International Journal for Numerical Methods in Engineering最新文献

{"title":"Topology Optimization of Elastoplastic Structure Based on Shakedown Strength","authors":"Songhua Huang,&nbsp;Lele Zhang,&nbsp;Geng Chen,&nbsp;Yugong Xu,&nbsp;Min Chen,&nbsp;Zhiyuan Liu,&nbsp;Eng Gee Lim","doi":"10.1002/nme.7627","DOIUrl":"https://doi.org/10.1002/nme.7627","url":null,"abstract":"<div>\u0000 \u0000 <p>The traditional approach to structural lightweight optimization design, which is based on the elastic limit rule, often results in a structure that exhibits either weight redundancy or strength redundancy to some extent. This study introduces a novel integration of shakedown analysis with structural topology optimization, departing from the conventional elastic limit rule. Shakedown analysis identifies a non-failure external load region beyond the elastic limit but below the plastic limit, independent of loading history. The proposed method, for the first time, accounts for the influence of self-equilibrium residual stress at the element level, redefining effective and ineffective elements in topology optimization. Shakedown total stress replaces elastic equivalent stress, offering a comprehensive measure. Utilizing Melan's lower bound theorem, a gradient-based topology optimization framework for shakedown analysis is developed, ensuring structures stay within the elastic–plastic range, preventing excessive plastic deformation. The approach, employing the moving asymptotes method after adjoint sensitivity analysis of shakedown total stress, is applied to a three-dimensional L-shaped bracket. Even with a remarkable 50% reduction in weight, the maximum total shakedown stress of the bracket reveals that it only increases by a modest 17.20% from its initial value. Moreover, compared to traditional topology optimization methods based on either elastic stress or stiffness, the proposed method based on total shakedown stress leads to a higher shakedown limit. Specifically, the configuration designed using the total shakedown stress exhibited increases of 2.01% and 9.82% in the shakedown limit compared to those obtained using stiffness and equivalent elastic stress, respectively. This suggests that the proposed method can effectively balance the trade-off between shakedown strength and structural stiffness, achieving a 2.01% rise in shakedown strength with only a 2.24% compromise in structural stiffness. These findings highlight the method's effectiveness and potential, emphasizing the benefit of redefining effective and ineffective elements using shakedown stress in topology optimization.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362897","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 Discrete Element Method for Smooth Polyhedrons and Its Application to Modeling Flows of Concave-Shaped Particles","authors":"Siqiang Wang,&nbsp;Qingwei Xu,&nbsp;Dongfang Liang,&nbsp;Shunying Ji","doi":"10.1002/nme.7628","DOIUrl":"https://doi.org/10.1002/nme.7628","url":null,"abstract":"<div>\u0000 \u0000 <p>The smooth polyhedral model has been commonly used to construct non-spherical particles with smooth surfaces, whereas it is mainly constrained to numerical simulations involving concave-shaped particles. This constraint arises from the limitations imposed by the contact algorithm. In this study, the contact detection between smooth polyhedrons is simplified to that between dilated triangular elements, and a discrete element method for concave polyhedral particles with smooth surfaces is developed. Subsequently, an automatic mesh simplification algorithm is established to enhance the computational efficiency without compromising accuracy. In validating the smooth polyhedral model, the simulation results of a hexahedron colliding with a plane are found to agree favorably with the experimental results. Then, the elastic collisions between the convex and concave particles are analyzed, and the total kinetic energy before and after the particle collision remains unchanged. Furthermore, the influences of particle morphology on the packing fraction, flow fluctuation, flow rate, mixing rate, velocity distribution, and system energy in hoppers and rotating drums are analyzed, revealing the underlying flow characteristics of concave polyhedral granular materials with smooth surfaces.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362899","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 Finite Interface Element for Modeling Inclusion-Matrix Interaction in Magneto-Active Elastomers","authors":"Will Klausler,&nbsp;Michael Kaliske","doi":"10.1002/nme.7625","DOIUrl":"https://doi.org/10.1002/nme.7625","url":null,"abstract":"<p>Magneto-active elastomers (MAEs) are an emerging smart composite material consisting of a compliant elastomer matrix filled with stiff, magnetizable inclusions. Meso-scale models, which treat the matrix and inclusions as discrete, are currently formulated with the assumption of perfect bonding at the interface. We apply a model for cohesive damage at the material interface and introduce a treatment for the transmission of the magnetic field in the gap. Examples demonstrate the concept and the difference in structural response between samples treated with the conventional and presented approaches.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7625","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362877","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":"Convergence of Damped Polarization Schemes for the FFT-Based Computational Homogenization of Inelastic Media With Pores","authors":"Elodie Donval,&nbsp;Matti Schneider","doi":"10.1002/nme.7632","DOIUrl":"https://doi.org/10.1002/nme.7632","url":null,"abstract":"<p>Porous microstructures represent a challenge for the convergence of FFT-based computational homogenization methods. In this contribution, we show that the damped Eyre–Milton iteration is linearly convergent for a class of nonlinear composites with a regular set of pores, provided the damping factor is chosen between zero and unity. First, we show that an abstract fixed-point method with non-expansive fixed-point operator and non-trivial damping converges linearly, provided the associated residual mapping satisfies a monotonicity condition on a closed subspace. Then, we transfer this result to the framework of polarization schemes and conclude the linear convergence of the damped Eyre–Milton scheme for porous materials. We present general arguments which apply to a class of nonlinear composites and mixed stress-strain loadings, as well. We show that the best contraction estimate is reached for a damping factor of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$$ 1/2 $$</annotation>\u0000 </semantics></math>, that is, for the polarization scheme of Michel–Moulinec–Suquet, and derive the corresponding optimal reference material. Our results generalize the recent work of Sab and co-workers who showed that an adaptively damped Eyre–Milton scheme leads to linear convergence for a class of linear composites with pores. Finally, we report on computational experiments which support our findings.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7632","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362876","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":"Sequential Maximal Updated Density Parameter Estimation for Dynamical Systems With Parameter Drift","authors":"Carlos del-Castillo-Negrete,&nbsp;Rylan Spence,&nbsp;Troy Butler,&nbsp;Clint Dawson","doi":"10.1002/nme.7618","DOIUrl":"https://doi.org/10.1002/nme.7618","url":null,"abstract":"<div>\u0000 \u0000 <p>We present a novel method for generating sequential parameter estimates and quantifying epistemic uncertainty in dynamical systems within a data-consistent (DC) framework. The DC framework differs from traditional Bayesian approaches due to the incorporation of the push-forward of an initial density, which performs selective regularization in parameter directions not informed by the data in the resulting updated density. This extends a previous study that included the linear Gaussian theory within the DC framework and introduced the maximal updated density (MUD) estimate as an alternative to both least squares and maximum a posterior (MAP) estimates. In this work, we introduce algorithms for operational settings of MUD estimation in real- or near-real time where spatio-temporal datasets arrive in packets to provide updated estimates of parameters and identify potential parameter drift. Computational diagnostics within the DC framework prove critical for evaluating (1) the quality of the DC update and MUD estimate and (2) the detection of parameter value drift. The algorithms are applied to estimate (1) wind drag parameters in a high-fidelity storm surge model, (2) thermal diffusivity field for a heat conductivity problem, and (3) changing infection and incubation rates of an epidemiological model.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362849","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":"Heterogeneous Smoothed Finite Element Method: Convergence/Superconvergence Proof and Its Performance in High-Contrast Composite Materials","authors":"Yun Chen,&nbsp;Guirong Liu,&nbsp;Junzhi Cui,&nbsp;Qiaofu Zhang,&nbsp;Ziqiang Wang","doi":"10.1002/nme.7636","DOIUrl":"https://doi.org/10.1002/nme.7636","url":null,"abstract":"<div>\u0000 \u0000 <p>Smoothed Finite Element Method (S-FEM) has been widely used in many engineering simulations. However, there are still a lot of theoretical problems to be solved, especially with regard to composite materials and convergence proof. Based on a novel least-squares approximation and conservation property, we extend S-FEM to heterogeneous materials. Firstly, the orthogonality, Softening Effect, and energy function are checked. Secondly, the interpolation error in the maximum norm is estimated in any dimension. Consequently, we get a theoretical convergence rate which has been sought since the year 2010. When restricted to one-dimensional problems, we construct a special test function to prove the superconvergence: (1) S-FEM flux is exact in the meaning of element-wise integral; (2) numerical flux is exact at some point in each element; (3) physical flux can be quadratically approximated at the center of each element. At last, we present two numerical experiments: (1) conventional S-FEM fails in high-contrast composite materials while our new scheme performs well; (2) our flux converges quadratically.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362847","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":"On the Use of Block Low Rank Preconditioners for Primal Domain Decomposition Methods","authors":"Christophe Bovet,&nbsp;Théodore Gauthier,&nbsp;Pierre Gosselet","doi":"10.1002/nme.7623","DOIUrl":"https://doi.org/10.1002/nme.7623","url":null,"abstract":"<p>This article investigates the use of the block low rank (BLR) factorization, recently proposed in the MUMPS solver, to define efficient and cheap preconditioners for primal domain decomposition methods, such as the Balancing Domain Decomposition method (BDD) and its adaptive multipreconditioned variant. To be scalable, these methods are equipped with an augmentation projector built from the local preconditioners nullspaces. The determination of these nullspaces is a complex task in the case of ill conditioned system, the use of block low rank compression makes this task even more complex as MUMPS' automatic detection no longer works properly. Two alternatives based on incomplete factorization with a well-chosen Schur complement are proposed. Also, the first massively parallel implementation of the adaptive multipreconditioned BDD solver (AMPBDD) is introduced. The performance of the methods is assessed with two weak scalability studies on problems up to 24,576 cores and about 790 millions of unknowns, on the Sator and Topaze supercomputers. BLR preconditioning proves to be an interesting strategy both in terms of memory usage and time to solution for reasonably conditioned problems.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7623","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362910","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 Finite Operator Learning Technique for Mapping the Elastic Properties of Microstructures to Their Mechanical Deformations","authors":"Shahed Rezaei,&nbsp;Reza Najian Asl,&nbsp;Shirko Faroughi,&nbsp;Mahdi Asgharzadeh,&nbsp;Ali Harandi,&nbsp;Rasoul Najafi Koopas,&nbsp;Gottfried Laschet,&nbsp;Stefanie Reese,&nbsp;Markus Apel","doi":"10.1002/nme.7637","DOIUrl":"https://doi.org/10.1002/nme.7637","url":null,"abstract":"<p>To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. We propose directly utilizing the available discretized weak form in finite element packages to construct the loss functions algebraically, thereby demonstrating the ability to find solutions even in the presence of sharp discontinuities. Our focus is on micromechanics as an example, where knowledge of deformation and stress fields for a given heterogeneous microstructure is crucial for further design applications. The primary parameter under investigation is the Young's modulus distribution within the heterogeneous solid system. Our investigations reveal that physics-based training yields higher accuracy compared with purely data-driven approaches for unseen microstructures. Additionally, we offer two methods to directly improve the process of obtaining high-resolution solutions, avoiding the need to use basic interpolation techniques. The first one is based on an autoencoder approach to enhance the efficiency for calculation on high resolution grid points. Next, Fourier-based parametrization is utilized to address complex 2D and 3D problems in micromechanics. The latter idea aims to represent complex microstructures efficiently using Fourier coefficients. The proposed approach draws from finite element and deep energy methods but generalizes and enhances them by learning parametric solutions without relying on external data. Compared with other operator learning frameworks, it leverages finite element domain decomposition in several ways: (1) it uses shape functions to construct derivatives instead of automatic differentiation; (2) it automatically includes node and element connectivity, making the solver flexible for approximating sharp jumps in the solution fields; and (3) it can handle arbitrary complex shapes and directly enforce boundary conditions. We provided some initial comparisons with other well-known operator learning algorithms, further emphasize the advantages of the newly proposed method.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7637","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113594","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":"Co-Simulation Interface Model Reduction for Large-Scale Coupled Simulations","authors":"Jari Peeters,&nbsp;Martijn Vermaut,&nbsp;Simon Vanpaemel,&nbsp;Frank Naets","doi":"10.1002/nme.7626","DOIUrl":"https://doi.org/10.1002/nme.7626","url":null,"abstract":"<div>\u0000 \u0000 <p>The paper presents a novel approach for reducing the co-simulation interface representation between multiple large-scale models. The methodology leverages model order reduction through component mode synthesis in some specific small deformation flexible multibody formulations that yield a constant transformation matrix between Cartesian coordinates and general multibody coordinates, such as the flexible natural coordinates formulation or the generalized component mode synthesis. The constant transformation matrix stemming from these techniques is further modified using modified Gram–Schmidt orthonormalization and the effective independence methodology to create a constant interface model reduction matrix. This matrix effectively connects a minimal set of interface nodes to the entire nodal domain, while simultaneously projecting the forces acting on the entire nodal domain onto the interface nodes. Notably, the proposed methodology scales the size of the required co-simulation interface representation with the considered set of mode shapes rather than the size of the numerical finite element mesh. This co-simulation interface model reduction strategy not only renders large distributed load models compatible with the Functional Mock-Up Interface but also extends its applicability to any structural model beyond the flexible multibody scope, provided that deformations remain relatively small. Numerical validation with a simply supported beam, connected to springs at each node, demonstrates that the interface model reduction error is significantly smaller than the co-simulation error. This suggests that substantial interface model reduction can be achieved without compromising accuracy. Moreover, additional numerical validation performed with a rotor-drum model showcases the versatility and scalability of the proposed approach, particularly in addressing dynamic structural systems.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113584","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 Multi-Time Stepping Algorithm for the Modelling of Heterogeneous Structures With Explicit Time Integration","authors":"Kin Fung Chan,&nbsp;Nicola Bombace,&nbsp;Duygu Sap,&nbsp;David Wason,&nbsp;Simone Falco,&nbsp;Nik Petrinic","doi":"10.1002/nme.7638","DOIUrl":"https://doi.org/10.1002/nme.7638","url":null,"abstract":"<p>Heterogeneous solids often exhibit complex dynamic behavior, requiring simulations to use varying time steps. However, the conventional use of a single-time step for the entire domain can be inefficient. This article proposes a multi-time stepping algorithm that addresses this challenge by relaxing the constraint for an integer or constant time step ratio between subdomains and eliminating the need for kinematic interpolation. The algorithm ensures the satisfaction of the Courant-Friedrichs-Lewy condition, deviating only to allow subdomains to remain in synchronization. Consequently, less integration steps are performed in comparison to state-of-the-art asynchronous integrators. We extend to the coupling of multiple subdomains, where each subdomain has its time step. Simulating stress wave propagation in metamaterials demonstrates that the proposed algorithm significantly accelerates simulation time, without sacrificing accuracy.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7638","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113652","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}