Finite Elements in Analysis and Design最新文献

{"title":"Application of a FEM-SPIM adaptive strategy to phase-field simulation of pressurized fracture","authors":"Eduarda Marques Ferreira ,&nbsp;Hugo Mouro Leão ,&nbsp;Roque Luiz da Silva Pitangueira ,&nbsp;Lapo Gori ,&nbsp;Larissa Novelli","doi":"10.1016/j.finel.2026.104536","DOIUrl":"10.1016/j.finel.2026.104536","url":null,"abstract":"<div><div>The problem of hydraulic fracturing has been studied in several areas of knowledge, including the oil industry, analysis of geological formations and structural engineering. Complex crack patterns are common, which are maximized by the presence of the fluid pressure load on the crack faces, with the occurrence of phenomena such as nucleation, branching and fracture joining. For this reason, the choice of a suitable model for treating the cracking process and the nonlinear behaviour of the material is very important. An interesting approach is the use of phase-field modelling (PFM), which treats the formation and propagation of any number of cracks automatically, as part of the solution of a variational problem. However, a negative aspect of PFM is that it requires very refined meshes in the crack propagation region to correctly represent the fracture process zone. This generates a high computational cost and can limit its use in large problems. The use of adaptive strategies, in which the refined regions follow the crack path, is an efficient approach to overcome this problem. In this respect, this paper proposes the use of an adaptive model with the coupling between the standard Finite Element Method (FEM) and meshless methods of the family of Smoothed Point Interpolation Methods (SPIMs), which possess the property of the Kronecker Delta function, allowing them to be directly coupled with the FEM. Both the coupling and the adaptive strategies are carried out automatically during the incremental-iterative process, using the value of the phase-field variable as the trigger parameter, ensuring that the region in which the inelastic process occurs is discretized by SPIM and properly refined. Numerical simulations are presented as a way of validating the proposed model as well as exemplifying its versatility, covering problems with realistic applications and large dimensions, the modelling of which would be difficult without the use of adaptive refinement strategies.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"256 ","pages":"Article 104536"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146192127","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 accurate coarse mesh-based analysis approach for nonlinear bending and post-buckling problems of plates and shells utilizing recurrent neural networks with Bayesian regularization back-propagation algorithm","authors":"Tan N. Nguyen ,&nbsp;Tan Khoa Nguyen ,&nbsp;Suppakit Eiadtrong ,&nbsp;Nuttawit Wattanasakulpong ,&nbsp;Mohamed-Ouejdi Belarbi ,&nbsp;Nader M. Okasha ,&nbsp;Masoomeh Mirrashid ,&nbsp;Aman Garg","doi":"10.1016/j.finel.2026.104525","DOIUrl":"10.1016/j.finel.2026.104525","url":null,"abstract":"<div><div>The fineness of element meshes strongly affects the accuracy and cost of solutions in computational mechanics. In this regards, an accurate coarse mesh-based analysis approach (CMA) for nonlinear bending and post-buckling problems of plates and shells utilizing nonlinear auto-regressive exogenous Bayesian neural networks (NARX-BNNs) is first proposed in this work. The CMA approach comprises two pivotal stages. Initially, a coarse mesh-based post-buckling isogeometric analysis is executed, yielding a preliminary equilibrium path quickly. The path includes a series of initial displacements and a series of initial loads. Subsequently, in the second stage, two initial series serve as the inputs for the trained networks to accurately predict displacements and loads. Finally, the resulting network outputs are a series of accurate displacements and a series of accurate loads leading to the attainment of an accurate equilibrium path. NARX-BNN is known as a recurrent neural network model utilizing Bayesian regularization back-propagation algorithm which can result in good generalization for difficult or noisy data sets. The post-buckling analyses were based on isogeometric analysis (IGA) and first-order shear deformation shell theory (FSDT) utilizing the von Karman assumption. Instabilities of shells considered in this work were snap-through, softening–hardening, and snap-back. High generalization, fast training and exactness of the proposed data-driven models were confirmed via solving five problems. The power, wide application, high exactness and effectiveness of the CMA approach for nonlinear bending and post-buckling problems of plates and shells were demonstrated. The concept of CMA approach can be applied and extended to a great number of problems in computational mechanics which uses element meshes in the numerical procedure to save time and labor.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"256 ","pages":"Article 104525"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Runge–Kutta–Chebyshev schemes to accelerate thermal modelling of additive manufacturing processes","authors":"Simon Essongue,&nbsp;Bourama Diarra,&nbsp;Eric Lacoste","doi":"10.1016/j.finel.2026.104527","DOIUrl":"10.1016/j.finel.2026.104527","url":null,"abstract":"<div><div>This work investigates the applicability of the Runge–Kutta–Chebyshev (RKC) time stepping scheme for conduction-based simulations of metal additive manufacturing (AM) processes, marking its first use in this context. RKC belongs to the underutilized class of stabilized explicit methods, combining the non-iterative, parallel-friendly nature of forward Euler (FE) with significantly relaxed stability constraints. Through comparisons with FE and backward Euler (BE) on a scan path-resolved, experimentally-validated simulation, we show that RKC offers substantial speedups while maintaining accuracy across both printing and cooling stages. The strong performance of RKC in this challenging test case – incorporating radiation, an evolving computational domain, and phase change, among other nonlinearities – underscores its potential and the need for its broader application within the applied numerical community.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"256 ","pages":"Article 104527"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Normalized energy-based physics-informed neural network: Theory and applications to solid mechanics problems","authors":"Thang Le-Duc ,&nbsp;H. Nguyen-Xuan ,&nbsp;Jaehong Lee","doi":"10.1016/j.finel.2026.104523","DOIUrl":"10.1016/j.finel.2026.104523","url":null,"abstract":"<div><div>Energy-based physics-informed neural networks (EPINNs) have recently achieved success for solving several partial differential equations (PDEs) in solid mechanics. In this study, we firstly indicate fundamental restrictions of the EPINN approach in terms of both analytical and practical perspectives, in which EPINN predictions perform poorly for non-trivial problems having small-intensity solutions and are intrinsically biased towards larger-intensity solutions when applied to coupled PDEs. To overcome these limitations of the traditional EPINN, this study subsequently proposes a normalized EPINN (nEPINN). In particular, the nEPINN uses a scaling vector to calibrate the network outputs to correct the total potential energy (TPE) error and the differences among prediction errors to achieve more uniformly high-quality solutions. Mathematical analyses are also deployed to examine the worst-case performance of the devised nEPINN from a theoretical perspective. Accordingly, two selection frameworks are devised afterwards to determine the scaling vector based on <em>a-posteriori</em> information about structural responses. Several solid mechanics examples, including one-dimensional (1D) linear and nonlinear beam bending models using both Euler–Bernoulli (EB) and Timoshenko theories, two-dimensional (2D) plane-stress and three-dimensional (3D) linear elasticity models, and real-world 72-bar truss, are selected to statistically validate the theoretical analyses on two EPINN models and the superiority of the nEPINN regarding prediction precision and stability. The obtained results confirm the correctness of the proposed theories and the practical efficiency of the devised method.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"256 ","pages":"Article 104523"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146160709","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":"Topology optimization under mixed transient dynamic loads: Explicit–implicit time integration","authors":"Jiaqi Qu ,&nbsp;Defu Lin ,&nbsp;Yusra Abdulrahman ,&nbsp;Yihao Dong","doi":"10.1016/j.finel.2026.104529","DOIUrl":"10.1016/j.finel.2026.104529","url":null,"abstract":"<div><div>Most existing topology optimization formulations for elastodynamic structures in the time domain adopt implicit integration schemes and treat either force or displacement (velocity) boundary conditions in isolation. Such approaches are not well suited to structures that are simultaneously subjected to different types of transient loads. In this paper we develop a density-based topology optimization framework for linear elastodynamics under mixed transient dynamic loads, in which time-dependent prescribed traction and prescribed loading rate act concurrently on different parts of the boundary. To balance solution accuracy and computational cost, the structural dynamics are solved using both the implicit HHT-<span><math><mi>α</mi></math></span> method and the explicit central difference method (CDM), and consistent adjoint sensitivities are derived for each scheme, with verification by the finite difference method. Structural performance is measured by the total mechanical work, which provides a unified metric that couples the work of external forces and the work associated with prescribed velocities over the entire loading history. Through a series of two-dimensional benchmark problems (half MBB beam, cantilever beam and clamped beam) we systematically investigate the influence of loading type, loading duration and time-integration scheme on the optimized topologies, dynamic responses and computational cost. The numerical results show that (i) mixed traction loading produces layouts that differ markedly from those obtained under single-type loading or static optimization, and (ii) the choice between HHT-<span><math><mi>α</mi></math></span> and CDM is crucial for short-duration, high-frequency excitations, where numerical damping in HHT-<span><math><mi>α</mi></math></span> significantly reduces the total mechanical work. These findings complement existing time-domain topology optimization studies and provide practical guidance for selecting appropriate loading representations and time-integration schemes in transient dynamic design.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"256 ","pages":"Article 104529"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146160711","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 accurate and robust quadrilateral shell element based on the Naghdi/Reissner/Mindlin shell theory","authors":"Qi Ran ,&nbsp;Huan Zhang ,&nbsp;She Li ,&nbsp;Xiangyang Cui","doi":"10.1016/j.finel.2026.104526","DOIUrl":"10.1016/j.finel.2026.104526","url":null,"abstract":"<div><div>The DKMQ24 element, based on the Naghdi–Mindlin–Reissner shell theory, performs well in bending- and shear-dominated problems but remains sensitive to mesh distortion and suffers from in-plane shear locking. In this study, the membrane strain field is reconstructed using the Mixed Interpolation of Tensorial Components (MITC) method to reduce mesh sensitivity, and the Enhanced Assumed Strain (EAS) method is applied to alleviate in-plane shear locking. An improper bending approximation and the artificial stiffness for drilling rotation in DKMQ24 hindered the element from fully passing rigid-body tests; this issue is successfully resolved by adopting the standard bending strain formulation and redefining the drilling stiffness. Benchmark examples demonstrate that the enhanced DKMQ24 element eliminates in-plane shear locking, exhibits improved robustness against mesh distortion, and successfully passes rigid-body tests, providing a reliable and high-precision quadrilateral shell element for engineering applications.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"256 ","pages":"Article 104526"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146102940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Data-Driven calibration and experimental observations of the main hypothesis employed in the definition of the wTCM finite element under compression","authors":"Juan Antonio López-Salido,&nbsp;Luis Saucedo-Mora","doi":"10.1016/j.finel.2026.104538","DOIUrl":"10.1016/j.finel.2026.104538","url":null,"abstract":"<div><div>Auxetic metamaterials, characterized by a negative Poisson’s ratio, exhibit distinctive deformation mechanisms that make them attractive for applications requiring enhanced energy absorption and stiffness control. In this work, a quasi-static compression test is performed on a 3D-printed coupon based on the General Auxetic Metamaterial (GAM) cell to experimentally characterize its global response and dominant deformation mechanisms. The experimental results are used to inform and support the calibration of a data-driven multiscale finite element methodology based on the wedge Topologically Consistent Metamaterial (wTCM) element. The approach establishes an energetic equivalence between the discrete strut architecture and an equivalent continuum representation, allowing geometric nonlinearities and effective stiffness degradation to be captured through pre-calibrated strut-level response curves. A detailed explicit finite element model is employed as a geometric reference to isolate geometric nonlinear effects, and the numerical responses obtained with the wTCM formulation are compared against both the experimental results and the explicit simulations. With appropriate calibration, the wTCM approach is shown to capture the relevant nonlinear structural response — including auxetic kinematics and strain localization — while retaining a reduced computational complexity.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"256 ","pages":"Article 104538"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146192126","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 mixed method for investigating free vibrations in fiber-reinforced shells with non-uniform curvature","authors":"D.A. Iannotta ,&nbsp;G. Giunta ,&nbsp;M. Montemurro","doi":"10.1016/j.finel.2026.104528","DOIUrl":"10.1016/j.finel.2026.104528","url":null,"abstract":"<div><div>The main goal of this work involves conducting numerical simulations to determine the vibrational behavior of composite shell structures. The introduction of doubly-curved laminated shells plays a pivotal role in diverse engineering applications, offering an expanded design space and the potential to enhance mechanical performance. However, the analysis of this kind of structures poses significant challenges due to the need to account for the curvature of the shell mid-surface. Moreover, the aspect ratio strongly influences the structural response in terms of free vibrations, also affecting the accuracy of the numerical solution. To address these complexities, this work employs the Carrera’s unified formulation, a well-established methodology for evaluating composites structural behavior which allows to set the expansion order of through-the-thickness polynomials as a free parameter of the simulation. In this context, the governing equations of the problem are derived through pure displacement and mixed formulations, within a finite element framework, ensuring a robust and adaptable analysis approach. This study extends the application of the unified formulation to complex shell geometries featuring non-uniform curvatures along the mid-surface principal directions. Free vibration analyses are performed to determine fundamental frequencies and mode shapes, with results benchmarked against 3D models from Abaqus and classical theoretical predictions. The comparison demonstrates the effectiveness of the proposed approach, establishing its efficacy for advanced structural investigation of fiber-reinforced shells with spatially varying curvatures, regardless of the considered slenderness ratio.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"256 ","pages":"Article 104528"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146160710","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":"Robust topology optimization of cellular structure for mitigating dynamic instability in elastic structure","authors":"Sol Ji Han ,&nbsp;Akihiro Takezawa ,&nbsp;Gil Ho Yoon","doi":"10.1016/j.finel.2026.104537","DOIUrl":"10.1016/j.finel.2026.104537","url":null,"abstract":"<div><div>This study presents an optimization method using cellular structures to mitigate dynamic instability. Dynamic instability, characterized by positive real parts of complex eigenvalues, arises from asymmetric system matrices. It often leads to problematic squeal noise and severe vibrations in engineering systems. The conventional optimization approach of cellular structures consists of three main steps: the homogenization to capture the material properties, the topology optimization considering the dynamic instability, and the reconstruction step to check the accuracy of the optimization result. First, homogenized constitutive matrices are computed and approximated using polynomial curves. Second, topology optimization is carried out based on these fitted curves. Finally, the reconstruction step is conducted to validate finite element analysis (FEA) results. The difference between the optimized and the reconstructed microstructure model in the conventional approach exists because the reconstruction does not satisfy the assumption of homogenization, and the shape of the unit cell differs between idealized and reconstructed models. This discrepancy between the optimal homogenized FE model and the reconstructed microstructure can cause serious dynamic instability after the reconstruction step. To mitigate this dynamic instability caused by the discrepancy, the present method employs an increased number of repeated structures by employing the concepts of unit cell groups and element groups. Additionally, a pseudo-robust optimization approach is presented to improve the robustness of the optimization result. Through this approach, a stable optimal objective value matching the reconstructed objective value is achieved, thereby successfully eliminating dynamic instability.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"256 ","pages":"Article 104537"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146192115","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":"Evaluation of locking mitigation techniques and development of locking-free ANCF shell elements for nearly incompressible materials based on the Yeoh model","authors":"Yanhu Li ,&nbsp;Yongjie Lu ,&nbsp;Shaopu Yang ,&nbsp;Jianxi Wang ,&nbsp;Haoyu Li","doi":"10.1016/j.finel.2026.104524","DOIUrl":"10.1016/j.finel.2026.104524","url":null,"abstract":"<div><div>To mitigate the volumetric locking observed in Absolute Nodal Coordinate Formulation (ANCF) shell elements for nearly incompressible materials, this study presents two locking-free formulations: one achieved by enhancing the standard ANCF shell element with the F-bar projection technique, and another through the development of a novel mixed-interpolation shell element. In nearly incompressible media, volumetric strain is determined by the derivatives of the position vector, which cannot be predicted as accurately as the position itself. Due to the small magnitude of volumetric strain and the large bulk modulus, any error in predicting volumetric strain can lead to significant stress inaccuracies. To tackle this issue, three approaches are employed to modify the volumetric part of the strain energy density function in ANCF shell elements. The first is to reduce the volume integral to a surface integral using the selective reduced integration method, assuming that the volumetric strain energy density is uniformly distributed through the thickness. The second approach introduces the F-bar projection technique into the ANCF framework to correct the volumetric strain. The third is to develop new mixed-interpolation shell elements based on the Hellinger–Reissner variational principle, which takes the position vector and the pressure as independent variables. Several benchmark problems dominated by bending deformation are used to evaluate the performance of these techniques. The results indicate that for lower-order elements with linear interpolation, none of the methods are fully effective in alleviating volumetric locking, and they usually lead to over-softening of the structure. In contrast, for the 4-node higher-order element, both the F-bar-enhanced and the newly developed mixed-interpolation elements are demonstrated to be locking-free, providing accurate displacement results while maintaining reasonable convergence rates. Compared with the existing 8-node higher-order shell element, they offer comprehensive advantages in terms of locking alleviation, reduced numbers of nodes and degrees of freedom, and guaranteed inter-element continuity. These features make them promising general-purpose formulations for simulating nearly incompressible media in flexible multibody systems.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"256 ","pages":"Article 104524"},"PeriodicalIF":3.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}