Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Autoregressive multiplier bootstrap for in-situ error estimation and quality monitoring of finite time averages in turbulent flow simulations","authors":"Christos Papagiannis ,&nbsp;Guillaume Balarac ,&nbsp;Pietro M. Congedo ,&nbsp;Olivier P. Le Maître","doi":"10.1016/j.cma.2025.118664","DOIUrl":"10.1016/j.cma.2025.118664","url":null,"abstract":"<div><div>In Computational Fluid Dynamics (CFD), and particularly within Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), the computational cost is largely dictated by the effort required to obtain statistically converged quantities such as time-averaged fields and higher-order moments. Despite the importance of accurately quantifying statistical uncertainty in unsteady simulations, no continuous and cost-effective, on-line method currently exists for monitoring the convergence quality of such statistics during runtime. This work introduces a novel, fully on-line bootstrapping approach to estimate the variance of finite-time averages without requiring the estimation of the flow’s Auto-Correlation Function (ACF). Unlike existing methods that rely on ACF estimation, which are often impractical due to excessive storage demands in large-scale simulations, or require off-line processing or a priori modeling assumptions, our method operates entirely during the simulation and incurs minimal overhead. The proposed technique employs a recursive update of bootstrap replicates of the time average, using correlated random weights generated via an autoregressive model. This formulation is computationally efficient: the update cost scales linearly with the number of bootstrap replicates and the dimensionality of the flow field, and the autoregressive model is inexpensive to evaluate. The method only requires storage of a small number of fields, making it suitable for large-scale CFD applications. We demonstrate the effectiveness of the approach on synthetic data from the Ornstein-Uhlenbeck process and on two canonical LES cases: a turbulent pipe flow and a round jet. We further discuss the method’s applicability to simulations with non-uniform time stepping, highlighting its flexibility and robustness.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118664"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941000","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":"Generating high-fidelity microstructures of polycrystalline materials with prescribed higher-order texture tensors","authors":"Maximilian Krause ,&nbsp;Thomas Böhlke ,&nbsp;Matti Schneider","doi":"10.1016/j.cma.2025.118690","DOIUrl":"10.1016/j.cma.2025.118690","url":null,"abstract":"<div><div>We introduce an efficient computational procedure for generating polycrystalline microstructures which permits studying the influence of specific texture-tensor orders on the resulting effective mechanical response, both in the linear elastic and the inelastic case. The crystallographic texture of a polycrystalline material is described by the Orientation Distribution Function (ODF). For practical computations, only the Fourier coefficients – called texture coefficients – of the ODF up to a certain order are of interest. In the work at hand, we wish to investigate this microstructure-property relationship. We interpret the task of approximating the texture coefficients of a microstructure realization as a <em>moment-matching</em>, i.e., quadrature, problem, and introduce efficient techniques for generating finite sets of orientations which exactly conform to prescribed polynomial texture terms. First, the microstructure morphology is generated via a well-established Laguerre-tessellation-based approach. Subsequently, the crystal grains are assigned a finite set of orientations which realize prescribed texture coefficients. We exploit the sparse representation of the action of the rotation group <em>SO</em>(3) on higher-order tensors to reduce the computational expense from exponential to cubic in the tensor order.</div><div>We consider polycrystalline copper as an example material and study the influence of texture terms of different polynomial order on the effective elastic properties and the anisotropy of initial yielding. For a large ensemble of polycrystal microstructures, we find that the elastic properties are mainly influenced by terms up to fourth order, whereas characterizing the yield function accurately requires higher-order texture terms.</div><div>To encourage further study of the texture dependence of nonlinear material properties, we provide an open-source python implementation of our algorithm.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118690"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941001","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 data-driven approach to cut-cell quadrature using spline interpolation","authors":"Michał Ł. Mika ,&nbsp;René R. Hiemstra ,&nbsp;Stein K.F. Stoter ,&nbsp;Dominik Schillinger","doi":"10.1016/j.cma.2025.118700","DOIUrl":"10.1016/j.cma.2025.118700","url":null,"abstract":"<div><div>This paper presents a data-driven approach to develop higher-order accurate tensor-product-stencil quadrature rules for implicitly defined two-dimensional domains. We construct a three-dimensional configuration space of possible domain cuts using a signed distance representation based on circular arcs, defined by their radius and center, and exploit symmetry to simplify its three-dimensional domain. The configuration space, being piecewise smooth, is carefully partitioned into smooth regions, enabling three-dimensional tensor-product spline interpolation to approximate quadrature data sampled from an established implicit domain quadrature technique. The resulting quadrature rules are simple to apply, highly accurate, efficient, and can be used as a black-box solution. We demonstrate compatibility with existing cut finite element techniques and illustrate their application through numerical examples.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118700"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940971","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":"Concurrent optimization of layups and stiffeners for stiffened laminated composite structures considering manufacturing constraints","authors":"Shanwei Li ,&nbsp;Zongliang Du ,&nbsp;Zunyi Duan ,&nbsp;Yibo Jia ,&nbsp;Chang Liu ,&nbsp;Zhifu Ge ,&nbsp;Xuefeng Mu ,&nbsp;Xu Guo","doi":"10.1016/j.cma.2025.118711","DOIUrl":"10.1016/j.cma.2025.118711","url":null,"abstract":"<div><div>Aiming to optimize thin-walled composite structures commonly used in the aerospace industry, the concurrent optimization of stiffeners and layup angles in stiffened laminated composite structures is achieved by combining the Moving Morphable Component (MMC) method and the Shape Function with Penalization (SFP) method. Based on the proposed explicit topology optimization framework for stiffened laminate structures, optimization formulations for maximizing stiffness and maximizing fundamental natural frequency, considering additive manufacturing constraints, are proposed. An efficient numerical algorithm is established, with analytical sensitivity analysis results derived. The constraints considered include stiffener thickness limits and laminate layup requirements. In addition, by fully leveraging the larger design space of synergies between stiffeners and laminates, it is demonstrated that the design result obtained through concurrent optimization exhibits better structural performance than the stiffened laminate structures achieved through the sequential optimization of stiffener and laminate layup angles.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118711"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940981","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":"Macro-element refinement schemes for THB-splines: Applications to Bézier projection and structure-preserving discretizations","authors":"Kevin Dijkstra ,&nbsp;Carlotta Giannelli ,&nbsp;Deepesh Toshniwal","doi":"10.1016/j.cma.2025.118707","DOIUrl":"10.1016/j.cma.2025.118707","url":null,"abstract":"<div><div>This paper introduces a novel adaptive refinement strategy for Isogeometric Analysis (IGA) using Truncated Hierarchical B-splines (THB-splines). The strategy is motivated by the fact that certain applications may benefit from adaptive refinement schemes, which lead to a higher degree of structure in the locally-refined mesh than usual, and building this structure a priori can simplify the implementation in those contexts. Specifically, we look at two applications: formulation of an <em>L</em>²-stable local projector for THB-splines a la Bézier projection [Dijkstra and Toshniwal (2023)], and adaptive structure-preserving discretizations using THB-splines [Evans et al. (2020), Shepherd and Toshniwal (2024)]. Previously proposed approaches for these applications require mesh modifications to preserve critical properties of the spline spaces, such as local linear independence or the exactness of the discrete de Rham complexes. Instead, we propose a macro-element-based refinement approach based on refining <span><math><mrow><mi>q</mi><mo>=</mo><msub><mi>q</mi><mn>1</mn></msub><mo>×</mo><mo>⋯</mo><mo>×</mo><msub><mi>q</mi><mi>n</mi></msub></mrow></math></span> blocks of elements, termed <strong>q</strong>-boxes, where the block size <strong>q</strong> is chosen based on the spline degree <strong>p</strong> and the specific application. • For the Bézier projection for THB-splines, we refine <strong>p</strong>-boxes (i.e., <span><math><mrow><mi>q</mi><mo>=</mo><mi>p</mi></mrow></math></span>). We show that THB-splines are locally linearly independent on <strong>p</strong>-boxes, which allows for a simple extension of the Bézier projection algorithm to THB-splines. This new formulation significantly improves upon the approach previously proposed by Dijkstra and Toshniwal (2023). • For structure-preserving discretizations, we refine <span><math><mrow><mo>(</mo><mi>p</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-boxes (i.e., <span><math><mrow><mi>q</mi><mo>=</mo><mi>p</mi><mo>+</mo><mn>1</mn></mrow></math></span>). We prove that this choice of <strong>q</strong> ensures that the mesh satisfies the sufficient conditions presented in Shepherd and Toshniwal (2024) for guaranteeing the exactness of the THB-spline de Rham complex a priori and in an arbitrary number of dimensions. This is crucial for structure-preserving discretizations, as it eliminates the need for additional mesh modifications to maintain the exactness of the complex during adaptive simulations.</div><div>The effectiveness of the proposed framework is demonstrated through theoretical proofs and numerical experiments, including optimal convergence for adaptive approximation and the simulation of the incompressible Navier-Stokes equations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118707"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145961744","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":"Wavelet-based enrichment for physics informed neural networks to approximate localized and heterogeneous solutions in solid mechanics","authors":"Duc-Vinh Nguyen ,&nbsp;Mohamed Jebahi ,&nbsp;Francisco Chinesta","doi":"10.1016/j.cma.2026.118768","DOIUrl":"10.1016/j.cma.2026.118768","url":null,"abstract":"<div><div>Recent research has highlighted the potential of physics-informed neural networks (PINNs) as an efficient methodology for approximating solutions of boundary value problems in solid mechanics. Nevertheless, their ability to accurately capture highly heterogeneous solutions of complex problems remains limited and requires further investigation. The present paper explores new strategies to address this challenge. In line with existing approaches based on local refinement of collocation (training) points, a weighted version of the loss function is first proposed to better balance the physical residuals across the entire computational domain. Although this modification improves overall performance, the approximation accuracy remains unsatisfactory. To overcome this limitation, an enriched version of PINN is developed to more effectively capture locally heterogeneous distributions of state variables. Specifically, wavelet-based enrichment functions are designed to approximate local high-frequency components of the full-field solution, thereby simplifying the task of the neural network, which is then required only to approximate the global smooth component of the solution. This approach achieves satisfactory accuracy even with relatively simple neural network architectures and few collocation points, as demonstrated through several benchmark problems. Therefore, the proposed enrichment concept represents a promising direction for further improving the performance of PINNs as solvers in computational mechanics, paving the way for their application to more complex problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118768"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023763","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 prospects of interpolatory spline bases for accurate mass lumping strategies in isogeometric analysis","authors":"Yannis Voet ,&nbsp;Espen Sande","doi":"10.1016/j.cma.2026.118762","DOIUrl":"10.1016/j.cma.2026.118762","url":null,"abstract":"<div><div>While interpolatory bases such as the Lagrange basis form the cornerstone of classical finite element methods, they have been replaced in the more general finite element setting of isogeometric analysis in favor of other desirable properties. Yet, interpolation is a key property for devising accurate mass lumping strategies that are ubiquitous in explicit dynamic analyses of structures. In this article, we explore the possibility of restoring interpolation for spline bases within isogeometric analysis for the purpose of mass lumping. Although reminiscent of the spectral element method, this technique comes with its lot of surprises and challenges, which are critically assessed.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118762"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023846","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":"Shape-topology-layout optimization of stiffened shell structures via the Feature-Driven Optimization (FDO) method","authors":"Hualin ZHANG,&nbsp;Weihong ZHANG","doi":"10.1016/j.cma.2026.118771","DOIUrl":"10.1016/j.cma.2026.118771","url":null,"abstract":"<div><div>In this work, an integrated shape-topology-layout optimization method is developed for stiffened shell structures to match the designs of the skin, openings and stiffeners. The proposed method takes full advantage of IsoGeometric Analysis (IGA), Finite Cell Method (FCM) and Feature-Driven Optimization (FDO). Specifically, the IGA enables accurate structural analysis and facilitates shape optimization of the skin by directly adjusting the control points of Non-Uniform Rational B-Splines (NURBS) skin surface. The FCM enables the use of the fixed structured mesh during the optimization process. The FDO adaptively inserts openings and stiffener features over the NURBS parametric domain for the optimization of skin topology and stiffener layout as easily as for 2D structures. Both implicit and parametric descriptions are jointly used to model openings and stiffener features. The implicit form concerns the level set function (LSF) in favor of the description of topological changes of the skin and the rapid identification of intersections of stiffeners. The parametric form concerns the use of a small number of design variables to produce optimized results with clear and smooth boundaries. Meanwhile, rigidity contributions of stiffeners are merged into the skin surface without the need of mesh conforming between the stiffeners and the skin surface. Representative examples are presented to demonstrate the effectiveness and advantages of the proposed design approach.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118771"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072454","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":"Graph neural networks with hybrid local-global attention for effective prediction of mechanical response in structures","authors":"Luca Patrignani,&nbsp;Silvestre T Pinho","doi":"10.1016/j.cma.2026.118753","DOIUrl":"10.1016/j.cma.2026.118753","url":null,"abstract":"<div><div>Graph Neural Networks (GNNs) are emerging as a transformative approach for predicting mechanical response in structures by naturally encoding unstructured finite element meshes as graphs. While traditional finite element analysis (FEA) provides trusted solutions for mechanics problems, it encounters significant computational and scalability bottlenecks. Existing machine learning approaches using regular grids fail to capture the irregular nature of real-world meshes, whereas standard GNNs suffer from over-smoothing and limited long-range information propagation that compromise accuracy. To overcome these limitations, we present a Graph Transformer methodology that implements an encoder-processor-decoder framework augmented with a frequency-controlled hybrid local-global attention mechanism, which systematically bridges local mesh connectivity with global information awareness across the computational domain. Our approach integrates seamlessly with real-world FEA workflows through an automated FEM-to-GNN pipeline that converts FE simulations to graph representations and generates training datasets directly from commercial solvers, enabling rapid deployment across various engineering applications without manual preprocessing bottlenecks. We validate our approach on open holes Carbon Fibre Reinforced Polymer (CFRP) laminate plates under various loading conditions and geometric configurations, and extend validation to nonlinear woven composites exhibiting plasticity and progressive damage under shear-dominated loadings, employing systematic hyperparameter optimisation with Tree-structured Parzen Estimator (TPE) sampling and mesh convergence studies. The linear case demonstrates excellent predictive accuracy (<span><math><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>=</mo><mn>0.98</mn></mrow></math></span>, <span><math><mrow><mi>R</mi><mi>M</mi><mi>S</mi><mi>E</mi><mo>=</mo><mn>0.00028</mn></mrow></math></span>) with 70 ×  speedup over equivalent-accuracy FEA and <span><math><mrow><mn>58</mn><mo>−</mo><mn>64</mn><mo>%</mo></mrow></math></span> reduction in training and validation loss compared to standard message-passing GNN architectures without attention mechanisms, while the nonlinear case achieves <span><math><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>=</mo><mn>0.97</mn></mrow></math></span> (<span><math><mrow><mi>R</mi><mi>M</mi><mi>S</mi><mi>E</mi><mo>=</mo><mn>0.0013</mn></mrow></math></span>) with 660 ×  speedup.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118753"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146000569","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":"Topology optimisation-based design of duct cross-sections for fully developed magnetohydrodynamic flows","authors":"Juan C. Àlvarez-Hostos ,&nbsp;Fernando R. Urgorri ,&nbsp;Javier Principe","doi":"10.1016/j.cma.2026.118787","DOIUrl":"10.1016/j.cma.2026.118787","url":null,"abstract":"<div><div>In this communication, duct cross-sections for fully developed inductionless magnetohydrodynamics (MHD) flows are designed via topology optimisation (TO). The objective function to be maximised is the volumetric flow rate that can be achieved along the duct under a prescribed pressure gradient, subject to an area constraint imposed on the cross-sectional geometry. The solid-liquid transition within the topology is modelled through a Darcy term, where the permeability is defined using the Carman-Kozeny equation as a function of an apparent liquid fraction, effectively enforcing zero velocity in solid regions. The well-known solid isotropic material with penalisation (SIMP) technique is used to define the apparent liquid fraction and to interpolate between the electrical conductivities of solid and fluid phases. A finite element framework is used for the multiphysics analysis, with a single design variable (artificial density) assigned to each finite element. Details of the adjoint-based sensitivity analysis within this multiphysics context are provided, and the influence of both the orientation and dominance of the magnetic field on the resulting topologies is also examined. The results demonstrate that the proposed optimisation strategy effectively yields solutions that maximise the flow rate, and that such topologies differ significantly from those expected in standard fluid dynamics problems, with strong dependence on magnetic field characteristics. Furthermore, the combined use of SIMP interpolation and the Carman-Kozeny-based Darcy term ensures stable convergence of the optimisation process within the inductionless MHD framework, even when accounting for the interpolation of electrical conductivity.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118787"},"PeriodicalIF":7.3,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134459","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}