Finite Elements in Analysis and Design最新文献

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Application of zonal Reduced-Order-Modeling to tire rolling simulation
IF 3.5 3区 工程技术
Finite Elements in Analysis and Design Pub Date : 2025-02-22 DOI: 10.1016/j.finel.2025.104330
D. Danan , R. Meunier , T. Dairay , T. Homolle , M. Yagoubi
{"title":"Application of zonal Reduced-Order-Modeling to tire rolling simulation","authors":"D. Danan ,&nbsp;R. Meunier ,&nbsp;T. Dairay ,&nbsp;T. Homolle ,&nbsp;M. Yagoubi","doi":"10.1016/j.finel.2025.104330","DOIUrl":"10.1016/j.finel.2025.104330","url":null,"abstract":"<div><div>Physic-based simulation remains a key enabler for real-world ever-growing complex industrial systems especially when crucial decisions are needed. While classical approaches have proven their accuracy and robustness over the years and come with a rich mathematical foundation, they suffer from several limitations depending of the underlying physics and use cases. For instance, especially concerning the resolution of Partial Differential Equations (PDEs) in 3 dimensions (3D), classical approaches are known to be computationally expensive. However, it turns out that simple pure data-driven approaches, while allegedly much more efficient from a computational point of view, do not necessarily hold up well regarding physical considerations. In this work, our aim is to investigate the tradeoff between accuracy and computational cost to design efficient and robust physical simulation methods under industrial constraints. In particular, as it is not easy to generate a large dataset through numerical simulations for such a problem, our aim is to design an approach addressing the data scarcity issue. To do so, we propose to hybridize a standard Finite Element Method (FEM) physics-based solver with a zonal Reduced Order Model (ROM) approach to simulate a rolling tire.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"246 ","pages":"Article 104330"},"PeriodicalIF":3.5,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143471709","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}
引用次数: 0
An enhanced single Gaussian point continuum finite element formulation using automatic differentiation
IF 3.5 3区 工程技术
Finite Elements in Analysis and Design Pub Date : 2025-02-19 DOI: 10.1016/j.finel.2025.104329
Njomza Pacolli , Ahmad Awad , Jannick Kehls , Bjorn Sauren , Sven Klinkel , Stefanie Reese , Hagen Holthusen
{"title":"An enhanced single Gaussian point continuum finite element formulation using automatic differentiation","authors":"Njomza Pacolli ,&nbsp;Ahmad Awad ,&nbsp;Jannick Kehls ,&nbsp;Bjorn Sauren ,&nbsp;Sven Klinkel ,&nbsp;Stefanie Reese ,&nbsp;Hagen Holthusen","doi":"10.1016/j.finel.2025.104329","DOIUrl":"10.1016/j.finel.2025.104329","url":null,"abstract":"<div><div>This contribution presents an improved low-order 3D finite element formulation with hourglass stabilization using automatic differentiation (AD). Here, the former Q1STc formulation is enhanced by an approximation-free computation of the inverse Jacobian. To this end, AD tools automate the computation and allow a direct evaluation of the inverse Jacobian, bypassing the need for a Taylor series expansion. Thus, the enhanced version, Q1STc+, is introduced. Numerical examples are conducted to compare the performance of both element formulations for finite strain applications, with particular focus on distorted meshes. Moreover, the performance of the new element formulation for an elasto-plastic material is investigated. To validate the obtained results, a volumetric locking-free element based on scaled boundary parametrization is used. Both the implementation of the element routine Q1STc+ and the corresponding material subroutine are made accessible to the public at <span><span>https://doi.org/10.5281/zenodo.14259791</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"246 ","pages":"Article 104329"},"PeriodicalIF":3.5,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143444282","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}
引用次数: 0
Robust multi-physical-material topology optimization with thermal-self-weight uncertain loads
IF 3.5 3区 工程技术
Finite Elements in Analysis and Design Pub Date : 2025-02-13 DOI: 10.1016/j.finel.2025.104319
Minh-Ngoc Nguyen , Joowon Kang , Soomi Shin , Dongkyu Lee
{"title":"Robust multi-physical-material topology optimization with thermal-self-weight uncertain loads","authors":"Minh-Ngoc Nguyen ,&nbsp;Joowon Kang ,&nbsp;Soomi Shin ,&nbsp;Dongkyu Lee","doi":"10.1016/j.finel.2025.104319","DOIUrl":"10.1016/j.finel.2025.104319","url":null,"abstract":"<div><div>Most topology optimization techniques for enhanced designs rely on the premise of deterministic loads. Nevertheless, in actuality, variables such as placements, weights, and orientations of applied loads may inadvertently fluctuate. Deterministic load-based designs may exhibit suboptimal structural performance in the presence of loading uncertainties. Uncertain aspects must be considered in topological optimization to provide robust outcomes. This work introduces an innovative robust multi-physics topology optimization technique for the design of multi-materials in response to unforeseen load variations. A combination of thermo-mechanical and self-weight loads, along with loading uncertainties, is provided based on the extended SIMP technique to achieve resilient designs. The optimized structures can be concurrently refined by minimizing the weighted sum of predicted compliance and standard deviation. The impact of self-weight and heat loads is examined through various cases to validate the proposed strategy.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"246 ","pages":"Article 104319"},"PeriodicalIF":3.5,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395080","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}
引用次数: 0
An assumed enhanced strain finite element formulation for modeling hydraulic fracture growth in a thermoporoelastic medium
IF 3.5 3区 工程技术
Finite Elements in Analysis and Design Pub Date : 2025-02-11 DOI: 10.1016/j.finel.2025.104320
Fushen Liu
{"title":"An assumed enhanced strain finite element formulation for modeling hydraulic fracture growth in a thermoporoelastic medium","authors":"Fushen Liu","doi":"10.1016/j.finel.2025.104320","DOIUrl":"10.1016/j.finel.2025.104320","url":null,"abstract":"<div><div>This paper presents an assumed enhanced strain finite element framework for simulating hydraulic fracture propagation in saturated thermoporoelastic media, considering the influence of thermal effects. The proposed approach combines classical thermoporoelasticity theory with a cohesive fracture model to describe the coupled behaviors of fluid flow, rock deformation and fracture propagation. Within this framework, fractures are represented using constant strain triangular elements enriched with constant displacement jumps. The mechanical response of fractures is governed by a trilinear cohesive law, and fracture initiation and propagation are both determined by using standard Newton’s method while maintaining global equilibrium. The numerical framework is verified through a series of examples, including cases without fractures, cases with rigid and deformable fractures, and hydraulic fracture propagation with thermal effects. The results show that thermal stress primarily affects the region near the injection point but has limited impact on fracture length evolution and fluid pressure distribution within the fracture. In contrast, temperature-dependent viscosity can significantly influence hydraulic fracture propagation. This work can be beneficial to our understanding of hydraulic fracture modeling in thermoporoelastic media and provide a potential useful numerical tool for simulating hydraulic fracturing processes with consideration of thermal effects.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"246 ","pages":"Article 104320"},"PeriodicalIF":3.5,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387536","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}
引用次数: 0
Sequential sensor placement for damage detection under frequency-domain dynamics
IF 3.5 3区 工程技术
Finite Elements in Analysis and Design Pub Date : 2025-02-11 DOI: 10.1016/j.finel.2025.104315
Mark J. Chen , Kavinayan Sivakumar , Gregory A. Banyay , Brian M. Golchert , Timothy F. Walsh , Michael M. Zavlanos , Wilkins Aquino
{"title":"Sequential sensor placement for damage detection under frequency-domain dynamics","authors":"Mark J. Chen ,&nbsp;Kavinayan Sivakumar ,&nbsp;Gregory A. Banyay ,&nbsp;Brian M. Golchert ,&nbsp;Timothy F. Walsh ,&nbsp;Michael M. Zavlanos ,&nbsp;Wilkins Aquino","doi":"10.1016/j.finel.2025.104315","DOIUrl":"10.1016/j.finel.2025.104315","url":null,"abstract":"<div><div>Identification and monitoring of damage have a growing importance in the maintenance of structures. A robust active sensing framework that integrates model-based inference and optimal sensor placement is proposed. By tightly coupling measured data and data acquisition scenarios, a <em>simultaneous</em> approach of damage estimation and sensor placement can be used to continuously and accurately assess a structure. In this work, a partial differential equation-constrained formulation for damage estimation is first developed using a conventional model-updating approach with a penalization damage parameter. Then, this formulation is linearized around the damage estimator to produce an Optimal Experimental Design (OED) problem for desirable sensor locations. Hence, the simultaneous sensing framework is postulated using a Fisher Information Matrix (FIM)-based approach as follows: given a current candidate damage state associated with the most up-to-date sensor information, find the next sensor location that minimizes some metric of the FIM and update the damage estimator. The sensing framework is also enhanced by introducing a Modified Error in Constitutive Equations (MECE) functional in the damage estimator. Adding MECE makes the framework more robust by limiting the damage estimator from being trapped in local minima. Through numerical examples, we show that our approach produces accurate damage estimators using a small number of sensor locations. In addition, we compare our results to those obtained using random sensor selections and expertly selected locations.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"246 ","pages":"Article 104315"},"PeriodicalIF":3.5,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143378073","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}
引用次数: 0
Stress-related topology optimization based on Isogeometric Analysis and global stress measures
IF 3.5 3区 工程技术
Finite Elements in Analysis and Design Pub Date : 2025-02-05 DOI: 10.1016/j.finel.2025.104317
Yupeng Huang, Song Yao, Xing Chen
{"title":"Stress-related topology optimization based on Isogeometric Analysis and global stress measures","authors":"Yupeng Huang,&nbsp;Song Yao,&nbsp;Xing Chen","doi":"10.1016/j.finel.2025.104317","DOIUrl":"10.1016/j.finel.2025.104317","url":null,"abstract":"<div><div>This paper presents a robust isogeometric topology optimization (ITO) framework that integrates Isogeometric Analysis (IGA) with global stress measures to enhance both accuracy and stability in stress-related structural optimization. Non-Uniform Rational B-Splines (NURBS)-based IGA is employed to ensure higher-order continuity and refined topology representation, enabling precise stress evaluation. The p-norm stress aggregation approximates maximum stress, while incorporating average stress into ITO mitigates oscillations for large p-norm parameters and further reduces sensitivity to <span><math><mi>P</mi></math></span>. Notably, this approach eliminates stress concentrations even when <span><math><mrow><mi>P</mi><mo>=</mo><mn>3</mn></mrow></math></span>, and maintains stable convergence as <span><math><mi>P</mi></math></span> increases up to 40 or more, thereby extending the feasible range of <span><math><mi>P</mi></math></span>-values. By examining various weight combinations of p-norm and average stress, we reveal how controlling both amplitude and mean stress leads to more uniform and lower stress levels. Additionally, an adaptive continuous scheme for stress constraints further improves convergence stability by gradually tightening stress limits from a relaxed state to the target value. Numerical results confirm that the proposed method consistently delivers accurate, stable, and efficient solutions for stress-related isogeometric topology optimization, marking a significant advancement in the field.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"245 ","pages":"Article 104317"},"PeriodicalIF":3.5,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143125222","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}
引用次数: 0
Computational modeling of a residually stressed thick-walled cylinder under the combined action of axial extension and inflation 轴向扩展和膨胀联合作用下残余应力厚壁圆筒的计算模型
IF 3.5 3区 工程技术
Finite Elements in Analysis and Design Pub Date : 2025-02-01 DOI: 10.1016/j.finel.2024.104309
Murtadha J. Al-Chlaihawi , Dariel Desena-Galarza , Heiko Topol , José Merodio
{"title":"Computational modeling of a residually stressed thick-walled cylinder under the combined action of axial extension and inflation","authors":"Murtadha J. Al-Chlaihawi ,&nbsp;Dariel Desena-Galarza ,&nbsp;Heiko Topol ,&nbsp;José Merodio","doi":"10.1016/j.finel.2024.104309","DOIUrl":"10.1016/j.finel.2024.104309","url":null,"abstract":"<div><div>Previous studies have shown that the mechanical response of incompressible hyperelastic materials is affected by the occurrence of residual stresses. In the context of biological soft tissues, such residual stresses result from factors that include growth and development processes. The detailed effect of these initial stresses on mechanical behavior remains to be explored in detail. The magnitude and distribution of residual stresses in arterial wall tissue affect the location of the occurrence of instabilities such as bulges. This study aims to develop a new approach to assess material behavior during bifurcation instability in the presence of residual stresses, especially non-planar stresses. A finite element protocol is developed for bifurcation and post-bifurcation of residually stressed thick-walled hyper-elastic circular hollow tubes subjected to axial stretches and internal pressure, incorporating three-dimensional residual stresses. A constitutive equation based on the strain energy function for these tubes is formulated and implemented in ABAQUS, using the Modified Riks method and a user-defined material subroutine (UMAT). Results indicate that bending bifurcation is likely for small axial stretches but becomes less probable with larger axial stretches while bulging bifurcation is expected for all axial stretch values. Pressures associated with pure bulging modes are higher than those for bulging induced by bending, suggesting aneurysms can be delayed by avoiding bending bifurcation. The bulging from bending bifurcation occurs on one side of the tubes, reflecting abdominal aortic aneurysm (AAA) conditions. The unsymmetrical bulge development aligns with the methodology used, whereas balloon-like bulging in pure modes is linked to arterial rupture.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104309"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142935962","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}
引用次数: 0
A hybrid stress finite element for the efficient nonlinear analysis of masonry walls based on a multi-failure strength domain 基于多破坏强度域的混合应力有限元对砌体墙体进行有效的非线性分析
IF 3.5 3区 工程技术
Finite Elements in Analysis and Design Pub Date : 2025-02-01 DOI: 10.1016/j.finel.2024.104310
G. Bertani , A. Bilotta , A.M. D’Altri , S. de Miranda , F.S. Liguori , A. Madeo
{"title":"A hybrid stress finite element for the efficient nonlinear analysis of masonry walls based on a multi-failure strength domain","authors":"G. Bertani ,&nbsp;A. Bilotta ,&nbsp;A.M. D’Altri ,&nbsp;S. de Miranda ,&nbsp;F.S. Liguori ,&nbsp;A. Madeo","doi":"10.1016/j.finel.2024.104310","DOIUrl":"10.1016/j.finel.2024.104310","url":null,"abstract":"<div><div>A novel 8-node hybrid stress finite element (FE) is proposed for the efficient nonlinear analysis of in-plane loaded masonry walls. To provide a robust, easy-to-characterize mechanically, and computationally efficient practice-oriented numerical framework, masonry is idealized as an elasto-plastic homogeneous continuum. Elasto-plasticity is considered at the FE level by means of a dual-decomposition approach, with plasticity controlled at Gauss–Lobatto points. A state-of-the-art single-surface multi-failure anisotropic strength domain specifically dedicated to masonry is employed. Multiple limit surfaces are considered and condensed into a unique surface through the RealSoftMax function, preserving the distinction between failure modes and the level of activation of each failure thanks to specific weights. The present numerical framework is tested though several structurally meaningful examples with available numerical and experimental reference solutions, comparing the efficiency of the proposed FE with standard displacement-based FEs, as well as other mixed FEs. As a result, the novel 8-node hybrid stress FE shows superior performance with respect to the other FEs, in terms of accuracy and convergence rate. Accordingly, the present numerical framework allows to simulate accurately the nonlinear response of masonry walls and to track realistically the evolution of the considered failure modes even with a few FEs per wall, so being particularly efficient and appealing in engineering common practice.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104310"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986239","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}
引用次数: 0
Advancing industrial finite element software: Developing Model Order Reduction for nonlinear transient thermal problems 工业有限元软件的发展:非线性瞬态热问题的模型降阶
IF 3.5 3区 工程技术
Finite Elements in Analysis and Design Pub Date : 2025-02-01 DOI: 10.1016/j.finel.2024.104299
Pierre-Eliot Malleval , Ronan Scanff , David Néron
{"title":"Advancing industrial finite element software: Developing Model Order Reduction for nonlinear transient thermal problems","authors":"Pierre-Eliot Malleval ,&nbsp;Ronan Scanff ,&nbsp;David Néron","doi":"10.1016/j.finel.2024.104299","DOIUrl":"10.1016/j.finel.2024.104299","url":null,"abstract":"<div><div>Over the past two decades, non-intrusive techniques have been used to develop reduced-order models for nonlinear structures in industrial environments. These techniques have placed a significant emphasis on <em>a posteriori</em> methods, which often rely on solutions derived from computationally expensive full-order models. Using <em>a priori</em> methods not relying on the full order model might be preferred as they reduce the computational burden upfront. The intrusiveness of the algorithms associated with these methods limits their introduction into commercial finite element software. Integrating robust and reliable approaches into a certified product is necessary for these methods to spread at an industrial level. This work aligns with this ambition, extending a weakly-intrusive implementation of the LATIN-PGD already embedded into commercial finite element software to transient thermal problems. The novelty of the approach stems from its extensive applicability, enabling the PGD method to address not just specific applications but also to seamlessly handle any nonlinearities, diverse element types, various boundary conditions, and other features inherent in such software. This results in a new comprehensive industrial nonlinear solver, including <em>a priori</em> model order reduction.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104299"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986346","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}
引用次数: 0
Plate finite elements with arbitrary displacement fields along the thickness 具有沿厚度任意位移场的板有限元
IF 3.5 3区 工程技术
Finite Elements in Analysis and Design Pub Date : 2025-02-01 DOI: 10.1016/j.finel.2024.104296
E. Carrera , D. Scano , E. Zappino
{"title":"Plate finite elements with arbitrary displacement fields along the thickness","authors":"E. Carrera ,&nbsp;D. Scano ,&nbsp;E. Zappino","doi":"10.1016/j.finel.2024.104296","DOIUrl":"10.1016/j.finel.2024.104296","url":null,"abstract":"<div><div>The present paper introduces a methodology for formulating two-dimensional structural theories featuring arbitrary kinematic fields. In the proposed approach, each displacement variable can be examined through an independent expansion function, enabling the integration of both classical and higher-order theories within a unified framework. The Carrera Unified Formulation is used to derive the governing equations in a unified form, independent of the expansion adopted for each displacement component. In this paper, plate structural theories are constructed by using polynomial expansions. The finite element method is used to discretize the structure in the reference plane of the plate, utilizing Lagrange-based elements. The Mixed Interpolation of Tensorial Components is adopted to alleviate the shear locking issues. In this study, isotropic plate structures are investigated under various loadings, boundary conditions, and different length-to-thickness ratios. Whenever possible, the present results are compared with analytical and literature solutions. The accuracy of the presented models is evaluated for both displacements and stress components. The findings indicate that the selection of the most appropriate model is strongly dependent on the specific parameters of the individual problem, however, choosing the right model can significantly enhance the efficiency of the numerical analysis.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104296"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841386","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}
引用次数: 0
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