Finite Elements in Analysis and Design最新文献_第7页

Integrating multiplicative Nitsche's method with HIGA platform: Isogeometric analysis of hydraulic tunnels lining thickness 基于HIGA平台的乘Nitsche法积分：水工隧洞衬砌厚度等几何分析

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-12-01 Epub Date: 2025-09-17 DOI: 10.1016/j.finel.2025.104445

Mingchao Li , Yixin Wang , Mengxi Zhang , Ang Li , Stéphane P.A. Bordas , Peng Yu , Yinpeng He

Isogeometric Analysis (IGA) is a novel numerical analysis method that can occupy the gap between geometrical and analytical models. IGA, when integrated with splicing algorithms, enables the splicing and coupling of multiple computational domains. This approach offers a novel solution for simulating complex hydraulic tunnels and similar practical engineering applications involving complex computational models. In this paper, a multiplicative Nitsche's method is proposed. The method determines the stabilization parameter

α

for contact models through a precise control coefficient computation equation, based on a chosen weighting parameter

γ

, and is integrated into the Hydraulic IsoGeometric Analysis (HIGA) platform. This method addresses the instability issues typically associated with the traditional Nitsche's method, which arise from empirically selected control parameters. Compared with the conventional Nitsche's method, multiplicative Nitsche's method significantly enhances the accuracy and stability of IGA while maintaining computational efficiency, according to the results of several 2D and 3D numerical examples. To demonstrate the engineering application prospects of multiplicative Nitsche's method, the proven applicability of IGA with the multiplicative Nitsche's method is showcased through a static analysis of a hydraulic tunnel model with complex geological features. The results demonstrate the method's capability to handle large-scale, multi-patch engineering problems, underscoring its potential for simulating and analyzing hydraulic tunnels under complex topographical and geological conditions.

等几何分析（IGA）是一种新颖的数值分析方法，可以填补几何模型与解析模型之间的空白。当IGA与剪接算法集成时，可以实现多个计算域的剪接和耦合。该方法为复杂水工隧道的模拟和涉及复杂计算模型的类似实际工程应用提供了一种新的解决方案。本文提出了一种乘法Nitsche方法。该方法基于选定的加权参数γ，通过精确的控制系数计算方程确定接触模型的稳定参数α，并集成到液压等几何分析（HIGA）平台中。该方法解决了通常与传统Nitsche方法相关的不稳定性问题，这些问题源于经验选择的控制参数。若干二维和三维数值算例结果表明，与传统的Nitsche方法相比，乘法Nitsche方法在保持计算效率的同时，显著提高了IGA的精度和稳定性。为了证明乘法Nitsche方法的工程应用前景，通过对具有复杂地质特征的水工隧道模型进行静力分析，证明了IGA与乘法Nitsche方法的适用性。结果表明，该方法具有处理大规模、多地块工程问题的能力，强调了其在复杂地形和地质条件下模拟和分析水工隧洞的潜力。

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引用次数: 0

An implicit coupled method of scaled boundary finite element and peridynamics for fracture analysis 断裂分析的尺度边界有限元与周动力隐式耦合方法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-12-01 Epub Date: 2025-09-16 DOI: 10.1016/j.finel.2025.104453

Wei Yu , Jun Liu , Haibo Wang , Lei Qin , Lei Gan , Quansheng Zang , Wenbin Ye

In this paper, firstly, an innovative multi-scale coupled method based on scaled boundary finite element (SBFEM) and peridynamics (PD) is proposed for predicting fracture propagation of elastic bodies in static/quasi-static problems. The coupled process in this method is established not by transition regions (overlapping regions), but by force equilibrium conditions at common points, which greatly reduces the complexity of modeling. The SBFEM is introduced to model the non-cracked domain and the PD is applied to model the cracked domain in this method. This reduces a great deal of computational time compared to the PD method. Moreover, the limitations of surface effects and troublesome load conditions for the PD calculation can be eliminated or mitigated. The SBFEM is different from FEM in that only the boundary of elastic bodies is discretized. Therefore, the computational efficiency is further improved compared with the coupled method of the FEM and PD. The SBFEM is also different from BEM in that it does not need to provide the fundamental solution and compute the singular integrals. Hence, the method is more convenient for solving complex problems compared with the coupled method of the BEM and PD. The accuracy of this coupled method is demonstrated by one example of accuracy analysis for single coupled and multiple coupled interfaces, and three examples of fracture propagation analysis (two pre-determined cracks and one spontaneous crack). The results show that the coupled method has a high accuracy. Furthermore, it is recommended that the spacing of the common points be set equal to the spacing of the PD material points so that the accuracy of the coupled method can be maximized. Finally, the cracking forms of a square plate with different shaped holes are explored. It shows that the proposed coupled method has potential for engineering applications.

本文首先提出了一种基于尺度边界有限元（SBFEM）和周动力学（PD）的多尺度耦合方法，用于静力/准静力问题中弹性体断裂扩展的预测。该方法不是通过过渡区域（重叠区域）建立耦合过程，而是通过共同点处的力平衡条件建立耦合过程，大大降低了建模的复杂性。该方法引入SBFEM对非裂纹区域进行建模，并采用局部局部化方法对裂纹区域进行建模。与PD方法相比，这大大减少了计算时间。此外，可以消除或减轻表面效应的限制和PD计算的麻烦负载条件。SBFEM与有限元法的不同之处在于它只对弹性体的边界进行离散化。因此，与有限元与PD耦合方法相比，进一步提高了计算效率。SBFEM与边界元法的不同之处在于，它不需要提供基本解和计算奇异积分。因此，该方法比边界元与PD的耦合方法更便于求解复杂问题。通过1个单耦合和多耦合界面精度分析算例以及3个断裂扩展分析算例（2个预定裂纹和1个自发裂纹）验证了该耦合方法的准确性。结果表明，该耦合方法具有较高的精度。此外，建议将公共点的间距设置为与PD材料点的间距相等，以使耦合方法的精度最大化。最后，探讨了不同孔型的方形板的开裂形式。表明所提出的耦合方法具有工程应用的潜力。

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引用次数: 0

Mesoscale FEM model of concrete: Statistical assessment of inherent stress concentrations in dependence on phase heterogeneity 混凝土的中尺度有限元模型：依赖于相非均质性的固有应力集中的统计评估

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-12-01 Epub Date: 2025-09-13 DOI: 10.1016/j.finel.2025.104442

Jan Mašek, Petr Miarka

Concrete heterogeneity originates from its production process, which involves bonding aggregates with a binder matrix. This study presents a mesoscale finite element model (MFEM) that offers detailed insights into the fracture process at the aggregate–cement matrix interface, focusing on one of concrete’s key properties: its mechanical response. Unlike discrete models, which often average out critical stress concentrations within the mesostructure, the MFEM approach captures detailed stress distributions, revealing localized effects crucial for understanding damage evolution. Although computationally more demanding, the MFEM leverages modern high-performance computing (HPC) to provide a detailed description of the stress field and material damage across different phases and interfaces. The proposed modeling framework integrates a collision-checked aggregate generation procedure, Voronoi-based mesostructure construction, and adaptive 3D meshing, forming a reusable methodology for stress analysis in heterogeneous composites. This approach offers transparent, physically interpretable parameterization of phase properties in contrast to black-box discrete models. Another methodological contribution is the statistical post-processing of stress data using histogram-based analysis across cross-sectional planes. This enables quantitative evaluation of stress concentration distributions, providing valuable insights into the mesoscale mechanical response and serving as a useful visualization tool for researchers working on heterogeneous material modeling. Various matrix-to-aggregate stiffness ratios are considered to evaluate the influence of material heterogeneity on the stress field. The results are based on a statistical evaluation of stress concentrations arising from variations in material stiffness. The model is applied to investigate the impact of using recycled crushed bricks as aggregates in concrete, with particular emphasis on the stiffness mismatch between the matrix and aggregates. The study examines how this stiffness contrast affects stress distribution and ultimately influences the composite’s failure mechanisms. Beyond this application, the MFEM framework provides a foundation for further investigations into nonlinear fracture processes, fatigue analysis, and mechanical optimization of alternative aggregate-matrix systems.

混凝土的非均质性源于其生产过程，该过程涉及将骨料与粘结剂基体粘合。本研究提出了一个中尺度有限元模型（MFEM），该模型提供了对骨料-水泥基体界面断裂过程的详细见解，重点关注混凝土的关键特性之一：力学响应。与离散模型不同，离散模型通常在细观结构中平均临界应力集中，而MFEM方法可以捕获详细的应力分布，揭示对理解损伤演变至关重要的局部效应。尽管计算要求更高，但MFEM利用现代高性能计算（HPC）提供了不同阶段和界面的应力场和材料损伤的详细描述。所提出的建模框架集成了碰撞检查聚合生成程序、基于voronoi的细观结构构建和自适应3D网格划分，形成了一种可重复使用的方法，用于异质复合材料的应力分析。与黑盒离散模型相比，这种方法提供了透明的、物理上可解释的相位特性参数化。另一个方法上的贡献是利用基于直方图的跨横截面分析对应力数据进行统计后处理。这可以定量评估应力集中分布，为中尺度力学响应提供有价值的见解，并为研究异质材料建模的研究人员提供有用的可视化工具。考虑不同的基体-骨料刚度比来评估材料非均质性对应力场的影响。结果是基于由材料刚度变化引起的应力集中的统计评估。该模型用于研究在混凝土中使用再生碎砖作为骨料的影响，特别强调基质和骨料之间的刚度不匹配。该研究考察了这种刚度对比如何影响应力分布并最终影响复合材料的破坏机制。除此之外，MFEM框架还为进一步研究非线性断裂过程、疲劳分析和替代集料基质系统的力学优化提供了基础。

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引用次数: 0

The polytopal composite element method for finite strain hyperelastic problems 有限应变超弹性问题的多面体复合元法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-12-01 Epub Date: 2025-09-18 DOI: 10.1016/j.finel.2025.104436

Y. Li , B.W. Wang , Z.Q. Feng

Polygonal elements have emerged as a cutting-edge discretization paradigm in computational solid mechanics, demonstrating significant potential for linear elasticity analyses. This work pioneers a robust computational framework extending polytopal composite elements to finite-strain hyperelasticity. The key idea by constructing a polynomial projection using least squares approximation for linear-compatible strain fields, followed by extending the derived linear operator to large deformation cases involving nonlinear strain. The computational framework of this method is fundamentally consistent with finite elements, allowing it to adapt and extend to various nonlinear problems. Through several numerical investigation we show that this approach maintains the excellent accuracy, convergence and stability, and is potentially offering new insights and references for polygonal elements in future nonlinear problems.

在计算固体力学中，多边形单元已经成为一种前沿的离散化范式，在线性弹性分析中显示出巨大的潜力。这项工作开创了一个强大的计算框架，将多面体复合元素扩展到有限应变超弹性。关键思想是利用最小二乘近似构造线性相容应变场的多项式投影，然后将导出的线性算子推广到涉及非线性应变的大变形情况。该方法的计算框架与有限元基本一致，使其能够适应和扩展到各种非线性问题。数值研究表明，该方法保持了良好的精度、收敛性和稳定性，为今后求解多边形单元的非线性问题提供了新的思路和参考。

引用次数: 0

Uzawa methods for the coupling of free flow and porous medium flow 自由流动与多孔介质流动耦合的Uzawa方法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-12-01 Epub Date: 2025-09-19 DOI: 10.1016/j.finel.2025.104460

Qingzhou Wang, Guangzhi Du

In this paper, two kinds of Uzawa algorithms are proposed and investigated to solve the coupling of free flow and porous medium flow, which is modeled by the mixed Stokes-Darcy problem with the Beavers-Joseph-Saffman interface condition. The first Uzawa method as an iterative method can avoid solving the saddle point problem at each iteration step. The second method aims to optimize the first one by combining the two-grid strategy. Rigorously theoretical analysis is established for these two algorithms. Some numerical experiments are carried out to verify the theoretical findings.

本文提出并研究了两种Uzawa算法来解决自由流动和多孔介质流动的耦合问题，该问题由带有beaver - joseph - saffman界面条件的混合Stokes-Darcy问题建模。第一种Uzawa方法作为一种迭代方法，可以避免在每个迭代步骤都求解鞍点问题。第二种方法旨在通过结合两网格策略对第一种方法进行优化。对这两种算法进行了严格的理论分析。通过数值实验对理论结果进行了验证。

引用次数: 0

An expandable local and parallel two-grid finite element scheme for Stokes problem Stokes问题的可扩展局部并行双网格有限元格式

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-12-01 Epub Date: 2025-09-08 DOI: 10.1016/j.finel.2025.104375

Hongwei Song , Jianping Zhao , Yanren Hou

A novel locally parallel finite element algorithm for addressing the Stokes problem has been developed, leveraging the two-grid method and the unit splitting technique. This innovative algorithm boasts several key advantages: (1) it operates independently of the hyperapproximation property, enhancing its applicability across various scenarios; (2) the decomposition of regions is solely dependent on the unit splitting technique, simplifying the computational process; and (3) by incorporating constraints on local corrections, the algorithm employs the penalized form of the Stokes problem. This strategic choice facilitates the exclusive resolution of the velocity field function under specific assumptions, thereby streamlining the solution process and potentially reducing computational complexity.

利用双网格法和单元分裂技术，提出了一种求解Stokes问题的局部并行有限元算法。该创新算法具有以下几个关键优势：(1)它独立于超逼近性质运行，增强了其在各种场景中的适用性；(2)区域分解完全依赖于单元分裂技术，简化了计算过程；(3)通过对局部修正的约束，该算法采用Stokes问题的惩罚形式。这种策略选择有助于在特定假设下对速度场函数进行独家解析，从而简化求解过程并可能降低计算复杂性。

引用次数: 0

The neural approximated virtual element method for elasticity problems 弹性问题的神经逼近虚元法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-12-01 Epub Date: 2025-10-09 DOI: 10.1016/j.finel.2025.104467

Stefano Berrone , Moreno Pintore , Gioana Teora

We present the Neural Approximated Virtual Element Method to numerically solve elasticity problems. This hybrid technique combines classical concepts from the Finite Element Method and the Virtual Element Method with recent advances in deep neural networks. Specifically, it is a polygonal method where the virtual basis functions are element-wise approximated by a neural network, eliminating the need for stabilization or projection operators typically required in the standard Virtual Element Method. We present the discrete formulation of the problem together with theoretical results, and we provide numerical tests on both linear and non-linear elasticity problems, demonstrating the advantages of a simple discretization, particularly in handling non-linearities.

提出了一种神经逼近虚元法来数值求解弹性问题。这种混合技术将有限元法和虚元法的经典概念与深度神经网络的最新进展相结合。具体来说，它是一种多边形方法，其中虚拟基函数由神经网络逐元逼近，消除了标准虚拟元方法中通常需要的稳定或投影算子。我们提出了问题的离散化形式和理论结果，并对线性和非线性弹性问题进行了数值测试，证明了简单离散化的优点，特别是在处理非线性问题时。

引用次数: 0

A simplified gradient-enhanced damage model based on energy limiters for crack propagation under time-dependent loading 基于能量限制器的时效加载下裂纹扩展梯度增强损伤简化模型

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-12-01 Epub Date: 2025-09-13 DOI: 10.1016/j.finel.2025.104443

Hung Thanh Tran

This paper presents the development and investigation of a simplified energy limiter-based nonlocal damage model for dynamic crack propagation in brittle media. The key idea underlying the proposed model is that crack growth under impact loading is primarily influenced by the tensile component of the strain tensor. Consequently, the energy-based damage-driving term is simplified to a strain-based counterpart, which is integrated using the first principal strain. This simplification leads to a model that is not only easier to implement but also more effective in capturing dynamic crack propagation compared to the original theory. In addition, the computational framework incorporates an energy limiter-based gradient damage formulation with a damage threshold, enabling natural crack initiation and propagation while significantly reducing spurious damage. One of the distinctive features of the proposed approach is the treatment of the nonlocal crack field as a primary unknown, alongside displacements. This allows the use of identical shape functions for both fields within the finite element analysis, enhancing consistency and computational efficiency. Consistent with classical continuum damage mechanics, the model can accurately simulate arbitrary and complex multiple crack paths, including three-dimensional (3D) crack propagation. Furthermore, to provide a more efficient numerical framework under time-dependent loading conditions with complex crack patterns, an explicit dynamic fracture algorithm is employed. This algorithm utilizes the central difference method, the row-sum technique for mass lumping, and a consistent procedure for updating the kinematic and damage-related terms. The advantages and modeling capabilities of the proposed strain-based gradient-enhanced damage formulation are demonstrated through representative numerical examples of dynamic fracture under shear, tension, and compression loading scenarios.

本文提出了一种基于能量限制器的脆性介质动态裂纹扩展非局部损伤简化模型。提出的模型的关键思想是，裂纹在冲击载荷下的扩展主要受应变张量的拉伸分量的影响。因此，基于能量的损伤驱动项被简化为基于应变的对应项，并使用第一主应变进行积分。与原始理论相比，这种简化导致的模型不仅更容易实现，而且在捕获动态裂纹扩展方面也更有效。此外，该计算框架结合了一个基于能量限制器的梯度损伤公式，该公式具有损伤阈值，可以实现自然裂纹的起始和扩展，同时显着减少虚假损伤。该方法的一个显著特点是将非局部裂纹场与位移一起作为主要未知数处理。这允许在有限元分析中对两个领域使用相同的形状函数，增强一致性和计算效率。该模型与经典连续介质损伤力学一致，能够准确模拟任意复杂的多重裂纹路径，包括三维裂纹扩展。此外，为了在具有复杂裂纹模式的时变加载条件下提供更有效的数值框架，采用了显式动态断裂算法。该算法利用中心差分法、行和技术进行质量集总，并采用一致的程序更新运动学和损伤相关项。通过具有代表性的剪切、拉伸和压缩加载情景下的动态断裂数值实例，证明了所提出的基于应变的梯度增强损伤公式的优势和建模能力。

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引用次数: 0

POD-RBF hyper-reduction method for fast finite element analysis of nonlinear dynamic problems 非线性动力问题快速有限元分析的POD-RBF超约简方法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-12-01 Epub Date: 2025-09-13 DOI: 10.1016/j.finel.2025.104455

Lam Vu-Tuong Nguyen, Hyun-Gyu Kim

This paper proposes a new hyper-reduction method for fast finite element analysis of nonlinear dynamic problems using proper orthogonal decomposition (POD) and radial basis function (RBF) interpolation. In the offline stage, displacement and internal force snapshots are collected from full-order FE simulations of nonlinear dynamic problems with training load cases. POD basis vectors are extracted from the displacement snapshots using the singular value decomposition (SVD). RBF coefficients for the internal force snapshots are also computed in the offline stage. The proposed POD-RBF hyper-reduction method efficiently estimates the reduced internal force vectors and the reduced tangent stiffness matrices using RBF interpolation with respect to reduced generalized coordinates. A snapshot selection strategy combining K-means clustering and greedy sampling algorithms is used to reduce the size of solution snapshots, which further enhances the efficiency of the present method. Numerical results show that the POD-RBF hyper-reduction method can be efficiently and effectively used to quickly solve nonlinear dynamic problems in a reduced-order space.

本文提出了一种利用正交分解和径向基函数插值的超约化方法，用于非线性动力问题的快速有限元分析。在离线阶段，从具有训练载荷的非线性动力问题的全阶有限元模拟中获取位移和内力快照。利用奇异值分解（SVD）从位移快照中提取POD基向量。在脱机阶段还计算了内力快照的RBF系数。提出的POD-RBF超约简方法利用RBF插值在广义约简坐标下有效地估计约简内力矢量和约简切刚度矩阵。采用k均值聚类和贪婪采样算法相结合的快照选择策略，减小了解快照的大小，进一步提高了方法的效率。数值结果表明，POD-RBF超约简方法可以高效、有效地快速求解降阶空间中的非线性动态问题。

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引用次数: 0

A novel interpolation scheme using partition-of-unity mapping for multi-material topology optimizations with compliance-based and stress-based designs 基于柔度和应力设计的多材料拓扑优化新插值方法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-12-01 Epub Date: 2025-10-23 DOI: 10.1016/j.finel.2025.104470

Tinh Quoc Bui, Minh Ngoc Nguyen

This paper presents an enhanced computational framework for multi-material topology optimization using a novel interpolation scheme with the partition-of-unity (PU) mapping. Inspired by the recent

p

-norm mapping scheme by Yi et al., (2023) the developed scheme inherits the easy-to-implement property, as the interpolation is written in a SIMP-like manner, and the sensitivity with respect to each material phase takes the same form. More importantly, the current scheme addresses the lack of PU property of the

p

-norm scheme, that is, the sum of volume fraction of all material phases within each element must be equal to one. In the

p

-norm scheme setting, the case when the physical densities of the materials are all equal to one is theoretically possible. This phenomenon means the duplication of the element volume. In the developed scheme, the mapping functions are computed in rational form, explicitly satisfying the PU property. The performance of the present method is investigated through six numerical examples: the first three are for the compliance-based designs and the other three are for the stress-based designs including the design of periodic meta-material with high bulk modulus. It is demonstrated in the numerical examples that although the lack of PU property in

p

-norm scheme does not seem to cause problematic issue in compliance-based design with only fixed load, erroneous patterns may appear in more complicated problems, e.g., in compliance-based design with consideration of self-weight load, and in stress-based design. The issue is successfully removed in the proposed PU mapping scheme.

本文提出了一种改进的多材料拓扑优化计算框架，该计算框架采用了一种新颖的统一分割（PU）映射插值方案。受Yi等人（2023）最近的p-范数映射方案的启发，开发的方案继承了易于实现的特性，因为插值是以类似simp的方式编写的，并且相对于每个材料相的灵敏度采用相同的形式。更重要的是，目前的方案解决了p-范数方案缺乏PU特性的问题，即每个单元内所有材料相的体积分数之和必须等于1。在p-范数方案设置中，材料的物理密度都等于1的情况在理论上是可能的。这种现象意味着元素体积的重复。在开发的方案中，映射函数以有理形式计算，显式地满足PU性质。通过六个数值算例研究了该方法的性能：前三个是基于柔度的设计，另外三个是基于应力的设计，包括高体积模量的周期性超材料的设计。数值算例表明，虽然在p范数方案中缺乏PU特性似乎不会导致仅固定荷载的基于柔度的设计出现问题，但在更复杂的问题中，例如在考虑自重荷载的基于柔度的设计中，以及在基于应力的设计中，可能会出现错误模式。在提出的PU映射方案中成功地消除了该问题。

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引用次数: 0