Pub Date : 2026-01-06DOI: 10.1016/j.finel.2025.104509
Christian Toderascu , Badadjida Wintiba , Karim Ehab Moustafa Kamel , Thierry J. Massart , Tine Tysmans
Textile Reinforced Cement (TRC) composites provide slender concrete material solutions. Using 3D textile reinforcements significantly improves the bending performance in the post-cracking stage compared to 2D textiles. Yet, no computational model takes into account explicitly the woven connections in 3D TRC. This contribution develops a novel strategy for generating the complex geometry of a mesoscale through-thickness Representative Volume Element (RVE) of 3D TRC shells, thanks to advanced geometric algorithms such as Rotation Minimising Frames (RMF), subsequently meshed and used in finite element (FE) analysis. The RVE with realistic reinforcement geometry enables the numerical evaluation of different fine scale processes contributing to the composite material performance, in particular the effect of the woven reinforcement architecture. RVE simulations under two types of bending loading conditions, using computational homogenisation procedures, illustrate that the proposed approach enables the investigation of the average macroscopic bending properties of 3D TRC based on the fine scale morphology of their reinforcement, together with an assessment of local strain fields.
{"title":"Modelling of 3D woven textile reinforced cement composites behaviour accounting for through-thickness reinforcement","authors":"Christian Toderascu , Badadjida Wintiba , Karim Ehab Moustafa Kamel , Thierry J. Massart , Tine Tysmans","doi":"10.1016/j.finel.2025.104509","DOIUrl":"10.1016/j.finel.2025.104509","url":null,"abstract":"<div><div>Textile Reinforced Cement (TRC) composites provide slender concrete material solutions. Using 3D textile reinforcements significantly improves the bending performance in the post-cracking stage compared to 2D textiles. Yet, no computational model takes into account explicitly the woven connections in 3D TRC. This contribution develops a novel strategy for generating the complex geometry of a mesoscale through-thickness Representative Volume Element (RVE) of 3D TRC shells, thanks to advanced geometric algorithms such as Rotation Minimising Frames (RMF), subsequently meshed and used in finite element (FE) analysis. The RVE with realistic reinforcement geometry enables the numerical evaluation of different fine scale processes contributing to the composite material performance, in particular the effect of the woven reinforcement architecture. RVE simulations under two types of bending loading conditions, using computational homogenisation procedures, illustrate that the proposed approach enables the investigation of the average macroscopic bending properties of 3D TRC based on the fine scale morphology of their reinforcement, together with an assessment of local strain fields.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"255 ","pages":"Article 104509"},"PeriodicalIF":3.5,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145903371","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}
Pub Date : 2026-01-02DOI: 10.1016/j.finel.2025.104505
Laura Rinaldi, Alvise Sommariva, Marco Vianello
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.
{"title":"Effective numerical integration on complex shaped elements by discrete signed measures","authors":"Laura Rinaldi, Alvise Sommariva, 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":"2026-01-02","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}
Pub Date : 2025-12-31DOI: 10.1016/j.finel.2025.104508
{"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":"2025-12-31","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}
The goal of this paper is to develop an enriched beam model using the asymptotic expansion method, that takes into account localized bearing effects by incorporating kinematics that capture the influence of external forces and support conditions. A stiffness matrix is derived for this model and a force-based method is introduced to include additional degrees of freedom for the implementation of support conditions or for the use of stiffeners. The aim is to demonstrate that the proposed enriched beam model, which considers the effects of external force distribution and localized effects specifically those resulting from supports, can be as effective as a volumetric or shell model of the same problem. The formulation is tested on two thin-walled box-girder benchmarks. For an unstiffened girder, the enriched element reproduces shell-model deflections with a maximum error of 0.83%. When five diagonal struts are inserted, global displacements and strut axial forces remain within 7% and 6% of the reference shell solution, respectively. This approach offers significant computational efficiency while effectively handling complex configurations, including struts and stiffeners.
{"title":"Localized bearing effects using an enriched beam model","authors":"Laila Limni , Youssef Derrazi , Mohammed-Khalil Ferradi","doi":"10.1016/j.finel.2025.104507","DOIUrl":"10.1016/j.finel.2025.104507","url":null,"abstract":"<div><div>The goal of this paper is to develop an enriched beam model using the asymptotic expansion method, that takes into account localized bearing effects by incorporating kinematics that capture the influence of external forces and support conditions. A stiffness matrix is derived for this model and a force-based method is introduced to include additional degrees of freedom for the implementation of support conditions or for the use of stiffeners. The aim is to demonstrate that the proposed enriched beam model, which considers the effects of external force distribution and localized effects specifically those resulting from supports, can be as effective as a volumetric or shell model of the same problem. The formulation is tested on two thin-walled box-girder benchmarks. For an unstiffened girder, the enriched element reproduces shell-model deflections with a maximum error of 0.83%. When five diagonal struts are inserted, global displacements and strut axial forces remain within 7% and 6% of the reference shell solution, respectively. This approach offers significant computational efficiency while effectively handling complex configurations, including struts and stiffeners.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104507"},"PeriodicalIF":3.5,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884253","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}
Pub Date : 2025-12-27DOI: 10.1016/j.finel.2025.104506
Shahed Rezaei , Reza Najian Asl , Kianoosh Taghikhani , Ahmad Moeineddin , Michael Kaliske , Markus Apel
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.
{"title":"Finite Operator Learning: Bridging neural operators and numerical methods for efficient parametric solution and optimization of PDEs","authors":"Shahed Rezaei , Reza Najian Asl , Kianoosh Taghikhani , Ahmad Moeineddin , Michael Kaliske , 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":"2025-12-27","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}
Pub Date : 2025-12-25DOI: 10.1016/j.finel.2025.104504
Kent T. Danielson , William M. Furr
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.
{"title":"Numerical properties of nodal mass lumping methods for arbitrary-order finite elements","authors":"Kent T. Danielson , 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":"2025-12-25","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}
Pub Date : 2025-12-24DOI: 10.1016/j.finel.2025.104499
Misganaw Abebe , Min-Geun Kim , Bonyong Koo
In this paper, Model-Agnostic Meta-Learning based on Deep Energy Method (MAML-DEM), a novel meta-learning framework is developed for the geometric parameterization. A single meta-trained neural network efficiently solves diverse 2D linear elasticity problems in plates with complex and varying topologies, including those containing multiple mixed circular and elliptical holes. Conceptual studies further demonstrate the framework's potential to generalize to non-uniform boundary conditions and more complex L-shaped hole geometries. By leveraging the variational principle of minimum potential energy, the model avoids the unstable gradients linked to second-order derivatives in standard Physics-Informed Neural Networks (PINNs). Additionally, a geometry-aware adaptive sampling method is employed to capture high-stress areas around geometric discontinuities precisely. During meta-training, the model learns a broad physical understanding applicable across various tasks. Results show that this approach can adapt very quickly to new and unseen geometries, achieving speeds up to 69x faster than training a specific model from scratch. The MAML-DEM framework exhibits superior accuracy and stability over conventional PINN methods, while also demonstrating strong generalization capability to tasks beyond its training data, effectively handling variations in topology, boundary conditions, and geometric complexity. This work highlights the potential of meta-learning to transform physics-informed simulations into practical and efficient tools for rapid engineering design and analysis.
{"title":"Physics-informed meta-learning for elasticity problems with geometric parameterization","authors":"Misganaw Abebe , Min-Geun Kim , Bonyong Koo","doi":"10.1016/j.finel.2025.104499","DOIUrl":"10.1016/j.finel.2025.104499","url":null,"abstract":"<div><div>In this paper, Model-Agnostic Meta-Learning based on Deep Energy Method (MAML-DEM), a novel meta-learning framework is developed for the geometric parameterization. A single meta-trained neural network efficiently solves diverse 2D linear elasticity problems in plates with complex and varying topologies, including those containing multiple mixed circular and elliptical holes. Conceptual studies further demonstrate the framework's potential to generalize to non-uniform boundary conditions and more complex L-shaped hole geometries. By leveraging the variational principle of minimum potential energy, the model avoids the unstable gradients linked to second-order derivatives in standard Physics-Informed Neural Networks (PINNs). Additionally, a geometry-aware adaptive sampling method is employed to capture high-stress areas around geometric discontinuities precisely. During meta-training, the model learns a broad physical understanding applicable across various tasks. Results show that this approach can adapt very quickly to new and unseen geometries, achieving speeds up to 69x faster than training a specific model from scratch. The MAML-DEM framework exhibits superior accuracy and stability over conventional PINN methods, while also demonstrating strong generalization capability to tasks beyond its training data, effectively handling variations in topology, boundary conditions, and geometric complexity. This work highlights the potential of meta-learning to transform physics-informed simulations into practical and efficient tools for rapid engineering design and analysis.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"254 ","pages":"Article 104499"},"PeriodicalIF":3.5,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822960","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}
Pub Date : 2025-12-18DOI: 10.1016/j.finel.2025.104503
Tao Nie, Jianli Liu, Wanpeng Zhao, Tao Zhang, Ruichen Zhang, Jinpeng Han, Zhaohui Xia
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.
{"title":"A novel data compression method for GPU accelerated large-scale isogeometric topology optimization with order-ascending strategy","authors":"Tao Nie, Jianli Liu, Wanpeng Zhao, Tao Zhang, Ruichen Zhang, Jinpeng Han, 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":"2025-12-18","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}
Pub Date : 2025-12-17DOI: 10.1016/j.finel.2025.104464
Taejung Lim , Minh-Chien Trinh , Hyungmin Jun
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.
{"title":"Partition of Unity-based four-node tetrahedral element for nonlinear structural analysis of nearly incompressible hyperelastic materials","authors":"Taejung Lim , Minh-Chien Trinh , 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":"2025-12-17","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}
Pub Date : 2025-12-16DOI: 10.1016/j.finel.2025.104498
Chenqi Li , Lingkuan Xuan , Jingfeng Gong , Hongyu Guo , Le Gu
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.
{"title":"An axisymmetric finite-volume method for thermal stress problems in heterogeneous materials","authors":"Chenqi Li , Lingkuan Xuan , Jingfeng Gong , Hongyu Guo , 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":"2025-12-16","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}
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