Engineering Analysis with Boundary Elements最新文献

英文中文

Numerical algorithm of concave polygon elements in solid mechanics: Theoretical analysis and performance evaluation of S-FEM and VEM 固体力学中凹多边形单元的数值计算：S-FEM和VEM的理论分析与性能评价

IF 3.3 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-02-03 DOI: 10.1016/j.enganabound.2025.106617

Shao-Wei Wu, Jun-Xiong Hu, Yu-Hang Ning, Zhang-Xing Xie, Kai Liu, Qi-Qi Li, Xin Liu

引用次数: 0

Modeling of rock failure based on a modified particle discontinuous deformation analysis 基于改进颗粒不连续变形分析的岩石破坏模型

IF 3.3 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-02-03 DOI: 10.1016/j.enganabound.2026.106666

Zongxin Jiang, Laping He, Zhao Long, Baoping Wang, Zhengxu Chen, Feng Liu

引用次数: 0

Electrochemical-mechanical analysis of ionic polymer gels based on the boundary element method 基于边界元法的离子聚合物凝胶电化学-力学分析

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-30 DOI: 10.1016/j.enganabound.2026.106656

Jingwen Liu , Changzheng Cheng , Yifan Huang , Feiyang Wang

Ionic polymer gels are employed in a number of electrochemical devices due to their exceptional electrical conductivity and electrochemical stability. These polymer gels serve in a complex working condition involving the interaction of multi-physical fields. In order to investigate the mechanical behavior of these materials in electrochemical field and enhance the computational efficiency of the numerical method under the complex boundary conditions, the boundary integral equations and internal stress integral equations are established in this paper to describe steady-state ionic polymer gels deformation state in the presence of an electric field. The boundary element method is used to solve for diffusion-induced stresses under the influence of concentration, while the radial integration method is used to deal with the domain integrals of the boundary integral equations containing the ion concentration field. The efficacy of the proposed method is substantiated through the deformation results of ionic polymer gels subjected to a steady-state electrochemical field. Furthermore, the boundary integral equations for multiple domains under diffusion effects are formulated on the basis of the multidomain boundary element method. The effect of steady-state diffusion-induced stresses to the ionic polymer gels and the current collector is studied. Additionally, the impact of diffusion-induced stresses to the current collectors and polymer gels is evaluated for varying current collector elastic moduli and widths.

离子聚合物凝胶由于其优异的导电性和电化学稳定性而被应用于许多电化学装置中。这些聚合物凝胶在涉及多物理场相互作用的复杂工作条件下服务。为了研究这些材料在电化学场中的力学行为，提高数值方法在复杂边界条件下的计算效率，本文建立了边界积分方程和内应力积分方程来描述稳态离子聚合物凝胶在电场作用下的变形状态。采用边界元法求解浓度影响下的扩散诱发应力，采用径向积分法求解含有离子浓度场的边界积分方程的域积分。离子聚合物凝胶在稳态电化学场作用下的变形结果证实了该方法的有效性。在此基础上，利用多域边界元法推导了扩散作用下多域边界积分方程。研究了稳态扩散诱导应力对离子聚合物凝胶和集流器的影响。此外，扩散引起的应力对电流集热器和聚合物凝胶的影响评估了不同的电流集热器弹性模量和宽度。

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引用次数: 0

A variationally consistent meshfree Galerkin formulation for three-dimensional strain gradient elasticity 三维应变梯度弹性的变一致无网格伽辽金公式

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-30 DOI: 10.1016/j.enganabound.2026.106659

JingYan Li , MingHao Zhao , Chunsheng Lu , JianWei Zhang , Yue Mei , BingBing Wang

In this paper, we develop a variationally consistent meshfree Galerkin formulation for three-dimensional strain gradient elasticity. A generalized five-variable variational principle is employed to derive an orthogonality condition, which forms the basis for a novel consistent integration scheme using tetrahedral background cells. This scheme incorporates first- and second-order smoothed nodal gradients and satisfies the discretized orthogonality condition, thereby ensuring full variational consistency. Numerical examples demonstrate that the proposed integration strategy achieves substantially higher accuracy and computational efficiency than conventional Gaussian quadrature, while effectively suppressing spurious numerical oscillations. Compared with simplified two-dimensional cases, the variationally consistent integration method is particularly suited for practical micro- and nano-scale device analysis and design.

本文建立了三维应变梯度弹性的变一致无网格伽辽金公式。利用广义的五变量变分原理推导出正交性条件，为四面体背景单元的一致性积分方案奠定了基础。该方案结合了一阶和二阶平滑节点梯度，满足离散正交性条件，从而保证了完全变分一致性。数值算例表明，所提出的积分策略比传统的高斯正交具有更高的精度和计算效率，同时有效地抑制了伪数值振荡。与简化的二维情况相比，变分一致积分法特别适合实际的微纳器件分析与设计。

引用次数: 0

Steady-state unconfined seepage in heterogeneous medium using an adaptive multi-patch isogeometric analysis 非均质介质中稳态无侧限渗流的自适应多块等几何分析

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-30 DOI: 10.1016/j.enganabound.2026.106658

Chen Wu , Lin Wang , Sundararajan Natarajan , Weihua Fang , Tiantang Yu

For seepage problems with free surfaces, traditional approaches use either moving mesh strategies or fixed mesh strategies. Both these approaches have inherent challenges, on one hand, the moving mesh methods often encounter computational instability caused by mesh distortion, whereas the fixed mesh methods face challenges in balancing computational accuracy and efficiency. To overcome these limitations, this paper presents a two-dimensional steady-state unconfined seepage framework based on adaptive multi-patch isogeometric analysis, designed to enable efficient, stable, and precise numerical simulations. The proposed framework incorporates a Zienkiewicz–Zhu error estimator to drive local mesh refinement, and utilizes truncated hierarchical non-uniform rational B-splines (TH-NURBS) for accurate modeling and localized adaptive refinement. The multi-patch technique, integrated with Nitsche’s method, is adopted for the simulation of complex geometries. Validation with several numerical examples shows that the framework provides favorable computational accuracy and efficiency, highlighting its potential for application in complex engineering problems.

对于自由表面的渗流问题，传统的方法要么采用移动网格策略，要么采用固定网格策略。这两种方法都存在固有的挑战，一方面，运动网格法经常遇到网格畸变引起的计算不稳定，而固定网格法则面临计算精度和效率平衡的挑战。为了克服这些限制，本文提出了一个基于自适应多补丁等几何分析的二维稳态无侧限渗流框架，旨在实现高效、稳定和精确的数值模拟。该框架采用Zienkiewicz-Zhu误差估计器驱动局部网格细化，并利用截断的分层非均匀有理b样条（TH-NURBS）进行精确建模和局部自适应细化。采用多贴片技术，结合Nitsche方法，对复杂几何图形进行模拟。数值算例验证表明，该框架具有良好的计算精度和效率，在复杂工程问题中具有应用潜力。

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引用次数: 0

A meshless Schwarz-MFS framework for identifying time-dependent thermal contact conductance in layered materials 一种无网格Schwarz-MFS框架用于识别层状材料中随时间变化的热接触电导

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-29 DOI: 10.1016/j.enganabound.2026.106649

Igor Falcão Tosi , Luiz Alberto da Silva Abreu , Julio Cesar Sampaio Dutra , Wellington Betencurte da Silva

This paper investigates the Method of Fundamental Solutions (MFS) for solving transient heat conduction problems in layered materials, in conjunction with the domain decomposition method. The study specifically examines the impact of Schwarz iterative algorithms by testing both overlapping and non-overlapping configurations between subdomains. In contrast to previous approaches where fictitious sources were placed outside the spatial domain in a circular arrangement, the present work arranges these sources in a rectangular configuration for each domain, introducing small additional distances at the boundaries to minimize singular values. The analysis addresses the stability of the method with respect to key parameters such as the number of collocation points, the distance between domains, the regularization parameter, and various error metrics. Numerical results are compared with reference solutions obtained using COMSOL, and the calculated errors demonstrate the excellent viability and robustness of the meshless method when combined with domain decomposition and Schwarz iteration schemes for solving multilayer transient heat conduction problems.

本文研究了层状材料瞬态热传导问题的基本解方法（MFS）与区域分解方法的结合。该研究通过测试子域之间的重叠和非重叠配置，具体检查了Schwarz迭代算法的影响。与之前将虚拟光源以圆形排列放置在空间域外的方法相反，本研究将这些光源以矩形配置排列在每个域，在边界处引入小的额外距离以最小化奇异值。分析了该方法在关键参数方面的稳定性，如配点数、域间距离、正则化参数和各种误差指标。数值结果与COMSOL参考解进行了比较，计算误差证明了无网格方法结合区域分解和Schwarz迭代方法求解多层瞬态热传导问题的可行性和鲁棒性。

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引用次数: 0

Long-time dynamic analysis of damped wave propagation using a time-spectral BEM with discontinuous triangular elements 用带有不连续三角单元的时谱边界元分析阻尼波传播的长时间动力

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-28 DOI: 10.1016/j.enganabound.2026.106657

Wenzhen Qu , Yan Gu , Bo Yu

In this work, a time-spectral boundary element method (TSBEM) with discontinuous triangular elements is proposed for long-time dynamic analysis of damped wave propagation in two dimension. Within this framework, the first- and second-order time derivatives of displacement in the governing equations are treated as nonhomogeneous terms and incorporated into the kernel functions of the domain integrals in the boundary integral equation using Green’s second identity. These time derivatives are approximated as weighted linear combinations of displacements values at Gaussian nodes within each temporal interval, following an inverse spectral integration technique. To evaluate domain integrals whose kernels involve unknown or non-functional physical quantities, discontinuous quadratic triangular elements are introduced to accurately approximate these quantities. Consequently, the developed approach accommodates large time steps while maintaining stability in long-time dynamic simulations. Notably, the coefficient matrix generated in the TSBEM is independent of the time variable, meaning it only needs to be computed once throughout the entire time marching process. To validate the accuracy and computational efficiency of the proposed approach, several numerical experiments are conducted. The numerical results obtained using the TSBEM are compared with those from traditional approaches.

本文提出了一种具有不连续三角单元的时谱边界元方法，用于二维阻尼波传播的长时间动力学分析。在此框架内，控制方程中的一阶和二阶位移时间导数被视为非齐次项，并使用格林二阶恒等式将其纳入边界积分方程中域积分的核函数中。这些时间导数近似为每个时间间隔内高斯节点位移值的加权线性组合，遵循逆光谱积分技术。为了计算核包含未知或非泛函物理量的域积分，引入了不连续二次三角元来精确逼近这些物理量。因此，所开发的方法可以适应大的时间步长，同时保持长时间动态模拟的稳定性。值得注意的是，TSBEM中生成的系数矩阵与时间变量无关，这意味着在整个时间推进过程中只需要计算一次。为了验证该方法的精度和计算效率，进行了数值实验。并与传统方法的数值结果进行了比较。

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引用次数: 0

Semi-analytical boundary element method for transient uncoupled thermoelastic analysis with coupling singularities 具有耦合奇点的瞬态非耦合热弹性分析的半解析边界元法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-24 DOI: 10.1016/j.enganabound.2026.106654

Yifan Huang , Jingwen Liu , Changzheng Cheng , Zhongrong Niu , Changyun Shi , Qi He , Fen Wang

This paper proposes a novel semi-analytical boundary element method (SABEM) for analyzing singular fields in transient uncoupled thermoelastic problems. The boundary-domain integral equations are formulated by integrating the governing equations of the transient uncoupled thermoelastic problems. To preserve the advantage of boundary-only discretization, the dual reciprocity method (DRM) and the particular integral formulation (PIF) are employed to convert domain integrals into boundary integrals. The radial basis functions are used in the DRM and PIF to approximate the distribution of physical fields across the domain. To accurately capture the singular fields, novel semi-analytical elements (SAEs) are constructed based on asymptotic expansions. Different from the conventional boundary element, where the unknowns are the singular physical quantities themselves, the undetermined amplitude coefficients in the SAEs are set as unknowns. Thus, the ill-conditioned system equations containing the undetermined singular physical fields in the conventional BEM can be improved without any mesh refinement. By solving the final system equations, the undetermined amplitude coefficients as well as the physical quantities in the entire domain can be obtained directly. The efficiency and validity of the proposed method are demonstrated through two numerical examples.

提出了一种新的半解析边界元法（SABEM），用于分析非耦合热弹性问题中的奇异场。通过对瞬态非耦合热弹性问题的控制方程进行积分，得到了边界域积分方程。为了保持边界离散化的优势，采用对偶互易法和特殊积分公式将域积分转化为边界积分。在DRM和PIF中使用径向基函数来近似物理场在域上的分布。为了准确地捕获奇异域，基于渐近展开构造了新的半解析元。与传统边界元中未知量是奇异物理量本身不同，边界元中的待定振幅系数被设置为未知量。因此，传统边界元法中包含待定奇异物理场的病态系统方程可以在不进行网格细化的情况下得到改进。通过求解最终的系统方程，可以直接得到整个区域的待定振幅系数和物理量。通过两个算例验证了该方法的有效性和有效性。

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引用次数: 0

A Morphing approach to a couple of peridynamic and classical continuum diffusion models for transient heat conduction 瞬态热传导的两个周期动力学和经典连续介质扩散模型的变形方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-23 DOI: 10.1016/j.enganabound.2026.106655

Shankun Liu, Hebang Qian, Fei Han

This study develops a coupled peridynamic/classical continuum (PD/CC) framework by the Morphing approach for transient heat conduction. By integrating the PD model with the Fourier-based CC model, a proposed hybrid model leverages the nonlocal formulation to characterize heat conduction in critical domains where sharp temperature gradients may occur due to flows or heat pulses, while employing the local formulation in the rest of the domains to reduce computational costs and be conducive to apply the traditional boundary conditions. The equivalence between PD and CC material parameters is established through a homogenized thermal potential, ensuring energy consistency across overlapping subdomains. A Morphing function strategically transitions between models, minimizing spurious “ghost heat” at interfaces. Theoretical dispersion analysis reveals distinct dissipation behaviors in PD and CC regimes, with numerical validations demonstrating agreements with analytical solutions and reference data. Case studies on 1D bars, 2D plates, and a 3D pillar with insulated cracks confirm the model’s accuracy and validity.

本研究利用Morphing方法建立了一个瞬态热传导的周动力学/经典连续体（PD/CC）耦合框架。通过将PD模型与基于傅里叶的CC模型相结合，提出了一种混合模型，该混合模型利用非局部公式来表征由于流动或热脉冲可能产生急剧温度梯度的关键区域的热传导，而在其余区域采用局部公式来减少计算成本并有利于应用传统边界条件。PD和CC材料参数之间的等效性通过均匀的热势建立，确保重叠子域之间的能量一致性。Morphing功能策略性地在模型之间转换，最大限度地减少界面上的虚假“鬼热”。理论色散分析揭示了PD和CC模式下不同的耗散行为，数值验证与解析解和参考数据一致。对1D杆、2D板和带有绝缘裂缝的3D柱的案例研究证实了模型的准确性和有效性。

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引用次数: 0

Tanh-B6 KAN-based PINN for solving thin plate bending problems 用于解决薄板弯曲问题的基于Tanh-B6 kan的PINN

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-23 DOI: 10.1016/j.enganabound.2026.106653

Shuo Liu, Yonghong Cao

Solving high-order partial differential equations, such as the governing equations of Kirchhoff thin plate bending, remains a significant challenge for traditional Physics-Informed Neural Networks (PINNs). Conventional Multi-Layer Perceptron (MLP) architectures often suffer from spectral bias and gradient instability when computing high-order derivatives. To address these limitations, this study introduces a novel framework: the Tanh-B6 KAN-based PINN. This method integrates Kolmogorov-Arnold Networks (KAN) featuring learnable Tanh activation functions and sixth-order B-spline basis functions into the PINN architecture. Specifically, the sixth-order B-splines ensure C⁴ continuity, providing stable analytical computation for high-order derivatives, while the Tanh activation captures global trends. The effectiveness of this approach is validated through comprehensive numerical experiments on elliptical, triangular, rectangular, and L-shaped thin plates subject to varying boundary and load conditions. Comparative results demonstrate that the Tanh-B6 KAN-based PINN significantly outperforms the traditional MLP-PINN, reducing the relative L₂ norm error and Mean Absolute Error (MAE) of the displacement field and boundaries by one to three orders of magnitude, while reducing the number of parameters by two to three orders of magnitude. The proposed method offers a robust, interpretable, and highly efficient solution for high-order mechanics problems.

求解高阶偏微分方程，如基尔霍夫薄板弯曲的控制方程，仍然是传统物理信息神经网络（pinn）面临的一个重大挑战。传统的多层感知器（MLP）结构在计算高阶导数时往往存在谱偏差和梯度不稳定性。为了解决这些限制，本研究引入了一种新的框架：基于Tanh-B6 kan的PINN。该方法将具有可学习Tanh激活函数和六阶b样条基函数的Kolmogorov-Arnold网络（KAN）集成到PINN体系结构中。具体来说，六阶b样条确保C4连续性，为高阶导数提供稳定的解析计算，而Tanh激活捕获全局趋势。通过椭圆、三角形、矩形和l型薄板在不同边界和载荷条件下的综合数值实验，验证了该方法的有效性。对比结果表明，基于Tanh-B6 kan的PINN显著优于传统的MLP-PINN，将位移场和边界的相对L2范数误差和平均绝对误差（MAE）降低了1 ~ 3个数量级，同时将参数数量减少了2 ~ 3个数量级。该方法为高阶力学问题提供了鲁棒性、可解释性和高效率的求解方法。

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