International Journal for Numerical Methods in Engineering最新文献

{"title":"Neural Level Set Topology Optimization Using Unfitted Finite Elements","authors":"Connor N. Mallon,&nbsp;Aaron W. Thornton,&nbsp;Matthew R. Hill,&nbsp;Santiago Badia","doi":"10.1002/nme.70004","DOIUrl":"https://doi.org/10.1002/nme.70004","url":null,"abstract":"<p>To facilitate the widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods with solvers capable of handling arbitrary problems. In this work, a topology optimization method for general multiphysics problems is presented. We leverage a convolutional neural parameterization of a level set for a description of the geometry and use this in an unfitted finite element method that is differentiable with respect to the level set everywhere in the domain. We construct the parameter to objective map in such a way that the gradient can be computed entirely by automatic differentiation at roughly the cost of an objective function evaluation. Without handcrafted initializations, the method produces regular topologies close to the optimal solution for standard benchmark problems whilst maintaining the ability to solve a more general class of problems than standard methods, for example, interface-coupled multiphysics.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689157","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 High-Precision Meshless Method for Time-Fractional Mixed Diffusion and Wave Equations","authors":"Zehui Ma,&nbsp;Rahmatjan Imin","doi":"10.1002/nme.70020","DOIUrl":"https://doi.org/10.1002/nme.70020","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, a meshless scheme based on Kernel Derivative Free Smoothed Particle Hydrodynamics (KDF-SPH) approximation is proposed to solve the time-fractional mixed diffusion and wave equations. The time fractional derivative is defined in the Caputo sense, and we use the finite difference method to discretize. The meshless method based on KDF-SPH is used for spatial discretization. Thus, a fully discrete meshless numerical scheme is obtained. At the same time, we use the obtained meshless discrete scheme to solve the initial boundary value problems of time-fractional mixed diffusion and wave equations in regular and irregular regions, and we get good results. By comparing the proposed method with many numerical methods, the accuracy and effectiveness of the proposed method are further verified.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645757","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":"Surrogate Computational Homogenization of Viscoelastic Composites","authors":"Yosuke Yamanaka,&nbsp;Norio Hirayama,&nbsp;Kenjiro Terada","doi":"10.1002/nme.70008","DOIUrl":"https://doi.org/10.1002/nme.70008","url":null,"abstract":"<p>We establish a surrogate model for computational homogenization of composite materials consisting of multiple viscoelastic constituents. A surrogate macroscopic material is identified by performing interpolation using radial basis functions (RBFs) and cubic spline functions on a constitutive database generated by a series of microscopic analyses or, equivalently, numerical material tests (NMTs) on a unit cell to represent anisotropic stress relaxation behavior as well as its dependence on strain rate and temperature. After briefly reviewing the two-scale boundary value problem derived based on homogenization theory, an RBF interpolation with a normalized kernel is formulated for a discrete dataset, and an optimization algorithm is applied to determine the three hyperparameters so as to achieve proper interpolation. Then, we formulate the surrogate homogenization model (SHM) using the interpolants to substitute for the macroscopic viscoelastic response. To show the specific procedure of the proposed surrogate modeling and demonstrate the performance of the created SHM, a representative numerical example is presented in the offline and online stages. In the offline stage, NMTs are carried out in the space of training data, including the temperature, to generate a dataset as long as the macroscopic stresses can be learned exhaustively, and then optimization is performed to determine the set of hyperparameters. Then, to validate the created SHM, its responses to unseen loading and temperature histories are compared with the corresponding NMT results. In the online stage, the created SHM is used to carry out a macroscopic analysis of a simple structure under specific loading and temperature conditions, and subsequently, the obtained macroscopic stresses are compared with those obtained from the localization analysis results. The results are also compared with those obtained from the single-scale direct numerical analyses.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645737","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":"Concurrent Optimization of Unit-Cell Topology and Tessellating Orientation for Finite Periodic Structures","authors":"Simon Thomas,&nbsp;Chi Wu,&nbsp;Qing Li,&nbsp;Grant P. Steven","doi":"10.1002/nme.70017","DOIUrl":"https://doi.org/10.1002/nme.70017","url":null,"abstract":"<p>Finite periodic layout for multicomponent systems signifies a compelling design strategy for constructing complex larger structures through assembling repeating representative unit-cells with various orientations. In addition to better transportability, handleability and replaceability, design with structural segmentation has been considered particularly valuable for additive manufacturing of large workpiece due to limited printing dimension of machine. However, existing design optimization of periodic structures has been largely restricted to simple translational placements of unit-cells, sophisticated tessellation with differently oriented topological unit-cells remains underexplored. This paper presents an efficient and adaptable topology optimization framework for concurrently optimizing periodic structures comprised of repeating topological unit-cells and their tailored orientations. By introducing a weighting factor associated with different orientation states of unit-cells, a dominant orientation for each unit-cell can gradually emerge in the course of optimization process. The proposed procedure combines the solid isotropic material with penalization (SIMP) model for topology optimization of unit-cell and the discrete material optimization (DMO) technique for the optimization of its orientation. The optimization objective is to minimize structural compliance subject to volume fraction constraint. Through sensitivity analysis, optimality criteria can be applied to simultaneously optimize a representative unit-cell (RUC) topology and the orientation weighting factors in the periodic macrostructure. Several 2D and 3D examples are investigated to demonstrate significant enhancement in compliance reduction of up to 34% compared to conventional periodic design without orientation optimization. This represents a notable improvement in finite periodic structural optimization, particularly leveraging the topology optimization to tailor unit-cell orientation rather than relying on brute-force search approaches. Our methodology paves a new avenue for designing more efficient and readily manufacturable lightweight structures with enhanced performance metrics.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645738","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":"Study on Reference Displacement Method Based on Radial Basis Functions With Boundary Orthogonality Correction and Spatial Multiple Point Selection","authors":"Han Tang,&nbsp;Guannan Zheng,&nbsp;Yuchen Zhang,&nbsp;Xinjiang Wang,&nbsp;Chengde Huang","doi":"10.1002/nme.70023","DOIUrl":"https://doi.org/10.1002/nme.70023","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;The process of elastic deformation is performed using the radial basis functions (RBF) method for the background mesh and the volume-weighted interpolation method for the computational mesh. The RBF method performs interpolation independently in different directions and does not ensure boundary orthogonality during elastic deformation. This study proposes a strategy to improve the quality and efficiency of the dynamic mesh method. Based on the automatically generated adaptive background mesh, a reference displacement method for spatial points is first developed to obtain reasonable reference displacements with rotational correction for spatial control points. The RBF is then used to interpolate the rotation angle of the boundary represented by the quaternion. Therefore, the large angle deformation can be more smoothly propagated to the spatial region. In the background mesh, the translational deformation is obtained by the damping function based on the minimum distance, the rotational deformation is calculated by rotating around a small number of nodes with the minimum distance from the wall surface, and the final rotational displacement is obtained by inverse distance weighting. This method ensures boundary orthogonality. Afterwards, the one-step reference displacement method is developed. A subset of mesh nodes on the boundary surface and one layer outside the boundary are automatically selected using a greedy algorithm and considered as control points. The spatial point is assigned a value using a reference displacement. The deformation displacement of the background mesh is calculated using the RBF method, and then interpolated into the computational grid. The obtained results show that this method can significantly improve the orthogonality of the boundary layer and retain the high accuracy of the RBF method for elastic deformation. In addition, a two-step spatial multi-point selection method is developed. Using a spatial peak selection method of high flexibility based on the quality change before and after mesh deformation, multiple spatial points are selected and considered as control points at a time, which allows for increased stability and robustness of the dynamic mesh method for the one-step reference displacement method. The deformation ability of the two-step spatial multi-point selection method is increased by 20% compared with that of the one-step reference displacement method in a single deformation step. The criterion for point selection is general, and the algorithm has high efficiency, which allows spatial control points to be selected in multiple regions. The two-step spatial multi-point selection method provides a smooth mesh, stretching the overlapped and squeezed mesh. The CPU cost is comparable to the RBF, and iteration is not required. The time complexity of the proposed multiple point selection method is reduced to 2/(M + 1) times that of the single-point selection method, which adds one spat","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645736","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":"Formulation of Correction Term in QUBO Form for Phase-Field Model","authors":"Shiori Aoki,&nbsp;Katsuhiro Endo,&nbsp;Yoshiki Matsuda,&nbsp;Yuya Seki,&nbsp;Shu Tanaka,&nbsp;Mayu Muramatsu","doi":"10.1002/nme.70019","DOIUrl":"https://doi.org/10.1002/nme.70019","url":null,"abstract":"<p>In this study, we developed a method of estimating the correction terms that makes the Hamiltonian used in phase-field analysis by quantum annealing correspond to the free energy functional of the conventional phase-field analysis using the finite difference method. For the estimation of the correction terms, we employed a factorization machine. The inputs to the factorization machine were the phase-field variables in domain-wall encoding and the differences between the Gibbs free energy and Hamiltonian. We obtained the difference value in quadratic unconstrained binary optimization (QUBO) form as the output of learning using the factorization machine. The QUBO form difference was subjected to the original Hamiltonian as the correction term. The performance of this correction term was evaluated by calculating the energy for a equilibrium state of diblock copolymer. In phase-field analysis, the time evolution equation is formulated so that the total free energy decreases; hence, a lower the free energy means a more accurate result close to that of a conventional method. When we performed annealing with correction terms, the microstructure showed a Gibbs free energy that was lower than that obtained without the correction terms.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645755","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 New Approach to Asynchronous Variational Integrators for a Phase Field Model of Dynamic Fracture","authors":"Deepak B. Jadhav,&nbsp;Dhananjay Phansalkar,&nbsp;Kerstin Weinberg,&nbsp;Michael Ortiz,&nbsp;Sigrid Leyendecker","doi":"10.1002/nme.70025","DOIUrl":"https://doi.org/10.1002/nme.70025","url":null,"abstract":"<p>Phase field modeling of fracture has gained attention as a relatively simple and fundamental approach to predict crack propagation. However, the significant computational demands still pose challenges, particularly in dynamic simulations. To mitigate these challenges, we present a newly devised asynchronous variational integrator (AVI) for phase field modeling of dynamic fracture, implemented within the framework of the finite element library FEniCS. The AVI allows each spatial mesh element to progress independently with its own characteristic time step. In the new approach, displacement updates occur as usual at each time step, while the phase field is globally solved after the displacement update of the largest spatial mesh element rather than after each time step. Benchmark problems are investigated to assess the performance and reliability of the new method, revealing notable computational savings while effectively capturing intricate dynamic fracture behavior.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70025","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143645756","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":"Inverse Design of Planar Clamped-Free Elastic Rods From Noisy Data","authors":"Dezhong Tong,&nbsp;Zhuonan Hao,&nbsp;Jiahao Li,&nbsp;Weicheng Huang","doi":"10.1002/nme.70018","DOIUrl":"https://doi.org/10.1002/nme.70018","url":null,"abstract":"<p>Slender structures, such as rods, often exhibit large deformations even under moderate external forces (e.g., gravity). This characteristic results in a rich variety of morphological changes, making them appealing for engineering design and applications, such as soft robots, submarine cables, decorative knots, and more. Prior studies have demonstrated that the natural shape of a rod significantly influences its deformed geometry. Consequently, the natural shape of the rod should be considered when manufacturing and designing rod-like structures. Here, we focus on an inverse problem: Can we determine the natural shape of a suspended 2D planar rod so that it deforms into a desired target shape under the specified loading? We begin by formulating a theoretical framework based on the statics of planar rod equilibrium that can compute the natural shape of a planar rod given its target shape. Furthermore, we analyze the impact of uncertainties (e.g., noise in the data) on the accuracy of the theoretical framework. The results reveal the shortcomings of the theoretical framework in handling uncertainties in the inverse problem, a fact often overlooked in previous works. To mitigate the influence of the uncertainties, we combine the statics of the planar rod with the adjoint method for parameter sensitivity analysis, constructing a learning framework that can efficiently explore the natural shape of the designed rod with enhanced robustness. This framework is validated numerically for its accuracy and robustness, offering valuable insights into the inverse design of soft structures for various applications, including soft robotics and animation of morphing structures.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581869","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 Non-Intrusive, Online Reduced Order Method for Non-Linear Micro-Heterogeneous Materials","authors":"Yasemin von Hoegen,&nbsp;Rainer Niekamp,&nbsp;Jörg Schröder","doi":"10.1002/nme.70007","DOIUrl":"https://doi.org/10.1002/nme.70007","url":null,"abstract":"<p>In this contribution we present an adaptive model order reduction technique for non-linear finite element computations of micro-heterogeneous materials. The presented projection-based method performs updates of the reduced basis during the iterative process and at the end of each load step. Convergence is achieved in all stages of the simulation and the best choice of basis vectors is assured. A novel technique for the choice of basis, the recursive Proper Orthogonal Decomposition, is introduced and compared to an existing technique, the comparative Proper Orthogonal Decomposition, in an academic two-dimensional unit cell example. Numerical examples of real two- and three-dimensional microstructures unveil the performance of the adaptive technique for industrial applications.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564722","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":"Topology Optimization for Large-Scale Unsteady Flow With the Building-Cube Method","authors":"Ryohei Katsumata,&nbsp;Koji Nishiguchi,&nbsp;Hiroya Hoshiba,&nbsp;Junji Kato","doi":"10.1002/nme.70016","DOIUrl":"https://doi.org/10.1002/nme.70016","url":null,"abstract":"<p>This study proposes a novel framework for solving large-scale unsteady flow topology optimization problems. While most previous studies on fluid topology optimization assume steady-state flows, an increasing number of recent studies deal with unsteady flows, which are more general in engineering. However, unsteady flow topology optimization involves solving the governing and adjoint equations of a time-evolving system, which requires a significant computational cost for topology optimization with a fine mesh. Therefore, we propose a large-scale unsteady flow topology optimization based on the building-cube method (BCM), which is one of the hierarchical Cartesian mesh methods. Although the BCM has been confirmed to have excellent scalability and is suitable for massively parallel computing, there are no studies that have applied it to unsteady flow topology optimization. In the proposed method, the governing and adjoint equations are discretized by a cell-centered finite volume method based on the BCM, which can achieve high parallel efficiency even with a fine mesh. The effectiveness of the proposed method for large-scale computing is discussed through several examples of optimization and verification of computational efficiency by weak scaling.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143533956","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}