Computer Methods in Applied Mechanics and Engineering最新文献_第10页

Corrosion-fatigue degradation in reinforced concrete structures: A multiphysics phase-field modeling approach 钢筋混凝土结构的腐蚀疲劳退化：一种多物理场相场建模方法

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: 2026-02-02 DOI: 10.1016/j.cma.2025.118693

Abedulgader Baktheer, Manikandan Gopakumar, Ghandi Kenjo, Fadi Aldakheel

Corrosion-fatigue interaction is a complex and strongly coupled chemo-mechanical degradation process that critically impacts the durability of reinforced concrete (RC) structures exposed to aggressive environments and cyclic loading. This work presents a holistic multiphysics phase-field modeling framework for simulating the full spectrum of coupled physical mechanisms that govern corrosion-fatigue degradation in RC structures. The proposed framework captures: (i) chloride transport and binding in the concrete matrix leading to corrosion initiation, (ii) reactive transport and precipitation of Fe

^{2 +}

and Fe

^{3 +}

ions in concrete pores, (iii) pressure accumulation due to rust formation and precipitation around steel reinforcement, (iv) corrosion diffusion and material degradation in steel representing softening due to film rupture and material dissolution, (v) fatigue degradation in steel reinforcement, (vi) fatigue crack propagation in concrete as well as splitting fracture due to corrosion, and (vii) degradation-dependent diffusivity enabling interaction between mechanical cracking and ionic transport. These processes are fully coupled within a unified chemo-mechanical phase-field formulation. Key components of the corrosion and fatigue submodels are validated against experimental data to ensure physical fidelity. The framework is then used to investigate the bidirectional interaction between corrosion and fatigue in both 2D and 3D settings, demonstrating how corrosion accelerates fatigue failure and, conversely, how early-stage fatigue cracking promotes corrosion progression. This comprehensive approach offers a robust tool for assessing service life and designing more durable RC structures under coupled environmental and mechanical loading. The corresponding source codes are openly available at [https://doi.org/10.25835/3duuzvj4 ], allowing reproducibility by interested researchers.

腐蚀-疲劳相互作用是一个复杂的、强耦合的化学-力学降解过程，它严重影响钢筋混凝土（RC）结构在恶劣环境和循环荷载下的耐久性。这项工作提出了一个整体的多物理场相场建模框架，用于模拟控制RC结构腐蚀疲劳退化的耦合物理机制的全谱。建议的架构包括：(i)氯化物在混凝土基体中的传递和结合导致腐蚀起始，（ii）混凝土孔隙中Fe2+和Fe3+离子的反应性传递和沉淀，（iii）钢筋周围锈形成和沉淀导致的压力积累，（iv）腐蚀扩散和材料降解，代表钢材薄膜破裂和材料溶解的软化，(v)钢筋的疲劳降解，（vi）混凝土中的疲劳裂纹扩展以及腐蚀引起的劈裂断裂；（vii）与退化相关的扩散系数，使机械开裂和离子传输之间能够相互作用。这些过程在统一的化学-机械相场公式中完全耦合。腐蚀和疲劳子模型的关键部件根据实验数据进行验证，以确保物理保真度。然后使用该框架在2D和3D环境下研究腐蚀与疲劳之间的双向相互作用，展示腐蚀如何加速疲劳失效，反过来，早期疲劳开裂如何促进腐蚀进展。这种综合方法为评估RC结构在环境和机械耦合载荷下的使用寿命和设计更耐用的RC结构提供了强大的工具。相应的源代码可以在[https://doi.org/10.25835/3duuzvj4]上公开获得，允许感兴趣的研究人员复制。

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引用次数: 0

Efficiently training SciML models with derivative-informed training data using order truncated imaginary numbers 利用序截断虚数有效训练具有导数信息的SciML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: 2026-02-07 DOI: 10.1016/j.cma.2026.118789

Krishna Prasath Logakannan , Mauricio Aristizabal , Geoffrey Bomarito , Zhitong Xu , Shandian Zhe , Robert M. Kirby , Harry Millwater , Jacob Hochhalter

The SciML community constantly faces challenges in data acquisition, which often results in sparse data for training. Incorporating derivatives during training has been shown to improve predictions from learned models in cases with sparse data. However, acquiring training data derivatives and computing corresponding model derivatives during fitness evaluations significantly increases the time required for both steps, which mitigates the benefits of leveraging derivatives in practice. Additionally, these issues are increased with increasing derivative order. In this work, these training steps are accelerated by using a hypercomplex algebra method, Order Truncated Imaginary (OTI) numbers, for efficient and accurate acquisition and computation of the requisite derivatives. Also presented is an assessment of using derivatives of arbitrary order in the training of symbolic regression (SR) models, termed derivative-informed training data for genetic programming with SR (DITD-GPSR). The effectiveness of the DITD-GPSR method is demonstrated using an optimization test function, a nonlinear oscillatory function, and a thick-walled cylinder solid mechanics problem. The results show that the DITD-GPSR method commonly requires just 10% of the training data to achieve similar accuracy to conventional GPSR, and the DITD-GPSR evolves to the exact equations in far fewer evolution steps, up to 100 times in some cases. Implementing OTI numbers enabled the computation of higher-order derivatives with negligible increase in compute time compared to exponential growth using conventional auto-differentiation.

SciML社区在数据获取方面不断面临挑战，这往往导致用于训练的数据稀疏。在训练过程中加入导数已被证明可以在数据稀疏的情况下提高学习模型的预测。然而，在适应度评估过程中获取训练数据衍生物并计算相应的模型衍生物会大大增加这两个步骤所需的时间，从而降低了在实践中利用衍生物的好处。此外，这些问题随着导数阶数的增加而增加。在这项工作中，这些训练步骤通过使用超复杂代数方法，序截断虚数（OTI）数来加速，以便有效和准确地获取和计算必要的导数。还提出了在符号回归（SR）模型的训练中使用任意阶导数的评估，称为带有SR的遗传规划的导数通知训练数据（ddd - gpsr）。通过优化测试函数、非线性振荡函数和厚壁圆柱固体力学问题验证了ddd - gpsr方法的有效性。结果表明，ddd -GPSR方法通常只需要10%的训练数据就能达到与传统GPSR相似的精度，并且ddd -GPSR方法进化到精确方程的进化步骤要少得多，在某些情况下高达100次。实现OTI数可以计算高阶导数，与使用传统的自微分进行指数增长相比，计算时间的增加可以忽略不计。

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引用次数: 0

A bridging-domain approach for multiscale modeling of anisotropic fracture in large-scale heterogeneous structures 大型非均质结构中各向异性裂缝多尺度建模的桥域方法

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: 2026-01-28 DOI: 10.1016/j.cma.2026.118774

Zakaria Chafia , Julien Yvonnet , Jérémy Bleyer

The prediction of the mechanical response of strongly heterogeneous structures containing defects critically depends on accurately capturing crack nucleation at micro scale. Fully resolved (high-fidelity) models are costly, whereas homogenized approaches may fail to represent initiation near heterogeneities. An efficient multiscale method is proposed in this work to simulate crack nucleation and propagation by bridging a high-fidelity micro-subdomain, dedicated to initiation, with a homogenized macro-subdomain used for propagation. The two subdomains overlap, may be discretized with nonconforming meshes, and are coupled through an energy-based formulation. The main contribution lies in the use, at the macro scale, of a surrogate anisotropic damage model constructed offline within the DDHAD (Data-Driven Harmonic Analysis of Damage) framework. This model reproduces direction-dependent crack propagation, while nucleation is resolved at the micro scale by the high-fidelity model. Significant computational speed-ups are achieved as compared to high-resolution simulations of the entire structure, and by accurately capturing initiation of the cracks in the microstructure. Examples on heterogeneous media exhibiting strong preferred crack orientations are presented to illustrate the potential of the approach.

含缺陷强非均相结构的力学响应预测关键取决于在微观尺度上准确捕捉裂纹形核。完全分辨（高保真度）的模型是昂贵的，而均质化的方法可能无法表示接近异质的起始。本文提出了一种有效的多尺度方法，通过桥接用于裂纹萌生的高保真微观子域和用于裂纹扩展的均匀化宏观子域来模拟裂纹的成核和扩展。两个子域重叠，可以用不一致的网格离散，并通过基于能量的公式耦合。主要贡献在于，在宏观尺度上，在DDHAD（数据驱动的损伤谐波分析）框架下离线构建了替代各向异性损伤模型。该模型再现了依赖于方向的裂纹扩展，而高保真模型在微观尺度上解决了成核问题。与整个结构的高分辨率模拟相比，通过准确捕获微观结构中裂纹的起始，实现了显著的计算速度提高。在非均质介质中表现出强优先裂纹取向的例子说明了该方法的潜力。

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引用次数: 0

Symmetrisation and hyperbolicity of first-order conservation laws in large strain compressible viscoelasticity using the smoothed particle hydrodynamics method 大应变可压缩粘弹性一阶守恒律的对称性和双曲性

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: 2026-01-28 DOI: 10.1016/j.cma.2026.118742

Chun Hean Lee , Antonio J. Gil , Tadas Jaugielavičius , Thomas Richardson , Sébastien Boyaval , Damien Violeau , Javier Bonet

This paper presents a new first-order hyperbolic framework with relaxation (or dissipation) terms for large strain viscoelastic solids. The framework is based on a compressible Maxwell-type viscoelastic model and integrates linear momentum conservation, geometric conservation laws, and evolution equations for internal variables. First, we propose a polyconvex strain energy function that is jointly convex with respect to the deformation measures and internal variables. Second, we introduce a generalised convex entropy function to symmetrise the hyperbolic system in terms of dual conjugate (entropy) variables. Third, we demonstrate that the system is hyperbolic (i.e., real wave speeds) under all deformation states, and that the relaxation terms correctly capture viscoelastic dissipation. Fourth, we present an upwinding Smoothed Particle Hydrodynamics (SPH) [1–3] scheme that enforces the second law of thermodynamics semi-discretely and uses the time rate of the generalised convex entropy to monitor internal dissipation and stabilise the simulation. Finally, the proposed framework is validated through numerical examples and benchmarked against the in-house Updated Reference Lagragian SPH [2,3] and vertex-centred finite volume [4–7] algorithms, demonstrating stability, accuracy, and consistent energy dissipation.

针对大应变粘弹性固体，提出了一种新的带松弛项的一阶双曲框架。该框架基于可压缩麦克斯韦型粘弹性模型，并集成了线性动量守恒、几何守恒定律和内部变量的演化方程。首先，我们提出了一个多凸应变能函数，该函数相对于变形量和内部变量是联合凸的。其次，我们引入了一个广义凸熵函数，以对偶共轭（熵）变量来对称双曲系统。第三，我们证明了系统在所有变形状态下都是双曲的（即实际波速），并且松弛项正确地捕获了粘弹性耗散。第四，我们提出了一种上旋光滑粒子流体力学（SPH）[1-3]方案，该方案半离散地执行热力学第二定律，并使用广义凸熵的时间率来监测内部耗散并稳定模拟。最后，通过数值算例验证了所提出的框架，并与内部更新的参考Lagragian SPH[2,3]和以顶点为中心的有限体积[4-7]算法进行了基准测试，证明了该框架的稳定性、准确性和一致的能量消耗。

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引用次数: 0

Smoothed particle hydrodynamics of anisotropic diffusions 各向异性扩散的光滑粒子流体力学

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-01 Epub Date: 2026-01-05 DOI: 10.1016/j.cma.2025.118697

Xiaojing Tang, Xiangyu Hu, Oskar Haidn

Diffusion problems with anisotropic features arise in various scientific and engineering disciplines. However, accurately describing these processes in numerical simulations poses challenges due to the erroneous approximation and the appearance of spurious oscillations and negative concentrations. As a Lagrangian mesh-less method, Smoothed Particle Hydrodynamics (SPH) offers unified framework for addressing multi-physics problems involving diffusion process. Despite these benefits, its application to anisotropic diffusion remains limited, due to the lack of accurate and stable particle approximation. In this paper, we developed a complete Hessian matrix formulation for anisotropic diffusion to achieve 2nd-order accuracy and numerical stability. Specifically, the 2nd-order reproducing approximation of the complete Hessian matrix is used for the coordinate transformation to obtain the anisotropic diffusion operator. The formulation is further applied for simulating diffusion processes in thin structures, where anisotropic resolution is handled with the adaptive SPH method.

To validate the proposed formulation, firstly, anisotropic contaminant diffusion in a fluid is simulated, showing strong consistency with analytical solutions and producing smooth, oscillation-free results even in the presence of discontinuities. Secondly, the diffusion of a physical field with a predefined initial distribution is modeled using anisotropic resolution and the adaptive SPH method. Across various anisotropic ratios, the accuracy is examined in relation to the truncation error. Finally, this formulation is applied to modeling practical applications, including fluid-structure interaction in a thin porous membrane and anisotropic transmembrane potential transport in the left ventricle. These results demonstrate that the proposed formulation can accurately and stably solve complex anisotropic diffusion problems and diffusion problem using anisotropic kernel and spatial resolutions in diverse physical settings.

具有各向异性特征的扩散问题出现在各种科学和工程学科中。然而，由于错误的近似和虚假振荡和负浓度的出现，在数值模拟中准确描述这些过程带来了挑战。光滑粒子流体动力学（SPH）作为一种拉格朗日无网格方法，为解决涉及扩散过程的多物理场问题提供了统一的框架。尽管有这些优点，但由于缺乏精确和稳定的粒子近似，它在各向异性扩散中的应用仍然有限。在本文中，我们建立了一个完整的各向异性扩散的Hessian矩阵公式，以达到二阶精度和数值稳定性。具体来说，利用完全Hessian矩阵的二阶再现近似进行坐标变换，得到各向异性扩散算子。该公式进一步应用于薄结构中扩散过程的模拟，其中采用自适应SPH方法处理各向异性分辨率。为了验证所提出的公式，首先，模拟了流体中各向异性污染物的扩散，显示出与解析解的强一致性，即使在存在不连续的情况下也能产生光滑、无振荡的结果。其次，利用各向异性分辨率和自适应SPH方法对具有预定义初始分布的物理场的扩散进行建模；在不同的各向异性比率下，准确度与截断误差的关系进行了检验。最后，将该公式应用于模拟实际应用，包括薄多孔膜中的流固相互作用和左心室各向异性跨膜电位传递。结果表明，该公式可以准确稳定地求解复杂的各向异性扩散问题，以及在不同物理环境下使用各向异性核和空间分辨率的扩散问题。

{"title":"Smoothed particle hydrodynamics of anisotropic diffusions","authors":"Xiaojing Tang, Xiangyu Hu, Oskar Haidn","doi":"10.1016/j.cma.2025.118697","DOIUrl":"10.1016/j.cma.2025.118697","url":null,"abstract":"<div><div>Diffusion problems with anisotropic features arise in various scientific and engineering disciplines. However, accurately describing these processes in numerical simulations poses challenges due to the erroneous approximation and the appearance of spurious oscillations and negative concentrations. As a Lagrangian mesh-less method, Smoothed Particle Hydrodynamics (SPH) offers unified framework for addressing multi-physics problems involving diffusion process. Despite these benefits, its application to anisotropic diffusion remains limited, due to the lack of accurate and stable particle approximation. In this paper, we developed a complete Hessian matrix formulation for anisotropic diffusion to achieve 2nd-order accuracy and numerical stability. Specifically, the 2nd-order reproducing approximation of the complete Hessian matrix is used for the coordinate transformation to obtain the anisotropic diffusion operator. The formulation is further applied for simulating diffusion processes in thin structures, where anisotropic resolution is handled with the adaptive SPH method.</div><div>To validate the proposed formulation, firstly, anisotropic contaminant diffusion in a fluid is simulated, showing strong consistency with analytical solutions and producing smooth, oscillation-free results even in the presence of discontinuities. Secondly, the diffusion of a physical field with a predefined initial distribution is modeled using anisotropic resolution and the adaptive SPH method. Across various anisotropic ratios, the accuracy is examined in relation to the truncation error. Finally, this formulation is applied to modeling practical applications, including fluid-structure interaction in a thin porous membrane and anisotropic transmembrane potential transport in the left ventricle. These results demonstrate that the proposed formulation can accurately and stably solve complex anisotropic diffusion problems and diffusion problem using anisotropic kernel and spatial resolutions in diverse physical settings.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"451 ","pages":"Article 118697"},"PeriodicalIF":7.3,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bayesian updating using multi-fidelity active learning Kriging models 基于多保真主动学习Kriging模型的贝叶斯更新

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-01 Epub Date: 2025-12-24 DOI: 10.1016/j.cma.2025.118658

Ioannis Prentzas, Michalis Fragiadakis

The paper presents a multi-fidelity framework for efficient Bayesian updating using active learning Kriging models. The updating problem is solved as an equivalent probabilistic problem using the Bayesian updating with Structural reliability (BUS) method. The proposed approach leverages an ensemble surrogate modeling strategy that combines two Kriging models of multiple fidelities, thereby enhancing predictive capacity while reducing computational cost by exploiting information from models of different fidelity levels. A key contribution is the integration of multi-fidelity Bayesian optimization in order to determine the optimal BUS constant, ensuring accurate transformation of the posterior into a reliability problem. Furthermore, an improved version of the Quantified Active Learning Subset Simulation (qAK-SuS) method, previously proposed by the authors, is proposed in order to efficiently estimate small failure probabilities and obtain the posterior distribution. The proposed framework, called qAK-BUS, offers a robust solution for Bayesian inference in engineering systems by smartly balancing model fidelity, prediction variance, and learning efficiency. Three numerical examples and an engineering application that involves the updating of a reinforced concrete bridge are examined for demonstrating and validating the proposed framework.

提出了一种基于主动学习克里格模型的高效贝叶斯更新的多保真度框架。采用结构可靠性（BUS）方法的贝叶斯更新将更新问题作为一个等效概率问题来解决。该方法利用集成代理建模策略，结合了两个多保真度的克里格模型，从而提高了预测能力，同时通过利用不同保真度模型的信息降低了计算成本。一个关键的贡献是多保真贝叶斯优化的集成，以确定最优的总线常数，确保准确的后验转换为可靠性问题。此外，为了有效地估计小故障概率并获得后验分布，提出了一种改进的量化主动学习子集模拟方法（qAK-SuS）。提出的框架，称为qAK-BUS，通过巧妙地平衡模型保真度，预测方差和学习效率，为工程系统中的贝叶斯推理提供了一个强大的解决方案。三个数值实例和一个涉及钢筋混凝土桥梁更新的工程应用进行了检验，以证明和验证所提出的框架。

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引用次数: 0

A higher-order time-domain boundary element formulation based on isogeometric analysis and the convolution quadrature method 基于等几何分析和卷积求积法的高阶时域边界元公式

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-01 Epub Date: 2025-12-22 DOI: 10.1016/j.cma.2025.118609

T. Kramer, B. Marussig, M. Schanz

An isogeometric boundary element method (BEM) is presented to solve scattering problems in an isotropic, homogeneous medium. We consider wave propagation problems governed by the scalar wave equation as in acoustics and the Lamé-Navier equations for elastodynamics considering the theory of linear elasticity. The underlying boundary integral equations imply time-dependent convolution integrals and allow us to determine the sought quantities in the bounded interior or the unbounded exterior after solving for the unknown Cauchy data. In the present work, the time-dependent convolution integrals are approximated by multi-stage Runge-Kutta (RK)-based convolution quadratures that involve steady-state solutions in the Laplace domain. The proposed method discretizes the spatial variable in the framework of isogeometric analysis (IGA), entailing a patchwise smooth spline basis. While previous studies have struggled to develop higher-order discretization methods for evolutionary boundary value problems, the present work introduces a novel combination of multi-stage RK-based convolution quadratures and isogeometric spatial approximation, yielding a fully higher-order method with high convergence rates in both space and time. The implementation scheme follows an element structure defined by the non-empty knot spans in the knot vectors and local, uniform Bernstein polynomials as basis functions. The algorithms to localize the basis functions on the elements are outlined and explained. The solutions of the mixed problems are approximated by the BEM based on a symmetric Galerkin variational formulation and a collocation method. We investigate convergence rates of the approximate solutions in a mixed space-and-time error norm.

提出了一种求解各向同性均匀介质散射问题的等几何边界元法。我们考虑由声学中的标量波动方程和考虑线弹性理论的弹性动力学中的lam - navier方程控制的波传播问题。潜在的边界积分方程意味着时间相关的卷积积分，并允许我们在求解未知的柯西数据后确定有界内部或无界外部的求量。在目前的工作中，时间相关的卷积积分是由多阶段龙格-库塔（RK）为基础的卷积正交近似，涉及稳态解在拉普拉斯域。该方法在等几何分析（IGA）框架中离散化空间变量，得到一个拼接光滑样条基。虽然以前的研究一直在努力开发用于进化边值问题的高阶离散化方法，但本研究引入了一种基于rq的多阶段卷积正交和等几何空间近似的新组合，从而产生了一种在空间和时间上都具有高收敛率的全高阶方法。实现方案遵循由结向量中的非空结跨度和局部一致Bernstein多项式作为基函数定义的单元结构。对基函数在元素上的定位算法进行了概述和说明。基于对称伽辽金变分公式和配点法，用边界元逼近了混合问题的解。研究了混合时空误差范数下近似解的收敛速率。

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引用次数: 0

A Nitsche’s extended Morley-type virtual element method for the biharmonic interface problem 双谐波界面问题的Nitsche扩展morley型虚元法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-01 Epub Date: 2025-12-31 DOI: 10.1016/j.cma.2025.118708

Guodong Ma , Jinru Chen , Feng Wang

In this paper, a Nitsche’s extended Morley-type virtual element method is proposed to discretize the biharmonic interface problem. By modifying the Galerkin projection on the interface element and adding some special terms along the edges of interface elements, we present the discrete approximation problem. The well-posedness of the discrete scheme is proved and the optimal convergence is derived, which is independent of the location of the interface relative to the mesh and the material parameter quotient. Numerical experiments verify the theoretical results.

本文提出了一种Nitsche扩展的morley型虚元方法来离散双谐波界面问题。通过修正界面元上的伽辽金投影，并在界面元边缘添加一些特殊项，给出了离散逼近问题。证明了离散格式的适定性，并导出了与网格界面位置和材料参数商无关的最优收敛性。数值实验验证了理论结果。

引用次数: 0

Robust topology optimization of continuum structures under material uncertainties using multifidelity Monte Carlo 材料不确定性下连续体结构的多保真蒙特卡罗鲁棒拓扑优化

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-01 Epub Date: 2026-01-03 DOI: 10.1016/j.cma.2025.118714

Jaeyub Hyun , Anirban Chaudhuri , Karen E. Willcox , H. Alicia Kim

We present a multifidelity robust topology optimization (mfRTO) method under material uncertainty for computationally efficient robust topology optimization. The standard Monte-Carlo-based approach typically requires numerous evaluations of an expensive high-fidelity physics model at each optimization iteration making its application in topology optimization under uncertainty computationally prohibitive. The mfRTO method uses multifidelity Monte Carlo, which combines many evaluations of multiple cheap-to-evaluate low-fidelity models with few evaluations from an expensive-to-evaluate high-fidelity model, to estimate the robust optimization objective function in each optimization iteration. The density-based topology optimization method is used for the inverse design of continuum structures, and the sensitivities are computed by the adjoint method. The results on various benchmark problems show that the mfRTO method can optimally allocate resources between the different fidelity models for a given budget in each optimization iteration to achieve significant speed-ups compared to the standard Monte Carlo approach while maintaining the same level of accuracy.

提出了一种材料不确定性条件下的多保真鲁棒拓扑优化方法，以实现计算效率高的鲁棒拓扑优化。标准的基于蒙特卡罗的方法通常需要在每次优化迭代中对昂贵的高保真物理模型进行大量评估，这使得其在不确定性条件下的拓扑优化中的应用在计算上令人望而却步。mfRTO方法采用多保真蒙特卡罗方法，结合对多个低保真度模型的多次评估和对高保真度模型的少量评估，在每次优化迭代中估计鲁棒优化目标函数。采用基于密度的拓扑优化方法对连续体结构进行反设计，并采用伴随法计算灵敏度。在各种基准问题上的结果表明，在每次优化迭代中，mfRTO方法可以在给定预算的不同保真度模型之间最优地分配资源，与标准蒙特卡罗方法相比，在保持相同精度水平的情况下，获得显著的加速。

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引用次数: 0

Wasserstein crossover for evolutionary algorithm-based topology optimization 基于进化算法的Wasserstein交叉拓扑优化

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-04-01 Epub Date: 2026-01-03 DOI: 10.1016/j.cma.2025.118713

Taisei Kii , Kentaro Yaji , Hiroshi Teramoto , Kikuo Fujita

Evolutionary algorithms (EAs) are promising approaches for non-differentiable or strongly multimodal topology optimization problems, but they often suffer from the curse of dimensionality, generally leading to low-resolution optimized results. This limitation stems in part from the difficulty of producing effective offspring through traditional crossover operators, which struggle to recombine complex parent design features in a meaningful way. In this paper, we propose a novel crossover operator for topology optimization, termed Wasserstein crossover, and develop a corresponding EA-based optimization framework. Our method leverages a morphing technique based on the Wasserstein distance—a distance metric between probability distributions derived from the optimal transport theory. Its key idea is to treat material distributions as probability distributions and generate offspring as Wasserstein barycenters, enabling smooth and interpretable interpolation between parent designs while preserving their structural features. The proposed framework incorporates Wasserstein crossover into an EA under a multifidelity design scheme, where low-fidelity optimized initial designs evolve through iterations of Wasserstein crossover and selection based on high-fidelity evaluation. We apply the proposed framework to three topology optimization problems: maximum stress minimization in two- and three-dimensional structural mechanics, and turbulent heat transfer in two-dimensional thermofluids. The results demonstrate that candidate solutions evolve iteratively toward high-performance designs through Wasserstein crossover, highlighting its potential as an effective crossover operator and validating the usefulness of the proposed framework for solving intractable topology optimization problems.

进化算法（EAs）是解决不可微或强多模态拓扑优化问题的一种很有前途的方法，但它们经常受到维数诅咒的影响，通常导致低分辨率的优化结果。这种限制部分源于传统的交叉操作难以产生有效的后代，因为传统的交叉操作难以以有意义的方式重组复杂的亲代设计特征。本文提出了一种新的拓扑优化交叉算子Wasserstein交叉算子，并开发了相应的基于ea的优化框架。我们的方法利用了一种基于瓦瑟斯坦距离的变形技术，这是一种从最优输运理论推导出的概率分布之间的距离度量。其关键思想是将材料分布视为概率分布，并产生后代作为Wasserstein质心，在保留其结构特征的同时，在母设计之间实现平滑和可解释的插值。提出的框架将Wasserstein交叉集成到多保真设计方案下的EA中，其中低保真优化的初始设计通过Wasserstein交叉的迭代和基于高保真评估的选择来发展。我们将提出的框架应用于三个拓扑优化问题：二维和三维结构力学中的最大应力最小化问题，以及二维热流体中的湍流传热问题。结果表明，候选解决方案通过Wasserstein交叉迭代地向高性能设计发展，突出了其作为有效交叉算子的潜力，并验证了所提出的框架在解决棘手的拓扑优化问题方面的实用性。

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引用次数: 0