Engineering Analysis with Boundary Elements最新文献_第3页

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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引用次数: 0

An explicit dynamic face-based smoothed finite element approach to thermoelastic modeling in thermal ablation therapy 基于显式动态面光滑有限元方法的热消融治疗热弹性建模

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-19 DOI: 10.1016/j.enganabound.2026.106648

Ruiping Niu, Yi Cai, Chengtao Wu

Computer-assisted thermal ablation therapy techniques depend on precise and effective soft tissue temperature prediction. This paper proposes an accurate explicit dynamics face-based smoothed finite element algorithm (FS-FEM) for thermoelastic analysis of soft tissue, grounded in large deformation thermoselasticity and total Lagrangian formulation. A tightly coupled model is proposed to capture the interactive behavior: (i) bioheat transfer with tissue deformation, (ii) tissue deformation due to thermal expansion. Then the weakened weak form of the presented coupled model is derived, and the explicit dynamic face-based smoothed finite element approach is formulated. Finally, the effectiveness and compatibility of the established methodology are verified using a human liver modelling with publicly available CT scan datasets to illustrate a clinically pertinent scenario of thermal ablation for hepatocellular carcinoma. The results demonstrate that our proposed numerical algorithm efficiently solves the simulation of liver thermal ablation, with temperature and tissue deformation predictions being more accurate than those obtained by the finite element method (FEM).

计算机辅助热消融治疗技术依赖于精确有效的软组织温度预测。基于大变形热弹性理论和全拉格朗日公式，提出了一种精确的基于显式动力学面光滑有限元法（FS-FEM）。提出了一个紧密耦合模型来捕捉相互作用行为：(i)生物热传递与组织变形，（ii）由于热膨胀引起的组织变形。然后推导了该耦合模型的弱化弱形式，并建立了基于显式动态面的光滑有限元方法。最后，使用公开可用的CT扫描数据集的人类肝脏模型验证了既定方法的有效性和兼容性，以说明肝细胞癌热消融的临床相关场景。结果表明，本文提出的数值算法有效地解决了肝脏热消融的模拟问题，其温度和组织变形的预测比有限元法（FEM）更准确。

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引用次数: 0

Multi-physics smoothed particle hydrodynamics (SPH) model for icing channel in cold regions 寒区结冰通道的多物理场光滑粒子流体力学模型

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-19 DOI: 10.1016/j.enganabound.2025.106623

Yuxiao Li , Haitao Wu , Shenglong Gu , Chi Zhang , Songdong Shao

This study proposed a multi-physics mesh-free Smoothed Particle Hydrodynamics (SPH)-based model for ice cover growth, which is designed to simulate ice dynamic evolutions in a cold-regional water conveyance channel. The model addressed the limitations of grid-based methods in multiphase interface treatment, free-surface tracking, and phase-change coupling. A three-dimensional (3D) computational model integrating the heat transfer, flow, and phase changes has been developed via modification of the open-source Smoothed Particle Hydrodynamics for industrial complex systems (SPHinXsys) framework. Natural convection is incorporated to dynamically simulate the ice cover growth in conveyance channels. Benchmark validations include two-dimensional (2D) Stefan problems and natural convection in square cavity. Simulations of three-dimensional channel flows with natural convection showed good agreement with the grid-based method. In the proposed multi-physics ice growth simulations, the maximum root mean square error of ice thickness is 1.93 mm with the growth rate deviations below 2.19 %. These results confirm the model’s capability for complex flows and its potential applications in cold-region anti-icing designs.

本文提出了一种基于多物理场无网格光滑粒子水动力学（SPH）的冰盖生长模型，用于模拟寒冷地区输水通道的冰动力演变。该模型解决了基于网格的方法在多相界面处理、自由表面跟踪和相变耦合方面的局限性。通过修改开放源代码的工业复杂系统平滑粒子流体动力学（SPHinXsys）框架，开发了一个集成传热、流动和相变的三维（3D）计算模型。采用自然对流的方法，动态模拟了输送通道中冰盖的增长。基准验证包括二维（2D） Stefan问题和方形腔内的自然对流。对自然对流的三维通道流动的模拟结果与基于网格的方法吻合较好。在多物理场冰生长模拟中，冰厚度的最大均方根误差为1.93 mm，生长速率偏差小于2.19%。这些结果证实了该模型对复杂流动的能力及其在寒冷地区防冰设计中的潜在应用。

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引用次数: 0

High-order meshless approach for solving the 3D nonlinear Bratu problem 求解三维非线性Bratu问题的高阶无网格方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-17 DOI: 10.1016/j.enganabound.2026.106651

El-Houssaine El-Asri , Abdeljalil Tri , Bouazza Braikat , Hamid Zahrouni

In this work, we study the nonlinear Bratu problem in three dimensions (3D), known for its complexity due to the presence of multiple solutions and bifurcations. We employ the Method of Fundamental Solutions (MFS) and Radial Basis Functions (RBF), combined with a High Order Continuation Method (HOCM), to compute the entire solution branch. The nonlinearity of the problem is handled by reformulating it into a sequence of linear problems using a Taylor series expansion. The resulting linear problems are approximated using MFS and RBF. The core idea is to represent the solution as a linear combination of fundamental solutions associated with source points located outside the domain, along with a particular solution constructed at collocation points within the domain. This approach enables the solution to be computed branch by branch through the continuation method. Bifurcation points are detected using a scalar indicator along the solution branches, based on a common tangent operator. This methodology allows for the efficient resolution of nonlinear problems in complex three-dimensional geometries. Our results demonstrate the accuracy and effectiveness of the proposed approach in solving the nonlinear Bratu equation.

在这项工作中，我们研究了三维（3D）的非线性Bratu问题，由于存在多个解和分支而以其复杂性而闻名。我们采用基本解法（MFS）和径向基函数法（RBF），结合高阶延拓法（HOCM）来计算整个解分支。该问题的非线性是通过使用泰勒级数展开将其重新表述为一系列线性问题来处理的。用MFS和RBF对得到的线性问题进行近似。其核心思想是将解表示为与位于域外的源点相关的基本解的线性组合，以及在域内的并置点构造的特定解。这种方法可以通过延拓法逐个分支地计算解。根据公切算子，沿着解分支使用标量指示器来检测分岔点。这种方法允许在复杂的三维几何非线性问题的有效解决。我们的结果证明了该方法在求解非线性Bratu方程中的准确性和有效性。

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引用次数: 0

A novel anisotropic lattice spring model for elastically-homogeneous modelling of layered rocks 层状岩石弹性均匀建模的一种新型各向异性晶格弹簧模型

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-17 DOI: 10.1016/j.enganabound.2026.106642

Weichen Sun , Qiang Xie , Kai Wu , Zhilin Cao , Hexing Zhang , Xiang Fu , Yuxin Ban

This paper proposes a novel Anisotropic Lattice Spring Model (ALSM) to address the limitations of traditional LSMs in simulating anisotropic deformation of layered rocks such as schist, shale, and slate. The model introduces two key innovations: (1) normal-tangential coupled spring bonds that form a full stiffness matrix with non-zero off-diagonal terms, overcoming the inherent Poisson's ratio constraints of LSMs; and (2) a dual-constraint stiffness matching method that incorporates stress symmetry into the energy equivalence framework, ensuring physical consistency in macroscopic constitutive relations and enabling prescise mapping between microscopic parameters and macroscopic elastic constants. Verification results show that the ALSM significantly broadens the achievable range of Poisson's ratios and accurately simulates strongly anisotropic rocks. In uniaxial compression and Brazilian disc tests, the ALSM yields apparent elastic moduli consistent with theory/experiment, captures non-monotonic anisotropy, and markedly reduces displacement/stress errors compared to traditional models. The model allows direct input of macroscopic anisotropic parameters, avoiding complex microscopic calibration. The established elastic homogenization framework supports further study of anisotropic fracture and offers a new approach for bottom-up design of anisotropic materials.

针对传统的各向异性网格弹簧模型在模拟片岩、页岩和板岩等层状岩石各向异性变形时的局限性，提出了一种新的各向异性网格弹簧模型（ALSM）。该模型引入了两个关键创新：(1)法向-切向耦合弹簧键形成非零非对角线项的完整刚度矩阵，克服了lsm固有的泊松比约束；(2)将应力对称性纳入能量等效框架的双约束刚度匹配方法，保证宏观本构关系的物理一致性，实现微观参数与宏观弹性常数的精确映射。验证结果表明，该方法显著拓宽了泊松比的可实现范围，能较准确地模拟强各向异性岩石。在单轴压缩和巴西盘测试中，ALSM得到了与理论/实验一致的表观弹性模量，捕获了非单调各向异性，与传统模型相比，显著降低了位移/应力误差。该模型允许直接输入宏观各向异性参数，避免了复杂的微观标定。所建立的弹性均质框架为进一步研究各向异性断裂提供了支撑，为各向异性材料的自底向上设计提供了新途径。

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引用次数: 0

A novel quasi-interpolation radial integration BEM for non-homogeneous problems 非齐次问题的一种新的准插值径向积分边界元

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-16 DOI: 10.1016/j.enganabound.2026.106645

Bin Hu , Cong Li

A novel quasi-interpolation radial integration boundary element method (QIRIBEM) is proposed for solving non-homogeneous problems in this study. For domain integrals involving unknowns, the conventional methods use compactly supported radial basis functions (CSRBFs) to interpolate these unknowns directly. The direct interpolation scheme requires the introduction of an interpolation matrix, followed by matrix inversion and matrix multiplication operations. To overcome this limitation, a quasi-interpolator based on CSRBFs is first introduced to approximate the unknowns, where the unknown serves as the interpolation coefficient, eliminating the requirement for the interpolation matrix. Subsequently, a new interaction list is proposed to improve the computational efficiency of constructing the quasi-interpolator. Finally, the quasi-interpolator is incorporated into the radial integration method to transform domain integrals into boundary integrals. In contrast to the direct interpolation radial integration boundary element method (DIRIBEM), the proposed method achieves good accuracy by use a smaller supported domain and avoid a series of calculation and storage operations related to the interpolation matrix, which can save considerable computational time and memory spaces for large-scale models.

提出了一种求解非齐次问题的准插值径向积分边界元法。对于涉及未知数的域积分，传统方法使用紧支持径向基函数（csrbf）直接插值这些未知数。直接插补方案需要引入插补矩阵，然后进行矩阵反演和矩阵乘法运算。为了克服这一限制，首先引入基于csrbf的准插值器来逼近未知量，其中未知量作为插值系数，消除了对插值矩阵的要求。为了提高拟插值器的计算效率，提出了一种新的相互作用表。最后，将拟插值器引入到径向积分法中，将域积分转化为边界积分。与直接插值径向积分边界元法（DIRIBEM）相比，该方法利用更小的支持域，避免了与插值矩阵相关的一系列计算和存储操作，获得了较好的精度，可为大规模模型节省大量的计算时间和存储空间。

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引用次数: 0

Scattering of capillary-gravity waves by surface-piercing porous barriers in the presence of uniform current over a porous sea bed 在多孔海床上存在均匀水流时，穿透表面的多孔屏障对毛细管重力波的散射

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-15 DOI: 10.1016/j.enganabound.2026.106646

Gagan Sahoo, Harekrushna Behera, Tai-Wen Hsu

Capillary–gravity waves, influenced by both surface tension and gravity, interact strongly with marine structures, especially in the presence of uniform currents. Despite extensive studies on wave scattering by porous structures, the combined effects of surface tension, current, and porous barriers over a porous bottom remain insufficiently explored. This study examines the scattering of such waves by two thin surface-piercing porous barriers in the presence of a uniform current over a porous sea bed. A linear wave–structure interaction model is solved numerically through a hybrid Boundary Element-Finite Difference Method (BEM–FDM) and analytically through an eigenfunction expansion combined with a least-squares approach. The hybrid BEM–FDM efficiently handles higher-order boundary conditions that cannot be directly addressed by conventional BEM, while the analytical method eliminates the need for eigenfunction orthogonality and explicit mode coupling. The effects of surface tension, current velocity and direction, porous effect parameters of barriers as well as bottom, barrier length and spacing between them on reflection, transmission, and energy dissipation are analyzed. Results show that surface tension enhances reflection and dissipation while reducing transmission. Current direction strongly affects scattering: following currents enhance transmission, whereas opposing currents increase reflection and dissipation. Longer barriers and larger porous-effect parameters of both porous barriers and porous bottom enhance energy dissipation, while spacing between porous barriers induce interference driven oscillations.

毛细重力波受表面张力和重力的影响，与海洋结构有强烈的相互作用，特别是在有均匀洋流的情况下。尽管对多孔结构的波散射进行了广泛的研究，但表面张力、电流和多孔底部上的多孔屏障的综合影响仍然没有得到充分的探索。本研究考察了在多孔海床上均匀水流存在的情况下，两个薄的穿透表面的多孔屏障对这种波的散射。采用混合边界元-有限差分法（BEM-FDM）对线性波-结构相互作用模型进行数值求解，采用特征函数展开结合最小二乘方法对线性波-结构相互作用模型进行解析求解。该方法有效地处理了传统边界元法无法直接解决的高阶边界条件，而解析法消除了特征函数正交性和显式模态耦合的需要。分析了表面张力、电流速度和方向、阻挡层及底部的多孔效应参数、阻挡层长度和阻挡层间距对反射、透射和能量耗散的影响。结果表明，表面张力增强了反射和耗散，降低了透射。电流方向强烈影响散射：顺电流增强透射，相反电流增强反射和耗散。更长的势垒和更大的孔效应参数增强了能量耗散，而多孔势垒之间的间距引起干涉驱动振荡。

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引用次数: 0

Graph-based compactly supported radial basis function neural network 基于图的紧支持径向基函数神经网络

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-01-15 DOI: 10.1016/j.enganabound.2026.106644

Hongjin Ren , Dengao Li , Hongen Jia , Ruiping Niu , Hongbin Wang

In this paper, a novel graph-based compactly supported radial basis function physics-informed neural network (G-CS-RBN) is proposed for partial differential equations. Compactly supported radial basis functions are employed to replace the linear interpolation to construct an efficient one-hidden-layer neural network. An adaptive support radius is proposed that allows each point to automatically learn its local support according to the loss function. This overcomes the drawback of the traditional numerical compactly supported radial basis functions using fixed empirical support radius, which restricts the accuracy of models. A graph structure is used to store the collocation points and their respective center points to improve the interpretability of the network, storage efficiency, and network learning. Besides, the adaptive center point is also suggested to aid the adaptive support radius, which can further boost the performance of G-CS-RBN. Finally, extensive numerical experiments on 2D and 3D PDEs demonstrate that G-CS-RBN achieves consistently better accuracy and efficiency compared with classical numerical CS-RBF methods and standard PINNs, while showing improved robustness across different PDEs.

本文提出了一种新的基于图的紧支持径向基函数物理信息神经网络（G-CS-RBN）。采用紧支持径向基函数代替线性插值，构造了高效的单隐层神经网络。提出了一种自适应支持半径，使每个点能够根据损失函数自动学习其局部支持。这克服了传统数值紧支撑径向基函数采用固定经验支持半径的缺点，限制了模型的精度。采用图结构存储并置点及其各自的中心点，提高了网络的可解释性、存储效率和网络学习能力。此外，还提出了自适应中心点来辅助自适应支撑半径，进一步提高了G-CS-RBN的性能。最后，在二维和三维偏微分方程上进行的大量数值实验表明，与经典的数值CS-RBF方法和标准pin相比，G-CS-RBN方法的精度和效率始终更高，同时在不同偏微分方程上表现出更好的鲁棒性。

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引用次数: 0