International Journal for Numerical Methods in Engineering最新文献_第2页

A Novel Petrov-Galerkin 4-Node Quadrilateral Element With Radial Polynomial Interpolation for Linear Elastic Analysis

IF 2.7 3区工程技术

International Journal for Numerical Methods in Engineering Pub Date : 2025-05-14 DOI: 10.1002/nme.70049

Lu-Zhen Dou, Ying-Qing Huang, Yuan-Fan Yang, Yan-Liang Ju, Hai-Bo Chen

{"title":"A Novel Petrov-Galerkin 4-Node Quadrilateral Element With Radial Polynomial Interpolation for Linear Elastic Analysis","authors":"Lu-Zhen Dou, Ying-Qing Huang, Yuan-Fan Yang, Yan-Liang Ju, Hai-Bo Chen","doi":"10.1002/nme.70049","DOIUrl":"https://doi.org/10.1002/nme.70049","url":null,"abstract":"<div>\u0000 \u0000 Based on the virtual work principle, a novel Petrov-Galerkin 4-node quadrilateral element is proposed in this article with different sets of test and trial functions. The virtual displacements are assumed by standard isoparametric interpolation which satisfies the interelement continuity requirement. It also ensures that the imposition of prescribed displacement boundary conditions and the calculation of equivalent nodal forces are the same as the conventional isoparametric elements. A support domain is formed for each element and all nodes within it are used to interpolate the actual displacements through the radial and polynomial basis functions. The nodal shape functions obtained by the radial polynomial interpolation possess the Kronecker delta property and sufficient completeness order for convergence. The resulted element stiffness matrix is unsymmetric, generally nonsquare, due to the Petrov-Galerkin formulation. However, the global unsymmetric stiffness matrix is square, sparse and structurally symmetric. Moreover, the determinant of the Jacobian matrix can be removed from the element stiffness matrix and this improves the immunity of the numerical accuracy to mesh distortion significantly. Numerical investigations demonstrate that the present element effectively combines the advantages of both finite element methods and radial basis meshless methods. Especially, the stress continuity and interelement smoothness are improved remarkedly.\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 10","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944707","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

Cell Agglomeration Strategy for Cut Cells in eXtended Discontinuous Galerkin Methods 扩展不连续伽辽金方法中切割细胞的细胞团聚策略

IF 2.7 3区工程技术

International Journal for Numerical Methods in Engineering Pub Date : 2025-05-08 DOI: 10.1002/nme.70013

Teoman Toprak, Matthias Rieckmann, Florian Kummer

{"title":"Cell Agglomeration Strategy for Cut Cells in eXtended Discontinuous Galerkin Methods","authors":"Teoman Toprak, Matthias Rieckmann, Florian Kummer","doi":"10.1002/nme.70013","DOIUrl":"https://doi.org/10.1002/nme.70013","url":null,"abstract":"In this work, a cell agglomeration strategy for the cut cells arising in the eXtended discontinuous Galerkin (XDG) method is presented. Cut cells are a fundamental aspect of unfitted mesh approaches, where complex geometries or interfaces separating subdomains are embedded into structured background grids to facilitate the mesh generation process. In such methods, arbitrary small cells occur due to the intersections of background cells with embedded geometries and lead to discretization difficulties due to their diminutive sizes. Furthermore, temporal evolutions of these geometries may lead to topological changes across different time steps. Both of these issues, that is, small-cut cells and topological changes, can be addressed with a cell agglomeration technique, independent of discretization. However, cell agglomeration encounters significant difficulties in three dimensions due to the complexity of neighborship and issues like cycles and parallel agglomeration chains. The proposed strategy introduces a robust framework that mitigates these problems by incorporating methods for cycle prevention, chain agglomeration, and parallelization. Implemented in the open-source software package BoSSS, this strategy has been successfully tested on multiprocessor systems using dynamic multiphase test cases in both two and three dimensions, enabling simulations that were previously infeasible.","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 9","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143926029","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

A Fundamentally New Coupled Approach to Contact Mechanics via the Dirichlet-Neumann Schwarz Alternating Method 一种基于Dirichlet-Neumann - Schwarz交替方法的全新接触力学耦合方法

IF 2.7 3区工程技术

International Journal for Numerical Methods in Engineering Pub Date : 2025-05-08 DOI: 10.1002/nme.70039

Alejandro Mota, Daria Koliesnikova, Irina Tezaur, Jonathan Hoy

{"title":"A Fundamentally New Coupled Approach to Contact Mechanics via the Dirichlet-Neumann Schwarz Alternating Method","authors":"Alejandro Mota, Daria Koliesnikova, Irina Tezaur, Jonathan Hoy","doi":"10.1002/nme.70039","DOIUrl":"https://doi.org/10.1002/nme.70039","url":null,"abstract":"<div>\u0000 \u0000 Contact phenomena are crucial for understanding the behavior of mechanical systems. However, existing computational approaches for simulating mechanical contact often face numerical challenges, such as inaccurate physical predictions, energy conservation errors, and unwanted oscillations. We introduce an alternative technique for simulating dynamic contact based on the non-overlapping Schwarz alternating method, originally developed for domain decomposition. In multibody contact scenarios, this method treats each body as a separate, non-overlapping domain and prevents interpenetration using an alternating Dirichlet–Neumann iterative process. This approach has a strong theoretical foundation, eliminates the need for contact constraints, and offers flexibility, making it ideal for multiscale and multiphysics applications. We conducted a numerical comparison between the Schwarz method and traditional methods, such as the Lagrange multiplier and penalty methods, focusing on a benchmark impact problem. Our results indicate that the Schwarz alternating method outperforms traditional methods in several key areas: it provides more accurate predictions for various measurable quantities and demonstrates exceptional energy conservation capabilities. To address unwanted oscillations in contact velocities and forces, we explored various algorithms and stabilization techniques, ultimately opting for the naïve-stabilized Newmark scheme for its simplicity and effectiveness. Additionally, we validated the efficiency of the Schwarz method in a three-dimensional impact problem, highlighting its inherent capacity to accommodate different mesh topologies, time-integration schemes, and time steps for each interacting body.\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 9","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143919349","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

Bridging Overlapping 2D Coarse and Fine Meshes Within the Phase Field Fracture Method 相场断裂法内桥接重叠二维粗、细网格

IF 2.7 3区工程技术

International Journal for Numerical Methods in Engineering Pub Date : 2025-05-07 DOI: 10.1002/nme.70043

Zakaria Chafia, Julien Yvonnet, Jérémy Bleyer

{"title":"Bridging Overlapping 2D Coarse and Fine Meshes Within the Phase Field Fracture Method","authors":"Zakaria Chafia, Julien Yvonnet, Jérémy Bleyer","doi":"10.1002/nme.70043","DOIUrl":"https://doi.org/10.1002/nme.70043","url":null,"abstract":"A framework is proposed to bridge coarse and fine meshes in a single simulation within the phase field method for fracture. Fine meshes are used in the vicinity of localized defects to accurately capture crack initiation, while coarse meshes are used away from initial defects and include only crack propagation paths. This reduces the prohibitive computational times associated with uniformly fine meshes over the entire domain, or with the use of complex adaptive meshes in the phase field method. The coupling between the two overlapping meshes is achieved using a variational formulation in which the energies of the models associated with the fine and coarse meshes are weighted in the superposition zone. Two situations are considered. The first includes the resolution of the phase field problem only in the fine mesh, while the coarse mesh is limited to the undamaged elastic problem. In the second situation, cracks can propagate in both the fine and coarse mesh. Variational formulations and associated finite element implementations are detailed. Numerical examples are presented, showing the potential of this approach to significantly reduce computational costs in the phase field method for cracking without affecting the accuracy.","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 9","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70043","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143914446","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

Data-Driven Optimization for the Evolve-Filter-Relax Regularization of Convection-Dominated Flows 对流主导流演化-滤波-松弛正则化的数据驱动优化

IF 2.7 3区工程技术

International Journal for Numerical Methods in Engineering Pub Date : 2025-05-07 DOI: 10.1002/nme.70042

Anna Ivagnes, Maria Strazzullo, Michele Girfoglio, Traian Iliescu, Gianluigi Rozza

{"title":"Data-Driven Optimization for the Evolve-Filter-Relax Regularization of Convection-Dominated Flows","authors":"Anna Ivagnes, Maria Strazzullo, Michele Girfoglio, Traian Iliescu, Gianluigi Rozza","doi":"10.1002/nme.70042","DOIUrl":"https://doi.org/10.1002/nme.70042","url":null,"abstract":"Numerical stabilization techniques are often employed in under-resolved simulations of convection-dominated flows to improve accuracy and mitigate spurious oscillations. Specifically, the evolve–filter–relax (EFR) algorithm is a framework that consists of evolving the solution, applying a filtering step to remove high-frequency noise, and relaxing through a convex combination of filtered and original solutions. The stability and accuracy of the EFR solution strongly depend on two parameters, the filter radius <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 </mrow>\u0000 <annotation>$$ delta $$</annotation>\u0000 </semantics></math> and the relaxation parameter <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>χ</mi>\u0000 </mrow>\u0000 <annotation>$$ chi $$</annotation>\u0000 </semantics></math>. Standard choices for these parameters are usually fixed in time, and related to the full order model setting, that is, the grid size for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 </mrow>\u0000 <annotation>$$ delta $$</annotation>\u0000 </semantics></math> and the time step for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>χ</mi>\u0000 </mrow>\u0000 <annotation>$$ chi $$</annotation>\u0000 </semantics></math>. The key novelties with respect to the standard EFR approach are: (i) time-dependent parameters <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ delta (t) $$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>χ</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ chi (t) $$</annotation>\u0000 </semantics></math>, and (ii) data-driven adaptive optimization of the parameters in time, considering a fully-resolved simulation as reference. In particular, we propose three different classes of optimized-EFR (Opt-EFR) strategies, aiming to optimize one or both parameters. The new Opt-EFR strategies are tested in the under-resolved simulation of a turbulent flow past a cylinder at <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mi>e</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>000</mn>\u0000 </mrow>\u0000 ","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 9","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70042","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143919452","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

Component-Based Model-Order Reduction With Mortar Tied Contact for Nonlinear Quasi-Static Mechanical Problems 非线性准静态力学问题基于构件的砂浆捆绑接触模型阶数约简

IF 2.7 3区工程技术

International Journal for Numerical Methods in Engineering Pub Date : 2025-04-27 DOI: 10.1002/nme.70041

Stephan Ritzert, Jannick Kehls, Stefanie Reese, Tim Brepols

引用次数: 0

KATO: Neural-Reparameterized Topology Optimization Using Convolutional Kolmogorov-Arnold Network for Stress Minimization 基于卷积Kolmogorov-Arnold网络的应力最小化神经重参数化拓扑优化

IF 2.7 3区工程技术

International Journal for Numerical Methods in Engineering Pub Date : 2025-04-21 DOI: 10.1002/nme.70034

Shengyu Yan, Jasmin Jelovica

{"title":"KATO: Neural-Reparameterized Topology Optimization Using Convolutional Kolmogorov-Arnold Network for Stress Minimization","authors":"Shengyu Yan, Jasmin Jelovica","doi":"10.1002/nme.70034","DOIUrl":"https://doi.org/10.1002/nme.70034","url":null,"abstract":"Topology optimization (TO) has been a cornerstone of advanced structural design for decades, yet it continues to face challenges in terms of convergence, optimality, and numerical stability, particularly for complex, non-convex problems like stress minimization. This paper introduces a novel approach to stress-based topology optimization through the development of neural-reparameterized topology optimization using the convolutional Kolmogorov-Arnold network (KATO). KATO uses the neural network to reparameterize the optimization problem, offering a unique solution to the challenges posed by stress minimization in TO. It also simplifies the penalization scheme by reducing sensitivity to certain parameters, which reduces the non-convexity of the stress minimization problem, enhancing convergence and stability. Our method demonstrates better performance in stress minimization compared to conventional approaches and a different neural network-based approach, achieving up to 10% lower maximum stress in common benchmark cases. KATO also shows remarkable efficiency, reducing computational time by up to 67% compared to conventional methods for stress minimization problems. We conduct a comprehensive analysis of KATO's performance, computational cost, scalability, and the impact of various neural network architectures. Our results indicate that KATO not only improves stress optimization but also offers insights into the relationship between neural network design and topology optimization performance, paving the way for more efficient and effective structural design processes.","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143852806","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

Fluid-Structure Interaction Simulation of Mitral Valve Structures in a Left Ventricle Model 左心室模型中二尖瓣结构的流体-结构相互作用模拟

IF 2.7 3区工程技术

International Journal for Numerical Methods in Engineering Pub Date : 2025-04-21 DOI: 10.1002/nme.70031

Joel Kronborg, Johan Hoffman

{"title":"Fluid-Structure Interaction Simulation of Mitral Valve Structures in a Left Ventricle Model","authors":"Joel Kronborg, Johan Hoffman","doi":"10.1002/nme.70031","DOIUrl":"https://doi.org/10.1002/nme.70031","url":null,"abstract":"Simulations of blood flow in patient-specific models of heart ventricles is a rapidly developing field of research, showing promise to improve future treatment of heart diseases. Fluid-structure interaction simulation of the mitral valve, with its complex structure including leaflets, chordae tendineae, and papillary muscles, provides additional prospects as well as challenges to such models. In this study, we combine a patient-specific model of the left ventricle with an idealized unified continuum fluid-structure interaction model of the mitral valve, to simulate the intraventricular diastolic blood flow. To the best of our knowledge, no monolithic fluid-structure interaction model, without the need for remeshing, has ever been used before to simulate the native mitral valve within the left ventricle. The chordae tendineae are simulated as a region of porous medium, to partially hinder the flow. Simulation results from this model are compared to those of a model with the same patient-specific left ventricle, but with the mitral valve simply modeled as a time-variant inflow boundary condition. The blood flow is analyzed with the E-wave propagation index, and by use of the triple decomposition of the velocity gradient tensor, which decomposes the flow into rigid body rotational flow, shearing flow, and irrotational straining flow. The triple decomposition enables analysis of the formation of initially large dominant flow features, such as the E-wave jet and the vortex ring around it, and their subsequent decay into smaller turbulent flow structures. This analysis of the development of flow structures over the duration of diastole appears to be in general agreement with the theory of the stability of rotation, shear, and strain structures. Elevated shear levels are investigated, but are found only in limited amounts that do not indicate significant risks of thrombus formation or other blood damage, which is to be expected in this healthy ventricle. The highest shear levels are localized at the leaflets in the fluid-structure interaction model, and at the ventricle wall in the planar model. The computed E-wave propagation indices are 1.21 for the fluid-structure interaction model and 1.90 for the planar valve model, which indicates proper washout in the apical region with no significant risk of blood stasis that could lead to left ventricular thrombus formation.","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70031","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143852804","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

Forward and Inverse Approaches for Uncertainty Quantification of the In-Plane Elastic Properties of Cellular Structures 元胞结构面内弹性特性不确定量化的正、逆方法

IF 2.7 3区工程技术

International Journal for Numerical Methods in Engineering Pub Date : 2025-04-21 DOI: 10.1002/nme.70035

Zhiyong Zhao, Hao Yuan, Jaan-Willem Simon, Lishuai Sun, Yujun Li

{"title":"Forward and Inverse Approaches for Uncertainty Quantification of the In-Plane Elastic Properties of Cellular Structures","authors":"Zhiyong Zhao, Hao Yuan, Jaan-Willem Simon, Lishuai Sun, Yujun Li","doi":"10.1002/nme.70035","DOIUrl":"https://doi.org/10.1002/nme.70035","url":null,"abstract":"<div>\u0000 \u0000 Uncertainty quantification is essential to exploiting the complete potential of cellular structures. Forward methods allow quantifying the uncertainties in the mechanical properties of cellular structures by propagating the uncertainties of the input parameters, while inverse methods allow using experimental data to indirectly infer the uncertainty of the input parameters. In this paper, a closed-loop forward and inverse quantification of the in-plane elastic properties of cellular structures was proposed. A polynomial chaos expansion model was used in the forward model for uncertainty propagation and quantification of the in-plane elastic properties using the results from the Fast Fourier Transform simulations. The random input parameters field in the Fast Fourier Transform simulations, including geometry and material parameters of cellular structures, was involved by Karhunen–Loève expansion. Furthermore, the inverse uncertainty quantification was conducted in the framework of Markov Chain Monte Carlo sampling-based Bayesian inference using the constructed polynomial chaos surrogate model. The approach introduced was applied to analyze the uncertainty quantification in two types of cellular structures. The results showed that the thickness of the cell wall dramatically influences the effective in-plane elastic modulus of the cellular structures. The PCE could significantly reduce the iterations compared to the Monte Carlo simulation while ensuring the accuracy of uncertainty quantification of the in-plane elastic modulus. In addition, effective evaluation and calibration of the geometry and material parameters of the cellular structures based on the obtained posterior probability distribution have been achieved. This addresses the problem of uncertainty quantification of the in-plane elastic properties and the difficulty in measuring the geometry and material parameters of cellular structures.\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143852863","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 Novel Strain-Continuous Finite Element Formulation for Geometrically Exact Thin-Walled Beam on Lie Algebra 李代数上几何精确薄壁梁的新型应变-连续有限元计算公式

IF 2.7 3区工程技术

International Journal for Numerical Methods in Engineering Pub Date : 2025-04-21 DOI: 10.1002/nme.70024

Ziheng Huang, Ju Chen, Shixing Liu, Yongxin Guo

{"title":"A Novel Strain-Continuous Finite Element Formulation for Geometrically Exact Thin-Walled Beam on Lie Algebra","authors":"Ziheng Huang, Ju Chen, Shixing Liu, Yongxin Guo","doi":"10.1002/nme.70024","DOIUrl":"https://doi.org/10.1002/nme.70024","url":null,"abstract":"<div>\u0000 \u0000 Most existing geometrically exact thin-walled beam formulations on Lie group SE(3)<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>×</mo>\u0000 </mrow>\u0000 <annotation>$$ times $$</annotation>\u0000 </semantics></math><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <annotation>$$ mathbb{R} $$</annotation>\u0000 </semantics></math> considering warping are <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <annotation>$$ C $$</annotation>\u0000 </semantics></math><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mo> </mo>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {}^0 $$</annotation>\u0000 </semantics></math>-continuous. In this study, a novel strain-continuous element for geometrically exact thin-walled beam on Lie algebra <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 </mrow>\u0000 <annotation>$$ mathfrak{s} $$</annotation>\u0000 </semantics></math><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 <annotation>$$ mathfrak{e} $$</annotation>\u0000 </semantics></math>(3)<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>×</mo>\u0000 </mrow>\u0000 <annotation>$$ times $$</annotation>\u0000 </semantics></math><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <annotation>$$ mathbb{R} $$</annotation>\u0000 </semantics></math> is originally proposed, in which the torsion-related Wagner effect and warping are considered in the constitutive relations. The proposed beam element is not only locking-free intrinsically, but also is <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <annotation>$$ C $$</annotation>\u0000 </semantics></math><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mo> </mo>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {}^1 $$</annotation>\u0000 </semantics></math>-continuous by using the proposed geometrical Hermite interpolation on Lie algebra. This interpolation based on Magnus expansion can simplify the description of interpolated element stress tensor and strain energy. Then, the sim","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 8","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143852803","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