Engineering Analysis with Boundary Elements最新文献_第2页

Seismic patterns in two-dimensional multilayer sediments using a hybrid boundary-finite element approach 基于边界-有限元混合方法的二维多层沉积物地震模式

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-04-01 Epub Date: 2026-02-03 DOI: 10.1016/j.enganabound.2026.106671

Bahman Ansari, Alireza Firoozfar, Bahram Ansari

This study proposes a hybrid boundary-finite element approach for calculating the seismic response of multilayered surface sediments with arbitrarily shaped topography. The system is subjected to oblique incident SH waves of varying frequencies. The method begins by introducing the hybrid formulation, which is then developed for multilayered problems by enforcing displacement and traction continuity at the interfaces. The free-field motion is incorporated into the solution by accounting for incident and reflected wave components. The developed method is implemented in a computer algorithm, and its accuracy is validated by solving several seismic problems with known solutions. Finally, a parametric study is conducted, analyzing both single-layer and two-layer sediment systems over a base soil layer. The sediments feature triangular, semi-square, and semi-circular geometries under incident SH waves, and the resulting seismic amplification patterns are presented. The results showed that the average dimensionless amplification across all frequencies and incident angles was 1.16 for the triangular shape, 1.18 for the semi-square, and 1.16 for the semi-circular shape in the single-layer case. For the two-layer case, these values increased to 1.47, 1.73, and 1.30, respectively. Furthermore, the single-layer triangular and semi-circular sediments demonstrated a greater capacity to absorb and trap wave energy, preventing it from propagating into the underlying layers.

本文提出了一种计算任意形状多层表层沉积物地震响应的边界-有限元混合方法。系统受到不同频率的斜入射SH波的作用。该方法首先引入混合公式，然后通过在界面处加强位移和牵引连续性来发展多层问题。通过考虑入射波和反射波分量，将自由场运动纳入到解决方案中。该方法在计算机上实现，并通过求解若干已知解的地震问题验证了其准确性。最后，进行了参数化研究，分析了基础土层上的单层和双层沉积物系统。在SH波作用下，沉积物呈三角形、半正方形和半圆形，并呈现出相应的地震放大模式。结果表明，在所有频率和入射角下，三角形的平均无量纲放大为1.16，半正方形的为1.18，半圆形的为1.16。对于两层情况，这些值分别增加到1.47、1.73和1.30。此外，单层三角形和半圆形沉积物显示出更大的吸收和捕获波能的能力，从而阻止波能传播到下层。

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引用次数: 0

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 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-04-01 Epub 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

This research focuses on the theoretical and computational aspects of numerical methods for handling concave polygonal elements in solid mechanics, namely smoothed finite element method (S-FEM) and virtual element method (VEM). Commencing with the principle of virtual work, the study uniformly formulates and discretizes the governing equations using the same mathematical symbols for both methodologies, meticulously deriving and implementing their respective stiffness matrices rooted in the elemental strain energy formulations. The equivalence between the smoothing stiffness matrix of S-FEM with smoothing domains and the consistent stiffness matrix of VEM has been demonstrated through theoretical analysis and numerical examples using various types of polygonal elements. The equivalence is directly verified by using numerical values of stiffness matrices with different concave convex grids, but the different characteristics of the two methods are also verified from a physical perspective (strain energy). Subsequently, a series of benchmark problems and real-world engineering instances are leveraged to scrutinize and contrast the efficacies and constraints of S-FEM and VEM about concave polygon. Results attest to the substantial applicability and robustness of these methods on irregularly-shaped concave polygons, advancing numerical techniques for non-standard geometric shapes in solid mechanics. This scholarly work offers insights for researchers and practitioners in selecting optimal computational strategies when analyzing the behavior of concave polygon elements.

本文主要研究了固体力学中凹多边形单元处理的理论和计算方法，即光滑有限元法（S-FEM）和虚拟元法（VEM）。该研究从虚功原理出发，使用相同的数学符号对两种方法的控制方程进行统一的表述和离散化，细致地推导并实现了基于元素应变能公式的各自的刚度矩阵。通过理论分析和数值算例，证明了具有光滑域的S-FEM的光滑刚度矩阵与VEM的一致刚度矩阵之间的等价性。采用不同凹凸网格的刚度矩阵数值直接验证了等效性，但也从物理角度（应变能）验证了两种方法的不同特性。随后，利用一系列基准问题和实际工程实例，仔细对比了S-FEM和VEM在凹多边形问题上的有效性和约束条件。结果证明了这些方法对不规则形状凹多边形的适用性和鲁棒性，推动了固体力学中非标准几何形状的数值计算技术。这项学术工作为研究人员和实践者在分析凹多边形元素的行为时选择最佳计算策略提供了见解。

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引用次数: 0

The T-stress evaluation for cracked functionally graded material structures by the BEM based on Erdogan’s Green’s functions 基于埃尔多安格林函数的边界元法评价裂纹功能梯度材料结构的t应力

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-04-01 Epub Date: 2026-02-05 DOI: 10.1016/j.enganabound.2026.106672

C.Z. Shi , J. Sladek , V. Sladek , P.H. Wen

This study extends a boundary element method (BEM) based on Erdogan’s Green’s functions (EGFs) to evaluate the T-stress of two-dimensional stationary cracks in functionally graded materials (FGMs). The EGFs corresponding to a straight crack in an infinite homogeneous plane subjected to a couple of point forces do not only inherently characterize the crack but also automatically ensure the traction-free boundary conditions on the crack surface. Owing to the identical singularity of the asymptotic stress field at the crack tip in both homogeneous and functionally graded materials, the integral equations for cracked FGMs can be established by regarding the material gradient as an equivalent body force. For FGMs with multiple cracks, the multi-domain technique (MDT) is used. Nine-node quadrilateral elements are employed to calculate the domain integrals. The T-stress is extracted from the contour-domain type interaction integral with incompatibility auxiliary fields. Comparative analyses with existing literature confirm the high accuracy of the developed BEM.

本研究扩展了一种基于埃尔多安格林函数（EGFs）的边界元法（BEM）来评估功能梯度材料（fgm）中二维静止裂纹的t应力。无限均质平面上的直裂纹在多点力作用下的egf不仅具有裂纹的固有特征，而且能自动保证裂纹表面无牵引力的边界条件。由于均匀材料和功能梯度材料裂纹尖端的渐近应力场具有相同的奇异性，因此可以将材料梯度视为等效的体力来建立裂纹fgm的积分方程。对于具有多裂纹的fgm，采用多域技术（MDT）。采用九节点四边形单元计算域积分。t应力从具有不相容辅助场的轮廓域型相互作用积分中提取。与已有文献的对比分析证实了所建立的边界元法具有较高的精度。

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引用次数: 0

A fourth-order RBF-FD scheme based on integral representations of the multiquadric for high-dimensional Black–Scholes PDEs 高维Black-Scholes偏微分方程基于多重曲面积分表示的四阶RBF-FD格式

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-04-01 Epub Date: 2026-02-04 DOI: 10.1016/j.enganabound.2026.106673

Yanlai Song

The valuation of multi-asset European options poses major challenges due to the curse of dimensionality. We present a fourth-order meshless radial basis function-produced finite difference (RBF-FD) approach based on a modified multiquadric kernel and its integral representations. This construction yields analytical differentiation weights on specific five-point stencils and enables efficient spatial discretization. Numerical experiments confirm the method’s stability, efficiency and convergence.

多资产欧式期权的估值由于维度的诅咒而面临重大挑战。提出了一种基于改进的多重二次核及其积分表示的四阶无网格径向基函数产生有限差分（RBF-FD）方法。这种结构在特定的五点模板上产生分析微分权重，并实现有效的空间离散化。数值实验验证了该方法的稳定性、有效性和收敛性。

引用次数: 0

A unified solution for buckling and free vibration analysis of sandwich plates with auxetic honeycomb core and perovskite-based solar cell face sheets under elastic boundary conditions 弹性边界条件下蜂窝芯夹层板与钙钛矿基太阳能电池面板屈曲与自由振动分析的统一解

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-04-01 Epub Date: 2026-02-05 DOI: 10.1016/j.enganabound.2026.106674

Hossein Pakdaman , Yaser Kiani

Perovskite-based sandwich structures with honeycomb cores have emerged as promising candidates for lightweight satellite solar panels; however, their mechanical stability and vibrational behavior under coupled photonic and electric fields remain poorly understood. This paper presents a unified formulation for analyzing the buckling and free vibration of sandwich plates with an auxetic core and perovskite-based face sheets under general boundary conditions (BCs), incorporating coupled photo-electro-thermal-mechanical effects. Within this solution approach, a general first-order shear deformation plate theory is developed, employing artificial spring technique for boundary modeling. The displacement components of perovskite-based sandwich plates are represented by orthogonal polynomials via a Gram-Schmidt procedure in both directions, irrespective of BCs. Precise results are then derived using the Rayleigh–Ritz technique, based on the energy functional of perovskite-based sandwich plates. The reliability and precision of this approach are confirmed by numerous convergence tests and comparative analyses. Detailed parametric studies are conducted to evaluate the impacts of light exposure, electric field, and geometrical parameters on the free vibration properties and buckling responses of perovskite-based sandwich plates with classical and elastic BCs. Findings show that the negative impacts of light and electric fields on the stability and vibrational characteristics of perovskite-based sandwich plates can be alleviated by using an auxetic core and adjusting their geometrical properties, thereby enhancing the accuracy and reliability of structural design for advanced engineering applications.

基于钙钛矿的蜂窝芯夹层结构已成为轻型卫星太阳能电池板的有希望的候选者；然而，它们在光子和电场耦合作用下的力学稳定性和振动行为仍然知之甚少。本文提出了在一般边界条件（BCs）下，考虑耦合光-电-热-力效应的钙钛矿基夹层板和缺氧性芯板的屈曲和自由振动分析的统一公式。在此求解方法中，建立了一阶剪切变形板理论，采用人工弹簧技术进行边界建模。钙钛矿基夹层板的位移分量通过Gram-Schmidt过程在两个方向上用正交多项式表示，而不考虑bc。然后使用瑞利-里兹技术，基于钙钛矿基夹层板的能量函数，得出精确的结果。大量的收敛性试验和对比分析证实了该方法的可靠性和精确性。通过详细的参数研究，评估了光照、电场和几何参数对钙钛矿基夹层板的自由振动性能和屈曲响应的影响。研究结果表明，采用消声芯和调整钙钛矿夹层板的几何特性可以减轻光、电场对钙钛矿夹层板稳定性和振动特性的负面影响，从而提高结构设计的精度和可靠性，面向先进工程应用。

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引用次数: 0

Geometrically nonlinear coupled thermo-mechanical thermally induced vibration response of FGM plate under sudden thermal shock 突发性热冲击下FGM板的几何非线性耦合热-机热激振动响应

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-04-01 Epub Date: 2026-02-06 DOI: 10.1016/j.enganabound.2026.106670

A. Salmanizadeh , M.R. Eslami , Y. Kiani

The present research investigates the large-amplitude thermally induced vibrations of functionally graded (FG) plates subjected to time-dependent thermal shock. One surface of the plate is insulated, while the opposite surface is exposed to a time-dependent heat flux. The thermomechanical properties of the functionally graded material (FGM) plate are evaluated using the rule of mixtures. Based on the von Kármán kinematic assumptions and the first-order shear deformation theory (FSDT), and by applying Hamilton’s principle, the governing equations of motion along with the associated boundary conditions are derived. The energy equations are formulated within the framework of the classical coupled thermoelastic theory, assuming a linear temperature distribution through the thickness. The resulting set of coupled equations of motion and energy is solved using a hybrid generalized differential quadrature (GDQ) method-Newmark–Picard algorithm. After thorough validation, parametric studies are conducted to examine the effects of coupled thermoelasticity, different boundary conditions, thermal boundary conditions at the edges, and the influence of the power law index.

本文研究了功能梯度（FG）板在时间相关热冲击作用下的大振幅热激振动。板的一个表面是绝缘的，而另一个表面则暴露在随时间变化的热通量中。采用混合规律对功能梯度材料（FGM）板的热力学性能进行了评价。基于von Kármán运动学假设和一阶剪切变形理论（FSDT），应用Hamilton原理，导出了运动控制方程及其边界条件。在经典耦合热弹性理论框架内，假设温度随厚度呈线性分布，建立了能量方程。采用混合广义微分正交（GDQ）方法- newmark - picard算法求解得到的运动和能量耦合方程组。在充分验证后，进行了参数化研究，考察了耦合热弹性、不同边界条件、边缘热边界条件以及幂律指数的影响。

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引用次数: 0

Corrigendum to “A molecular dynamics investigation of the atomic structural behavior of the interaction between amyloid beta protein and Aspirin within an aqueous nanodomain” [Engineering Analysis with Boundary Elements 146 (2023) 851-858] “淀粉样蛋白和阿司匹林在水纳米结构域内相互作用的原子结构行为的分子动力学研究”的更正[边界元工程分析146 (2023)851-858]

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-04-01 Epub Date: 2026-02-06 DOI: 10.1016/j.enganabound.2026.106650

Quynh Hoang Le , Shokoufeh Heydaripour , Bita Farhadi , Rzgar Farooq Rashid , Mustafa Inc

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 : 2026-04-01 Epub 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 : 2026-04-01 Epub 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

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 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2026-04-01 Epub Date: 2026-02-03 DOI: 10.1016/j.enganabound.2026.106666

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

As a special form of discontinuous deformation analysis (DDA), the particle DDA has gained more and more attention. In this study, a modified particle DDA is presented and applied to rock failure simulation. First, inspired by the discrete element method, a modified contact geometry model is introduced by decomposing the relative shear displacement of a contact pair into a translational and a rotational component. Based on this model, the contact related submatrices are derived which have more compact forms compared to the traditional ones. Then, a cumulative incremental update scheme is adopted in both shear and rolling directions, and the corresponding formulations are deduced. Moreover, a bonded particle model with rolling resistance, which employs tensile and Mohr-Coulomb failure criteria, is also implemented. A main feature of the modified formulation is that the contact points do not need to be explicitly defined and the displacement transformation matrix is not involved in the contact related submatrices. The proposed formulation is first validated by a single disk test, and then applied to two rock failure problems. The numerical results indicate that the proposed method can effectively simulate rock fracture under both static and dynamic loading.

作为不连续变形分析（DDA）的一种特殊形式，颗粒不连续变形分析（DDA）越来越受到人们的关注。本文提出了一种改进的粒子DDA方法，并将其应用于岩石破坏模拟。首先，受离散元法的启发，将接触副的相对剪切位移分解为平移分量和旋转分量，提出了一种改进的接触几何模型；在此基础上，导出了接触相关子矩阵，其形式比传统的接触相关子矩阵更加紧凑。然后，在剪切方向和滚动方向上采用累积增量更新方案，并推导出相应的计算公式。此外，采用拉伸破坏准则和Mohr-Coulomb破坏准则建立了具有滚动阻力的粘结颗粒模型。修正公式的一个主要特点是不需要明确定义接触点，并且位移变换矩阵不涉及接触相关子矩阵。提出的公式首先通过单盘试验验证，然后应用于两个岩石破坏问题。数值结果表明，该方法可以有效地模拟静、动载荷作用下的岩石破裂。

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引用次数: 0