Pub Date : 2026-02-06DOI: 10.1016/j.finel.2026.104525
Tan N. Nguyen, Tan Khoa Nguyen, Suppakit Eiadtrong, Nuttawit Wattanasakulpong, Mohamed-Ouejdi Belarbi, Nader M. Okasha, Masoomeh Mirrashid, Aman Garg
{"title":"An accurate coarse mesh-based analysis approach for nonlinear bending and post-buckling problems of plates and shells utilizing recurrent neural networks with Bayesian regularization back-propagation algorithm","authors":"Tan N. Nguyen, Tan Khoa Nguyen, Suppakit Eiadtrong, Nuttawit Wattanasakulpong, Mohamed-Ouejdi Belarbi, Nader M. Okasha, Masoomeh Mirrashid, Aman Garg","doi":"10.1016/j.finel.2026.104525","DOIUrl":"https://doi.org/10.1016/j.finel.2026.104525","url":null,"abstract":"","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"51 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134779","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 : 2026-02-05DOI: 10.1016/j.finel.2026.104527
Simon Essongue, Bourama Diarra, Eric Lacoste
{"title":"Runge–Kutta–Chebyshev schemes to accelerate thermal modelling of additive manufacturing processes","authors":"Simon Essongue, Bourama Diarra, Eric Lacoste","doi":"10.1016/j.finel.2026.104527","DOIUrl":"https://doi.org/10.1016/j.finel.2026.104527","url":null,"abstract":"","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"92 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134781","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 : 2026-02-05DOI: 10.1016/j.finel.2026.104524
Yanhu Li, Yongjie Lu, Shaopu Yang, Jianxi Wang, Haoyu Li
{"title":"Evaluation of locking mitigation techniques and development of locking-free ANCF shell elements for nearly incompressible materials based on the Yeoh model","authors":"Yanhu Li, Yongjie Lu, Shaopu Yang, Jianxi Wang, Haoyu Li","doi":"10.1016/j.finel.2026.104524","DOIUrl":"https://doi.org/10.1016/j.finel.2026.104524","url":null,"abstract":"","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"46 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2026-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134780","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 : 2026-02-04DOI: 10.1016/j.finel.2026.104526
Qi Ran , Huan Zhang , She Li , Xiangyang Cui
The DKMQ24 element, based on the Naghdi–Mindlin–Reissner shell theory, performs well in bending- and shear-dominated problems but remains sensitive to mesh distortion and suffers from in-plane shear locking. In this study, the membrane strain field is reconstructed using the Mixed Interpolation of Tensorial Components (MITC) method to reduce mesh sensitivity, and the Enhanced Assumed Strain (EAS) method is applied to alleviate in-plane shear locking. An improper bending approximation and the artificial stiffness for drilling rotation in DKMQ24 hindered the element from fully passing rigid-body tests; this issue is successfully resolved by adopting the standard bending strain formulation and redefining the drilling stiffness. Benchmark examples demonstrate that the enhanced DKMQ24 element eliminates in-plane shear locking, exhibits improved robustness against mesh distortion, and successfully passes rigid-body tests, providing a reliable and high-precision quadrilateral shell element for engineering applications.
{"title":"An accurate and robust quadrilateral shell element based on the Naghdi/Reissner/Mindlin shell theory","authors":"Qi Ran , Huan Zhang , She Li , Xiangyang Cui","doi":"10.1016/j.finel.2026.104526","DOIUrl":"10.1016/j.finel.2026.104526","url":null,"abstract":"<div><div>The DKMQ24 element, based on the Naghdi–Mindlin–Reissner shell theory, performs well in bending- and shear-dominated problems but remains sensitive to mesh distortion and suffers from in-plane shear locking. In this study, the membrane strain field is reconstructed using the Mixed Interpolation of Tensorial Components (MITC) method to reduce mesh sensitivity, and the Enhanced Assumed Strain (EAS) method is applied to alleviate in-plane shear locking. An improper bending approximation and the artificial stiffness for drilling rotation in DKMQ24 hindered the element from fully passing rigid-body tests; this issue is successfully resolved by adopting the standard bending strain formulation and redefining the drilling stiffness. Benchmark examples demonstrate that the enhanced DKMQ24 element eliminates in-plane shear locking, exhibits improved robustness against mesh distortion, and successfully passes rigid-body tests, providing a reliable and high-precision quadrilateral shell element for engineering applications.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"256 ","pages":"Article 104526"},"PeriodicalIF":3.5,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146102940","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 : 2026-01-26DOI: 10.1016/j.finel.2025.104489
Max von Zabiensky, Dustin R. Jantos, Philipp Junker
In several engineering applications, self-contact is a major effect or even desired feature, e.g., energy absorption in severe structural deformations, gripper in (soft-)robotics, and the optimization of those. Usual contact approaches require extensive calculation effort, but a fast and robust simulation approach could lead to remarkable improvements in product design. The third medium contact is a very promising approach, which can fulfill the requirements mentioned above. This method was also already applied in topology optimization approaches. However, the most concurrent regularization approaches require at least quadratic shape functions for hexahedron finite elements and at least cubic shape functions for tetrahedrons. In recent works, a new regularization technique was developed: herein, the gradients of deformation measures are computed by additional nodal degrees of freedom in the finite elements, i.e., as additional fields of unknowns. This is accompanied by a reduction of the order of the shape function. In this work, we derive a special discretization of the additional unknowns which enables self-contact based on the neighbored element method. This approach leads to a fast algorithm for the computation of the regularized set of partial differential equations: the displacements are the only nodal degrees of freedom and can be computed with linear finite element shape functions while the additional unknowns are discretized in the quadrature points of the mesh and solved in a staggered manner. The results are critically analyzed and illustrated for several two-dimensional problems.
{"title":"A fast and robust third medium contact approach using the neighbored element method","authors":"Max von Zabiensky, Dustin R. Jantos, Philipp Junker","doi":"10.1016/j.finel.2025.104489","DOIUrl":"10.1016/j.finel.2025.104489","url":null,"abstract":"<div><div>In several engineering applications, self-contact is a major effect or even desired feature, e.g., energy absorption in severe structural deformations, gripper in (soft-)robotics, and the optimization of those. Usual contact approaches require extensive calculation effort, but a fast and robust simulation approach could lead to remarkable improvements in product design. The third medium contact is a very promising approach, which can fulfill the requirements mentioned above. This method was also already applied in topology optimization approaches. However, the most concurrent regularization approaches require at least quadratic shape functions for hexahedron finite elements and at least cubic shape functions for tetrahedrons. In recent works, a new regularization technique was developed: herein, the gradients of deformation measures are computed by additional nodal degrees of freedom in the finite elements, i.e., as additional fields of unknowns. This is accompanied by a reduction of the order of the shape function. In this work, we derive a special discretization of the additional unknowns which enables self-contact based on the neighbored element method. This approach leads to a fast algorithm for the computation of the regularized set of partial differential equations: the displacements are the only nodal degrees of freedom and can be computed with linear finite element shape functions while the additional unknowns are discretized in the quadrature points of the mesh and solved in a staggered manner. The results are critically analyzed and illustrated for several two-dimensional problems.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"255 ","pages":"Article 104489"},"PeriodicalIF":3.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047949","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 : 2026-01-20DOI: 10.1016/j.finel.2025.104510
Ilaria Fiore, Francesco Cannizzaro
This study presents a Displacement-Based (DB) finite element formulation of the multi-cracked planar circular arch within the Timoshenko theory. The cracks presence is simulated with the localised flexibility approach, considering the tangential, radial and rotational kinematic jumps at the damaged sections. The kinematic discontinuities are modelled with Dirac's deltas in the generalised governing equations defined over a unique domain for a generic number of damaged sections, which represents a significant computational advantage over classic approaches requiring enforcement of continuity conditions at the discontinuous sections. The governing equations of the statics of the multi-cracked Timoshenko circular arch are integrated, leading to the closed-form response as a function of six boundary conditions only. Then, the static discontinuous shape functions are inferred and exploited to obtain the stiffness and consistent mass matrices of the multi-cracked circular arch, considering just three degrees of freedom for each end of the member irrespective of the amount of cracks along the axis of the element. The obtained circular multi-cracked element, which is completely locking-free, is implemented in a finite element environment that encompasses an analogous finite element introduced for cracked straight members, thus allowing the study of general planar damaged frames both in the static and dynamic contexts.
{"title":"A displacement-based Timoshenko finite element of multi-cracked circular arch","authors":"Ilaria Fiore, Francesco Cannizzaro","doi":"10.1016/j.finel.2025.104510","DOIUrl":"10.1016/j.finel.2025.104510","url":null,"abstract":"<div><div>This study presents a Displacement-Based (DB) finite element formulation of the multi-cracked planar circular arch within the Timoshenko theory. The cracks presence is simulated with the localised flexibility approach, considering the tangential, radial and rotational kinematic jumps at the damaged sections. The kinematic discontinuities are modelled with Dirac's deltas in the generalised governing equations defined over a unique domain for a generic number of damaged sections, which represents a significant computational advantage over classic approaches requiring enforcement of continuity conditions at the discontinuous sections. The governing equations of the statics of the multi-cracked Timoshenko circular arch are integrated, leading to the closed-form response as a function of six boundary conditions only. Then, the static discontinuous shape functions are inferred and exploited to obtain the stiffness and consistent mass matrices of the multi-cracked circular arch, considering just three degrees of freedom for each end of the member irrespective of the amount of cracks along the axis of the element. The obtained circular multi-cracked element, which is completely locking-free, is implemented in a finite element environment that encompasses an analogous finite element introduced for cracked straight members, thus allowing the study of general planar damaged frames both in the static and dynamic contexts.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"255 ","pages":"Article 104510"},"PeriodicalIF":3.5,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014797","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 : 2026-01-17DOI: 10.1016/j.finel.2026.104522
P. Wriggers
The third medium contact approach has been successfully employed in structural applications and extended to various optimization problems. This discretization technique replaces classical contact formulations and algorithms by introducing a compliant interfacial layer – referred to as the third medium – between the contacting bodies. Unlike traditional contact methods, this formulation naturally accommodates finite deformations at the interface. As the two bodies approach each other, the third medium undergoes compression and effectively acts as a deformable barrier, preventing interpenetration and transmitting contact forces in a smooth and numerically stable manner. In thermo-mechanical problems, heat conduction must be incorporated into the model, which typically requires specialized interface laws when using classical contact formulations. These laws aim to capture the complex thermal behavior at the contact interface, including discontinuities and varying conductance. In contrast, the third medium approach offers a significant advantage: the thermo-mechanical formulation inherently accounts for the interface behavior without the need for additional interface conditions. This includes the gradual heat transfer through the surrounding gas when the bodies are near each other, as well as the localized heat conduction that occurs upon physical contact. As a result, the third medium naturally captures both non-contact and contact-phase thermal conduction within a unified framework. In this paper, we propose a new thermo-mechanical model based on a continuum formulation for finite strains and show by means of examples the behavior of the associated finite element formulation based on linear ansatz functions.
{"title":"A third medium approach for thermo-mechanical contact based on low order ansatz spaces","authors":"P. Wriggers","doi":"10.1016/j.finel.2026.104522","DOIUrl":"10.1016/j.finel.2026.104522","url":null,"abstract":"<div><div>The third medium contact approach has been successfully employed in structural applications and extended to various optimization problems. This discretization technique replaces classical contact formulations and algorithms by introducing a compliant interfacial layer – referred to as the third medium – between the contacting bodies. Unlike traditional contact methods, this formulation naturally accommodates finite deformations at the interface. As the two bodies approach each other, the third medium undergoes compression and effectively acts as a deformable barrier, preventing interpenetration and transmitting contact forces in a smooth and numerically stable manner. In thermo-mechanical problems, heat conduction must be incorporated into the model, which typically requires specialized interface laws when using classical contact formulations. These laws aim to capture the complex thermal behavior at the contact interface, including discontinuities and varying conductance. In contrast, the third medium approach offers a significant advantage: the thermo-mechanical formulation inherently accounts for the interface behavior without the need for additional interface conditions. This includes the gradual heat transfer through the surrounding gas when the bodies are near each other, as well as the localized heat conduction that occurs upon physical contact. As a result, the third medium naturally captures both non-contact and contact-phase thermal conduction within a unified framework. In this paper, we propose a new thermo-mechanical model based on a continuum formulation for finite strains and show by means of examples the behavior of the associated finite element formulation based on linear ansatz functions.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"255 ","pages":"Article 104522"},"PeriodicalIF":3.5,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995152","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 : 2026-01-13DOI: 10.1016/j.finel.2026.104521
Max Nezdyur , Lynn Munday , Wilkins Aquino
Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. To address these challenges, this paper introduces a novel Element Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method’s modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to nuclear engineering.
{"title":"Parametric reduced order models for graded lattice structures","authors":"Max Nezdyur , Lynn Munday , Wilkins Aquino","doi":"10.1016/j.finel.2026.104521","DOIUrl":"10.1016/j.finel.2026.104521","url":null,"abstract":"<div><div>Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. To address these challenges, this paper introduces a novel Element Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method’s modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to nuclear engineering.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"255 ","pages":"Article 104521"},"PeriodicalIF":3.5,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962065","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 : 2026-01-12DOI: 10.1016/j.finel.2026.104520
S.M. Mallikarjunaiah , Pavithra Venkatachalapthy
An -adaptive continuous Galerkin finite element method is developed to analyze a static anti-plane shear crack embedded in a nonlinear, strain-limiting elastic body. The geometrically linear material is described by a constitutive law relating stress and strain that is algebraically nonlinear. Such a formulation is advantageous as it regularizes the stress and strain fields in the neighborhood of a crack-tip, thereby circumventing the non-physical strain singularities inherent to linear elastic fracture mechanics. In this investigation, the constitutive relation utilized is uniformly bounded, monotone, coercive, and Lipschitz continuous, ensuring the well-posedness of the mathematical model. The governing equation, derived from the balance of linear momentum coupled with the nonlinear constitutive relationship, is formulated as a second-order quasi-linear elliptic partial differential equation. For a body with an edge crack, this governing equation is augmented with a classical traction-free boundary condition on the crack faces. An -adaptive finite element scheme is proposed for the numerical approximation of the resulting boundary value problem. The adaptive strategy is driven by a dual-component error estimation scheme: mesh refinement (-adaptivity) is guided by a residual-based a posteriori error indicator of the Kelly type, while the local polynomial degree (-adaptivity) is adjusted based on an estimator of the local solution regularity. The performance, accuracy, and convergence characteristics of the proposed method are demonstrated through numerical experiments. The structure of the regularized crack-tip fields is examined for various modeling parameters. Furthermore, the presented framework establishes a robust foundation for extension to more complex and computationally demanding problems, including quasi-static and dynamic crack propagation in brittle materials. A comparative analysis reveals that while standard -refinement yields only algebraic convergence due to the crack-tip singularity, the proposed -scheme recovers exponential convergence, reducing the degrees of freedom required for high-precision solutions by nearly two orders of magnitude.
{"title":"hp-adaptive finite element simulation of a static anti-plane shear crack in a nonlinear strain-limiting elastic solid","authors":"S.M. Mallikarjunaiah , Pavithra Venkatachalapthy","doi":"10.1016/j.finel.2026.104520","DOIUrl":"10.1016/j.finel.2026.104520","url":null,"abstract":"<div><div>An <span><math><mrow><mi>h</mi><mi>p</mi></mrow></math></span>-adaptive continuous Galerkin finite element method is developed to analyze a static anti-plane shear crack embedded in a nonlinear, strain-limiting elastic body. The geometrically linear material is described by a constitutive law relating stress and strain that is algebraically nonlinear. Such a formulation is advantageous as it regularizes the stress and strain fields in the neighborhood of a crack-tip, thereby circumventing the non-physical strain singularities inherent to linear elastic fracture mechanics. In this investigation, the constitutive relation utilized is <em>uniformly bounded</em>, <em>monotone</em>, <em>coercive</em>, and <em>Lipschitz continuous</em>, ensuring the well-posedness of the mathematical model. The governing equation, derived from the balance of linear momentum coupled with the nonlinear constitutive relationship, is formulated as a second-order quasi-linear elliptic partial differential equation. For a body with an edge crack, this governing equation is augmented with a classical traction-free boundary condition on the crack faces. An <span><math><mrow><mi>h</mi><mi>p</mi></mrow></math></span>-adaptive finite element scheme is proposed for the numerical approximation of the resulting boundary value problem. The adaptive strategy is driven by a dual-component error estimation scheme: mesh refinement (<span><math><mi>h</mi></math></span>-adaptivity) is guided by a residual-based a posteriori error indicator of the <em>Kelly type</em>, while the local polynomial degree (<span><math><mi>p</mi></math></span>-adaptivity) is adjusted based on an estimator of the local solution regularity. The performance, accuracy, and convergence characteristics of the proposed method are demonstrated through numerical experiments. The structure of the regularized crack-tip fields is examined for various modeling parameters. Furthermore, the presented framework establishes a robust foundation for extension to more complex and computationally demanding problems, including quasi-static and dynamic crack propagation in brittle materials. A comparative analysis reveals that while standard <span><math><mi>h</mi></math></span>-refinement yields only algebraic convergence due to the crack-tip singularity, the proposed <span><math><mrow><mi>h</mi><mi>p</mi></mrow></math></span>-scheme recovers exponential convergence, reducing the degrees of freedom required for high-precision solutions by nearly two orders of magnitude.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"255 ","pages":"Article 104520"},"PeriodicalIF":3.5,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957280","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 : 2026-01-12DOI: 10.1016/j.finel.2026.104511
Jun-Sik Kim , Tuan Anh Bui , Junyoung Park
Thin-walled beams with complex cross-sections require efficient reduced-order models to overcome the high computational cost of three-dimensional finite element analyses. Among existing approaches, the Formal Asymptotic Method (FAM) provides an efficient framework for slender beams through a two-step procedure: a cross-sectional analysis to determine warping-related quantities, followed by the construction of an equivalent one-dimensional beam model within a Timoshenko-type framework. The resulting macroscopic model involves only six degrees of freedom per node and is therefore very compact.
In conventional FAM formulations, the cross-sectional analysis is based on three-dimensional solid elasticity and requires discretization using two-dimensional finite elements, which can be computationally expensive, especially for thin-walled and multilayer composite structures. In this paper, a new one-dimensional beam formulation is proposed by integrating shell theory into the FAM framework. The cross-section is represented by its reference surface and discretized using two-node line elements, leading to a significant reduction in the computational cost of the sectional analysis while preserving the essential deformation characteristics of thin to moderately thick walls.
The accuracy and efficiency of the proposed formulation are demonstrated through numerical examples, including rectangular box beams and a wind turbine blade. Comparisons with other reduced-order models and with three-dimensional finite element results obtained using Abaqus show that the proposed approach accurately predicts global displacements at a significantly lower computational cost.
{"title":"Formal asymptotic derivation of one-dimensional models for thin-walled beams based on shell theory","authors":"Jun-Sik Kim , Tuan Anh Bui , Junyoung Park","doi":"10.1016/j.finel.2026.104511","DOIUrl":"10.1016/j.finel.2026.104511","url":null,"abstract":"<div><div>Thin-walled beams with complex cross-sections require efficient reduced-order models to overcome the high computational cost of three-dimensional finite element analyses. Among existing approaches, the Formal Asymptotic Method (FAM) provides an efficient framework for slender beams through a two-step procedure: a cross-sectional analysis to determine warping-related quantities, followed by the construction of an equivalent one-dimensional beam model within a Timoshenko-type framework. The resulting macroscopic model involves only six degrees of freedom per node and is therefore very compact.</div><div>In conventional FAM formulations, the cross-sectional analysis is based on three-dimensional solid elasticity and requires discretization using two-dimensional finite elements, which can be computationally expensive, especially for thin-walled and multilayer composite structures. In this paper, a new one-dimensional beam formulation is proposed by integrating shell theory into the FAM framework. The cross-section is represented by its reference surface and discretized using two-node line elements, leading to a significant reduction in the computational cost of the sectional analysis while preserving the essential deformation characteristics of thin to moderately thick walls.</div><div>The accuracy and efficiency of the proposed formulation are demonstrated through numerical examples, including rectangular box beams and a wind turbine blade. Comparisons with other reduced-order models and with three-dimensional finite element results obtained using Abaqus show that the proposed approach accurately predicts global displacements at a significantly lower computational cost.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"255 ","pages":"Article 104511"},"PeriodicalIF":3.5,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957281","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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