Finite Elements in Analysis and Design最新文献

{"title":"A simple hybrid linear and nonlinear interpolation finite element for the adaptive Cracking Elements Method","authors":"Xueya Wang ,&nbsp;Yiming Zhang ,&nbsp;Minjie Wen ,&nbsp;Herbert A. Mang","doi":"10.1016/j.finel.2024.104295","DOIUrl":"10.1016/j.finel.2024.104295","url":null,"abstract":"<div><div>The Cracking Elements Method (CEM) is a numerical tool for simulation of quasi-brittle fracture. It neither needs remeshing, nor nodal enrichment, or a complicated crack-tracking strategy. The cracking elements used in the CEM can be considered as a special type of Galerkin finite elements. A disadvantage of the CEM is that it uses nonlinear interpolation of the displacement field (e.g. Q8 and T6 elements for 2D problems), introducing more nodes and consequently requiring greater computing efforts than in case of elements based on linear interpolation of the displacement field. With the aim to solve this problem we propose a hybrid linear and nonlinear interpolation finite element for the adaptive CEM presented in this work. A simple strategy is proposed for treating elements with <span><math><mi>p</mi></math></span> edge nodes, where <span><math><mrow><mi>p</mi><mo>∈</mo><mfenced><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></mfenced></mrow></math></span>, with <span><math><mi>n</mi></math></span> as the edge number of the considered element. Only a few program codes are needed. Then, by just adding edge and center nodes to the elements experiencing cracking, while keeping linear interpolation of the displacement field for the elements outside the cracking domain, the number of total nodes is reduced to almost one half of the number in case of using the conventional CEM. Numerical investigations have shown that the new approach not only preserves all of the advantages of the CEM, but also results in a significantly enhanced computing efficiency.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104295"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841420","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":"Development of C1 smooth isogeometric functions for planar multi-patch domains for NURBS based analysis","authors":"Lokanath Barik,&nbsp;Abinash Kumar Swain","doi":"10.1016/j.finel.2024.104300","DOIUrl":"10.1016/j.finel.2024.104300","url":null,"abstract":"<div><div>This paper proposes a novel framework for constructing <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> smooth isogeometric functions on the planar multipatch domain. We extend the concept of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> coupling, wherein the null space approach was used to construct geometrically continuous basis functions as linear combinations of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> basis functions near patch junctions. However, due to the lack of continuity constraints, the resulting approximate basis functions violated the partition of unity and non-negativity properties. The proposed framework enforces the partition of unity and non-negativity conditions through additional equations, preserving higher-order continuity across the interface. The patch coupling algorithm provided generates <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> smooth isogeometric functions for arbitrarily shaped planar multipatch geometries. The advantage of this proposed approach is a reduced degree of approximation and a smooth transition from 1D to 2D patch coupling methodology. The computational effort to determine a new set of basis functions is significantly reduced due to the partition of unity property. Numerical studies are performed for the Kirchhoff–Love plate and biharmonic equations on various curved multipatch geometries, including an additional patch test. Enhanced numerical accuracy is observed for geometries with curved interfaces and boundaries. The accuracy and numerical efficiency of the proposed framework are analysed through <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> errors, showing optimal convergence behaviour for different polynomial orders. Furthermore, well-conditioned global matrices are observed with increasing refinement levels, demonstrating the efficiency of the methodology.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104300"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911621","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":"An hp-finite element for vibration analysis of laminates reinforced with curvilinear fibres","authors":"Pedro Camacho,&nbsp;Pedro Ribeiro,&nbsp;Hamed Akhavan","doi":"10.1016/j.finel.2024.104280","DOIUrl":"10.1016/j.finel.2024.104280","url":null,"abstract":"<div><div>In this paper, an approach to model thin composite plates reinforced with curvilinear fibres is presented and applied to analyse modes of vibration. Particular attention is given to plates with non-standard geometries, which are less commonly addressed in studies on this topic. Aiming to achieve accuracy with a small number of degrees-of-freedom, the model is based on Kirchhoff’s plate theory, combined with an <em>hp</em>-version finite element method. Assembling <em>p</em>-version Kirchhoff plate elements, while ensuring continuity, presents a significant challenge. Elastic connections are introduced to address this issue. Additionally, elastic boundaries are also considered to impose the boundary conditions. Regarding the reinforcing fibres, cubic polynomial splines are employed to represent the path of the fibres, which also adds to the proposed model generality. To discretise the displacement field of the plate, three sets of interpolation functions are investigated. The convergence properties of the model, and the effects of the intervening features, are analysed based on <em>hp</em>-refinement. The proposed approach is shown to require fewer degrees-of-freedom to effectively analyse irregular-shaped plates, when compared to the more commonly used <em>h</em>-version finite elements. Moreover, the capability of cubic polynomial splines to represent fibre paths is validated. The paper concludes with modal analysis of a composite plate with a complex shape to verify tailoring abilities of reinforcing curvilinear fibres.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104280"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142804886","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}

{"title":"An innovative beam element with section components cohesive interaction for reinforced concrete frames","authors":"S.Hamed Ebrahimi","doi":"10.1016/j.finel.2024.104307","DOIUrl":"10.1016/j.finel.2024.104307","url":null,"abstract":"<div><div>The behavior of a Timoshenko concrete beam reinforced by ribbed steel rebars is a function of the cohesive interaction between the concrete and reinforcement provided via bond-slip or traction-separation law. Bond-slip interactions between top/bottom reinforcements and the concrete beam section considering the shear deformations have been studied in this paper in static loading and nonlinear material and geometry conditions.</div><div>In this regard, the hybrid beam element has been enriched with two additional interactive degrees of freedom which incorporate the constituted freedom of the top and bottom unions of compressive and tensile reinforcements.</div><div>For this purpose, a two-dimensional mesh of the section is added as considered in the multi-fiber and multiscale approaches to non-homogeneous materials simulation whereas, several benefits are provided among which are non-prismatic reinforced concrete beam analysis, arbitrary composite beam section architecture, processing damage, and tracking cracks through the beam section and accordingly through the length of the beam, Fiber Reinforced Polymer reinforcement and wrapping laminates analysis and design, considering prestressing beam sections and many other advantages.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104307"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142935954","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":"Formulating finite elements representing a given microstructure without using homogenisation","authors":"Kazem Ghabraie","doi":"10.1016/j.finel.2024.104306","DOIUrl":"10.1016/j.finel.2024.104306","url":null,"abstract":"<div><div>A framework is proposed to directly calculate the stiffness matrix of a macro-element equivalent to a desired microstructure. In a sense, this approach enables the estimation of the “homogenised” properties of microstructures without using the homogenisation theory. The proposed framework is based on assumed displacement fields within equivalent macro-elements. Different displacement assumptions are briefly discussed and two equivalent macro-elements are formulated. Several numerical tests are performed and discussed to show the potentials and limitations of the equivalent macro-elements. The numerical results show that one of the formulated elements can provide reasonable accuracy improvements, particularly in stress calculations. A sensitivity analysis is provided allowing the proposed equivalent macro-elements to be used in topology optimisation. The numerical results show that the formulated elements can effectively enhance the resolution of the boundaries in optimised solutions to obtain smooth designs.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104306"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142935964","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}

{"title":"An adaptive mesh refinement algorithm for stress-based phase field fracture models for heterogeneous media: Application using FEniCS to ice-rock cliff failures","authors":"Duc Tien Nguyen ,&nbsp;Abhinav Gupta ,&nbsp;Ravindra Duddu ,&nbsp;Chandrasekhar Annavarapu","doi":"10.1016/j.finel.2024.104311","DOIUrl":"10.1016/j.finel.2024.104311","url":null,"abstract":"<div><div>Fracture propagation in heterogeneous ice-rock cliffs and hanging glaciers is complicated by the presence of internal interfaces and material property mismatch, so their failure risk is difficult to assess. Despite recent advances, phase-field fracture modeling is computationally expensive for large-scale homogeneous and heterogeneous material media. Here, we present an adaptive mesh refinement algorithm for the stress-based phase-field fracture model for heterogeneous media, implemented within the open-source finite element software package FEniCS. The novelty of the proposed algorithm includes its ability to handle material heterogeneity by representing elastic and fracture properties as fields via material distribution functions. These properties, along with the solution fields, are then appropriately transferred during the mesh refinement process without requiring a redefinition. We present several numerical studies to benchmark the method and analyze fracture predictions in idealized homogeneous and heterogeneous rock and ice-rock domains. Through these studies, we demonstrate the method’s accuracy and efficiency of simulations in multi-dimensions, and examine the effect of material properties and the interface inclination on fracture propagation. The results indicate that the mismatch of material properties at the rock-rock and ice-rock interfaces and the critical stress for fracture initiation can have a significant influence on crack propagation, including depth, length, and orientation. In three-dimensional geological fracture simulations, non-adaptive meshes would require handling billions of elements, whereas the proposed algorithm reduces the final mesh size to fewer than a million, demonstrating substantial computational savings and making it a practical approach for geological fracture simulation.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104311"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986238","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}

{"title":"Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media","authors":"Sumanta Roy ,&nbsp;Dibakar Roy Sarkar ,&nbsp;Chandrasekhar Annavarapu ,&nbsp;Pratanu Roy ,&nbsp;Brice Lecampion ,&nbsp;Dakshina Murthy Valiveti","doi":"10.1016/j.finel.2024.104305","DOIUrl":"10.1016/j.finel.2024.104305","url":null,"abstract":"<div><div>We model transient diffusion in heterogeneous materials using a novel physics-informed neural networks framework (PINNs) termed Adaptive interface physics-informed neural networks or AdaI-PINNs (Roy et al. arXiv preprint arXiv:2406.04626, 2024). AdaI-PINNs utilize different activation functions with trainable slopes tailored to each material region within the computational domain, allowing for a fully automated and adaptive PINNs approach to model interface problems with strongly and weakly discontinuous solutions. To enhance its performance in highly heterogeneous transient diffusion systems, we prescribe a suite of robust practices, including appropriate non-dimensionalization of equations, a biased sampling method, Glorot initialization, and the hard enforcement of boundary and initial conditions. We evaluate the efficacy of the proposed method on several benchmark forward and inverse problems. Comparative studies on one-dimensional and two-dimensional benchmark problems reveal that the modified AdaI-PINNs outperform its unmodified counterpart, achieving root-mean-square errors that are at least two orders of magnitude better in forward problems. For inverse problems, the maximum errors in the approximated diffusion coefficients by modified AdaI-PINNs are four orders of magnitude better than those of the unmodified version. Additionally, modified AdaI-PINNs demonstrate improved stability in problems with large material mismatches.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104305"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986240","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":"Conditional value at risk for damage identification in structural digital twins","authors":"Facundo N. Airaudo ,&nbsp;Harbir Antil ,&nbsp;Rainald Löhner","doi":"10.1016/j.finel.2025.104316","DOIUrl":"10.1016/j.finel.2025.104316","url":null,"abstract":"<div><div>Given measurements from sensors and a set of standard forces, an optimization based approach to perform damage identification in structures is introduced. The key novelty lies in letting the loads and measurements to be random variables. Subsequently, the conditional-value-at-risk (CVaR) is minimized subject to the elasticity equations as constraints. CVaR is a risk measure that leads to minimization of rare and low probability events which the standard expectation cannot. The optimization variable is the (deterministic) strength factor which appears as a coefficient in the elasticity equation, thus making the problem nonconvex. Due to uncertainty, the problem is high dimensional and, due to CVaR, the problem is nonsmooth. An adjoint based approach is developed with quadrature in the random variables. This approach would enable the implementation of risk-averse digital twins. Numerical results are presented in the context of a plate, a large structure with trusses similar to those used in solar arrays or cranes, and a footbridge.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"245 ","pages":"Article 104316"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143125160","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":"Finite element analysis-enabled optimization of process parameters in additive manufacturing","authors":"Jingyi Wang,&nbsp;Panayiotis Papadopoulos","doi":"10.1016/j.finel.2024.104282","DOIUrl":"10.1016/j.finel.2024.104282","url":null,"abstract":"<div><div>A design optimization framework is proposed for process parameters in additive manufacturing. A finite element approximation of the coupled thermomechanical model is used to simulate the fused deposition of heated material and compute the objective function for each analysis. Both gradient-based and gradient-free optimization methods are developed. The gradient-based approach, which results in a balance law-constrained optimization problem, requires sensitivities computed from the fully discretized finite element model. These sensitivities are derived and subsequently applied to a projected gradient-descent algorithm. For the gradient-free approach, two distinct algorithms are proposed: a search algorithm based on local variations and a Bayesian optimization algorithm using a Gaussian process. Two design optimization examples are considered in order to illustrate the effectiveness of these approaches and explore the range of their usefulness.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104282"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841385","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":"Designing novel vascular stents with enhanced mechanical behavior through topology optimization of existing devices","authors":"Nicola Ferro ,&nbsp;Francesco Mezzadri ,&nbsp;Dario Carbonaro ,&nbsp;Emanuele Galligani ,&nbsp;Diego Gallo ,&nbsp;Umberto Morbiducci ,&nbsp;Claudio Chiastra ,&nbsp;Simona Perotto","doi":"10.1016/j.finel.2024.104304","DOIUrl":"10.1016/j.finel.2024.104304","url":null,"abstract":"<div><div>A variety of different vascular stent designs are currently available on the market, featuring different geometries, manufacturing materials, and physical characteristics. Here, we propose a framework for designing innovative stents that replicate and enhance the mechanical properties of existing devices. The framework includes a Solid Isotropic Material with Penalization (SIMP)-based topology optimization formulation, assisted by the homogenization theory to constrain the mechanical response, along with a minimum length scale requirement to ensure manufacturability to the designed devices. The optimization problem, discretized on a sequence of computational meshes anisotropically adapted, generates a 2D stent unit cell, which can be automatically converted into a 3D digital version of the device. This virtual prototype is validated through <em>in silico</em> testing via a radial crimping simulation to assess the stent insertion into the catheter, prior to implantation. The results prove that the proposed framework can identify stent designs that are competitive with respect to existing devices in terms of relevant clinical requirements, such as foreshortening, radial stiffness and surface contact area.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"244 ","pages":"Article 104304"},"PeriodicalIF":3.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986347","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}