Computer Methods in Applied Mechanics and Engineering最新文献_第7页

An inter-scale stiffness propagation method with nonintrusive modeling of stochastic porosity in unidirectional composites 单向复合材料随机孔隙度的尺度间刚度传播非侵入建模方法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-06 DOI: 10.1016/j.cma.2025.118720

Yu-Cheng Yang , Zi-Qian Wang , Jian-Jun Gou , Xiao-Bing Ma , Chun-Lin Gong

Porosity is a primary source of stiffness uncertainty in fiber-reinforced composites. However, explicitly modeling pores with prescribed geometry at the composite-scale leads to prohibitive computational cost for uncertainty quantification. This study proposes an inter-scale stiffness propagation method linking matrix-scale stochastic porosity to stiffness uncertainty of unidirectional fiber-reinforced (UD) composites. In such nonintrusive modeling of porosity, the local volume effect strongly influences the quantification accuracy. Pores in the matrix are modeled as spheres distributed by a Poisson point process. Their radius follows a truncated Gaussian law, leading to a porosity field whose covariance follows a Matérn-type form independent of local volume. The decay of porosity variance with increasing volume size, attributed to local volume averaging, is confirmed, indicating a similar behavior in finite element (FE) homogenization at the matrix-scale. The variance of matrix stiffness is found to decrease with growing local volume size, and its consistent negative correlation with porosity is thereby established. The stiffness-porosity joint distribution is then constructed by the conditional Gaussian mapping method. Finally, the stiffness calculation model at the composite-scale is developed, and the uncertainty induced by pores at the matrix-scale is quantified by Monte Carlo simulation. The results show that the nonintrusive modeling of stochastic porosity enables reliable stiffness propagation and efficient pore-induced uncertainty quantification.

孔隙率是纤维增强复合材料刚度不确定性的主要来源。然而，在复合尺度上明确地用规定的几何形状建模孔隙会导致不确定性量化的计算成本过高。本文提出了一种将单向纤维增强（UD）复合材料的基体尺度随机孔隙度与刚度不确定性联系起来的尺度间刚度传播方法。在这种非侵入式孔隙度建模中，局部体积效应严重影响定量精度。孔隙在基质中被建模为球体，通过泊松点过程进行分布。它们的半径遵循截断高斯定律，导致孔隙度场的协方差遵循独立于局部体积的matsamrn型形式。孔隙度随体积大小的增加而衰减，归因于局部体积平均，表明在矩阵尺度上的有限元（FE）均质化具有类似的行为。基体刚度方差随局部体积尺寸的增大而减小，并与孔隙率呈一致的负相关关系。然后采用条件高斯映射法构造刚度-孔隙度节理分布。最后，建立了复合尺度下的刚度计算模型，并通过蒙特卡罗模拟量化了基体尺度下孔隙引起的不确定性。结果表明，随机孔隙度的非侵入式建模能够实现可靠的刚度传播和有效的孔隙诱导不确定性量化。

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引用次数: 0

Error estimates and graded mesh refinement for isogeometric analysis in the vicinity of polar corners 极角附近等距分析的误差估计和梯度网格细化

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-06 DOI: 10.1016/j.cma.2025.118695

Thomas Apel, Philipp Zilk

Isogeometric analysis (IGA) combines exact geometric representations with higher-order accuracy for the numerical solution of partial differential equations. However, in geometrically complex settings – such as domains with corner singularities or non-standard parameterizations – these advantages may not be fully realized by standard IGA techniques. In particular, commonly used NURBS parameterizations can result in polar mappings, where one edge of the parametric domain is collapsed onto a single point, known as the polar point. Although widely used in computer-aided design, such configurations lack a full convergence theory. Additionally, reduced solution regularity near corners can significantly limit the performance of standard IGA, as higher-order convergence is no longer attainable.

In this work, both challenges are addressed by analyzing parameterizations in which the polar point coincides with a corner of the physical domain. To tackle the resulting singularity, a simple and effective local refinement strategy is proposed based on mesh grading toward the collapsed edge. This produces a locally refined mesh in the vicinity of the polar corner that accurately captures the singular behavior of the PDE solution.

To support this strategy, a numerical analysis tailored to polar domains with corners is developed. The framework includes the definition of polar function spaces on the parametric domain, a quasi-interpolant for polar splines, and the derivation of error estimates in weighted Sobolev norms. Optimal convergence is proven for smooth solutions under uniform refinement and for singular solutions using appropriately graded meshes. Numerical experiments on benchmark domains confirm the theoretical predictions and demonstrate the practical efficiency of the proposed method.

等几何分析（IGA）结合了精确的几何表示和偏微分方程数值解的高阶精度。然而，在几何上复杂的环境中-例如具有角点奇点或非标准参数化的域-这些优势可能无法通过标准IGA技术完全实现。特别是，常用的NURBS参数化可以导致极坐标映射，其中参数化域的一条边被折叠成一个点，称为极坐标点。虽然在计算机辅助设计中得到了广泛的应用，但这种构型缺乏完整的收敛理论。此外，在拐角附近降低的解正则性会极大地限制标准IGA的性能，因为不再能够实现高阶收敛。在这项工作中，这两个挑战都是通过分析参数化来解决的，其中极点与物理域的一个角落重合。为了解决由此产生的奇异性，提出了一种简单有效的基于网格向崩塌边缘分级的局部细化策略。这在极角附近产生了一个局部细化的网格，可以准确地捕获PDE解决方案的奇异行为。为了支持这一策略，开发了适合具有角的极域的数值分析。该框架包括参数域上极坐标函数空间的定义，极坐标样条的拟插值，以及加权Sobolev范数误差估计的推导。证明了均匀细化下的光滑解和适当分级网格下的奇异解的最优收敛性。在基准域上的数值实验验证了理论预测，并验证了该方法的实际有效性。

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引用次数: 0

Reinforcement learning closures for underresolved partial differential equations using synthetic data 使用合成数据的欠解偏微分方程的强化学习闭包

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-22 DOI: 10.1016/j.cma.2026.118767

Lothar Heimbach , Sebastian Kaltenbach , Petr Karnakov , Francis J. Alexander , Petros Koumoutsakos

Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-world applications remains prohibitively expensive because of the necessity of resolving a broad range of spatiotemporal scales. In turn, practitioners often rely on coarse-grained approximations of the original PDEs, trading off accuracy for reduced computational resources. To mitigate the loss of detail inherent in such approximations, closure models are employed to represent unresolved spatiotemporal interactions. We present a framework for developing closure models for PDEs using synthetic data acquired through the method of manufactured solutions. These data are used in conjunction with reinforcement learning to provide closures for coarse-grained PDEs. We illustrate the efficacy of our method using the one-dimensional and two-dimensional Burgers’ equations and the two-dimensional advection equation. Moreover, we demonstrate that closure models trained for inhomogeneous PDEs can be effectively generalized to homogeneous PDEs. The results demonstrate the potential for developing accurate and computationally efficient closure models for systems with scarce data.

偏微分方程（PDEs）描述从湍流和流行病到量子力学和金融市场的各种现象。尽管计算科学在最近取得了进展，但由于需要解决大范围的时空尺度，因此在实际应用中解决这种偏微分方程仍然非常昂贵。反过来，从业者通常依赖于原始偏微分方程的粗粒度近似值，以降低计算资源的准确性为代价。为了减轻这种近似中固有的细节损失，闭合模型被用来表示未解决的时空相互作用。我们提出了一个框架，利用通过制造解决方案的方法获得的合成数据来开发pde的闭合模型。这些数据与强化学习一起使用，为粗粒度的pde提供闭包。我们用一维和二维Burgers方程以及二维平流方程来说明我们的方法的有效性。此外，我们证明了针对非齐次偏微分方程训练的闭包模型可以有效地推广到齐次偏微分方程。研究结果表明，为具有稀缺数据的系统开发精确且计算效率高的闭包模型具有潜力。

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引用次数: 0

Topology-aware stress analysis in shell structures 壳结构的拓扑感知应力分析

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-23 DOI: 10.1016/j.cma.2026.118770

Junpeng Wang , Yingjian Liu , Jun Wu , Rüdiger Westermann

We present a stable and accurate algorithm for tracing principal stress lines (PSLs) in shell structures, applicable to both first- and second-order triangular and quadrilateral elements. The algorithm operates directly in the isoparametric space of the elements, leveraging their inherent shape functions to account for curved geometry without resorting to artificial subdivision. This approach enables, for the first time, a consistent stress topology analysis for shell elements, including a rigorous treatment of stress degeneracies. Our PSL seeding strategy integrates stress topology with the curved shell surface, ensuring a uniform and consistent PSL distribution. We evaluate the algorithm’s performance through a series of numerical experiments, demonstrating its utility for advanced stress analysis. Furthermore, we demonstrate the generation of a globally consistent, space-filling PSL structure, which is directly applicable to downstream tasks such as lightweight structural design. To support practical use, we provide a publicly available MATLAB implementation. The implementation features a unified file interface that supports diverse mesh types and is compatible with standard finite element method (FEM) output, offering a versatile tool for stress investigation and design evaluation in computational mechanics. The code is available at https://github.com/PSLer/PSLshell.

本文提出了一种稳定、准确的壳结构主应力线追踪算法，适用于一阶和二阶三角形和四边形单元。该算法直接在元素的等参空间中操作，利用其固有的形状函数来解释弯曲的几何形状，而无需诉诸人工细分。该方法首次实现了对壳单元的一致应力拓扑分析，包括对应力退化的严格处理。我们的PSL播种策略将应力拓扑与弯曲的壳表面相结合，确保PSL分布均匀一致。我们通过一系列的数值实验来评估算法的性能，证明了它在高级应力分析中的实用性。此外，我们还展示了一种全球一致的、填充空间的PSL结构的生成，它直接适用于轻量化结构设计等下游任务。为了支持实际使用，我们提供了一个公开可用的MATLAB实现。该实现具有统一的文件接口，支持多种网格类型，并与标准有限元方法（FEM）输出兼容，为计算力学中的应力调查和设计评估提供了一个通用的工具。代码可在https://github.com/PSLer/PSLshell上获得。

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引用次数: 0

A multiscale lattice Boltzmann model for simulating Stokes to pre-Darcy flow 模拟Stokes - pre-Darcy流动的多尺度晶格Boltzmann模型

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-29 DOI: 10.1016/j.cma.2026.118775

Catherine Choquet, Théo Coiffard

This paper presents a unified numerical modeling framework for simulating fluid flow across heterogeneous media and multiple flow regimes, from very low-velocity porous flows to free-fluid Navier-Stokes regimes. The proposed approach builds upon the Lattice-Boltzmann (LB) method, exploiting its kinetic formulation and inherent multiscale character. Unlike conventional continuum models that rely on distinct partial differential equations (Darcy, Brinkman, Forchheimer, or Navier-Stokes) and require complex coupling strategies at interfaces, the present scheme introduces a scaling parameter

θ = ϵ^{α}

(with ϵ the Knudsen number and

α \in R_{+}

) to incorporate the effects of both microscopic structure and observation scale within a single LB formulation. We show that adjusting α, even abruptly, enables simulations in highly heterogeneous media without invoking separate PDE models and interface conditions, or introducing ad hoc force terms. Theoretical analysis based on Chapman-Enskog expansions demonstrates that the proposed LB scheme recovers well-known continuum (PDE) limits under appropriate scaling. Numerical benchmarks validate its accuracy and stability across Darcy, Brinkman, Forchheimer, and Stokes regimes, as well as intermediate transitions, confirming the potential of the method as a fully kinetic and genuinely multiscale alternative to traditional PDE-based approaches.

本文提出了一个统一的数值模拟框架，用于模拟非均质介质和多种流动形式的流体流动，从极低速多孔流动到自由流体Navier-Stokes流动。提出的方法建立在晶格-玻尔兹曼（LB）方法的基础上，利用其动力学公式和固有的多尺度特征。与依赖不同偏微分方程（Darcy, Brinkman， Forchheimer或Navier-Stokes）的传统连续体模型不同，并且需要在界面处采用复杂的耦合策略，本方案引入了一个缩放参数θ=ϵα（其中Knudsen数为λ， α∈R+），以将微观结构和观察尺度的影响纳入单个LB公式中。我们表明，调整α，即使是突然调整，也可以在高度异构的介质中进行模拟，而无需调用单独的PDE模型和界面条件，或引入特别的力项。基于Chapman-Enskog展开的理论分析表明，在适当的尺度下，所提出的LB方案可以恢复众所周知的连续体（PDE）极限。数值基准验证了其在Darcy， Brinkman， Forchheimer和Stokes体系以及中间过渡中的准确性和稳定性，证实了该方法作为传统基于pde的方法的完全动力学和真正的多尺度替代方案的潜力。

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引用次数: 0

Unsupervised Constitutive Model Discovery from Sparse and Noisy Data 基于稀疏和噪声数据的无监督本构模型发现

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-07 DOI: 10.1016/j.cma.2025.118722

Vahab Knauf Narouie , Jorge-Humberto Urrea-Quintero , Fehmi Cirak , Henning Wessels

Recently, unsupervised constitutive model discovery has gained attention through frameworks based on the Virtual Fields Method (VFM), most prominently the EUCLID approach. However, the performance of VFM-based approaches, including EUCLID, is affected by measurement noise and data sparsity, which are unavoidable in practice. The statistical finite element method (statFEM) offers a complementary perspective by providing a Bayesian framework for assimilating noisy and sparse measurements to reconstruct the full-field displacement response, together with quantified uncertainty. While statFEM recovers displacement fields under uncertainty, it does not strictly enforce consistency with constitutive relations. In this work, we integrate statFEM with unsupervised constitutive model discovery in the EUCLID framework, yielding statFEM–EUCLID. The framework is demonstrated for isotropic hyperelastic materials. The results show that this integration reduces sensitivity to noise and data sparsity, while ensuring that the reconstructed fields remain consistent with both equilibrium and constitutive laws.

近年来，基于虚拟场方法（VFM）的框架（最突出的是EUCLID方法）引起了无监督本构模型发现的关注。然而，包括EUCLID在内的基于vfm的方法的性能受到测量噪声和数据稀疏性的影响，这在实践中是不可避免的。统计有限元法（statFEM）提供了一个互补的视角，它提供了一个贝叶斯框架，用于吸收噪声和稀疏测量来重建全场位移响应，以及量化的不确定性。statFEM恢复不确定条件下的位移场，但并不严格遵守本构关系。在这项工作中，我们将statFEM与EUCLID框架中的无监督本构模型发现相结合，得到statFEM - EUCLID。对各向同性超弹性材料的框架进行了论证。结果表明，该方法降低了对噪声的敏感性和数据稀疏性，同时保证了重构场符合平衡和本构律。

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引用次数: 0

Conservative data-driven finite element framework with adaptive hp-refinement for diffusion problems with material uncertainty 具有材料不确定性扩散问题的自适应hp精化保守数据驱动有限元框架

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-10 DOI: 10.1016/j.cma.2025.118703

Adriana Kuliková , Andrei G. Shvarts , Łukasz Kaczmarczyk , Chris J. Pearce

This paper presents a new data-driven finite element framework that is applicable to a broad range of engineering simulation problems. In the data-driven approach, the conservation laws and boundary conditions are satisfied by means of the finite element method, while the experimental data is used directly in numerical simulations, avoiding material models. Critically, we introduce a “weaker” mixed finite element formulation, which relaxes the regularity requirements on the approximation space for the primary field. At the same time, the continuity of the normal flux component is enforced across inner boundaries, allowing the conservation law to be satisfied in the strong sense. The relaxed regularity of the approximation spaces makes it easier to observe how imperfections in the datasets, such as missing or noisy data, result in non-uniqueness of the solution. This can be quantified to predict the uncertainty of the results using methods such as Markov chain Monte Carlo. Furthermore, this formulation provides a posteriori error indicators tailored for the data-driven approach, providing confidence in the results and enabling efficient solution schemes via adaptive hp-refinement. The capabilities of the formulation are demonstrated on an example of the nonlinear heat transfer in nuclear graphite using synthetically generated material datasets. This work provides an essential component for numerical frameworks for complex engineering systems such as digital twins.

本文提出了一种新的数据驱动有限元框架，适用于广泛的工程仿真问题。在数据驱动方法中，通过有限元方法满足守恒定律和边界条件，而直接将实验数据用于数值模拟，避免了材料模型。重要的是，我们引入了一个“较弱”的混合有限元公式，它放宽了对初级场近似空间的正则性要求。同时，法向通量分量的连续性被强制跨越内部边界，使得守恒定律在强意义上得到满足。近似空间的松弛规则使得更容易观察数据集中的缺陷，例如缺失或噪声数据，如何导致解的非唯一性。这可以用马尔科夫链蒙特卡罗等方法来量化预测结果的不确定性。此外，该公式提供了为数据驱动方法量身定制的后验误差指标，提供了对结果的信心，并通过自适应hp细化实现了有效的解决方案。利用合成生成的材料数据集，以核石墨中的非线性传热为例，证明了该公式的能力。这项工作为数字孪生等复杂工程系统的数值框架提供了重要的组成部分。

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引用次数: 0

Assessing coronary microvascular dysfunction using angiography-based data-driven methods 使用基于血管造影的数据驱动方法评估冠状动脉微血管功能障碍

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-12 DOI: 10.1016/j.cma.2026.118743

Haizhou Yang , Jiyang Zhang , Brahmajee K. Nallamothu , Krishna Garikipati , C. Alberto Figueroa

Coronary microvascular dysfunction (CMD), characterized by impaired regulation of blood flow in the coronary microcirculation, plays a key role in the pathogenesis of ischemic heart disease and is increasingly recognized as a contributor to adverse cardiovascular outcomes. Despite its clinical importance, CMD remains underdiagnosed due to the reliance on invasive procedures such as pressure wire-based measurements of the index of microcirculatory resistance (IMR) and coronary flow reserve (CFR), which are costly, time-consuming, and carry procedural risks. To date, no study has sought to quantify CMD indices using data-driven approaches while leveraging the rich information contained in coronary angiograms. To address these limitations, this study proposes a novel data-driven framework for inference of CMD indices based on coronary angiography. A physiologically validated multi-physics model was used to generate synthetic datasets for data-driven model training, consisting of CMD indices and computational angiograms with corresponding contrast intensity profiles (CIPs). Two neural network architectures were developed: a single-input-channel encoder-MLP model for IMR prediction and a dual-input-channel encoder-MLP model for CFR prediction, both incorporating epistemic uncertainty estimation to quantify prediction confidence. Results demonstrate that the data-driven models achieve high predictive accuracy when evaluated against physics-based synthetic datasets, and that the uncertainty estimates are positively correlated with prediction errors. Furthermore, the utility of CIPs as informative surrogates for coronary physiology is demonstrated, underscoring the potential of the proposed framework to enable accurate, real-time, image-based CMD assessment using routine angiography without the need for more invasive approaches.

冠状动脉微血管功能障碍（CMD）以冠状动脉微循环血流调节受损为特征，在缺血性心脏病的发病机制中起着关键作用，并越来越被认为是心血管不良结局的一个因素。尽管其具有重要的临床意义，但由于依赖于侵入性手术，如基于压力丝测量微循环阻力指数（IMR）和冠状动脉血流储备（CFR），这些手术成本高，耗时长，并且存在手术风险，因此CMD仍未得到充分诊断。迄今为止，还没有研究试图利用冠状动脉造影中包含的丰富信息，利用数据驱动的方法量化CMD指数。为了解决这些局限性，本研究提出了一种新的数据驱动框架，用于基于冠状动脉造影的CMD指数推断。使用生理验证的多物理模型生成用于数据驱动模型训练的合成数据集，包括CMD指数和具有相应对比度强度曲线（cip）的计算血管图。开发了两种神经网络架构：用于IMR预测的单输入通道编码器- mlp模型和用于CFR预测的双输入通道编码器- mlp模型，两者都采用认知不确定性估计来量化预测置信度。结果表明，数据驱动模型对基于物理的合成数据集具有较高的预测精度，且不确定性估定值与预测误差呈正相关。此外，cip作为冠状动脉生理学的信息替代品的实用性被证明，强调了所提出的框架的潜力，可以使用常规血管造影进行准确、实时、基于图像的CMD评估，而无需更多的侵入性方法。

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引用次数: 0

A smoothly varying quadrature approach for 3D IgA-BEM discretizations: Application to Stokes flow simulations 三维IgA-BEM离散化的光滑变正交方法：在Stokes流模拟中的应用

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-01-30 DOI: 10.1016/j.cma.2026.118773

Cesare Bracco , Francesco Patrizi , Alessandra Sestini

We introduce a novel quadrature strategy for Isogeometric Analysis (IgA) boundary element discretizations, specifically tailored to collocation methods. Thanks to the dimensionality reduction and the natural handling of unbounded domains, boundary integral formulations are particularly appealing in the IgA framework. However, they require the evaluation of boundary integrals whose kernels exhibit singular or nearly singular behavior. Even when the kernel is not singular, its numerical evaluation becomes challenging whenever the integration region lies close to a collocation point. These integrals of polar and nearly singular functions represent the main computational difficulty of IgA-BEM and motivate the development of efficient and accurate quadrature rules. Unlike traditional methods that classify integrals as singular, nearly singular, or regular, our approach employs a desingularizing change of variables that smoothly adapts to the physical distance from singularities in the boundary integral kernels. The transformation intensifies near the polar point and progressively weakens when integrating over portions of the domain that are farther from it, ultimately leaving the integrand unchanged in the limit of a diametrically opposed region. This automatic calibration enhances accuracy and robustness by eliminating the traditional classification step, to which the approximation quality is often highly sensitive. Moreover, integration is performed directly over B-spline supports rather than over individual elements, reducing computational cost, particularly for higher-degree splines. The proposed method is validated through boundary element benchmarks for the three dimensional Stokes problem, where we achieve excellent convergence rates.

我们引入了一种新的正交策略，用于等几何分析（IgA）边界元离散化，专门针对搭配方法。由于降维和无界域的自然处理，边界积分公式在IgA框架中特别有吸引力。然而，它们要求计算核表现出奇异或近似奇异行为的边界积分。即使核函数不是奇异的，当积分区域靠近一个配点时，核函数的数值计算也会变得困难。这些极函数和近奇异函数的积分代表了IgA-BEM的主要计算困难，并推动了高效准确的求积分规则的发展。与将积分分类为奇异、近奇异或正则的传统方法不同，我们的方法采用了一种去奇异化的变量变化，可以平滑地适应边界积分核中与奇点的物理距离。变换在极点附近增强，在离极点较远的区域上积分时逐渐减弱，最终使被积函数在完全相反区域的极限内保持不变。这种自动校准消除了传统的分类步骤，从而提高了精度和鲁棒性，而传统的分类步骤往往对逼近质量非常敏感。此外，积分直接在b样条支撑上执行，而不是在单个元素上执行，减少了计算成本，特别是对于高次样条。通过对三维Stokes问题的边界元基准测试验证了该方法的有效性，并取得了较好的收敛速度。

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引用次数: 0

Level set topology optimization for fluid-structure interaction using the modified immersed finite element method 基于改进浸入有限元法的流固耦合水平集拓扑优化

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-15 Epub Date: 2026-02-02 DOI: 10.1016/j.cma.2026.118754

Andreas Neofytou , Lucy T. Zhang , H. Alicia Kim

This work presents level set topology optimization method (LSTO) for fluid-structure interaction (FSI) problems. For the solution of the FSI problem the modified immersed finite element method (mIFEM) is used. The proposed formulation provides several advantages compared to the existing methods that rely on unified formulations or remeshing approaches. First it results in separate solid and fluid domains, thus allowing any discretization to be used for each physics. This allows for well established independent fluid and solid solvers to be utilized. Further, this modularity is possible without requiring re-meshing, which maintains efficiency especially for the fluid solver. The finite element method (FEM) is used to solve the flow equations efficiently on an Eulerian grid. The Lagrangian solid is analyzed with the reproducing kernel particle method (RKPM) which is a Galerkin-based meshfree method. The combination of LSTO and RKPM provides a well-defined solid interface which can be maintained on the computational domain by laying particles in the solid and on the level set boundary. The solid and fluid sensitivities are then computed to optimize the fully coupled problem, which is the fundamental challenge in this modular formulation. To identify and remove solid free-floating volumes that emerge during optimization within the flow field, an algorithm based on neighbor information is also introduced. For verification of the approach, benchmarking examples are solved and analyzed based on the assumption of steady state conditions. Beyond the linear elastic solid case considered by the majority of FSI works, we also test our approach with a nonlinear solid with large deformation.

提出了求解流固耦合问题的水平集拓扑优化方法（LSTO）。对于FSI问题的求解，采用了改进的浸入有限元法。与依赖统一公式或重网格方法的现有方法相比，所提出的公式提供了几个优点。首先，它产生了分离的固体和流体域，从而允许对每种物理使用任何离散化。这允许使用完善的独立流体和固体求解器。此外，这种模块化可以在不需要重新划分网格的情况下实现，这可以保持效率，特别是对于流体求解器。采用有限元法在欧拉网格上求解流动方程。采用基于伽辽金的无网格再现核粒子法（RKPM）对拉格朗日固体进行分析。LSTO和RKPM的结合提供了一个定义良好的实体界面，通过在实体和水平集边界上铺设粒子，可以在计算域上维护该界面。然后计算固体和流体灵敏度以优化完全耦合问题，这是该模块化公式的基本挑战。为了识别和去除流场优化过程中出现的固体自由漂浮体，提出了一种基于邻域信息的算法。为了验证该方法的有效性，在稳态条件假设的基础上对基准算例进行了求解和分析。除了大多数FSI作品所考虑的线性弹性固体情况外，我们还用具有大变形的非线性固体测试了我们的方法。

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引用次数: 0