Finite Elements in Analysis and Design最新文献

{"title":"Reduced-integration hexahedral finite element for static and vibration analysis of micropolar continuum","authors":"Yu Yao ,&nbsp;Xin Zhao ,&nbsp;Linghao Chen ,&nbsp;Yujie Gu ,&nbsp;Tianqi Zhou","doi":"10.1016/j.finel.2025.104412","DOIUrl":"10.1016/j.finel.2025.104412","url":null,"abstract":"<div><div>The micropolar elasticity finite element method is widely used for analyzing advanced materials with complex microstructures, but existing implementations often suffer from computational inefficiency due to full integration schemes and shear locking in bending scenarios. This study proposes a high-performance, reduced-integration, first-order hexahedral micropolar element to address these limitations. The formulation combines standard Lagrange interpolation with uniform strain and curvature fields, ensuring patch test satisfaction and accuracy in skewed configurations. An artificial stiffness method is introduced to suppress displacement and rotational hourglass instabilities. Rigorous numerical validations, including force and displacement patch tests, cantilever beam bending, and free vibration analysis, demonstrate the superior accuracy and computational efficiency of the element. Furthermore, applications to star-shaped lattices and 3D chiral metamaterials highlight its effectiveness in capturing microstructure-dependent mechanical behaviors, such as unexpected bending deformation and tension-twist coupling. The proposed element significantly enhances computational efficiency in homogenization simulation, providing a robust and practical tool for the simulation-driven design of advanced mechanical metamaterials with complex deformation mechanisms.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104412"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144611919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Three-dimensional simulation of finite-strain debonding using immersed meshes","authors":"Andrew B. Groeneveld ,&nbsp;Pinlei Chen","doi":"10.1016/j.finel.2025.104404","DOIUrl":"10.1016/j.finel.2025.104404","url":null,"abstract":"<div><div>We propose a method for modeling interfacial damage and debonding under quasi-static loads using immersed meshes in 3D at finite strains. This is an extension of our previous work on an immersed variational multiscale discontinuous Galerkin (VMDG) method in 2D. The variational approach remains the same, but transitioning from 2D to 3D introduces significant complications in the computational geometry aspects. The immersed VMDG method is a stabilized interface formulation derived using variational multiscale (VMS) ideas to apply discontinuous Galerkin (DG) treatment to the interface while employing a continuous Galerkin (CG) approximation elsewhere. Key benefits of VMDG are the variationally derived stabilization terms that evolve during deformation and are free of user-defined parameters. Also, the transition from perfect bond to damage behavior at the interface is handled naturally by incorporating an interfacial gap variable governed by a yield criterion and a flow rule. To support 3D simulations, we introduce algorithms for integrating cut elements, forming interface segments, and computing the VMDG stabilization tensor. Cut-element integration is performed using voxel-based moment-fitting integration to avoid the robustness issues associated with using mesh Booleans and tetrahedral integration cells. A simplification of the stabilization tensor is also proposed to reduce the computational cost while retaining the variational character of the stabilization. Several numerical examples are presented to demonstrate the robustness, efficiency, and range of applicability of the method.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"250 ","pages":"Article 104404"},"PeriodicalIF":3.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144536086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Runge–Kutta discontinuous Galerkin method based on flux vector splitting for hyperbolic conservation laws","authors":"Zhengrong Xie","doi":"10.1016/j.finel.2025.104398","DOIUrl":"10.1016/j.finel.2025.104398","url":null,"abstract":"<div><div>The flux vector splitting (FVS) method has firstly been incorporated into the Runge–Kutta Discontinuous Galerkin (RKDG) framework for reconstructing the numerical fluxes required for the spatial semi-discrete formulation, setting it apart from the conventional RKDG approaches that typically utilize the Lax–Friedrichs flux scheme or classical Riemann solvers such as HLLC. The control equations are initially reformulated into a flux-split form. Subsequently, a variational approach is applied to this flux-split form, from which a DG spatial semi-discrete scheme based on FVS is derived. Then, FVS-RKDG is implemented in two-dimensional case by splitting the normal flux on cell interfaces instead of splitting dimension by dimension in the x and y directions Finally, the concept of “flux vector splitting based on Jacobian eigenvalue decomposition” has been applied to the conservative linear scalar transport equations and the nonlinear Burgers’ equation. This approach has led to the rederivation of the classical Lax–Friedrichs flux scheme and the provision of a Steger–Warming flux scheme for scalar cases.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"250 ","pages":"Article 104398"},"PeriodicalIF":3.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144518096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A finite element implementation of the SRTD algorithm for an Oldroyd 3-parameter viscoelastic fluid model","authors":"Christian Austin ,&nbsp;Sara Pollock ,&nbsp;L. Ridgway Scott","doi":"10.1016/j.finel.2025.104399","DOIUrl":"10.1016/j.finel.2025.104399","url":null,"abstract":"<div><div>In this paper, we discuss a finite element implementation of the SRTD algorithm described by Girault and Scott for the steady-state case of a certain 3-parameter subset of the Oldroyd models. We compare it to the well-known EVSS method, which, though originally described for the upper-convected Maxwell model, can easily accommodate the Oldroyd 3-parameter model. We obtain numerical results for both methods on two benchmark problems: the lid-driven cavity problem and the journal-bearing, or eccentric rotating cylinders, problem. We find that the resulting finite element implementation of SRTD is stable with respect to mesh refinement and is generally faster than EVSS, though is not capable of reaching as high a Weissenberg number as EVSS.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"250 ","pages":"Article 104399"},"PeriodicalIF":3.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stress-based topology optimization of continuum structures incorporating a piecewise P-norm stabilization strategy","authors":"Shi-An Zhou,&nbsp;Song Yao","doi":"10.1016/j.finel.2025.104401","DOIUrl":"10.1016/j.finel.2025.104401","url":null,"abstract":"<div><div>In this paper, a combined Floating Projection Topology Optimization (FPTO) method is applied to stress-based topology optimization of continuum structures. To balance the need for a stable optimization process under a low P-norm and the goal of achieving a uniform stress distribution at a higher P-norm, the FPTO method here is combined with piecewise P-norm strategy. A new parameter, solid rate, is introduced, serving not only as an additional convergence criterion but also as a decision criterion for adaptively increasing the P-norm value. To validate the effectiveness of the proposed FPTO method incorporating both piecewise P-norm stabilization and the solid rate control strategy, this study conducts stiffness maximization optimization with stress constraints on various typical structures. The results show that the method effectively reduces computational oscillations in stress-based topology optimization for structures with stress concentrations, which helps to the discovery of superior designs.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"250 ","pages":"Article 104401"},"PeriodicalIF":3.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144480638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A parallel FreeFEM framework for topology optimization of structures into three spatial dimensions","authors":"J.M.M. Luz Filho,&nbsp;A.T.A. Gomes,&nbsp;A.A. Novotny","doi":"10.1016/j.finel.2025.104384","DOIUrl":"10.1016/j.finel.2025.104384","url":null,"abstract":"<div><div>This article presents a simple and compact parallel FreeFEM implementation for topology optimization of structures into three spatial dimensions. The topology optimization algorithm relies on the topological derivative concept together with a level-set domain representation method, in which the topological derivative is used as a steepest descent direction evolving the level-set function within the optimization procedure. In addition, adaptive mesh refinement is performed in the optimization scheme for enhancing the boundary representation of the resulting structure and reducing the computational cost of structured mesh refinements. In addition, a rich and thorough discussion of the main aspects of the parallel FreeFEM implementation is given in full detail. In particular, a version of the resulting code is provided for the reader convenience, including two benchmark examples for structural stiffness maximization and for the design of compliant mechanisms, showing the simplicity and effectiveness of the proposed implementation. Besides, we also show how the resulting code can be easily converted into a SIMP-based topology design algorithm. Since all the background knowledge on the topological derivative method is presented and the complete FreeFEM implementation is provided as supplementary material, this paper may also be used as educational/pedagogical material for graduate students and/or newcomers to the field of topology optimization.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"250 ","pages":"Article 104384"},"PeriodicalIF":3.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A physically based Proper Orthogonal Decomposition for structural mechanics involving dissipative processes","authors":"L. Cimatti Lucarelli ,&nbsp;N. Blal ,&nbsp;A. Platzer ,&nbsp;A. Gravouil ,&nbsp;D. Iampietro","doi":"10.1016/j.finel.2025.104386","DOIUrl":"10.1016/j.finel.2025.104386","url":null,"abstract":"<div><div>This paper proposes a framework for a physically based POD (Proper Orthogonal Decomposition), denoted <span><math><mi>φ</mi></math></span>POD. The proposed Reduced Order Model (ROM) is set to respect one of the evolution equations of an elasto-viscoplastic material. The <span><math><mi>φ</mi></math></span>POD is obtained through the solution of a constrained minimization problem over the reduced coordinates of the POD. Furthermore, a physically based Reduced Order Surrogate Model (ROSM) is constructed based on <em>Interpolation on a Tangent Space to the Grassmann manifold</em> (ITSGM). This paper uses the 2D Cook’s membrane under plane strain hypothesis as an application case. The performance metrics to compare the <span><math><mi>φ</mi></math></span>POD to the regular POD are the residual of the constrained equation, projection energies, and interpolation error for mechanical fields.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"250 ","pages":"Article 104386"},"PeriodicalIF":3.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Profilometry-based indentation plastometry (PIP) integrated finite element (FE) model validation using neutron diffraction","authors":"Gaurav Vithalani ,&nbsp;Stuart Bell ,&nbsp;Rezwanul Haque ,&nbsp;Edmund Pickering ,&nbsp;Mark Reid ,&nbsp;Geoffrey Will ,&nbsp;Richard Clegg ,&nbsp;Theodore A. Steinberg","doi":"10.1016/j.finel.2025.104400","DOIUrl":"10.1016/j.finel.2025.104400","url":null,"abstract":"<div><div>Stress assisted corrosion can lead to premature failure of structural alloys such as stainless steel 316. The mechanisms governing the various failure modes are poorly understood due to the complexities involved in testing the combined effects of stress and corrosion at high temperatures. Modified Turski (MT) specimens are an invaluable tool for studying these mechanisms as they can be pre-stressed to induce residual stresses and exposed to a corrosive environment without needing specialised equipment. However, it is challenging to measure the stresses experimentally without altering the stress state. To overcome this, finite element (FE) modelling can be used, but validated models are scarce, particularly for MT specimen geometry. In this work, an FE model was developed based on the non-destructive characterisation of material using profilometry-based indentation Plastometry (PIP) and validated for residual stresses using enhanced neutron diffraction (ND) measurement. The model results showed significant correlations with experimentally observed deflection and residual stress profile. The deviation observed between the model and experiment was analysed and discussed to understand the evolution of strain field in materials. To conclude, this validated model, and approach is reliable and enables rapid material compatibility assessment for stress assisted corrosion, which is particularly important in emerging industries like concentrated solar thermal (CST) and hydrogen energy, amongst many others.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"250 ","pages":"Article 104400"},"PeriodicalIF":3.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-material structure topology optimization considering length scale control based on isogeometric analysis approach","authors":"Jianping Zhang,&nbsp;Ou Guo,&nbsp;Yaping Zhao,&nbsp;Zhijian Zuo,&nbsp;Mintao Chen,&nbsp;Haishan Lu,&nbsp;Shuguang Gong","doi":"10.1016/j.finel.2025.104391","DOIUrl":"10.1016/j.finel.2025.104391","url":null,"abstract":"<div><div>The multi-material structure topology optimization method considering length scale control (LSC) using the isogeometric analysis approach is put forward. The density distribution function (DDF) is applied for improving structural smoothness, and the resulting structure has smoother and clearer boundaries compared to the conventional finite element method. The alternating active-phase algorithm and gradient algorithm are utilized for building the multi-material interpolation model and updating the design variable, respectively. The effects of different LSC scheme, the maximum length scale control (MaxLSC) domain radius <span><math><mrow><msub><mi>R</mi><mi>max</mi></msub></mrow></math></span>, the radius of DDF influence domain <span><math><mrow><msub><mi>r</mi><mtext>fil</mtext></msub></mrow></math></span> and the aggregation factor <span><math><mrow><msub><mi>p</mi><mi>n</mi></msub></mrow></math></span> on the structure performance are investigated. The results show the structure with both MaxLSC and MinLSC applied exhibits a more uniform material distribution, the structural manufacturability is effectively guaranteed. When <span><math><mrow><msub><mi>r</mi><mtext>fil</mtext></msub><mo>≤</mo><mn>3</mn><mi>h</mi></mrow></math></span>, the jagged boundaries appear in the structure, and when <span><math><mrow><msub><mi>r</mi><mtext>fil</mtext></msub><mo>≥</mo><mn>5</mn><mi>h</mi></mrow></math></span>, the branching structures decrease. The topological structure obtained when <span><math><mrow><msub><mi>r</mi><mtext>fil</mtext></msub><mo>=</mo><mn>3.5</mn><mi>h</mi><mo>−</mo><mn>4</mn><mi>h</mi></mrow></math></span> has the relatively uniform material distribution. When <span><math><mrow><msub><mi>R</mi><mi>max</mi></msub><mo>=</mo><mn>5</mn><mi>h</mi></mrow></math></span>, the island phenomenon appears in the structure. When <span><math><mrow><msub><mi>R</mi><mi>max</mi></msub><mo>=</mo><mn>10</mn><mi>h</mi></mrow></math></span>, the branching structure is reduced and thickened simultaneously, the recommended range for <span><math><mrow><msub><mi>R</mi><mi>max</mi></msub></mrow></math></span> is <span><math><mrow><mn>6</mn><mi>h</mi><mo>−</mo><mn>8</mn><mi>h</mi></mrow></math></span>. When <span><math><mrow><msub><mi>p</mi><mi>n</mi></msub><mo>=</mo><mn>80</mn><mo>−</mo><mn>110</mn></mrow></math></span>, the topological structure exhibits more branching structure in both materials. It is proved that the effectiveness of the LSC method can still be guaranteed in the three-dimensional problem and curved edge structure.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"250 ","pages":"Article 104391"},"PeriodicalIF":3.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144280979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two-grid domain decomposition methods for the coupled Dual-Porosity-Navier-Stokes system with Beavers-Joseph interface condition","authors":"Chongxin Zhang,&nbsp;Guangzhi Du,&nbsp;Xinxin Sun","doi":"10.1016/j.finel.2025.104403","DOIUrl":"10.1016/j.finel.2025.104403","url":null,"abstract":"<div><div>In this paper, two kinds of two-grid domain decomposition methods for the coupled Dual-Porosity-Navier-Stokes system are proposed and analyzed by integrating the established robin-type domain decomposition approach with a two-grid strategy. Initially, we apply the established robin-type domain decomposition approach on a coarse grid to address the coupled problem. Subsequently, on a fine grid, we employ two distinct approaches: first, to solve the matrix and microfracture subproblems, followed by the Navier–Stokes subproblem. Both approaches fundamentally approximate the interface term using the coarse-grid solution. The proposed algorithms integrate the two-grid approach with the established domain decomposition method, capitalizing on the strengths of both techniques while addressing their respective limitations. Comprehensive theoretical analysis is established, and four in-depth numerical investigations are conducted to assess the efficiency, accuracy, and robustness of the proposed algorithms by comparing them with the domain decomposition method.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"250 ","pages":"Article 104403"},"PeriodicalIF":3.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501860","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}