Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"A novel stability-preserving load regulation for coupled thermomechanical buckling optimization of shell structures","authors":"Thanh T. Banh ,&nbsp;Minh-Chien Trinh ,&nbsp;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}

{"title":"Monotone peridynamic neural operator for nonlinear material modeling with conditionally unique solutions","authors":"Jihong Wang ,&nbsp;Xiaochuan Tian ,&nbsp;Zhongqiang Zhang ,&nbsp;Stewart Silling ,&nbsp;Siavash Jafarzadeh ,&nbsp;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}

{"title":"Isogeometric fluid-structure interaction using a mixed continuous/discontinuous Galerkin scheme","authors":"Régis Duvigneau","doi":"10.1016/j.cma.2026.118795","DOIUrl":"10.1016/j.cma.2026.118795","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118795"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146152930","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}

{"title":"On the evolution of damage-induced localization in a deformable-director Cosserat continuum","authors":"Andrea Panteghini ,&nbsp;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}

{"title":"Adaptive beta update scheme in heaviside projection method of topology optimization","authors":"Won Seok Song ,&nbsp;Haram Park ,&nbsp;Jeonghyun Park ,&nbsp;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}

{"title":"A naturally sharpened level-set formulation for incompressible free-surface flows","authors":"Jongmin Rim ,&nbsp;Jinhui Yan ,&nbsp;Yuri Bazilevs","doi":"10.1016/j.cma.2026.118798","DOIUrl":"10.1016/j.cma.2026.118798","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118798"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191977","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}

{"title":"MultiLevel variational MultiScale (ML-VMS) framework for large-scale simulation","authors":"Lei Zhang ,&nbsp;Jiachen Guo ,&nbsp;Shaoqiang Tang ,&nbsp;Thomas J.R. Hughes ,&nbsp;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 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.</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}

{"title":"Variational data-consistent assimilation","authors":"Rylan Spence ,&nbsp;Troy Butler ,&nbsp;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}

{"title":"Interface filtering structural optimization for two-fluid heat exchanger","authors":"Xinyi Yu,&nbsp;Xiaoping Qian","doi":"10.1016/j.cma.2026.118818","DOIUrl":"10.1016/j.cma.2026.118818","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"453 ","pages":"Article 118818"},"PeriodicalIF":7.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191975","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}

{"title":"A continuous topology optimization framework using an explicit binarization constraint","authors":"Tao Xu ,&nbsp;Yi Min Xie ,&nbsp;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}