的改进有限粒子方法（MFPM）与用于求解结果分段线性系统的皮卡德迭代技术相结合来克服这些挑战。该方法采用自适应模板选择方法，保证了条件数适中的结果线性系统。一种自适应无网格细化方法提高了自由边界的分辨率，特别是在先验捕获未知自由边界方面。数值实验证实了该方法在一系列节点布局（包括笛卡尔网格、PNP节点和Halton点）上的灵活性和鲁棒性，证明了它作为解决双边障碍问题的有效工具的潜力，并扩大了PDE和变分不等式模型的适用性。

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引用次数: 0

A high-order meshless method for the Allen-Cahn phase-field model Allen-Cahn相场模型的一种高阶无网格方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-01 DOI: 10.1016/j.enganabound.2025.106559

Yuqian Xu, Wentao Ma

Accurately capturing interface dynamics in phase-field models remains a significant challenge, especially in the presence of narrow interfacial layers and geometrically complex domains. In this work, we propose a high-order meshless method based on the Generalized Finite Difference Method (GFDM) to efficiently solve the Allen-Cahn (AC) equation. The spatial discretization is constructed via Taylor expansions combined with moving least-squares approximations, achieving arbitrary-order accuracy without requiring mesh generation. Moreover, the method supports localized node refinement near interfaces and direct boundary treatment in irregular geometries, significantly enhancing computational efficiency and geometric adaptability. A Crank-Nicolson (CN) scheme is employed for time discretization to preserve the energy dissipation property of the model. Extensive numerical experiments, including mean curvature flow and phase separation in both regular and irregular domains, demonstrate the proposed method’s accuracy, energy stability, and geometric adaptability.

在相场模型中准确捕获界面动力学仍然是一个重大挑战，特别是在存在窄界面层和几何复杂区域的情况下。在本文中，我们提出了一种基于广义有限差分法（GFDM）的高阶无网格方法来有效地求解Allen-Cahn （AC）方程。空间离散化是通过泰勒展开结合移动最小二乘逼近，实现任意阶精度而不需要网格生成。此外，该方法支持界面附近的局部节点细化和不规则几何的直接边界处理，显著提高了计算效率和几何适应性。采用Crank-Nicolson （CN）格式进行时间离散，以保持模型的能量耗散特性。大量的数值实验，包括规则和不规则域的平均曲率流动和相分离，证明了该方法的准确性、能量稳定性和几何适应性。

引用次数: 0

An improved Tchebychev-radial point interpolation method for large deformation analysis of hyperelastic model 一种用于超弹性模型大变形分析的改进tchebychevv -径向点插值方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-01 DOI: 10.1016/j.enganabound.2025.106566

Nha Thanh Nguyen, Thai Van Vu, Pham Toan Thang

In this study, an improvement for the Tchebychev-radial point interpolation method (TRPIM) is proposed for the finite deformation analysis of the hyperelastic structure. The TRPIM shape function is developed by integrating the radial basis function with the Tchebychev polynomial basis function instead of traditional polynomial basis functions, and this combination produces a more accurate interpolation. Both the first and second kinds of Tchebychev polynomial are tested and evaluated for the proposed method. The modification revolves around integrating the Cartesian transformation method into the TRPIM approach to make it a truly meshfree method that does not use background cells system for numerical integration. The nonlinear behavior of hyperelastic models (Neo-Hookean, Mooney–Rivlin, and Ogden) under a finite deformation state is simulated with the total Lagrange formulation and standard Newton–Raphson algorithm. To assess the large deformation behavior of two-dimensional hyperelastic problems, a series of numerical tests are carried out. The reliability and performance of the proposed method is confirmed by comparing its results with those of available solutions.

本文提出了一种改进的tchebychevv -radial点插值法（TRPIM），用于超弹性结构的有限变形分析。将径向基函数与Tchebychev多项式基函数相结合，取代了传统的多项式基函数，得到了TRPIM形状函数，这种组合可以实现更精确的插值。对所提出的方法进行了第一类和第二类切比切夫多项式的检验和评价。改进的核心是将笛卡尔变换方法与TRPIM方法相结合，使其成为一种真正的无网格方法，不使用背景单元系统进行数值积分。采用全拉格朗日公式和标准Newton-Raphson算法模拟了有限变形状态下的超弹性模型（Neo-Hookean、Mooney-Rivlin和Ogden）的非线性行为。为了评估二维超弹性问题的大变形行为，进行了一系列数值试验。通过与已有解的结果比较，验证了所提方法的可靠性和性能。

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引用次数: 0

A meshfree RBF-PUM method for solving variable-order time-fractional transport equations with an illustrative case in intelligent transportation systems 求解智能交通系统中变阶时分数阶输运方程的无网格RBF-PUM方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-11-30 DOI: 10.1016/j.enganabound.2025.106570

Marzieh Raei, Seyyed-Mahdi Hosseini-Motlagh, Mohammad Reza Gholamian

This paper develops a robust meshfree numerical framework based on the Radial Basis Function Partition of Unity Method (RBF-PUM) for solving two- and three-dimensional variable-order time-fractional transport equations. The temporal derivative is approximated using the Weighted and Shifted Grünwald–Letnikov (WSGD) scheme, which ensures second-order accuracy and unconditional stability, while spatial discretization is handled by localized RBF-PUM collocation for improved conditioning and flexibility on irregular domains. Extensive numerical experiments confirm second-order convergence, stability, and robustness against geometric perturbations and noise. Benchmark tests with different variable-order profiles and a representative transport scenario in intelligent mobility systems demonstrate that the proposed framework accurately captures heterogeneous memory effects and spatio-temporal transport dynamics beyond classical diffusion. The results highlight the method’s effectiveness for modeling anomalous transport and its potential use in engineering analyses of complex multi-dimensional systems, including applications in intelligent transportation networks.

本文提出了一种基于统一方法径向基函数划分（RBF-PUM）的鲁棒无网格数值框架，用于求解二维和三维变阶时间分数输运方程。时间导数的近似采用加权移位格 nwald - letnikov （WSGD）格式，保证了二阶精度和无条件稳定性；空间离散化采用局部RBF-PUM配置，提高了不规则域上的调节和灵活性。广泛的数值实验证实二阶收敛性，稳定性和抗几何扰动和噪声的鲁棒性。在智能移动系统中，基于不同变序特征和典型传输场景的基准测试表明，所提出的框架准确地捕捉了超越经典扩散的异构记忆效应和时空传输动态。研究结果强调了该方法对异常运输建模的有效性及其在复杂多维系统的工程分析中的潜在应用，包括在智能交通网络中的应用。

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引用次数: 0

A Feature-Enhanced Physics Informed Neural Network for trajectory simulation of charged particles 用于带电粒子轨迹模拟的特征增强物理信息神经网络

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-11-29 DOI: 10.1016/j.enganabound.2025.106562

Fan Yang, Xuan Liu, Pengbo Wang, Xinheng Li

Trajectory simulation of charged particles is a complex multiphysics problem with dynamic field involved. With the mesh-free essence, Physics-Informed Neural Networks (PINNs) offers high capability in conformal modeling and dynamic field mapping. By integrating governing physical laws with real-time or experimental data, PINNs can accurately capture dynamic field variation and system response, demonstrating substantial potential for field–particle coupling simulations. However, conventional PINNs still face challenges caused by space charge effect and multi-scale field variations. This paper proposes a Feature-Enhanced PINN (FE-PINN) framework for the simulation of charged particle dynamics. For electromagnetic fields with evolving internal sources and complex geometries, Feature-Enhanced PINN eliminates the need for network retraining under varying space charge distributions, and applies targeted enhancement in collocation strategies and network structure to improve convergence and accuracy in domains of localized high-gradient. Built upon FE-PINN electromagnetic field solutions, particle trajectory simulation is achieved by iteratively solving the Poisson’s equation and particle motion equation under a fixed magnetic field. The proposed method is validated using the magnetron injection gun (MIG) of an 800 GHz gyrotron with results compared with that of CST Studio Suite.

带电粒子的轨迹模拟是一个涉及动力学场的复杂多物理场问题。物理信息神经网络（PINNs）具有无网格的本质，在保形建模和动态场映射方面具有很高的能力。通过将控制物理定律与实时或实验数据相结合，pinn可以准确地捕获动态场变化和系统响应，显示出场-粒子耦合模拟的巨大潜力。然而，传统的pin - ns仍然面临着空间电荷效应和多尺度场变化带来的挑战。本文提出了一种特征增强的pin - n （fe - pin）框架，用于模拟带电粒子动力学。对于具有演化的内源和复杂几何形状的电磁场，Feature-Enhanced PINN消除了在不同空间电荷分布下对网络进行再训练的需要，并对配置策略和网络结构进行了有针对性的增强，以提高局部高梯度域的收敛性和准确性。在FE-PINN电磁场解的基础上，通过迭代求解固定磁场下的泊松方程和粒子运动方程实现粒子轨迹仿真。利用800 GHz回旋管的磁控管注射枪（MIG）对该方法进行了验证，并与CST Studio Suite的结果进行了比较。

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引用次数: 0

Coupled role of mineral heterogeneity and cross fractures in the macro–meso mechanical behavior of granite: Insights from image-informed numerical modeling 矿物非均质性和交叉裂缝在花岗岩宏观细观力学行为中的耦合作用：来自图像信息数值模拟的见解

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-11-29 DOI: 10.1016/j.enganabound.2025.106564

Tingting Liu , Shenghao Yang , Luyang Ding , Xiaohan Xie , Hui Shen , Xinping Li

Tectonic evolution induces discontinuities and mineral heterogeneity in rock masses, complicating mechanical behavior. This study examines how mineral composition affects the response of granite with cross fractures, a key issue for underground engineering stability. The discrete element method (DEM) was implemented using the particle flow code in two dimensions (PFC2D). Parameters were calibrated through a digital image processing grain-based model (DIP–GBM), on which a random distribution properties grain-based model (RDP–GBM) was established to simulate mechanical response, fracture evolution, and energy characteristics under varied mineral compositions. Results show that fracture connectivity (ω) is the primary control: uniaxial compressive strength (UCS) decreases with increasing connectivity, while the elastic modulus (E) increases slightly at ω = 0.141 before declining. Mineral composition exerts a secondary influence, with higher biotite content and feldspar-to-quartz (λ) ratios reducing strength. In intact granite, failure is governed by mineral heterogeneity, whereas in cross-fractured granite, fracture geometry dominates. Low-stress region exists in granite with cross fractures and is linked to crack evolution. With increasing connectivity, total and elastic strain energy decrease, while biotite-rich rocks show reduced total energy. These findings highlight the coupled effects of fractures and minerals and provide a basis for stability evaluation in underground engineering.

构造演化导致岩体中的不连续和矿物非均质性，使力学行为复杂化。本文研究了矿物成分如何影响具有交叉裂缝的花岗岩的响应，这是地下工程稳定性的一个关键问题。采用二维粒子流代码（PFC2D）实现离散元法（DEM）。通过数字图像处理颗粒模型（DIP-GBM）标定参数，在此基础上建立随机分布属性颗粒模型（RDP-GBM），模拟不同矿物成分下的力学响应、裂缝演化和能量特征。结果表明，裂缝连通性（ω）是主要控制因素，单轴抗压强度（UCS）随连通性的增加而降低，而弹性模量(E)在ω = 0.141时略有增加，然后下降。矿物组成是次要影响，较高的黑云母含量和长石与石英（λ）比降低了强度。在完整的花岗岩中，破坏是由矿物非均质性决定的，而在交叉断裂的花岗岩中，裂缝几何形状占主导地位。低应力区存在于具有交叉裂缝的花岗岩中，与裂缝演化有关。随着连通性的增加，总应变能和弹性应变能降低，而富含黑云母的岩石总应变能降低。这些发现突出了裂缝与矿物的耦合作用，为地下工程稳定性评价提供了依据。

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引用次数: 0