Computer Methods in Applied Mechanics and Engineering最新文献_第2页

A novel stability-preserving load regulation for coupled thermomechanical buckling optimization of shell structures 一种壳体结构热-力耦合屈曲优化的保稳载荷调节方法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-05-01 Epub Date: 2026-02-14 DOI: 10.1016/j.cma.2026.118809

Thanh T. Banh , Minh-Chien Trinh , Hyungmin Jun

In realistic operating environments, thermal and mechanical fields interact in a highly complex manner, generating coupled responses that exert a profound influence on structural stability. Despite their practical importance, most existing topology optimization studies addressing stability have modeled thermal effects as uniform or independent, thereby overlooking the intrinsic coupling between temperature variation and mechanical deformation. Moreover, for decoupled buckling problems, a critical limitation that has received insufficient attention in prior research is the occurrence of complex eigenvalues resulting from the loss of spectral consistency. To overcome these issues, the present study introduces a comprehensive multimaterial topology optimization framework that directly incorporates coupled thermomechanical behavior into buckling design, wherein the temperature field is treated as a design-dependent load to fully capture its interaction with the evolving structural layout. In parallel, a novel stability-preserving load regulation (SPLR) scheme is proposed for decoupled buckling analysis to address the long-standing problem of numerical instability in conventional thermomechanical buckling formulations. The SPLR procedure maintains the positive definiteness of the baseline stiffness matrix and suppresses the emergence of complex-valued eigenmodes, ensuring reliable and physically meaningful buckling evaluation throughout the optimization process. Furthermore, the refined adaptive continuation method (RACM) is extended to coupled thermomechanical and multimaterial settings to enhance convergence and numerical robustness. The overall framework is subsequently formulated for curved shell structures using the mixed interpolation of tensorial components (MITC4) element, enabling the effective elimination of shear-locking effects, while a refined stabilization strategy is introduced to suppress artificial buckling modes frequently encountered in coupled stability analyses. Analytical sensitivities are derived through adjoint formulations employing auxiliary vectors, and the optimization problems are solved using the method of moving asymptotes (MMA). Numerical studies confirm the accuracy, robustness, and broad applicability of the proposed methodology under a wide range of complex coupled thermomechanical loading.

在实际操作环境中，热场和机械场以高度复杂的方式相互作用，产生对结构稳定性产生深远影响的耦合响应。尽管具有实际意义，但大多数现有的解决稳定性的拓扑优化研究都将热效应建模为均匀或独立的，从而忽略了温度变化与机械变形之间的内在耦合。此外，对于解耦屈曲问题，一个在之前的研究中没有得到足够重视的关键限制是由于谱一致性的丧失而导致的复特征值的出现。为了克服这些问题，本研究引入了一种综合的多材料拓扑优化框架，该框架直接将耦合热力学行为纳入屈曲设计中，其中温度场被视为设计相关载荷，以充分捕捉其与不断变化的结构布局的相互作用。同时，提出了一种新的保持稳定的载荷调节（SPLR）方案，用于解耦屈曲分析，以解决传统热机械屈曲公式中长期存在的数值不稳定性问题。SPLR程序保持了基线刚度矩阵的正确定性，抑制了复杂值特征模态的出现，确保了在整个优化过程中可靠且具有物理意义的屈曲评估。此外，将改进的自适应延拓方法（RACM）推广到热力学和多材料耦合的情况下，以提高收敛性和数值鲁棒性。随后，利用张拉分量混合插值（MITC4）单元制定了弯曲壳结构的总体框架，从而有效地消除了剪切锁定效应，同时引入了一种精细的稳定策略，以抑制耦合稳定性分析中经常遇到的人为屈曲模式。利用辅助向量的伴随公式推导了解析灵敏度，并利用移动渐近线法求解了优化问题。数值研究证实了该方法在大范围复杂耦合热-机械载荷下的准确性、鲁棒性和广泛适用性。

{"title":"A novel stability-preserving load regulation for coupled thermomechanical buckling optimization of shell structures","authors":"Thanh T. Banh , Minh-Chien Trinh , Hyungmin Jun","doi":"10.1016/j.cma.2026.118809","DOIUrl":"10.1016/j.cma.2026.118809","url":null,"abstract":"<div><div>In realistic operating environments, thermal and mechanical fields interact in a highly complex manner, generating coupled responses that exert a profound influence on structural stability. Despite their practical importance, most existing topology optimization studies addressing stability have modeled thermal effects as uniform or independent, thereby overlooking the intrinsic coupling between temperature variation and mechanical deformation. Moreover, for decoupled buckling problems, a critical limitation that has received insufficient attention in prior research is the occurrence of complex eigenvalues resulting from the loss of spectral consistency. To overcome these issues, the present study introduces a comprehensive multimaterial topology optimization framework that directly incorporates coupled thermomechanical behavior into buckling design, wherein the temperature field is treated as a design-dependent load to fully capture its interaction with the evolving structural layout. In parallel, a novel stability-preserving load regulation (SPLR) scheme is proposed for decoupled buckling analysis to address the long-standing problem of numerical instability in conventional thermomechanical buckling formulations. The SPLR procedure maintains the positive definiteness of the baseline stiffness matrix and suppresses the emergence of complex-valued eigenmodes, ensuring reliable and physically meaningful buckling evaluation throughout the optimization process. Furthermore, the refined adaptive continuation method (RACM) is extended to coupled thermomechanical and multimaterial settings to enhance convergence and numerical robustness. The overall framework is subsequently formulated for curved shell structures using the mixed interpolation of tensorial components (MITC4) element, enabling the effective elimination of shear-locking effects, while a refined stabilization strategy is introduced to suppress artificial buckling modes frequently encountered in coupled stability analyses. Analytical sensitivities are derived through adjoint formulations employing auxiliary vectors, and the optimization problems are solved using the method of moving asymptotes (MMA). Numerical studies confirm the accuracy, robustness, and broad applicability of the proposed methodology under a wide range of complex coupled thermomechanical loading.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118809"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146192982","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

Monotone peridynamic neural operator for nonlinear material modeling with conditionally unique solutions 具有条件唯一解的非线性材料建模的单调周动力神经算子

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-05-01 Epub Date: 2026-02-11 DOI: 10.1016/j.cma.2026.118792

Jihong Wang , Xiaochuan Tian , Zhongqiang Zhang , Stewart Silling , Siavash Jafarzadeh , Yue Yu

Nonlocal continuum mechanics models, including peridynamics, have emerged as powerful tools for describing the mechanical responses of complex nonlinear materials. In typical applications of peridynamics, the functional form of the material model is prescribed in advance, based on the analyst’s preferences and insight, creating the need for time-consuming calibration and validation for the particular material at hand. Although data-driven methods were proposed to streamline the modeling process, the well-posedness of these learned peridynamic models is generally not guaranteed, which creates the possibility of non-physical solutions in downstream simulation tasks.

In this study, we address this challenge of developing an accurate data-driven model with known uniqueness properties. To do this, we introduce the monotone peridynamic neural operator (MPNO), a novel approach for learning a data-driven nonlocal constitutive model with guaranteed well-posedness for certain classes of problems. Our approach learns a nonlocal kernel together with a nonlinear constitutive relation, while ensuring solution uniqueness through a monotone gradient network. This architectural constraint on the gradient induces the convexity of the learnt energy density function. This guarantees the uniqueness of solutions in the small deformation regime. To validate our approach, we evaluate MPNO’s performance on both synthetic and real-world datasets. On synthetic datasets generated with a manufactured kernel and constitutive relation, we show, both theoretically and numerically, that the learnt model converges to the ground-truth as the measurement grid size decreases. Additionally, our MPNO exhibits superior generalization capabilities in comparison with conventional neural networks. It yields smaller displacement solution errors in down-stream tasks with unseen loadings that are outside of the distribution of training samples. Finally, we showcase the practical utility of our approach through applications in learning a homogenized model from molecular dynamics data, highlighting the model’s expressivity and physical interpretability in real-world scenarios.

包括周动力学在内的非局部连续介质力学模型已经成为描述复杂非线性材料力学响应的有力工具。在周动力学的典型应用中，材料模型的功能形式是根据分析人员的偏好和见解预先规定的，这就需要对手头的特定材料进行耗时的校准和验证。虽然提出了数据驱动的方法来简化建模过程，但通常不能保证这些学习到的周动力学模型的适定性，这就为下游仿真任务中的非物理解创造了可能性。在本研究中，我们解决了开发具有已知唯一性属性的准确数据驱动模型的挑战。为了做到这一点，我们引入了单调周期动态神经算子（MPNO），这是一种学习数据驱动的非局部本构模型的新方法，对于某些类别的问题具有保证的适定性。该方法学习非局部核和非线性本构关系，同时通过单调梯度网络保证解的唯一性。梯度上的结构约束导致了学习到的能量密度函数的凸性。这保证了小变形区解的唯一性。为了验证我们的方法，我们在合成数据集和真实数据集上评估了MPNO的性能。在使用人造核和本构关系生成的合成数据集上，我们从理论上和数值上表明，随着测量网格大小的减小，学习模型收敛于基本事实。此外，与传统神经网络相比，我们的MPNO表现出优越的泛化能力。在训练样本分布之外的未见负载的下游任务中，它产生更小的位移解误差。最后，我们通过从分子动力学数据中学习均匀化模型的应用，展示了我们方法的实际效用，突出了模型在现实世界场景中的表现力和物理可解释性。

{"title":"Monotone peridynamic neural operator for nonlinear material modeling with conditionally unique solutions","authors":"Jihong Wang , Xiaochuan Tian , Zhongqiang Zhang , Stewart Silling , Siavash Jafarzadeh , Yue Yu","doi":"10.1016/j.cma.2026.118792","DOIUrl":"10.1016/j.cma.2026.118792","url":null,"abstract":"<div><div>Nonlocal continuum mechanics models, including peridynamics, have emerged as powerful tools for describing the mechanical responses of complex nonlinear materials. In typical applications of peridynamics, the functional form of the material model is prescribed in advance, based on the analyst’s preferences and insight, creating the need for time-consuming calibration and validation for the particular material at hand. Although data-driven methods were proposed to streamline the modeling process, the well-posedness of these learned peridynamic models is generally not guaranteed, which creates the possibility of non-physical solutions in downstream simulation tasks.</div><div>In this study, we address this challenge of developing an accurate data-driven model with known uniqueness properties. To do this, we introduce the monotone peridynamic neural operator (MPNO), a novel approach for learning a data-driven nonlocal constitutive model with guaranteed well-posedness for certain classes of problems. Our approach learns a nonlocal kernel together with a nonlinear constitutive relation, while ensuring solution uniqueness through a monotone gradient network. This architectural constraint on the gradient induces the convexity of the learnt energy density function. This guarantees the uniqueness of solutions in the small deformation regime. To validate our approach, we evaluate MPNO’s performance on both synthetic and real-world datasets. On synthetic datasets generated with a manufactured kernel and constitutive relation, we show, both theoretically and numerically, that the learnt model converges to the ground-truth as the measurement grid size decreases. Additionally, our MPNO exhibits superior generalization capabilities in comparison with conventional neural networks. It yields smaller displacement solution errors in down-stream tasks with unseen loadings that are outside of the distribution of training samples. Finally, we showcase the practical utility of our approach through applications in learning a homogenized model from molecular dynamics data, highlighting the model’s expressivity and physical interpretability in real-world scenarios.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118792"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146152928","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

Isogeometric fluid-structure interaction using a mixed continuous/discontinuous Galerkin scheme 使用混合连续/不连续伽辽金格式的等几何流固相互作用

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-05-01 Epub Date: 2026-02-11 DOI: 10.1016/j.cma.2026.118795

Régis Duvigneau

A mixed continuous / discontinuous Galerkin scheme is introduced for the simulation of fluid-structure interaction problems in an isogeometric analysis framework. The properties of Non-Uniform Rational B-Spline basis functions are leveraged to enable an exact transfer of the structural displacement to the fluid domain, while using different discretizations and refinements on the two sides of the coupling interface. The proposed approach is applied to the simulation of a compressible flow around an elastic wing membrane and to a classical fluid-structure benchmark involving the flow around a cylinder equipped with a hyper-elastic bar. For both cases, the results obtained are compared to those found in the literature to assess the accuracy of the proposed method.

采用连续/不连续混合Galerkin格式在等几何分析框架下模拟流固耦合问题。利用非均匀有理b样条基函数的性质，在耦合界面两侧采用不同的离散化和细化方法，使结构位移精确地传递到流体域。将该方法应用于弹性翼膜周围可压缩流动的模拟和一个经典的流体结构基准，该基准涉及装有超弹性杆的圆柱体周围的流动。对于这两种情况，所获得的结果将与文献中发现的结果进行比较，以评估所提出方法的准确性。

引用次数: 0

On the evolution of damage-induced localization in a deformable-director Cosserat continuum 变形导向coserat连续体中损伤局部化的演化

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-05-01 Epub Date: 2026-02-14 DOI: 10.1016/j.cma.2026.118797

Andrea Panteghini , M.B. Rubin

This paper analyzes a small-deformation, size-dependent Cosserat continuum, which in addition to the usual kinematics and balance laws admits a deformable triad of director vectors at each material point. Deformations of these directors are determined by additional director-momentum balance laws. The constitutive equations enrich elastic response with rate-independent damage that reduces the integrity of the effective resistance to distortional deformations of the material in the macro-continuum only, while leaving the stiffnesses associated with the deformable director triad unchanged. A finite element formulation for the resulting field equations is developed.

Two benchmark problems (biaxial isochoric loading and a notched plate) are analyzed to assess mesh objectivity and evolution of localization patterns. The results show that, for the examined problems, the Cosserat model with a deformable director triad predicts size-dependent yet mesh-independent shear-band initiation, width, and progression, with band thickness governed by the internal length ℓ rather than by the mesh. In contrast, the classical Cosserat baseline with a rigid director triad retains mesh sensitivity once multiple bands nucleate and evolve.

Overall, the benchmark problems examined indicate that the deformable Cosserat model has strong potential to be interpreted as a physically motivated continuum description of localized regions, rather than solely as a numerical regularization device.

本文分析了一个小变形，尺寸相关的Cosserat连续体，除了通常的运动学和平衡定律外，它还允许在每个质点处有可变形的三方向向量。这些董事的变形是由额外的董事-动量平衡定律决定的。本构方程丰富了弹性响应与速率无关的损伤，仅在宏观连续体中降低了材料对扭曲变形的有效阻力的完整性，同时保持与变形指示三角相关的刚度不变。给出了计算结果场方程的有限元公式。分析了两个基准问题（双轴等线加载和缺口板），以评估网格的客观性和局部化模式的演变。结果表明，对于所研究的问题，具有可变形方向的coserat模型预测剪切带的起始、宽度和进展与尺寸无关，而与网格无关，剪切带的厚度由内部长度而不是网格控制。相比之下，经典的coserat基线具有刚性的定向三位一体，一旦多个波段成核并演变，则保留网格灵敏度。总的来说，测试的基准问题表明，可变形的Cosserat模型具有很强的潜力，可以被解释为局部区域的物理驱动连续体描述，而不仅仅是一个数值正则化装置。

{"title":"On the evolution of damage-induced localization in a deformable-director Cosserat continuum","authors":"Andrea Panteghini , M.B. Rubin","doi":"10.1016/j.cma.2026.118797","DOIUrl":"10.1016/j.cma.2026.118797","url":null,"abstract":"<div><div>This paper analyzes a small-deformation, size-dependent Cosserat continuum, which in addition to the usual kinematics and balance laws admits a deformable triad of director vectors at each material point. Deformations of these directors are determined by additional director-momentum balance laws. The constitutive equations enrich elastic response with rate-independent damage that reduces the integrity of the effective resistance to distortional deformations of the material in the macro-continuum only, while leaving the stiffnesses associated with the deformable director triad unchanged. A finite element formulation for the resulting field equations is developed.</div><div>Two benchmark problems (biaxial isochoric loading and a notched plate) are analyzed to assess mesh objectivity and evolution of localization patterns. The results show that, for the examined problems, the Cosserat model with a deformable director triad predicts size-dependent yet mesh-independent shear-band initiation, width, and progression, with band thickness governed by the internal length ℓ rather than by the mesh. In contrast, the classical Cosserat baseline with a rigid director triad retains mesh sensitivity once multiple bands nucleate and evolve.</div><div>Overall, the benchmark problems examined indicate that the deformable Cosserat model has strong potential to be interpreted as a physically motivated continuum description of localized regions, rather than solely as a numerical regularization device.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118797"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191972","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

Adaptive beta update scheme in heaviside projection method of topology optimization 拓扑优化重面投影法中的自适应beta更新方案

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-05-01 Epub Date: 2026-02-11 DOI: 10.1016/j.cma.2026.118805

Won Seok Song , Haram Park , Jeonghyun Park , Seungjae Min

The Heaviside projection method is widely used to obtain binary solutions in topology optimization, and the projection steepness parameter beta is typically increased by doubling at fixed update intervals. However, such interval-based schemes often lead to excessive iterations and numerical oscillations during the optimization process. In this study, we propose an adaptive beta update strategy that extends the role of the gray-level indicator, a measure of non-discreteness, to an adaptive parameter governing the progression of beta throughout the optimization. The proposed method consists of two phases: a stability-based Phase 1 that guides a gradual reduction of intermediate densities, and a prediction-based Phase 2 that adjusts beta when beta-update congestion is detected to ensure continuous and stable projection progression. Numerical experiments across various physical problems and parameter settings demonstrate that the proposed approach significantly reduces the number of iterations required to reach convergence while maintaining or improving the final objective performance. These results indicate that the adaptive beta update strategy can serve as a consistent and effective beta update framework for the Heaviside projection in topology optimization.

Heaviside投影法在拓扑优化中被广泛应用于二进制解的求解，其投影陡峭度参数β通常通过在固定的更新间隔加倍来增加。然而，这种基于区间的方案在优化过程中往往会导致过多的迭代和数值振荡。在本研究中，我们提出了一种自适应beta更新策略，该策略将灰度指标（非离散性度量）的作用扩展为一个自适应参数，该参数在整个优化过程中控制beta的进展。提出的方法包括两个阶段：基于稳定性的第一阶段，指导中间密度的逐渐减少；基于预测的第二阶段，当检测到beta更新拥塞时调整beta，以确保持续稳定的投影进度。针对各种物理问题和参数设置的数值实验表明，该方法显著减少了在保持或提高最终目标性能的同时达到收敛所需的迭代次数。这些结果表明，自适应beta更新策略可以作为拓扑优化中Heaviside投影一致有效的beta更新框架。

{"title":"Adaptive beta update scheme in heaviside projection method of topology optimization","authors":"Won Seok Song , Haram Park , Jeonghyun Park , Seungjae Min","doi":"10.1016/j.cma.2026.118805","DOIUrl":"10.1016/j.cma.2026.118805","url":null,"abstract":"<div><div>The Heaviside projection method is widely used to obtain binary solutions in topology optimization, and the projection steepness parameter beta is typically increased by doubling at fixed update intervals. However, such interval-based schemes often lead to excessive iterations and numerical oscillations during the optimization process. In this study, we propose an adaptive beta update strategy that extends the role of the gray-level indicator, a measure of non-discreteness, to an adaptive parameter governing the progression of beta throughout the optimization. The proposed method consists of two phases: a stability-based Phase 1 that guides a gradual reduction of intermediate densities, and a prediction-based Phase 2 that adjusts beta when beta-update congestion is detected to ensure continuous and stable projection progression. Numerical experiments across various physical problems and parameter settings demonstrate that the proposed approach significantly reduces the number of iterations required to reach convergence while maintaining or improving the final objective performance. These results indicate that the adaptive beta update strategy can serve as a consistent and effective beta update framework for the Heaviside projection in topology optimization.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118805"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146152925","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

A naturally sharpened level-set formulation for incompressible free-surface flows 不可压缩自由表面流的自然锐化水平集公式

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-05-01 Epub Date: 2026-02-13 DOI: 10.1016/j.cma.2026.118798

Jongmin Rim , Jinhui Yan , Yuri Bazilevs

The level set method is widely employed in two-phase flow simulations due to its robustness in handling complex interface topological changes. However, it suffers from two main limitations. First, the method is not inherently mass conservative. Second, the signed-distance property of the level set field can deteriorate under strong convection, particularly in high Reynolds-number flows. Consequently, conventional level set methods often require auxiliary procedures such as sharpening (or re-distancing) and mass correction, which rely on and are sensitive to user-defined parameters and also increase implementation complexity and computational cost. Here, we present a naturally sharpened level-set formulation for incompressible air-water flows that is mass conservative and eliminates the need for these additional algorithmic steps. The resulting free-surface flow modeling and simulation framework is more efficient and robust as demonstrated through several challenging numerical test cases.

水平集方法在处理复杂界面拓扑变化方面具有鲁棒性，在两相流模拟中得到了广泛的应用。然而，它有两个主要的限制。首先，该方法本身并不是质量保守的。其次，在强对流条件下，特别是在高雷诺数流动条件下，水平集场的带符号距离性质会变差。因此，传统的水平集方法通常需要辅助过程，如锐化（或重新距离）和质量校正，这些过程依赖于用户定义的参数，并且对用户定义的参数很敏感，也增加了实现的复杂性和计算成本。在这里，我们提出了一个自然锐化的不可压缩空气-水流动的水平集公式，它是质量保守的，并且消除了这些额外算法步骤的需要。通过几个具有挑战性的数值测试案例证明，由此产生的自由表面流建模和仿真框架更加高效和鲁棒。

引用次数: 0

MultiLevel variational MultiScale (ML-VMS) framework for large-scale simulation 大规模模拟的多级变分多尺度（ML-VMS）框架

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-05-01 Epub Date: 2026-02-13 DOI: 10.1016/j.cma.2026.118807

Lei Zhang , Jiachen Guo , Shaoqiang Tang , Thomas J.R. Hughes , Wing Kam Liu

In this paper, we propose the MultiLevel Variational MultiScale (ML-VMS) method, a novel approach that seamlessly integrates a multilevel mesh strategy into the Variational Multiscale (VMS) framework. A key feature of the ML-VMS method is the use of the Convolution Hierarchical Deep-learning Neural Network (C-HiDeNN) as the approximation basis, which enables fine-grained control over the trade-off between computational efficiency and interpolation accuracy. The framework employs a coarse mesh throughout the domain, with localized fine meshes placed only in subdomains of high interest, such as those surrounding a source. Solutions at different resolutions are robustly coupled through the variational weak form and interface conditions. Crucially, our method departs from existing VMS-based multilevel approaches by approximating the fine-scale solution directly using the fine-scale basis functions. Compared to existing multilevel methods, ML-VMS (1) can couple an arbitrary number of mesh levels across different scales using variational multiscale framework; (2) allows approximating functions with arbitrary orders with linear finite element mesh due to the C-HiDeNN basis; (3) is supported by a rigorous theoretical error analysis; (4) features several tunable hyperparameters (e.g., order p, patch size s) with a systematic guide for their selection. We first show the theoretical error estimates of ML-VMS. Then through numerical examples, we demonstrate that ML-VMS with the C-HiDeNN takes less computational time than the FEM basis given comparable accuracy. Furthermore, we incorporate a space-time reduced-order model (ROM) based on C-HiDeNN-Tensor Decomposition (TD) into the ML-VMS framework. For a large-scale single-track laser powder bed fusion (LPBF) transient heat transfer problem that is equivalent to a full-order finite element model with 10¹⁰ spatial degrees of freedom (DoFs), our three-level ML-VMS C-HiDeNN-TD demonstrates a promising speedup of approximately 5,000x speedup on a single CPU over a single-level linear FEM-TD ROM. We further validate the generality of ML-VMS through a 3D elasticity case study. Compared to the linear FEM-TD ROM, our approach achieves theoretical convergence rates and provides significant speedups with higher precision.

本文提出了多层次变分多尺度（ML-VMS）方法，这是一种将多层次网格策略无缝集成到变分多尺度（VMS）框架中的新方法。ML-VMS方法的一个关键特征是使用卷积层次深度学习神经网络（C-HiDeNN）作为近似基础，它可以对计算效率和插值精度之间的权衡进行细粒度控制。该框架在整个域中使用粗网格，而局部细网格仅放置在高兴趣的子域中，例如源周围的子域。不同分辨率下的解通过变分弱形式和界面条件进行鲁棒耦合。关键是，我们的方法与现有的基于vms的多层方法不同，它直接使用精细尺度基函数逼近精细尺度解。与现有的多尺度方法相比，ML-VMS(1)使用变分多尺度框架，可以在不同尺度上耦合任意数量的网格层；(2)由于C-HiDeNN基，允许用线性有限元网格逼近任意阶函数；(3)有严格的理论误差分析支持；(4)具有几个可调的超参数（例如，顺序p，补丁大小s），并具有系统的选择指南。我们首先展示了ML-VMS的理论误差估计。通过数值算例表明，在精度相当的情况下，基于C-HiDeNN的ML-VMS比基于FEM的计算时间更少。此外，我们将基于c - hidenn张量分解（TD）的时空降阶模型（ROM）整合到ML-VMS框架中。对于相当于1010空间自由度（dfs）的全阶有限元模型的大规模单轨道激光粉末床熔合（LPBF）瞬态传热问题，我们的三级ML-VMS C-HiDeNN-TD在单级线性FEM-TD ROM上的单个CPU上显示了大约5,000倍的加速。我们通过三维弹性案例研究进一步验证了ML-VMS的通用性。与线性FEM-TD ROM相比，我们的方法实现了理论收敛率，并提供了更高精度的显着加速。

{"title":"MultiLevel variational MultiScale (ML-VMS) framework for large-scale simulation","authors":"Lei Zhang , Jiachen Guo , Shaoqiang Tang , Thomas J.R. Hughes , Wing Kam Liu","doi":"10.1016/j.cma.2026.118807","DOIUrl":"10.1016/j.cma.2026.118807","url":null,"abstract":"<div><div>In this paper, we propose the MultiLevel Variational MultiScale (ML-VMS) method, a novel approach that seamlessly integrates a multilevel mesh strategy into the Variational Multiscale (VMS) framework. A key feature of the ML-VMS method is the use of the Convolution Hierarchical Deep-learning Neural Network (C-HiDeNN) as the approximation basis, which enables fine-grained control over the trade-off between computational efficiency and interpolation accuracy. The framework employs a coarse mesh throughout the domain, with localized fine meshes placed only in subdomains of high interest, such as those surrounding a source. Solutions at different resolutions are robustly coupled through the variational weak form and interface conditions. Crucially, our method departs from existing VMS-based multilevel approaches by approximating the fine-scale solution directly using the fine-scale basis functions. Compared to existing multilevel methods, ML-VMS (1) can couple an arbitrary number of mesh levels across different scales using variational multiscale framework; (2) allows approximating functions with arbitrary orders with linear finite element mesh due to the C-HiDeNN basis; (3) is supported by a rigorous theoretical error analysis; (4) features several tunable hyperparameters (e.g., order <em>p</em>, patch size <em>s</em>) with a systematic guide for their selection. We first show the theoretical error estimates of ML-VMS. Then through numerical examples, we demonstrate that ML-VMS with the C-HiDeNN takes less computational time than the FEM basis given comparable accuracy. Furthermore, we incorporate a space-time reduced-order model (ROM) based on C-HiDeNN-Tensor Decomposition (TD) into the ML-VMS framework. For a large-scale single-track laser powder bed fusion (LPBF) transient heat transfer problem that is equivalent to a full-order finite element model with 10<sup>10</sup> spatial degrees of freedom (DoFs), our three-level ML-VMS C-HiDeNN-TD demonstrates a promising speedup of approximately 5,000x speedup on a single CPU over a single-level linear FEM-TD ROM. We further validate the generality of ML-VMS through a 3D elasticity case study. Compared to the linear FEM-TD ROM, our approach achieves theoretical convergence rates and provides significant speedups with higher precision.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118807"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191974","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

Variational data-consistent assimilation 变分数据一致同化

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-05-01 Epub Date: 2026-02-13 DOI: 10.1016/j.cma.2026.118804

Rylan Spence , Troy Butler , Clint Dawson

This work introduces a new class of four-dimensional variational data assimilation (4D-Var) methods grounded in data-consistent inversion (DCI) theory. The methods extend classical 4D-Var by incorporating a predictability-aware regularization term. The first method formulated is referred to as Data-Consistent 4D-Var (DC-4DVar), which is then enhanced using a Weighted Mean Error (WME) quantity-of-interest map to construct the DC-WME 4D-Var method. While the DC and DC-WME cost functions both involve a predictability-aware regularization term, the DC-WME function includes a modification to the model-data misfit, thereby improving estimation accuracy, robustness, and theoretical consistency in nonlinear and partially observed dynamical systems. Proofs are provided that establish the existence and uniqueness of the minimizer and analyze how a predictability assumption that is common within the DCI framework helps to promote solution stability. Numerical experiments are presented on benchmark dynamical systems (Lorenz-63 and Lorenz-96) as well as for the shallow water equations (SWE). In the benchmark dynamical systems, the DC-WME 4D-Var formulation is shown to consistently outperform standard 4D-Var in reducing both error and bias while maintaining robustness under high observation noise and short assimilation windows. Despite introducing modest computational overhead, DC-WME 4D-Var delivers improvements in estimation performance and forecast skill, demonstrating its potential practicality and scalability for high-dimensional data assimilation problems.

本文介绍了一种基于数据一致性反演（DCI）理论的新型四维变分数据同化（4D-Var）方法。该方法通过加入可预测性感知正则化项扩展了经典的4D-Var。制定的第一种方法被称为数据一致性4D-Var (DC-4DVar)，然后使用加权平均误差（WME）兴趣量图对其进行增强，以构建DC-WME 4D-Var方法。虽然DC和DC- wme代价函数都涉及可预测性感知的正则化项，但DC- wme函数包括对模型数据不拟合的修正，从而提高了非线性和部分观测动力系统的估计精度、鲁棒性和理论一致性。提供了证明，建立了最小化的存在性和唯一性，并分析了DCI框架中常见的可预测性假设如何有助于促进解决方案的稳定性。给出了Lorenz-63和Lorenz-96两种基准动力系统以及浅水方程（SWE）的数值实验。在基准动力系统中，DC-WME 4D-Var公式在降低误差和偏差方面始终优于标准4D-Var，同时在高观测噪声和短同化窗口下保持鲁棒性。尽管引入了适度的计算开销，DC-WME 4D-Var在估计性能和预测技能方面提供了改进，展示了其在高维数据同化问题上的潜在实用性和可扩展性。

{"title":"Variational data-consistent assimilation","authors":"Rylan Spence , Troy Butler , Clint Dawson","doi":"10.1016/j.cma.2026.118804","DOIUrl":"10.1016/j.cma.2026.118804","url":null,"abstract":"<div><div>This work introduces a new class of four-dimensional variational data assimilation (4D-Var) methods grounded in data-consistent inversion (DCI) theory. The methods extend classical 4D-Var by incorporating a predictability-aware regularization term. The first method formulated is referred to as Data-Consistent 4D-Var (DC-4DVar), which is then enhanced using a Weighted Mean Error (WME) quantity-of-interest map to construct the DC-WME 4D-Var method. While the DC and DC-WME cost functions both involve a predictability-aware regularization term, the DC-WME function includes a modification to the model-data misfit, thereby improving estimation accuracy, robustness, and theoretical consistency in nonlinear and partially observed dynamical systems. Proofs are provided that establish the existence and uniqueness of the minimizer and analyze how a predictability assumption that is common within the DCI framework helps to promote solution stability. Numerical experiments are presented on benchmark dynamical systems (Lorenz-63 and Lorenz-96) as well as for the shallow water equations (SWE). In the benchmark dynamical systems, the DC-WME 4D-Var formulation is shown to consistently outperform standard 4D-Var in reducing both error and bias while maintaining robustness under high observation noise and short assimilation windows. Despite introducing modest computational overhead, DC-WME 4D-Var delivers improvements in estimation performance and forecast skill, demonstrating its potential practicality and scalability for high-dimensional data assimilation problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118804"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191976","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

Interface filtering structural optimization for two-fluid heat exchanger 双流体换热器界面过滤结构优化

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2026-05-01 Epub Date: 2026-02-14 DOI: 10.1016/j.cma.2026.118818

Xinyi Yu, Xiaoping Qian

This work introduces an interface filtering structural optimization (IFSO) method featuring parameter-free interface movement, which combines a nonuniform filter radius with a proposed dual-filtering strategy for two-fluid counter-flow heat exchangers (HXs). The approach supports seeding from different initial geometries and maintains their sharp material interfaces, enforces prescribed minimum thickness through dual filtering, and employs an interpolation scheme to represent the two fluids and the solid within one stepped density field. The method is demonstrated on a conventional straight-channel HX and high-performance Gyroid-based HXs. Post-optimization simulations confirm the improvements, including  ∼ 50.96% higher heat transfer rate in straight pipes and over 123% enhancement in power density for Gyroid HXs, attributed to increased interfacial curvature and intensified mixing effects. These results establish the dual-filtering IFSO as a viable computational method for HX optimization.

本文介绍了一种基于无参数界面运动的界面过滤结构优化（IFSO）方法，该方法将非均匀过滤半径与提出的双过滤策略相结合，用于双流体逆流式换热器（HXs）。该方法支持不同初始几何形状的播种，并保持其锋利的材料界面，通过双重滤波强制规定最小厚度，并采用插值方案在一个阶梯密度场内表示两种流体和固体。该方法在传统直通道HX和高性能陀螺仪HX上进行了验证。优化后的模拟证实了这些改进，包括直管传热率 ~ 提高了50.96%，Gyroid HXs的功率密度提高了123%以上，这归因于界面曲率的增加和混合效应的增强。这些结果表明，双滤波IFSO是一种可行的HX优化计算方法。

引用次数: 0

A continuous topology optimization framework using an explicit binarization constraint 使用显式二值化约束的连续拓扑优化框架

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: 2026-01-07 DOI: 10.1016/j.cma.2025.118724

Tao Xu , Yi Min Xie , Jie Yang

Achieving crisp, manufacturable black-and-white (0/1) designs from element-based topology optimization methods is a critical and long-standing challenge. This paper introduces a novel continuous framework, termed Explicit Binarization Topology Optimization (EBTO), that addresses this challenge by treating binarization not as an implicit byproduct but as a direct mathematical constraint. The proposed method achieves this by introducing an explicit constraint formulated using a tunable function that directly measures and controls the global “greyness” of the design. This approach fundamentally decouples the binarization mechanism from the material model, allowing for the use of a linear material interpolation scheme that simplifies sensitivity analysis and provides a clearer physical interpretation for optimization problems. The versatility and robustness of the EBTO framework are demonstrated through a comprehensive set of 2D and 3D numerical examples, including compliance minimization, compliant mechanism design, and challenging stress-based optimization problems. The results consistently show that the proposed method generates clear 0/1 solutions with excellent structural performance, demonstrating superior results in benchmark cases compared to established methods. Furthermore, a set of guiding principles for formulating such explicit constraints is established, providing a foundation for future advancements in this class of topology optimization methods.

通过基于元素的拓扑优化方法实现清晰、可制造的黑白（0/1）设计是一个关键且长期存在的挑战。本文介绍了一种新的连续框架，称为显式二值化拓扑优化（EBTO），它通过将二值化视为直接的数学约束而不是隐含的副产品来解决这一挑战。提出的方法通过引入显式约束来实现这一目标，该约束使用可调函数来直接测量和控制设计的全局“灰色度”。这种方法从根本上将二值化机制与材料模型解耦，允许使用线性材料插值方案，简化灵敏度分析，并为优化问题提供更清晰的物理解释。EBTO框架的多功能性和鲁棒性通过一组全面的2D和3D数值示例得到了证明，包括合规最小化、合规机构设计和具有挑战性的基于应力的优化问题。结果一致表明，本文方法生成的0/1解清晰，结构性能优异，在基准案例中效果优于已有方法。此外，还建立了一套用于制定此类显式约束的指导原则，为该类拓扑优化方法的未来发展奠定了基础。

{"title":"A continuous topology optimization framework using an explicit binarization constraint","authors":"Tao Xu , Yi Min Xie , Jie Yang","doi":"10.1016/j.cma.2025.118724","DOIUrl":"10.1016/j.cma.2025.118724","url":null,"abstract":"<div><div>Achieving crisp, manufacturable black-and-white (0/1) designs from element-based topology optimization methods is a critical and long-standing challenge. This paper introduces a novel continuous framework, termed Explicit Binarization Topology Optimization (EBTO), that addresses this challenge by treating binarization not as an implicit byproduct but as a direct mathematical constraint. The proposed method achieves this by introducing an explicit constraint formulated using a tunable function that directly measures and controls the global “greyness” of the design. This approach fundamentally decouples the binarization mechanism from the material model, allowing for the use of a linear material interpolation scheme that simplifies sensitivity analysis and provides a clearer physical interpretation for optimization problems. The versatility and robustness of the EBTO framework are demonstrated through a comprehensive set of 2D and 3D numerical examples, including compliance minimization, compliant mechanism design, and challenging stress-based optimization problems. The results consistently show that the proposed method generates clear 0/1 solutions with excellent structural performance, demonstrating superior results in benchmark cases compared to established methods. Furthermore, a set of guiding principles for formulating such explicit constraints is established, providing a foundation for future advancements in this class of topology optimization methods.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118724"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940918","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