International Journal for Numerical Methods in Engineering最新文献

{"title":"Structural Topology Optimization With the Simultaneous Constraints to Maximum Contact Pressure and Fatigue Damage","authors":"Jiajia Li,&nbsp;Tong Gao,&nbsp;Ziad Moumni,&nbsp;Weihong Zhang","doi":"10.1002/nme.70071","DOIUrl":"https://doi.org/10.1002/nme.70071","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, we develop a topology optimization method for elastic contact problems involving fatigue constraints under proportional loads. The method is formulated by means of B-spline parameterization of the pseudo-density field to describe the material layout. Both the contact pressure control on the contact surface and fatigue constraint to the whole structure domain are taken into account simultaneously. The accumulated fatigue damage related to the fatigue constraint is calculated based upon the rainflow-counting scheme, Sines method, <i>S</i>–<i>N</i> curve and Palmgren–Miner's linear damage hypothesis. The Kreisselmeier–Steinhauser (KS) function is adopted as an aggregated measure for both the maximum contact pressure and the maximum fatigue damage. The design sensitivities are derived analytically using the adjoint method. Both frictionless and frictional contact problems are investigated. The influence of fatigue constraints on the optimization result is discussed in comparison with the standard compliance minimization. Frictional contact effects upon the optimized results and fatigue damage are highlighted. Results show that the maximum contact pressure and maximum fatigue damage can effectively be controlled to avoid fatigue failure and that the fatigue strength of the structure can be improved at the cost of structural stiffness.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Neural Ordinary Differential Equations for Model Order Reduction of Stiff Systems","authors":"Matteo Caldana,&nbsp;Jan S. Hesthaven","doi":"10.1002/nme.70060","DOIUrl":"https://doi.org/10.1002/nme.70060","url":null,"abstract":"<p>Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying neural ODEs in practical applications often encounters the challenge of stiffness, a condition where rapid variations in some components of the solution demand prohibitively small time steps for explicit solvers. This work addresses the stiffness issue when employing neural ODEs for model order reduction by introducing a suitable reparametrization in time. The considered map is data-driven, and it is induced by the adaptive time-stepping of an implicit solver on a reference solution. We show that the map produces a non-stiff system that can be cheaply solved with an explicit time integration scheme. The original, stiff, time dynamic is recovered by means of a map learnt by a neural network that connects the state space to the time reparametrization. We validate our method through extensive experiments, demonstrating improvements in efficiency for the neural ODE inference while maintaining robustness and accuracy when compared to an implicit solver applied to the stiff system with the original right-hand side.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70060","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144300261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization","authors":"Lucka Barbeau,&nbsp;Marc-Étienne Lamarche-Gagnon,&nbsp;Florin Ilinca","doi":"10.1002/nme.70068","DOIUrl":"https://doi.org/10.1002/nme.70068","url":null,"abstract":"<p>The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in the PGD algorithm, where an inertial step component has been introduced to improve efficiency in solving constrained optimization problems, this study introduces two key enhancements to further improve the algorithm's performance and adaptability in large-scale design spaces. First, univariate constraints (such as design variable bounds constraints) are directly incorporated into the projection step via the Schur complement and an improved active set algorithm with bulk constraints manipulation, avoiding issues with min–max clipping. Second, the update step is decomposed relative to the constraint vector space, enabling a post-projection adjustment based on the state of the constraints and an approximation of the Lagrangian, significantly improving the algorithm's robustness for problems with nonlinear constraints. Applied to a topology optimization problem for heat sink design, the proposed PGD algorithm demonstrates performance comparable to or exceeding that of the Method of Moving Asymptotes (MMA), with minimal parameter tuning. These results position the enhanced PGD as a robust tool for complex optimization problems with large variable spaces, such as topology optimization problems.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70068","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144299704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stress-Constrained Topology Optimization With the Augmented Lagrangian Method: A Comparative Study of Subproblem Solvers","authors":"Gustavo Assis da Silva,&nbsp;Hélio Emmendoerfer Jr.","doi":"10.1002/nme.70066","DOIUrl":"https://doi.org/10.1002/nme.70066","url":null,"abstract":"<div>\u0000 \u0000 <p>Incorporating stress constraints in topology optimization is a challenging task due to the large number of constraints in the formulation. One effective strategy to address this challenge is the augmented Lagrangian (AL) method, which transforms the original stress-constrained problem into a sequence of subproblems with only bound constraints. The effectiveness of the AL method heavily depends on the optimization method used to solve these subproblems. This work performs a comparative study of six optimization solvers: The method of moving asymptotes (MMA), the steepest descent method with move limits (SDM), the spectral projected gradient (SPG), and the limited-memory BFGS with bound constraints (L-BFGS-B), along with two proposed adaptations, steepest descent method with move limits—Barzilai–Borwein (SDMBB) and spectral projected gradient with move limits (SPGM). These methods are evaluated in the context of the volume minimization problem with local stress constraints. The solutions are compared in terms of performance, defined as the final volume fraction, and efficiency, measured by the number of state and adjoint analyses required. A mesh dependence study is conducted to assess the robustness of each method across different mesh sizes, including high-resolution cases with approximately 1.8 million elements. SDMBB exhibits the highest efficiency, while SPGM achieves the best performance, followed by SDM. The MMA, SPG, and L-BFGS-B show limitations in high-resolution problems or fail to meet specific stopping criteria. The results demonstrate that the choice of the optimization solver significantly affects the efficiency of the AL method, as well as the performance and mesh dependence of the solutions. Furthermore, this study identifies the most promising methods for solving large-scale stress-constrained problems.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144299995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Novel Approach to Thermo-Mechanically Coupled, Gradient-Enhanced Damage Modeling","authors":"Fangrui Liu,&nbsp;Dustin Roman Jantos,&nbsp;Philipp Junker","doi":"10.1002/nme.70065","DOIUrl":"https://doi.org/10.1002/nme.70065","url":null,"abstract":"<p>Thermo-mechanical damage, such as thermal shock, is a common engineering problem. It constitutes a challenging problem that damage and temperature are conversely interacting with each other: Material damage leads to an increase in temperature due to energy dissipation; temperature also influences damage evolution. On the one hand, an increase in temperature decreases the damage threshold, which makes damage more likely to occur. On the other hand, a non-uniform temperature distribution can cause internal stresses within the material, leading to the occurrence of damage. Taking all of the above points into account, we introduce a novel approach based on the Hamilton principle for thermo-mechanically coupled, gradient-enhanced damage modeling. To accelerate the computation speed, we adopt the Neighbored Element Method to calculate the Laplace operator in the governing equation of both the damage variable and temperature. The numerical examples show the robustness and efficiency of our method.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70065","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144292055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Decoupled Approach to Multidisciplinary System Analysis Under Uncertainty","authors":"Kais Zaman,&nbsp;Gulam Kibria","doi":"10.1002/nme.70062","DOIUrl":"https://doi.org/10.1002/nme.70062","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents an efficient probabilistic approach for uncertainty propagation in multidisciplinary system analysis (MDA) under aleatory uncertainty (i.e., natural or physical variability). To enhance computational efficiency, a decoupled method is employed to separate the MDA from the probabilistic analysis. Initially, the paper introduces a moment-matching technique to estimate the first four moments of the coupling variables. This technique utilizes Taylor series expansion, direct tensor product quadrature, sparse grid numerical integration, and univariate dimension reduction methods. After quantifying the uncertainty in the coupling variables, system-level uncertainty propagation is carried out using methods similar to those used in single-discipline problems. The proposed methods are suitable for both sampling and analytical approximation-based reliability analysis techniques. The effectiveness of these methods is demonstrated through a mathematical problem and a practical engineering problem.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144292516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Time-Adaptive Multirate Quasi-Newton Waveform Iteration for Coupled Problems","authors":"Niklas Kotarsky,&nbsp;Philipp Birken","doi":"10.1002/nme.70063","DOIUrl":"https://doi.org/10.1002/nme.70063","url":null,"abstract":"<p>We consider waveform iterations for dynamical coupled problems, or more specifically, PDEs that interact through a lower-dimensional interface. We want to allow for the reuse of existing codes for the subproblems, called a partitioned approach. To improve computational efficiency, different and adaptive time steps in the subsolvers are advisable. Using so-called waveform iterations in combination with relaxation, this has been achieved for heat transfer problems earlier. Alternatively, one can use a black box method like Quasi-Newton to improve the convergence behavior. These methods have recently been combined with waveform iterations for fixed time steps. Here, we suggest an extension of the Quasi-Newton method to the time-adaptive setting and analyze its properties. We compare the proposed Quasi-Newton method with state-of-the-art solvers on a heat transfer test case and a complex mechanical Fluid-Structure interaction case, demonstrating the method's efficiency.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70063","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144292056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Phase-Field Modeling of Ductile Fracture Across Grain Boundaries in Polycrystals","authors":"Kim Louisa Auth,&nbsp;Jim Brouzoulis,&nbsp;Magnus Ekh","doi":"10.1002/nme.70056","DOIUrl":"https://doi.org/10.1002/nme.70056","url":null,"abstract":"<p>In this study, we address damage initiation and microcrack formation in ductile failure of polycrystalline metals. We show how our recently published thermodynamic framework for ductile phase-field fracture of single crystals can be extended to polycrystalline structures. A key feature of this framework is that it accounts for size effects by adopting gradient-enhanced (crystal) plasticity. Gradient-enhanced plasticity requires the definition of boundary conditions representing the plastic slip transmission resistance of the boundaries. In this work, we propose a novel type of microflexible boundary condition for gradient-plasticity, which couples the slip transmission resistance with the phase-field damage such that the resistance locally changes during the fracturing process. The formulation allows maintaining the effect of grain boundaries as obstacles for plastic slip during plastification, while also accounting for weakening of their resistance during the softening phase. In numerical experiments, the new damage-dependent boundary condition is compared with classical microfree and microhard boundary conditions in polycrystals, and it is demonstrated that it indeed produces a response that transitions from microhard to microfree as the material fails. We show that the formulation maintains resistance to slip transmission during hardening, but can generate microcracks across grain boundaries during the fracture process. We further show examples of how the model can be used to simulate void coalescence and three-dimensional crack fronts in polycrystals.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 12","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70056","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144273074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Predictive Physics-Aware Hybrid Reduced Order Model for Reacting Flows","authors":"Adrián Corrochano,&nbsp;Rodolfo S. M. Freitas,&nbsp;Manuel López-Martín,&nbsp;Alessandro Parente,&nbsp;Soledad Le Clainche","doi":"10.1002/nme.70058","DOIUrl":"https://doi.org/10.1002/nme.70058","url":null,"abstract":"<p>This article introduces an innovative methodology that merges modal decomposition, extracting physical patterns, with deep learning networks (DLNs) for forecasting reacting flows. The model is generalizable and capable of predicting complex simulations with just one training of the model, showing transfer learning capabilities. The primary objective is to optimize computational resources while maintaining accuracy on the predictions. With the combination of proper orthogonal decomposition (POD) and DLNs, our approach offers an efficient and effective solution for flow dynamics prediction. The new hybrid (POD/DLN) predictive model is designed for solving reacting flow problems. The POD block segregates temporal and spatial information, while the DLN block operates solely on the temporal domain with significantly reduced dimensionality. The POD modes contain the main flow characteristics, turning the model into a physics-based model. This architecture leads to substantial enhancements in computational cost and memory requirements, while maintaining the precision in the predictions. Such advancements are particularly crucial for addressing the challenges posed by high-dimensional multivariate and complex time-series forecasting tasks. Two different deep learning architectures have been tested to predict the temporal coefficients, based on recursive (RNN) and convolutional (CNN) neural networks, introducing a novel physics-aware loss function. From each architecture, different models have been created to understand the behavior of each parameter of the neural network. The results show that these architectures are able to predict the temporal evolution of the reactive flow. To the authors' knowledge, this is the first time this type of hybrid models is used to temporal prediction in reactive flows. The generalization capabilities and robustness of this physics-aware ROM shed light on new development of predictive models for this research field.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70058","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144244240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Efficient Arbitrary Grid Material Point Method for Problems With Nonconforming Boundary Conditions","authors":"Hongyu Ma,&nbsp;Jiasheng Li,&nbsp;Zixian Sun,&nbsp;Xiong Zhang","doi":"10.1002/nme.70054","DOIUrl":"https://doi.org/10.1002/nme.70054","url":null,"abstract":"<div>\u0000 \u0000 <p>In the standard material point method (MPM), a Cartesian background grid is typically used to solve equations of motion. This can make imposing boundary conditions a challenging task when the boundary of the material domain does not align with the grid edge, as these nonconforming boundary conditions are difficult to apply directly to the nodes of the Cartesian grid. In this paper, we propose the Arbitrary Grid Material Point Method (AGMPM) to efficiently solve problems involving a nonconforming boundary conditions by converting them into conforming boundary conditions. In the AGMPM, boundaries with arbitrary geometries are constructed by using arbitrary convex polygonal grid cells. The Wachspress coordinates are introduced as the shape functions for these grid cells. To impose boundary conditions on the arbitrary grid, two specific types of boundary conditions are proposed as examples: roller boundary conditions, which are two-sided constraints, and rigid-wall-boundary conditions, which are single-sided constraints. These boundary conditions are extensions of those used in the standard MPM. To improve computational efficiency during the particle-to-mesh mapping, an efficient search algorithm based on the bucket search method is presented. Several numerical examples are studied to verify the proposed AGMPM, demonstrate its potential and flexibility in solving engineering problems, and showcase its improved accuracy compared to the standard MPM when dealing with nonconforming boundary conditions.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 11","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144244090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}