International Journal for Numerical Methods in Engineering最新文献

{"title":"On the Feasibility of Foundational Models for the Simulation of Physical Phenomena","authors":"Alicia Tierz,&nbsp;Mikel M. Iparraguirre,&nbsp;Icíar Alfaro,&nbsp;David González,&nbsp;Francisco Chinesta,&nbsp;Elías Cueto","doi":"10.1002/nme.70027","DOIUrl":"https://doi.org/10.1002/nme.70027","url":null,"abstract":"<div>\u0000 \u0000 <p>We explore the feasibility of foundation models for the simulation of physical phenomena, with emphasis on continuum (solid and fluid) mechanics. Although so-called “learned simulators” have shown some success when applied to specific tasks, it remains to be studied to what extent they can undergo severe changes in domain shape, boundary conditions, and/or constitutive laws and still provide robust (i.e., hallucination-free) and accurate results. In this paper, we perform an exhaustive study of these features, put ourselves in the worst-case scenario, and study their resistance to such strong changes in their domain of application.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689769","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":"Monolithic and Staggered Solution Strategies for Constrained Mechanical Systems in Optimal Control Problems","authors":"Ashutosh Bijalwan,&nbsp;Simeon Schneider,&nbsp;Peter Betsch,&nbsp;José J Muñoz","doi":"10.1002/nme.70026","DOIUrl":"https://doi.org/10.1002/nme.70026","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper deals with the optimal control of constrained mechanical systems, with potential additional kinematic constraints at the final time. Correspondingly, the equations of motion of the underlying mechanical system assume the form of differential-algebraic equations with end constraints. The proposed discretisation of the optimality conditions yields a scheme which is capable of preserving control angular momentum maps resulting from the rotational symmetry of the underlying optimal control problem. The numerical solution of the discretised system is first tested with two solution strategies: Monolithic and staggered approaches, and then also solved with hybrid approaches, which combine salient features of each individual strategy. The monolithic strategy solves all the optimality conditions for all time steps as a single system of non-linear equations and relies on a Newton-Raphson scheme, which guarantees quadratic rates of convergence in the vicinity of the optimal solution trajectory. The staggered strategy is based on the Forward-Backward Sweep Method (FBSM), where state and adjoint equations are solved separately, and the control equations provide an update of the control variables, which we here achieve with also a Newton-Raphson scheme. The proposed hybrid strategies combine the advantages of a conventional gradient-based FBSM with the individual Newton-based solution procedures once the solution is close to the optimal trajectory. The strategies are developed and compared through three representative numerical examples, which show that all schemes yield very similar solutions. However, the hybrid approaches become more advantageous in the computation time when the time-step decreases or the size of the problem increases.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689757","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":"Direct Load-Carrying Boundary Identification-Based Topology Optimization Method for Structures With Design-Dependent Boundary Load","authors":"Boyuan Fan,&nbsp;Huixin Huang,&nbsp;Jingyu Hu,&nbsp;Shutian Liu","doi":"10.1002/nme.70010","DOIUrl":"https://doi.org/10.1002/nme.70010","url":null,"abstract":"<div>\u0000 \u0000 <p>During topology optimization with design-dependent boundary load, updating the load conditions is necessary. However, it is challenging to identify the load-carrying boundary in density-based topology optimization frame. To address this issue, a direct load-carrying boundary identification method is proposed to describe and update the design-dependent boundary load, and a topology optimization method for structures with design-dependent boundary load is presented. First, a Flood Fill algorithm (FFA) based domain extension method is introduced to generate a new structure with a boundary equivalent to the load-carrying boundary of the original structure. Then, the erosion boundary identification method is applied to the new structure to identify the load-carrying boundary instead of the original structure. Finally, the load information (direction and magnitude) of the design-dependent boundary load is determined using a normalized gradient algorithm, which completes the update of the design-dependent boundary load. This method overcomes the difficulty of identifying the load-carrying boundary in density-based methods. The effectiveness of this method is demonstrated by several examples of minimum compliance (including 3D) and flexible mechanisms.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689768","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":"Concurrent Optimization of Structures and Anisotropic Materials for Mechanical Cloaking","authors":"Yifu Lu,&nbsp;Liyong Tong","doi":"10.1002/nme.70028","DOIUrl":"https://doi.org/10.1002/nme.70028","url":null,"abstract":"<p>This paper studies the concurrent optimization of structural topologies and material properties for mechanical cloaking problems, in which the macrostructures, microstructures, and novel spatially-varying microstructure orientations of the cloaking devices are simultaneously considered and form a multiscale topology optimization problem. In this work, we (1) propose a new element-based objective function for mechanical cloaking; (2) establish generic mathematical formulations to model the multiscale optimization problem, including a novel mathematical relation between the original objective function and material microstructures, and implement the formulated optimization problem via an extended moving iso-surface threshold (MIST) method; (3) investigate the concurrent optimization of the macrostructure and material microstructures and orientations; (4) propose a novel analytical method derived for fully anisotropic materials to compute the optimal material orientations. Benchmark numerical examples are investigated to validate the proposed method. The present numerical results show that the proposed method can improve the cloaking performance by up to 26.25% compared with the literature.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70028","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689767","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":"Modelling of Kirchhoff and Mindlin–Reissner Plate Bending With Hybrid-Trefftz Stress Elements","authors":"J. A. Teixeira de Freitas,&nbsp;Carlos Tiago,&nbsp;E. M. B. R. Pereira","doi":"10.1002/nme.7668","DOIUrl":"https://doi.org/10.1002/nme.7668","url":null,"abstract":"<div>\u0000 \u0000 <p>The polynomial bases usually applied in the implementation of hybrid-Trefftz stress elements for plate bending are extended to include the formal solutions necessary to model high-gradient stress fields associated with boundary layer and singular wedge effects. To this end, the approximation of the stress-resultant field includes the (Trefftz) solutions of the harmonic, biharmonic, and Helmholtz governing systems of differential equations. Numerical testing problems are selected to show that the element can be used to solve the Kirchhoff model and to adequately simulate both boundary layer and singular wedge effects in thin and moderately thick Mindlin–Reissner plates.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689954","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":"Laminated Composite Plate Model Considering Interfacial Imperfection Based on Quasi-Conforming Element Technique","authors":"Zhiyuan Zhu,&nbsp;Xiaobin Li","doi":"10.1002/nme.70029","DOIUrl":"https://doi.org/10.1002/nme.70029","url":null,"abstract":"<div>\u0000 \u0000 <p>Laminated composite plates widely used in industries are prone to various defects at the interfaces between layers in complex usage environments and manufacturing processes, also known as the interfacial imperfection. Therefore, based on the third-order zigzag displacement field and a layer-spring model, a four-node quadrilateral quasi-conforming plate element (QCQ4) is proposed to calculate the free vibration of the composite laminates with interfacial imperfection. In addition, combined with the numerical results from other literature, it is verified that the proposed plate element (QCQ4) can effectively obtain the stress and deflection of the composite laminates with interfacial imperfection, and accurately calculate the free vibration of laminates with different geometries, thicknesses and fiber directions. Furthermore, numerical results show that when the dimensionless interface parameter <i>R</i> characterizing the interfacial imperfection increases from 0.0 to 1.0 and 5.0, respectively, the maximum reduction in the natural frequency of the laminated thick and thin plates in the first six modes exceeds 33% and 37%. This means that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mo>=</mo>\u0000 <mn>1.0</mn>\u0000 </mrow>\u0000 <annotation>$$ R=1.0 $$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mo>=</mo>\u0000 <mn>5.0</mn>\u0000 </mrow>\u0000 <annotation>$$ R=5.0 $$</annotation>\u0000 </semantics></math> seem to be two critical values for evaluating whether thick and thin laminates will experience a significant decrease in stiffness due to interfacial imperfection. Besides, it is also found that as the increase of the dimensionless interface parameter <i>R</i>, the 4th and 5th mode shapes of the square and circular laminate, and the 5th and 6th mode shapes of the triangular laminate will change compared with the mode shapes of laminates without interfacial imperfection.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689391","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 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}