International Journal for Numerical Methods in Engineering最新文献

{"title":"Simple Harmonic Motion Analysis of Elastic Structures Using Hamiltonian Simulation via Quantum Singular Value Transformation","authors":"Koya Wagatsuma,&nbsp;Katsuhiro Endo,&nbsp;Kenjiro Terada","doi":"10.1002/nme.70407","DOIUrl":"https://doi.org/10.1002/nme.70407","url":null,"abstract":"<p>This study proposes a quantum computing algorithm for dynamic structural analysis, assuming the use of quantum computers. Specifically, we apply a quantum algorithm known as Hamiltonian Simulation (HS), which calculates the time evolution of the Schrödinger equation with time-independent coefficients, to the equations of motion governing the simple harmonic motion problem of a two-dimensional elastic structure. This is implemented by applying the Quantum Singular Value Transformation (QSVT) method to the finite-element-discretized equations. The performance of the proposed method is evaluated through several numerical experiments and compared with theoretical computational complexity and error estimates. Practical challenges are also discussed.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 16","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70407","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784760","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":"Partitioned Balancing Domain Decomposition Method for Heterogeneous Static Structures","authors":"Seung-Hoon Kang,&nbsp;K. C. Park,&nbsp;Gil-Eon Jeong,&nbsp;SangJoon Shin","doi":"10.1002/nme.70413","DOIUrl":"https://doi.org/10.1002/nme.70413","url":null,"abstract":"<p>This study proposes a partitioned balancing domain decomposition (P-BDD) method for static analysis of heterogeneous structures. The P-BDD method may be viewed as a localized version of traditional BDD approaches. Its principal solution vector consists of unassembled partition-boundary displacements, used to compute the partition-interior displacements. This differs from existing BDD methods whose primary solution vector consists of the assembled interface displacements along the partition boundaries. Two types of coarse-space preconditioners, Type-c and Type-ci, are introduced to enhance convergence. Numerical experiments demonstrate that the P-BDD method achieves high accuracy and computational efficiency in solving heterogeneous systems compared with traditional methods. As a byproduct of the P-BDD method, adopting the framework of localized Lagrange multipliers (LLMs) yields an efficient preconditioner for conventional BDD methods, referred to as LLM-BDD, which is applicable to nonconformal interface problems.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 16","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70413","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784758","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 QUBO Formulation for Multi-Material Topology Optimization With Quantum Annealing","authors":"Kenshin Nakano,&nbsp;Koji Nishiguchi,&nbsp;Junji Kato","doi":"10.1002/nme.70405","DOIUrl":"https://doi.org/10.1002/nme.70405","url":null,"abstract":"<p>Multi-material topology optimization (MMTO) seeks the optimal distribution of multiple materials within a given design domain to maximize structural performance. However, due to the high complexity of the solution space, MMTO problems are often trapped in local optima. To address this issue, a quantum annealing-based MMTO framework is proposed. The framework incorporates a quadratic unconstrained binary optimization (QUBO) formulation of the mutually exclusive material constraint (MEMC). The optimization procedure employs the generalized benders decomposition (GBD) method, which converts the original mixed-integer nonlinear program into a mixed-integer linear form which is subsequently embedded into a QUBO formulation suitable for quantum annealing. Several numerical examples are presented to validate the effectiveness of the proposed approach. The results show that multi-material designs yield better objective function values than single-material ones. The proposed method also matches or surpasses existing discrete MMTO methods in most cases and exhibits strong robustness against variations in the initial design and the material numbering order-issues that typically affect MMTO methods such as ordered solid isotropic material with penalization (SIMP). This robustness indicates that the proposed approach is less sensitive to initial conditions and provides a more reliable optimization framework. Overall, these findings confirm that the proposed QUBO-based framework is an effective and reliable approach for MMTO.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 16","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70405","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784759","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":"Peridynamics for Numerical Inversion of Laplace Transforms Using Post's Formula","authors":"Erdogan Madenci,&nbsp;Mehmet Dorduncu,&nbsp;Atila Barut","doi":"10.1002/nme.70422","DOIUrl":"https://doi.org/10.1002/nme.70422","url":null,"abstract":"<div>\u0000 \u0000 <p>Numerical inversion of the Laplace transform remains a challenging problem due to the need to select method-specific parameters. This study introduces a peridynamics-enabled Post inversion formula tailored for real-valued functions with smooth decay. The proposed approach employs the Peridynamic Differential Operator (PDDO) together with Peridynamic Least Squares Minimization (PDLSM) to accurately evaluate high-order derivatives in the Laplace domain. Numerical results first validate the method using test functions with known analytical inverses and subsequently demonstrate its applicability to solving differential and integral equations. The results indicate that the proposed approach yields accurate and stable time-domain solutions. This approach does not require prior knowledge of singularities, contour placement, or function-specific scaling.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 16","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784757","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 Multi-Scale Simulation of Progressive Damage in Laminated Composites Using Shell Finite Elements","authors":"Aewis K. W. Hii,&nbsp;Stephen R. Hallett,&nbsp;Bassam El Said","doi":"10.1002/nme.70404","DOIUrl":"https://doi.org/10.1002/nme.70404","url":null,"abstract":"<p>This paper presents a study on multi-scale modelling of progressive damage model in laminated composites using shell finite elements, with considerations for the effects of manufacturing defects. The approach utilises second-order homogenisation with 5-parameter shell formulation to capture the effects of complex sub-structural geometry and damage mechanisms in a smeared, equivalent single layer manner. During analysis, the shell constitutive tensors are continually updated and derived from high-fidelity unit cell simulations. The key benefits are two-fold. First, manufacturing defects can be directly introduced to targeted regions by assigning unit cells containing said defects. Second, the effects of progressive damage, including delamination, are accounted for in a smeared fashion without requiring complex mesh-stacking nor discontinuous kinematic enhancements. A series of numerical benchmarks are presented to demonstrate the model's ability to accurately predict damage/defect induced stiffness degradation, failure loads and damage morphology in laminated composites under loading conditions, including bending, shear, buckling and static indentation. Overall, the findings in this paper presents a proof-of-concept for a multi-scale framework that enables defect assessment and damage modelling in shell-based simulations of composite structures, and lays the groundwork for future computational acceleration via surrogate modelling.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 16","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70404","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783890","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 Generalized Shape Function Approach for Multimaterial Topology Optimization","authors":"Swagatam Islam Sarkar,&nbsp;Nikhil Singh,&nbsp;Anupam Saxena,&nbsp;Prabhat Kumar","doi":"10.1002/nme.70401","DOIUrl":"https://doi.org/10.1002/nme.70401","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents a generalized shape function (gSF) approach for multi-material topology optimization that utilizes a compact design space to produce optimized configurations featuring a large number of materials. Building upon 1D (linear), 2D (bilinear), and 3D (trilinear) shape functions, generalized <i>n</i>D (<i>n</i>-linear) shape functions are conceptualized to map the multi-material simplex domain. Natural coordinates of these shape functions are considered the design variables used to determine the material densities. These densities are mathematically proven to satisfy the essential barycentric properties, guaranteeing a physically valid material interpolation space. Furthermore, we demonstrate that applying density filtering directly to the natural coordinates is mathematically equivalent to filtering the densities themselves, and that the tailored projection scheme preserves these vital barycentric properties in the projected states. The versatility, efficacy, and success of the gSF approach are demonstrated across various 2D and 3D stiff-structure (SS) and compliant-mechanism (CM) design problems. Strain energy is minimized for SS, whereas a multicriteria objective is minimized for CMs with given volume constraints. Sensitivity analysis is performed using the adjoint variable method, and the optimization problem is solved using the method of moving asymptotes. Results for SSs and CMs in 2D and 3D, respectively, up to 24 and 15 different materials, are presented. Objective history plots indicate smooth convergence. The proposed approach removes practical restrictions on the number of candidate materials, offering excellent scalability for large-scale engineering applications.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 16","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784056","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 Convergence-Based Correction Framework for Finite Effects in Tensile Lattice Structures","authors":"Kevin Moj,&nbsp;Grzegorz Robak,&nbsp;Robert Owsiński,&nbsp;Dawid Wachowski","doi":"10.1002/nme.70403","DOIUrl":"https://doi.org/10.1002/nme.70403","url":null,"abstract":"<div>\u0000 \u0000 <p>The effective Young's modulus of periodic lattice structures is contingent not solely on topology and relative density, but also on the number of unit cells incorporated within the computational domain or specimen. This issue assumes particular significance in uniaxial tension, for which representativeness criteria are less well-defined than in compression. The present work proposes a convergence-based numerical framework for the quantitative description of finite effects and the correction of the effective Young's modulus determined for non-representative domains. The analysis was conducted for six periodic topologies, including three rod structures (BCC, Fluorite, Kelvin) and three TPMS-type structures (Fischer–Koch, Gyroid shell, Schwarz shell). The linear-elastic FEM simulations were performed for various relative densities and for cubic domains of <i>N</i> × <i>N</i> × N unit cells, with N from 1 to 12. It has been demonstrated that the convergence of the effective Young's modulus to the asymptotic value can be adequately described by an exponential model governed by a pair of parameters: the convergence length <i>τ</i>, which sets the decay rate, and the normalized amplitude <i>α</i>, which sets the magnitude of the initial deviation. Together they determine the minimum number of cells required for a given error level. On this basis, representativeness error maps and correction factor maps <i>C</i>(<i>N</i>, <i>ρ</i>_rel) were developed. These maps constitute a calibrated correction framework that allows the response of an underrepresented domain to be rescaled toward the asymptotic stiffness within the calibrated topology–density range, rather than an independent predictive model. A comparison with experimental tensile tests shows that the corrected predictions move closer to the measurements for most configurations. Direct simulations of elongated domains reveal, however, that a correction calibrated on isotropically scaled domains captures only a small part of the stiffness change produced by extending a specimen along the loading axis alone, so the framework is presented as a correction for isotropically scaled domains. At lower relative densities geometric deviations and manufacturing inaccuracies additionally contribute to the remaining discrepancy.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 16","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753533","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 Self-Correcting Adaptive Remeshing Strategy for Three-Dimensional Phase-Field Fracture Simulation","authors":"FengYu Cheng,&nbsp;Hao Yu,&nbsp;ChengSi Lyu,&nbsp;Bo Li,&nbsp;Quan Wang,&nbsp;Leong Hien Poh,&nbsp;HengAn Wu","doi":"10.1002/nme.70402","DOIUrl":"https://doi.org/10.1002/nme.70402","url":null,"abstract":"<div>\u0000 \u0000 <p>Three-dimensional phase-field fracture simulations are computationally demanding, as the geometric complexity and topological evolution of crack surfaces in 3D space require a vast number of degrees of freedom to achieve sufficient accuracy. Yet, most existing spatial adaptive schemes rely on rigid refinement patterns and empirical control parameters, which hinder local flexibility and effective adaptive mesh control. To address these limitations, a self-correcting global–local adaptive meshing method (SC-GL-AMM) is developed. A normalized nodal density field is first defined to provide a quantitative indicator of local resolution demand and guide adaptive refinement, enabling efficient and targeted mesh control. Subsequently, global crack sampling is conducted through filtering and clustering to capture 3D fracture features and perform Voronoi partitioning. Within each subdomain, a hexagonal close-packed node seeding algorithm is applied, supporting parallel processing and adaptively adjusting the distribution of mesh nodes according to the local nodal density field. Constrained Delaunay tetrahedralization is then employed to construct the adaptive mesh, ensuring geometric conformity and maintaining topological consistency across refined regions. Furthermore, a self-correcting framework is introduced, which is utilized to dynamically update the adaptive criterion based on the evolving solution-dependent indicators, enhancing robustness for complex 3D fracture scenarios. Comparative and ablation studies are conducted to assess the roles and effects of key algorithmic components. Numerical examples further demonstrate that the proposed method generates high-quality meshes with flexible adaptation, achieving up to a sixfold speed-up compared with the conventional tetrahedral subdivision strategy. This strategy thus constitutes a significant enhancement in adaptive mesh control, providing an efficient tool for large-scale three-dimensional phase-field fracture simulations.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 16","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704271","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":"Adaptive Matrix-Free Simulations of Fluid-Filled Phase-Field Fractures With Fixed-Stress Coupling and Fracture-Width Computation","authors":"Leon M. Kolditz,&nbsp;Viktor Kosin,&nbsp;Sanghyun Lee,&nbsp;Thomas Wick","doi":"10.1002/nme.70392","DOIUrl":"https://doi.org/10.1002/nme.70392","url":null,"abstract":"<p>Fluid-filled phase-field fracture simulations require robust, scalable solvers that can handle strongly nonlinear, non-smooth mechanics and tightly coupled flow on locally refined meshes. In this work, we develop an adaptive finite element framework for quasi-static, fluid-filled phase-field fractures that combines semi-smooth Newton methods, fixed-stress iterative coupling, and matrix-free geometric multigrid preconditioning. The geomechanics subproblem, with displacement and phase field as primary variables, is solved by a semi-smooth combined Newton method based on a primal-dual active set formulation. The resulting linear systems are treated with the generalized minimal residual method and matrix-free geometric multigrid preconditioners on locally refined meshes, with a local smoothing approach and careful treatment in the active set updates. The pressure equation is coupled to the geomechanics system via a fixed-stress iterative scheme which iterates until both subproblem residuals are sufficiently minimized, and each flow subproblem is likewise preconditioned by matrix-free geometric multigrid on the same adaptive meshes. In addition, we introduce an enhanced fracture-width computation, inspired by and extending existing phase-field aperture formulas, to obtain more accurate and mesh-robust width fields consistent with the regularized fracture profile. The overall computational framework is demonstrated on a set of two- and three-dimensional benchmark problems, highlighting its robustness, efficiency, and accuracy for simulating fluid-filled phase-field fractures with local mesh refinement.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 15","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70392","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752565","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":"Physics-Informed Neural Networks for Flexoelectric Boundary Value Problems: A Reformulated Architecture for High- and Mixed-Order Electromechanically Coupled Systems","authors":"Yihan Hao,&nbsp;Kai Tan,&nbsp;Leong Hien Poh,&nbsp;Zhongbo Yuan,&nbsp;Qian Deng","doi":"10.1002/nme.70400","DOIUrl":"https://doi.org/10.1002/nme.70400","url":null,"abstract":"<div>\u0000 \u0000 <p>Flexoelectricity denotes a universal electromechanical coupling in dielectric materials, whereby strain gradients break local inversion symmetry and induce electric polarization. The resulting boundary value problem (BVP) is governed by a coupled multi-physics system of high-order and mixed-order partial differential equations with nonstandard boundary conditions. Within this context, physics-informed neural networks (PINNs) offer an attractive mesh-free computational framework, providing <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}^{infty } $$</annotation>\u0000 </semantics></math>-continuous approximations of the solution fields and enabling the direct evaluation of high-order derivatives via automatic differentiation. However, we recognize that the distinctive differential structure of flexoelectric BVPs severely degrades the learning performance of naive PINN formulations. The direct use of primary field variables in strong-form residuals requires repeated evaluation of high-order derivatives, leading to unstable gradient propagation and degraded training efficiency. More critically, the problem exhibits a mixed-order structure across the coupled fields, which introduces conflicting gradients within a shared network and results in an ill-conditioned optimization landscape. In this work, we propose a reformulated PINN architecture for flexoelectric BVPs, retaining the strong-form and data-free manner. By incorporating pseudo outputs and auxiliary losses, the proposed architecture recasts the original high-order system into a lower-order reformulation; more importantly, it reduces the imbalance of differential orders across coupled fields within each loss component. This reformulation improves the compatibility between the differential structure of the governing equations and the PINN representation, thereby alleviating the associated optimization difficulty and enhancing training efficiency and accuracy. Numerical investigations on representative flexoelectric benchmark problems demonstrate strong performance as a promising numerical approach for flexoelectric BVPs and clear advantages over naive formulations. Beyond flexoelectricity, the present work provides new insights into the treatment of high- and/or mixed-order coupled partial differential systems within the PINN framework.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"127 15","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752601","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}