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

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

A staggered training framework for mechanics-informed neural networks in tractable multiscale homogenization with application to woven fabrics 可处理多尺度均匀化中力学信息神经网络的交错训练框架及其在机织织物中的应用

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-09 DOI: 10.1016/j.cma.2025.118666

Faisal As’ad, Charbel Farhat

We introduce a computationally tractable framework for multiscale homogenization of path-dependent heterogeneous materials that combines mechanics-informed artificial neural networks with a staggered training procedure. The proposed approach decomposes complex, multiscale problems into a sequence of two-scale subproblems, efficiently bridging the scales through data-driven, neural network-based surrogate models that are, by construction, consistent with fundamental laws of continuum mechanics. The staggered training strategy ensures that the offline computational cost scales linearly with the number of scales, rather than exponentially, thereby achieving substantial efficiency gains over conventional nested multiscale finite element methods. As an illustrative application, the framework is demonstrated on woven fabrics, capturing viscoelastic and fiber-resolved material behaviors while maintaining computational efficiency. The results demonstrate that the proposed method achieves high-fidelity predictions comparable to those of fully resolved models reconstructed from real-material imaging, establishing a general and flexible methodology for modeling complex materials with many interacting scales.

我们引入了一个计算易于处理的框架，用于路径依赖的非均质材料的多尺度均质化，该框架将力学信息人工神经网络与交错训练过程相结合。该方法将复杂的多尺度问题分解为一系列双尺度子问题，通过数据驱动的、基于神经网络的替代模型有效地桥接这些尺度，这些模型的构建符合连续介质力学的基本定律。交错训练策略确保离线计算成本随尺度数量线性增长，而不是指数增长，从而获得比传统嵌套多尺度有限元方法更大的效率提升。作为一个说明性应用，该框架在机织物上进行了演示，在保持计算效率的同时捕获粘弹性和纤维分解的材料行为。结果表明，该方法实现了与真实材料成像重建的全分辨率模型相当的高保真预测，为具有许多相互作用尺度的复杂材料建模建立了一种通用而灵活的方法。

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引用次数: 0

Optimal convergence of IgA collocation methods IgA配置方法的最优收敛性

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-09 DOI: 10.1016/j.cma.2025.118721

Maria Roberta Belardo , Francesco Calabrò

Isogeometric collocation discretizes the strong form of a PDE on smooth spline spaces and therefore avoids element integration, but its spatial accuracy is highly sensitive to the placement of the collocation nodes. For this reason methods are tested on linear elliptic problems in order to verify convergence properties. Classical choices such as Greville abscissae may yield suboptimal convergence in both H¹ and L² norms for several spline degrees and problem settings. Node sets derived from (estimated) superconvergent (Cauchy–Galerkin) points – e.g. alternating subsets, clustered variants, or least–squares sets – frequently improve the observed L² behaviour and in favourable cases approach the Galerkin benchmark, though this is not universal across all degrees, boundary conditions, and PDE types. In this paper we find for the first choices of points that recover optimal convergence for polynomial degrees

p = 4, 6, 8

. The construction is made in order to recover the symmetry inside every knot span also for even degrees, as done in the above mentioned methods. Although the exact reason for this behaviour could not be clearly identified, the numerical evidence suggests that restoring local symmetry recovers the optimal rate. Unfortunately, as most of the previously proposed methods, this results in a collocation system with more equations than degrees of freedom number of degrees of freedom, thus the overall system is solved in a least–square sense.

等几何配置使PDE在光滑样条空间上的强形式离散化，从而避免了单元积分，但其空间精度对配置节点的位置高度敏感。为此，在线性椭圆型问题上对该方法进行了检验，以验证其收敛性。经典的选择，如Greville abscissae，对于一些样条度和问题设置，可能在H1和L2规范中产生次优收敛。从（估计的）超收敛（柯西-伽辽金）点派生的节点集——例如交替子集、聚类变体或最小二乘集——经常改善观察到的L2行为，在有利的情况下接近伽辽金基准，尽管这并非适用于所有度、边界条件和PDE类型。在本文中，我们找到了对于多项式次p=4,6,8恢复最优收敛的第一选择点。构造是为了恢复对称内部的每个结跨度也为偶数度，如在上述方法中所做的。虽然这种行为的确切原因还不能清楚地确定，但数值证据表明，恢复局部对称可以恢复最佳速率。不幸的是，正如之前提出的大多数方法一样，这导致搭配系统的方程多于自由度数，因此整个系统在最小二乘意义上求解。

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引用次数: 0

A data-driven approach to cut-cell quadrature using spline interpolation 使用样条插值的数据驱动切割细胞正交方法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-08 DOI: 10.1016/j.cma.2025.118700

Michał Ł. Mika , René R. Hiemstra , Stein K.F. Stoter , Dominik Schillinger

This paper presents a data-driven approach to develop higher-order accurate tensor-product-stencil quadrature rules for implicitly defined two-dimensional domains. We construct a three-dimensional configuration space of possible domain cuts using a signed distance representation based on circular arcs, defined by their radius and center, and exploit symmetry to simplify its three-dimensional domain. The configuration space, being piecewise smooth, is carefully partitioned into smooth regions, enabling three-dimensional tensor-product spline interpolation to approximate quadrature data sampled from an established implicit domain quadrature technique. The resulting quadrature rules are simple to apply, highly accurate, efficient, and can be used as a black-box solution. We demonstrate compatibility with existing cut finite element techniques and illustrate their application through numerical examples.

本文提出了一种数据驱动的方法来开发隐定义二维域的高阶精确张量积模板求积规则。我们基于圆弧，利用圆弧的半径和圆心来定义有符号距离表示，构造了一个可能的区域切割的三维构形空间，并利用对称性来简化其三维区域。结构空间是分段光滑的，被仔细划分为光滑区域，使三维张量积样条插值能够近似从已建立的隐式域正交技术中采样的正交数据。由此产生的正交规则易于应用，精度高，效率高，并且可以用作黑盒解决方案。我们演示了与现有切割有限元技术的兼容性，并通过数值实例说明了它们的应用。

引用次数: 0

Autoregressive multiplier bootstrap for in-situ error estimation and quality monitoring of finite time averages in turbulent flow simulations 自回归乘子自举法用于湍流模拟中有限时间平均值的原位误差估计和质量监测

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-08 DOI: 10.1016/j.cma.2025.118664

Christos Papagiannis , Guillaume Balarac , Pietro M. Congedo , Olivier P. Le Maître

In Computational Fluid Dynamics (CFD), and particularly within Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), the computational cost is largely dictated by the effort required to obtain statistically converged quantities such as time-averaged fields and higher-order moments. Despite the importance of accurately quantifying statistical uncertainty in unsteady simulations, no continuous and cost-effective, on-line method currently exists for monitoring the convergence quality of such statistics during runtime. This work introduces a novel, fully on-line bootstrapping approach to estimate the variance of finite-time averages without requiring the estimation of the flow’s Auto-Correlation Function (ACF). Unlike existing methods that rely on ACF estimation, which are often impractical due to excessive storage demands in large-scale simulations, or require off-line processing or a priori modeling assumptions, our method operates entirely during the simulation and incurs minimal overhead. The proposed technique employs a recursive update of bootstrap replicates of the time average, using correlated random weights generated via an autoregressive model. This formulation is computationally efficient: the update cost scales linearly with the number of bootstrap replicates and the dimensionality of the flow field, and the autoregressive model is inexpensive to evaluate. The method only requires storage of a small number of fields, making it suitable for large-scale CFD applications. We demonstrate the effectiveness of the approach on synthetic data from the Ornstein-Uhlenbeck process and on two canonical LES cases: a turbulent pipe flow and a round jet. We further discuss the method’s applicability to simulations with non-uniform time stepping, highlighting its flexibility and robustness.

在计算流体动力学（CFD）中，特别是在直接数值模拟（DNS）和大涡模拟（LES）中，计算成本很大程度上取决于获得统计收敛量（如时间平均场和高阶矩）所需的努力。尽管在非定常模拟中准确量化统计不确定性很重要，但目前还没有一种连续的、经济有效的在线方法来监测这些统计数据在运行时的收敛质量。这项工作引入了一种新颖的、完全在线的自启动方法来估计有限时间平均值的方差，而不需要估计流的自相关函数（ACF）。与依赖于ACF估计的现有方法不同，由于大规模模拟中过度的存储需求，或者需要离线处理或先验建模假设，这些方法通常是不切实际的，我们的方法完全在模拟过程中运行，并且产生最小的开销。所提出的技术使用自回归模型生成的相关随机权重，对时间平均值的自举重复进行递归更新。该公式计算效率高：更新成本与自举复制的数量和流场的维数成线性关系，并且自回归模型的评估成本低。该方法只需要存储少量的字段，使其适合大规模的CFD应用。我们在Ornstein-Uhlenbeck过程的合成数据和两种典型的LES情况（湍流管流和圆形射流）上证明了该方法的有效性。进一步讨论了该方法在非均匀时间步进仿真中的适用性，突出了其灵活性和鲁棒性。

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引用次数: 0

Generating high-fidelity microstructures of polycrystalline materials with prescribed higher-order texture tensors 用规定的高阶织构张量生成高保真的多晶材料微观结构

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-08 DOI: 10.1016/j.cma.2025.118690

Maximilian Krause , Thomas Böhlke , Matti Schneider

We introduce an efficient computational procedure for generating polycrystalline microstructures which permits studying the influence of specific texture-tensor orders on the resulting effective mechanical response, both in the linear elastic and the inelastic case. The crystallographic texture of a polycrystalline material is described by the Orientation Distribution Function (ODF). For practical computations, only the Fourier coefficients – called texture coefficients – of the ODF up to a certain order are of interest. In the work at hand, we wish to investigate this microstructure-property relationship. We interpret the task of approximating the texture coefficients of a microstructure realization as a moment-matching, i.e., quadrature, problem, and introduce efficient techniques for generating finite sets of orientations which exactly conform to prescribed polynomial texture terms. First, the microstructure morphology is generated via a well-established Laguerre-tessellation-based approach. Subsequently, the crystal grains are assigned a finite set of orientations which realize prescribed texture coefficients. We exploit the sparse representation of the action of the rotation group SO(3) on higher-order tensors to reduce the computational expense from exponential to cubic in the tensor order.

We consider polycrystalline copper as an example material and study the influence of texture terms of different polynomial order on the effective elastic properties and the anisotropy of initial yielding. For a large ensemble of polycrystal microstructures, we find that the elastic properties are mainly influenced by terms up to fourth order, whereas characterizing the yield function accurately requires higher-order texture terms.

To encourage further study of the texture dependence of nonlinear material properties, we provide an open-source python implementation of our algorithm.

我们介绍了一种有效的计算程序来生成多晶微结构，它允许研究特定的纹理张量阶对产生的有效力学响应的影响，无论是在线弹性情况下还是在非弹性情况下。用取向分布函数（ODF）来描述多晶材料的晶体织构。在实际计算中，只有ODF的傅里叶系数（称为纹理系数）达到一定阶才有意义。在手头的工作中，我们希望研究这种微观结构-性能关系。我们将逼近微观结构实现的纹理系数的任务解释为一个矩匹配问题，即正交问题，并引入有效的技术来生成有限的方向集，这些方向集完全符合规定的多项式纹理项。首先，微观结构形态是通过一种完善的基于laguerre -tessellation的方法生成的。然后，为晶粒分配一组有限的取向，这些取向可以实现规定的织构系数。利用旋转群SO(3)在高阶张量上作用的稀疏表示，减少了从指数阶到三次阶的计算开销。以多晶铜为例，研究了不同多项式阶织构项对其有效弹性性能和初始屈服各向异性的影响。对于一个大的多晶微观结构系综，我们发现弹性性能主要受四阶项的影响，而准确表征屈服函数需要高阶织构项。为了鼓励对非线性材料属性的纹理依赖性的进一步研究，我们提供了一个开源的python算法实现。

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引用次数: 0

Dual-primal isogeometric tearing and interconnecting solvers for adaptively refined multi-patch configurations 自适应改进多贴片结构的双原始等距撕裂和互连求解器

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-01-08 DOI: 10.1016/j.cma.2025.118701

Stefan Takacs , Stefan Tyoler

Isogeometric Analysis is a variant of the finite element method, where spline functions are used for the representation of both the geometry and the solution. Splines, particularly those with higher degree, achieve their full approximation power only if the solution is sufficiently regular. Since solutions are usually not regular everywhere, adaptive refinement is essential. Recently, a multi-patch-based adaptive refinement strategy based on recursive patch splitting has been proposed, which naturally generates hierarchical, non-matching multi-patch configurations with T-junctions, but preserves the tensor-product structure within each patch. In this work, we investigate the application of the dual-primal Isogeometric Tearing and Interconnecting method (IETI-DP) to such adaptive multi-patch geometries. We provide sufficient conditions for the solvability of the local problems and propose a preconditioner for the overall iterative solver. We establish a condition number bound that coincides with the bound previously shown for the fully matching case. Numerical experiments confirm the theoretical findings and demonstrate the efficiency of the proposed approach in adaptive refinement scenarios.

等几何分析是有限元方法的一种变体，其中样条函数用于表示几何形状和解。样条曲线，特别是那些高次的样条曲线，只有在解足够规则的情况下才能达到完全的近似能力。由于解决方案通常不是在任何地方都是规则的，因此自适应改进是必不可少的。近年来，提出了一种基于递归补丁分割的多补丁自适应改进策略，该策略自然生成具有t结点的分层、不匹配的多补丁构型，但保留了每个补丁内的张量积结构。在这项工作中，我们研究了双原始等几何撕裂和互连方法（IETI-DP）在这种自适应多块几何形状中的应用。给出了局部问题可解的充分条件，并给出了整体迭代解的前提条件。我们建立了一个条件数界，它与前面所示的完全匹配情况的界一致。数值实验验证了理论结果，并证明了该方法在自适应细化场景下的有效性。

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引用次数: 0