Computer Methods in Applied Mechanics and Engineering最新文献_第8页

PACMANN: Point adaptive collocation method for artificial neural networks PACMANN：人工神经网络的点自适应配置方法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-14 DOI: 10.1016/j.cma.2025.118723

Coen Visser , Alexander Heinlein , Bianca Giovanardi

Physics-Informed Neural Networks (PINNs) have emerged as a tool for approximating the solution of Partial Differential Equations (PDEs) in both forward and inverse problems. PINNs minimize a loss function which includes the PDE residual determined for a set of collocation points. Previous work has shown that the number and distribution of these collocation points have a significant influence on the accuracy of the PINN solution. Therefore, the effective placement of these collocation points is an active area of research. Specifically, available adaptive collocation point sampling methods have been reported to scale poorly in terms of computational cost when applied to high-dimensional problems. In this work, we address this issue and present the Point Adaptive Collocation Method for Artificial Neural Networks (PACMANN). PACMANN incrementally moves collocation points toward regions of higher residuals using gradient-based optimization algorithms guided by the gradient of the PINN loss function, that is, the squared PDE residual. We apply PACMANN to several forward and inverse problems, including one with a low-regularity solution and 3D Navier Stokes, and demonstrate that this method matches the performance of state-of-the-art methods in terms of the accuracy/efficiency tradeoff for the low-dimensional problems, while outperforming available approaches for high-dimensional problems. Key features of the method include its low computational cost and simplicity of integration into existing physics-informed neural network pipelines. The code is available at https://github.com/CoenVisser/PACMANN.

物理信息神经网络（pinn）已经成为逼近偏微分方程（PDEs）正解和逆解的一种工具。pinn最小化一个损失函数，它包含一组并置点确定的PDE残差。先前的工作表明，这些配点的数量和分布对PINN解的精度有显著影响。因此，这些搭配点的有效放置是一个活跃的研究领域。具体而言，已有的自适应配点采样方法在应用于高维问题时，在计算成本方面伸缩性较差。在这项工作中，我们解决了这个问题，并提出了人工神经网络的点自适应配置方法（PACMANN）。PACMANN使用基于梯度的优化算法，以PINN损失函数的梯度（即PDE残差的平方）为指导，逐步将搭配点向残差较高的区域移动。我们将PACMANN应用于几个正反问题，包括一个具有低正则解和3D Navier Stokes的问题，并证明该方法在低维问题的精度/效率权衡方面与最先进的方法相匹配，同时优于高维问题的可用方法。该方法的主要特点是计算成本低，易于集成到现有的物理信息神经网络管道中。代码可在https://github.com/CoenVisser/PACMANN上获得。

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引用次数: 0

A unified multiscale framework for stress-Based topology optimization using local constraint enforcement 基于局部约束的应力拓扑优化统一多尺度框架

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-13 DOI: 10.1016/j.cma.2025.118692

George Kazakis , Nikos D. Lagaros

This study presents a robust multiscale formulation for stress-constrained topology optimization aimed at designing lightweight and structurally resilient components. Unlike classical compliance-based methods, which may result in topologies unable to support applied loads, the proposed approach minimizes structural volume while rigorously enforcing local stress constraints. A dual-scale framework integrates macro-structural optimization with periodic micro-structural design, leveraging the Solid Isotropic Material with Penalization (SIMP) method; though it remains adaptable to other established topology optimization techniques. To address the computational challenges arising from numerous local stress constraints, we implement an Augmented Lagrangian strategy combined with polynomial vanishing constraints, eliminating the need for aggregation functions such as the p-norm or Kreisselmeier-Steinhauser functions. The resulting optimization algorithm is accurate and scalable, supported by a detailed sensitivity analysis and adjoint-based gradient computation. Numerical experiments in two dimensions validate the effectiveness of the method, demonstrating superior stress distribution and structural efficiency compared to classical formulations. This work contributes a comprehensive and scalable methodology for multiscale topology optimization under stress constraints, suitable for high-performance engineering applications.

本研究提出了一种鲁棒的多尺度应力约束拓扑优化公式，旨在设计轻量化和结构弹性构件。与传统的基于顺应性的方法不同，这种方法可能导致拓扑结构无法支持施加的载荷，而所提出的方法在严格执行局部应力约束的同时最小化了结构体积。双尺度框架将宏观结构优化与周期性微观结构设计相结合，利用固体各向同性材料惩罚（SIMP）方法；尽管它仍然适用于其他已建立的拓扑优化技术。为了解决由众多局部应力约束引起的计算挑战，我们实现了一种结合多项式消失约束的增广拉格朗日策略，消除了对p-范数或Kreisselmeier-Steinhauser函数等聚集函数的需求。通过详细的灵敏度分析和基于伴随的梯度计算，所得到的优化算法具有准确性和可扩展性。二维数值实验验证了该方法的有效性，表明与经典公式相比，该方法具有更好的应力分布和结构效率。这项工作为应力约束下的多尺度拓扑优化提供了一种全面、可扩展的方法，适用于高性能工程应用。

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引用次数: 0

Macro-element refinement schemes for THB-splines: Applications to Bézier projection and structure-preserving discretizations thb样条的宏元细化方案：在bsamizier投影和结构保持离散化中的应用

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-12 DOI: 10.1016/j.cma.2025.118707

Kevin Dijkstra , Carlotta Giannelli , Deepesh Toshniwal

This paper introduces a novel adaptive refinement strategy for Isogeometric Analysis (IGA) using Truncated Hierarchical B-splines (THB-splines). The strategy is motivated by the fact that certain applications may benefit from adaptive refinement schemes, which lead to a higher degree of structure in the locally-refined mesh than usual, and building this structure a priori can simplify the implementation in those contexts. Specifically, we look at two applications: formulation of an L²-stable local projector for THB-splines a la Bézier projection [Dijkstra and Toshniwal (2023)], and adaptive structure-preserving discretizations using THB-splines [Evans et al. (2020), Shepherd and Toshniwal (2024)]. Previously proposed approaches for these applications require mesh modifications to preserve critical properties of the spline spaces, such as local linear independence or the exactness of the discrete de Rham complexes. Instead, we propose a macro-element-based refinement approach based on refining

q = q_{1} \times \dots \times q_{n}

blocks of elements, termed q-boxes, where the block size q is chosen based on the spline degree p and the specific application. • For the Bézier projection for THB-splines, we refine p-boxes (i.e.,

q = p

). We show that THB-splines are locally linearly independent on p-boxes, which allows for a simple extension of the Bézier projection algorithm to THB-splines. This new formulation significantly improves upon the approach previously proposed by Dijkstra and Toshniwal (2023). • For structure-preserving discretizations, we refine

(p + 1)

-boxes (i.e.,

q = p + 1

). We prove that this choice of q ensures that the mesh satisfies the sufficient conditions presented in Shepherd and Toshniwal (2024) for guaranteeing the exactness of the THB-spline de Rham complex a priori and in an arbitrary number of dimensions. This is crucial for structure-preserving discretizations, as it eliminates the need for additional mesh modifications to maintain the exactness of the complex during adaptive simulations.

The effectiveness of the proposed framework is demonstrated through theoretical proofs and numerical experiments, including optimal convergence for adaptive approximation and the simulation of the incompressible Navier-Stokes equations.

介绍了一种利用截断层次b样条（thb样条）进行等几何分析（IGA）的自适应改进策略。该策略的动机是某些应用程序可能受益于自适应细化方案，这导致局部细化网格的结构程度比通常更高，并且先验地构建这种结构可以简化这些上下文中的实现。具体来说，我们研究了两种应用：一种是基于bsamzier投影的thb样条的l2稳定局部投影公式[Dijkstra和Toshniwal(2023)]，另一种是使用thb样条的自适应结构保持离散化[Evans等人（2020），Shepherd和Toshniwal(2024)]。先前提出的这些应用方法需要修改网格以保持样条空间的关键特性，例如局部线性独立性或离散de Rham复合体的准确性。相反，我们提出了一种基于宏元素的细化方法，该方法基于细化q= q1x⋯×qn元素块，称为q盒，其中块大小q是根据样条度p和特定应用选择的。•对于thb样条的bsamzier投影，我们改进了p-box（即q=p）。我们证明了thb样条在p-box上是局部线性无关的，这允许将bsamzier投影算法简单地扩展到thb样条。这个新公式显著改进了Dijkstra和Toshniwal（2023）先前提出的方法。•对于保持结构的离散化，我们改进(p+1)-盒（即q=p+1）。我们证明，这种q的选择确保网格满足Shepherd和Toshniwal（2024）中提出的充分条件，以保证thb样条de Rham复合体先验和任意维数的准确性。这对于保持结构的离散化是至关重要的，因为它消除了在自适应模拟过程中需要额外的网格修改来保持复合体的准确性。通过理论证明和数值实验证明了该框架的有效性，包括自适应逼近的最优收敛性和不可压缩Navier-Stokes方程的模拟。

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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 : 2026-01-12 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

Multi-physics-enhanced Bayesian inverse analysis: Information gain from additional fields 多物理场增强贝叶斯逆分析：附加场的信息增益

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-12 DOI: 10.1016/j.cma.2026.118735

Lea J. Haeusel, Jonas Nitzler, Lea J. Köglmeier, Wolfgang A. Wall

Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available but seemingly useless data are ignored. This work proposes incorporating such data from additional physical fields into the inverse analysis, even when the forward model solves a single-physics problem. A Bayesian framework easily incorporates the additional data and quantifies the resulting uncertainty reduction. We formally introduce the proposed method, which we denote as multi-physics-enhanced Bayesian inverse analysis. Moreover, this work is the first to quantify the reduction in parameter uncertainty by comparing the information gain from the prior to the posterior when using single-physics versus multi-physics data. We demonstrate the potential of the proposed method in two exemplary applications. Our results show that even a few or noisy data points from an additional physical field can considerably increase the information gain, even when the physical field is only weakly or one-way coupled. Overall, this work proposes and promotes the future use of multi-physics-enhanced Bayesian inverse analysis as a cost- and time-saving game-changer across various fields of science and industry, particularly in medicine.

在复杂的现实世界场景中，反演分析，如模型校准，经常受到缺乏信息数据的困扰。标准的补救措施是设计新的实验装置，这往往既昂贵又耗时，而现成但看似无用的数据却被忽视了。这项工作建议将这些来自其他物理场的数据纳入反向分析，即使正演模型解决了单一物理问题。贝叶斯框架很容易包含额外的数据，并量化结果的不确定性减少。我们正式介绍了所提出的方法，我们称之为多物理增强贝叶斯逆分析。此外，这项工作是第一次量化参数不确定性的减少，通过比较使用单物理场和多物理场数据时从先验到后验的信息增益。我们在两个示例应用中展示了所提出方法的潜力。我们的研究结果表明，即使是来自额外物理场的少量或有噪声的数据点也可以大大增加信息增益，即使物理场只是弱耦合或单向耦合。总的来说，这项工作提出并促进了未来多物理增强贝叶斯逆分析的使用，作为在科学和工业各个领域，特别是在医学领域节省成本和时间的游戏规则改变者。

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引用次数: 0

Hetero-EUCLID: Interpretable model discovery for heterogeneous hyperelastic materials using stress-unsupervised learning 异质超弹性材料的可解释模型发现使用应力无监督学习

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-12 DOI: 10.1016/j.cma.2026.118729

Kanhaiya Lal Chaurasiya , Saurav Dutta , Siddhant Kumar , Akshay Joshi

We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) framework to efficiently solve the heterogenized formulation through parsimonious model selection using sparsity-promoting priors and Monte Carlo Markov Chain sampling. We utilize experimentally observable 3D surface displacement and boundary-averaged force data generated from Finite Element simulations of non-equi-biaxial tension tests on heterogeneous specimens. The framework broadly consists of two steps– residual force-based segmentation and constitutive parameter identification. We validate and demonstrate the ability of the proposed framework to segment the domain and characterize the constituent materials on various types of thin square heterogeneous domains. We validate the framework’s ability to segment and characterize materials with multiple levels of displacement noises and non-native mesh discretizations, i.e, using different meshes for the forward FE simulations and the inverse EUCLID problem. This demonstrates the applicability of the Hetero-EUCLID framework in Digital Image/Volume Correlation-based experimental scenarios. Furthermore, the proposed framework performs successful segmentation and material characterizations based on data from a single experiment, thereby making it viable for rapid, interpretable model discovery in domains such as aerospace and defense composites and for characterization of selective tissue stiffening in medical conditions such as fibroatheroma, atherosclerosis, or cancer.

我们提出了一个计算框架，Hetero-EUCLID，用于分割和参数识别，以表征非均质材料的所有成分的全超弹性行为。在这项工作中，我们利用贝叶斯- euclid（高效无监督本构律识别和发现）框架，通过使用稀疏性促进先验和蒙特卡洛马尔可夫链采样的简约模型选择，有效地解决异构化公式。我们利用实验观察到的三维表面位移和边界平均力数据，这些数据来自非均匀试件的非等双轴拉伸试验的有限元模拟。该框架大致包括两个步骤：基于剩余力的分割和本构参数识别。我们验证并展示了所提出的框架在各种类型的薄方形异构域上分割域和表征组成材料的能力。我们验证了该框架对具有多级位移噪声和非原生网格离散化的材料进行分割和表征的能力，即使用不同的网格进行正演有限元模拟和反EUCLID问题。这证明了Hetero-EUCLID框架在基于数字图像/体积相关的实验场景中的适用性。此外，所提出的框架基于单个实验的数据进行成功的分割和材料表征，从而使其能够在航空航天和国防复合材料等领域快速、可解释的模型发现，以及在纤维动脉粥样硬化、动脉粥样硬化或癌症等医疗条件下选择性组织硬化的表征。

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引用次数: 0

Formulation of a new shell-like reduced order model finite element for layered structures 层状结构新的类壳降阶有限元模型的建立

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-10 DOI: 10.1016/j.cma.2026.118730

Francesc Turon , Fermin Otero , Alex Ferrer , Xavier Martinez

This paper presents a weak work-based kinematic coupling formulation between layered Reissner-Mindlin (RM) shell models and non-overlapping contiguous solid models. This approach relies on the interface definition proposed by the Mixing Dimensional Coupling (MDC) method, extending it to layered cross-sections. To achieve this, additional weak kinematic conditions are added to the work and reaction equilibrium in order to ensure deformation compatibility along the coupling interface and through the laminate in its thickness direction. The first outcome of the presented work is the development of efficient hybrid models, which employ conventional shell elements in regions with uniform lamination and solid models in areas with discontinuities. This enables accurate capture of the structural stiffness while focusing computational resources on regions where the kinematic assumptions of shell elements are insufficient. Secondly, this work introduces a procedure for defining multi-nodal Shell-Like Reduced Order Models (SLROMs) that are compatible with conventional Reissner Mindlin shell elements. These SLROMs are derived from solid model representations of regions with laminates or discontinuities, such as holes, thickness variations, or laminate transitions. Once analyzed, they enable efficient shell-only analyses while still providing detailed solid model stress distribution. Both the coupling formulation and the SLROM approach are evaluated through illustrative numerical examples.

本文提出了层状Reissner-Mindlin （RM）壳模型与非重叠连续实体模型之间基于弱工作的运动耦合公式。该方法依赖于混合维度耦合（MDC）方法提出的接口定义，并将其扩展到分层截面。为了实现这一目标，在功和反作用力平衡中增加了额外的弱运动学条件，以确保沿耦合界面和通过层压板在其厚度方向上的变形兼容性。所提出的工作的第一个成果是高效混合模型的发展，该模型在均匀层合区域使用常规壳单元，在不连续区域使用实体模型。这可以准确捕获结构刚度，同时将计算资源集中在壳单元的运动学假设不足的区域。其次，本文介绍了一个定义多节点类壳降阶模型（slrom）的过程，该模型与传统的Reissner Mindlin壳元素兼容。这些slrom来源于具有层压或不连续的区域的实体模型表示，例如孔，厚度变化或层压过渡。一旦进行分析，它们就可以在提供详细的实体模型应力分布的同时进行有效的壳分析。通过数值算例对耦合公式和SLROM方法进行了评价。

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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 : 2026-01-10 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

Multiscale polymorphic uncertainty quantification based on physics-augmented neural networks 基于物理增强神经网络的多尺度多态不确定性量化

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-10 DOI: 10.1016/j.cma.2025.118726

Felix Harazin, Jakob Platen, F. Niklas Schietzold, Wolfgang Graf, Michael Kaliske

With this contribution, the aim is to incorporate and evaluate the uncertainty in multiscale structural analyses. The material properties of composites (e.g., concrete, spinoidal structures) consequently depend on structural parameters and actual realizations of the composite mesostructures. Uncertainties on the mesoscale lead to uncertain behavior on the macroscale. Based on scale separation and following the current homogenization methods, a surrogate model is introduced, which enables the uncertainty quantification of macroscopic structures based on uncertainties at the mesoscale. Through the usage of Neural Networks (NN)s as surrogate models for the composite material, sampling-based uncertainty quantification schemes are enabled in large elastic deformations. A formulation of NNs that incorporates physical information of hyperelastic materials in the network structure is used and expanded with uncertain parameters to further reduce the information needed for the training of the NN. The proposed procedure enables the consideration of aleatoric, epistemic, and polymorphic uncertainty. For the training of the NN, a domain separation is proposed, which allows the efficient pre-training of the neural network.

有了这个贡献，目的是纳入和评估多尺度结构分析中的不确定性。复合材料（如混凝土、螺旋结构）的材料性能取决于结构参数和复合材料细观结构的实际实现。中尺度上的不确定性导致宏观尺度上的不确定性行为。基于尺度分离，在现有均质化方法的基础上，提出了一种基于中尺度不确定性的替代模型，实现了宏观结构的不确定性量化。通过使用神经网络（NN）作为复合材料的替代模型，实现了基于采样的不确定性量化方案。在网络结构中引入超弹性材料物理信息的神经网络公式，并使用不确定参数进行扩展，以进一步减少神经网络训练所需的信息。所提出的程序能够考虑任意的、认知的和多态的不确定性。对于神经网络的训练，提出了一种域分离方法，使神经网络能够进行有效的预训练。

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引用次数: 0

An adaptive isogeometric boundary integral method using analysis-suitable T-splines for fluid-shell interactions at low Reynolds numbers 低雷诺数流壳相互作用的适合分析的t样条自适应等几何边界积分方法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-10 DOI: 10.1016/j.cma.2025.118725

Togo Hayashi, Shunichi Ishida, Yohsuke Imai

An adaptive isogeometric boundary integral method is developed for fluid–structure interaction analysis of the deformation of a hyperelastic sheet in a viscous fluid. An isogeometric Kirchhoff–Love shell formulation for solid mechanics is coupled with a boundary integral formulation for fluid mechanics at the Stokes flow regime. Knot insertion and removal based on analysis-suitable T-splines are applied to mesh refinement and coarsening. Compression- and curvature-dependent refinement and coarsening rules are used to capture complex fold formations. Flow-induced deformation due to extensional and simple shear flows, and growth-induced deformation due to swelling and shrinking are simulated. Protrusion and retraction of the leading edge of a membrane are also simulated. These numerical examples demonstrate that the developed method is capable of simulating a variety of fold formation problems in viscous environments while saving computational costs.

提出了一种自适应等几何边界积分法，用于分析粘性流体中超弹性片的流固耦合变形。固体力学的等几何Kirchhoff-Love壳公式与流体力学的边界积分公式在Stokes流态下耦合。基于适合分析的t样条的结点插入和去除应用于网格的细化和粗化。压缩和曲率相关的细化和粗化规则用于捕获复杂的褶皱构造。模拟了由拉伸和单纯剪切引起的流动诱导变形，以及由膨胀和收缩引起的生长诱导变形。还模拟了膜前缘的突出和收缩。数值算例表明，该方法在节省计算成本的同时，能够模拟各种粘性环境下的褶皱形成问题。

引用次数: 0