Finite Elements in Analysis and Design最新文献

{"title":"An axisymmetric finite-volume method for thermal stress problems in heterogeneous materials","authors":"Chenqi Li ,&nbsp;Lingkuan Xuan ,&nbsp;Jingfeng Gong ,&nbsp;Hongyu Guo ,&nbsp;Le Gu","doi":"10.1016/j.finel.2025.104498","DOIUrl":"10.1016/j.finel.2025.104498","url":null,"abstract":"<div><div>To reduce the computational cost of axisymmetric problems and to extend the applicability of the cell-vertex finite volume method (CV-FVM), this paper develops an axisymmetric cell-vertex finite volume method (ACV-FVM) for transient thermal stress analysis in heterogeneous materials with axisymmetric structures. The reduced two-dimensional domain is discretized using 3-node triangular ring elements and 4-node quadrilateral ring elements. A numerical solver based on the ACV-FVM is implemented in C++ and applied to solve thermo-mechanical coupling problems involving homogeneous materials, multilayered materials, functionally graded materials, and materials with temperature-dependent properties. The numerical results show good agreement with analytical solutions and other numerical results. The findings indicate that, compared to nodal-based output schemes, element-center-based output significantly suppresses spurious stress oscillations in multilayered materials. The proposed method has been successfully applied to the thermal stress analysis of a cylinder liner with thermal barrier coatings. Results reveal that temperature-dependent material properties lead to an approximate 1.5 % increase in temperature and a 3.4 % increase in thermal stress at the same location, highlighting the necessity of considering temperature-dependent thermo-mechanical behavior in such analyses.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104498"},"PeriodicalIF":3.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784762","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":"Editorial for the Special Issue on Digital Twins in Analysis and Design","authors":"","doi":"10.1016/j.finel.2025.104508","DOIUrl":"10.1016/j.finel.2025.104508","url":null,"abstract":"","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104508"},"PeriodicalIF":3.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894406","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":"Numerical properties of nodal mass lumping methods for arbitrary-order finite elements","authors":"Kent T. Danielson ,&nbsp;William M. Furr","doi":"10.1016/j.finel.2025.104504","DOIUrl":"10.1016/j.finel.2025.104504","url":null,"abstract":"<div><div>Higher-order finite elements using Lagrange and other bases provide distinct benefits over traditional first-order ones in nonlinear solid dynamics but pose additional challenges for explicit methods using nodal mass lumping. Row-summation nodal mass lumping is shown to have a variationally consistent mathematical foundation for explicit methods. Notorious problems with this procedure are caused by improper selection of bases that are not well-suited (suboptimal) for nodal mass lumping, by any method, and not by the lumping scheme. Nodal integration lumping, i.e., via Gauss-Lobatto quadrature using bases that satisfy the Kronecker-Delta property, is also seen to be just a specific case of row-summation lumping (off-diagonal terms innately sum to zero) with a fixed precision. The more general row-sum form, however, is theoretically sound for other appropriate bases and permits arbitrary precision quadrature rules that is shown can be important with distortion, including desirable curvature permitted by higher-order shape functions. Imprecise nodal quadrature lumping can sometimes produce instabilities. In other cases, it captures lower modes sufficiently for solution accuracy but still inadequately computes the largest mode to thus reduce the stable time increment size noticeably. The distinct imprecise over-calculation of the consistent mass matrix by Gauss-Lobatto nodal quadrature and its equivalency to row-summation nodal mass-lumping also reveals additional interesting numerical properties.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104504"},"PeriodicalIF":3.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822959","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":"Finite Operator Learning: Bridging neural operators and numerical methods for efficient parametric solution and optimization of PDEs","authors":"Shahed Rezaei ,&nbsp;Reza Najian Asl ,&nbsp;Kianoosh Taghikhani ,&nbsp;Ahmad Moeineddin ,&nbsp;Michael Kaliske ,&nbsp;Markus Apel","doi":"10.1016/j.finel.2025.104506","DOIUrl":"10.1016/j.finel.2025.104506","url":null,"abstract":"<div><div>We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach unifies aforementioned methods and we can parametrically solve partial differential equations in a data-free manner and provide accurate sensitivities. These capabilities enable gradient-based optimization without the typical sensitivity analysis costs, unlike adjoint methods that scale directly with the number of response functions. Our Finite Operator Learning (FOL) approach originally employs feed-forward neural networks to directly map the discrete design space to the discrete solution space, and can alternatively be combined with existing physics-informed neural operator techniques to recover continuous solution fields, while avoiding the need for automatic differentiation when formulating the loss terms. The discretized governing equations, as well as the design and solution spaces, can be derived from any well-established numerical techniques. In this work, we employ the Finite Element Method (FEM) to approximate fields and their spatial derivatives. Thanks to the finite-element formulation, Dirichlet boundary conditions are satisfied by construction, and Neumann boundary conditions are naturally included in the FE residual through the weak form. Subsequently, we conduct Sobolev training to minimize a multi-objective loss function, which includes the discretized weak form of the energy functional, boundary conditions violations, and the stationarity of the residuals with respect to the design variables. Our study focuses on the heat equation and the mechanical equilibrium problem. First, we primarily address the property distribution in heterogeneous materials, where Fourier-based parameterization is employed to significantly reduce the number of design variables. Second, we explore changes in the source term in such PDEs. Third, we investigate the solution under different boundary conditions. In the context of gradient-based optimization, we examine the tuning of the microstructure’s heat transfer characteristics. Our technique also simplifies to an efficient matrix-free PDE solver that can compete with standard available solvers. This is demonstrated by solving a nonlinear thermal and mechanical PDE on a complex 3D geometry.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104506"},"PeriodicalIF":3.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840875","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":"Effective numerical integration on complex shaped elements by discrete signed measures","authors":"Laura Rinaldi,&nbsp;Alvise Sommariva,&nbsp;Marco Vianello","doi":"10.1016/j.finel.2025.104505","DOIUrl":"10.1016/j.finel.2025.104505","url":null,"abstract":"<div><div>We discuss a cheap and stable approach to polynomial moment-based compression of multivariate measures by discrete signed measures. The method is based on the availability of an orthonormal basis and a low-cardinality algebraic quadrature formula for an auxiliary measure in a bounding set. Differently from other approaches, no conditioning issue arises since no matrix factorization or inversion is needed. We provide bounds for the sum of the absolute values of the signed measure weights, and we make two examples: efficient quadrature on curved planar elements with spline boundary (in view of the application to high-order FEM/VEM), and compression of QMC integration on 3D elements with complex shape.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104505"},"PeriodicalIF":3.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884254","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":"Integral constitutive equations based temporal finite element modeling for the static viscoelastic problem","authors":"Fengling Chen,&nbsp;Yiqian He,&nbsp;Haitian Yang","doi":"10.1016/j.finel.2025.104490","DOIUrl":"10.1016/j.finel.2025.104490","url":null,"abstract":"<div><div>A stepwise spatial–temporal finite element algorithm is developed to provide a general numerical tool for solving static viscoelastic problems with integral constitutive equations. The displacement, strain and stress are formulated by the hybrid basis functions based Temporal Finite Element Method (TFEM), and are incorporated into the constitutive relations. The framework is established based on the virtual work principle and the weighted residual technique, and is convenient to cooperate with kinds of numerical schemes for boundary value problems such as FEM and SBFEM. Two criteria are proposed to numerically evaluate error propagation during the step-marching process, which can be used to determine appropriate time-step sizes for prescribed temporal shape functions and spatial FE meshes. Compared with the TFEM algorithm based on differential viscoelastic constitutive equations, the present approach overcomes the order-restriction limitation by employing integral constitutive equations with Prony-series based relaxation moduli. Numerical examples demonstrate the capability and accuracy of the proposed method in handling viscoelastic problems involving material heterogeneity, stress singularity, various relaxation moduli, and different loading forms. The obtained results with various configurations of temporal shape functions and step sizes, exhibit good agreement with analytical solutions and ABAQUS simulations.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104490"},"PeriodicalIF":3.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685751","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":"Regularizing the linearly extrapolated BDF2 scheme for incompressible flows with time relaxation","authors":"Sean Breckling ,&nbsp;Jorge Reyes ,&nbsp;Sidney Shields ,&nbsp;Clifford Watkins","doi":"10.1016/j.finel.2025.104491","DOIUrl":"10.1016/j.finel.2025.104491","url":null,"abstract":"<div><div>This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. We also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104491"},"PeriodicalIF":3.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731679","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 data compression method for GPU accelerated large-scale isogeometric topology optimization with order-ascending strategy","authors":"Tao Nie,&nbsp;Jianli Liu,&nbsp;Wanpeng Zhao,&nbsp;Tao Zhang,&nbsp;Ruichen Zhang,&nbsp;Jinpeng Han,&nbsp;Zhaohui Xia","doi":"10.1016/j.finel.2025.104503","DOIUrl":"10.1016/j.finel.2025.104503","url":null,"abstract":"<div><div>This paper aims to address the common challenges of storage overhead and computational inefficiencies that arise in isogeometric topology optimization (ITO) when dealing with large-scale problems. To tackle these issues, the paper proposes a novel framework that combines a highly efficient data storage strategy with Graphics Processing Unit (GPU) accelerated optimization. By utilizing control point pairs and removing redundant matrix storage, the Isogeometric Compressed Sparse Row (IGA-CSR) technique effectively reduces storage requirements. Furthermore, the paper presents an order-ascending optimization strategy to avoid intensive calculations caused by large degrees of freedom in the early stage. What's more, the introduction of Graphics Processing Unit further improves the optimization process. Combining these methods, an efficient optimization framework is proposed, which allows efficient optimization even for problems that involve tens of millions of degrees of freedom via single NVIDIA GeForce RTX 3090 GPU with 24 GB. Validation through two 3D benchmark examples reveals that the IGA-CSR method shows the best performance comparing with existing methods in memory consumption. At the same time, it enhances computational efficiency about 65.4 % comparing with conventional second-order isogeometric topology optimization via GPU acceleration.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104503"},"PeriodicalIF":3.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784760","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":"Unsymmetric Serendipity finite elements: Performance analysis","authors":"S. Eisenträger ,&nbsp;E. Woschke ,&nbsp;E.T. Ooi","doi":"10.1016/j.finel.2025.104487","DOIUrl":"10.1016/j.finel.2025.104487","url":null,"abstract":"<div><div>This paper presents a comparative analysis of the conventional finite element method (FEM) and the unsymmetric finite element method (UFEM) for Serendipity elements (<span><math><mrow><mi>p</mi><mo>≤</mo><mn>3</mn></mrow></math></span>), focusing on two factors: (i) achievable accuracy and (ii) computational costs. The UFEM, based on a Petrov–Galerkin formulation, uses <em>metric</em> shape functions as <em>trial</em> functions and <em>parametric</em> shape functions as <em>test</em> functions. This unique approach enhances the resistance against mesh distortion, as it ensures polynomial completeness of the Ansatz space of unsymmetric finite elements. Hence, higher accuracy can be achieved in complex geometries. However, the unsymmetric nature of UFEM leads to increased computational costs as a result of the added complexity of solving the resulting system of equations. This study provides a quantitative evaluation of the computational burden associated with achieving specific error thresholds for both methods. By analyzing a range of benchmark problems, we identify scenarios in which each method performs optimally, offering practical insights for selecting the appropriate approach based on accuracy demands and computational constraints. Our findings suggest that, while UFEM can produce superior accuracy, its computational efficiency depends on application-specific requirements and available resources.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104487"},"PeriodicalIF":3.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145659097","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":"Partition of Unity-based four-node tetrahedral element for nonlinear structural analysis of nearly incompressible hyperelastic materials","authors":"Taejung Lim ,&nbsp;Minh-Chien Trinh ,&nbsp;Hyungmin Jun","doi":"10.1016/j.finel.2025.104464","DOIUrl":"10.1016/j.finel.2025.104464","url":null,"abstract":"<div><div>This study introduces a refined four-node tetrahedral finite element employing the Partition of Unity method for nonlinear static and modal analysis of nearly incompressible hyperelastic materials. The proposed Partition of Unity-based element effectively reduces volumetric locking and improves solution accuracy without increasing the number of nodes. The Partition of Unity method enriches the displacement field by incorporating additional polynomial basis functions, enabling higher-order displacement approximation, and effectively alleviating volumetric locking. Mooney–Rivlin and Neo-Hookean material models are integrated with the penalty method, ensuring robust handling of nearly incompressible behavior. Large deformations are addressed using a total Lagrangian formulation. In addition, a displacement-based direct iterative nonlinear modal analysis procedure is employed to derive nonlinear natural frequencies and corresponding mode shapes. In nonlinear static analysis, the proposed element is validated through various numerical cases including blocks under compression, cylinders under large deformation, mesh distortion sensitivity analysis, and tires under compression. The present element effectively alleviates the volumetric locking phenomenon and provides excellent performance even when using a coarse mesh. Nonlinear modal analysis has been performed on cases such as free vibration of distorted plates, truncated cylindrical shells, and hyperelastic soft robots. The proposed elements effectively capture nonlinear natural frequencies and mode shapes even with distorted and coarse meshes.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104464"},"PeriodicalIF":3.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784761","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}