Finite Elements in Analysis and Design最新文献

{"title":"Parametric model order reduction for dynamic non-linear thermoelastic problems in functionally graded materials","authors":"Ganesh S. Pawar ,&nbsp;Amar K. Gaonkar ,&nbsp;Salil S. Kulkarni","doi":"10.1016/j.finel.2025.104463","DOIUrl":"10.1016/j.finel.2025.104463","url":null,"abstract":"<div><div>Functionally graded materials subjected to thermoelastic loading are increasingly utilized in a wide range of industrial applications. The coupled temperature–displacement analysis of such complex structures is typically performed using finite element analysis. However, high-fidelity finite element models often result in significant computational costs. Furthermore, during the design phase, it is desirable to explore variations in material gradation to optimize performance, which further amplifies the computational demand. To address this, a parametric model order reduction framework is proposed in this study to accelerate the dynamic simulation of functionally graded materials under thermoelastic loading. In many applications, mechanical responses remain linear due to small deformations, while thermal non-linearity dominates due to high temperature. Exploiting this structure, a hybrid reduced-order model is introduced, which employs Krylov-based reduction for the mechanical model while retaining the thermal model at full-scale. This hybrid reduced order model is further extended to incorporate parametric dependencies inherent in functionally graded materials through various parametric model order reduction techniques. The spatial variation of material properties is captured using the generalized isoparametric formulation. Material gradation is modeled using either a power-law or exponential-law distribution, with the corresponding exponents treated as parameters of interest. Parametric variations are managed through interpolation of local bases and a locally reduced order model. Four distinct parametric reduced order models are developed based on different combinations of these interpolation strategies. The effectiveness and accuracy of the proposed models are validated using a 2D planar benchmark problem featuring spatially varying material properties. It is observed that, for the mechanical part, reduced order models employing interpolation of local bases achieve higher speed-ups than those based on interpolation of reduced system matrices. In the thermal part, all models utilize local basis interpolation with hyper-reduction via either the discrete empirical interpolation method or the energy conserving sampling and weighting method; among these, energy conserving sampling and weighting-based approaches offer better accuracy. The developed framework demonstrates speed-ups of up to 50 compared to full-scale simulations.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104463"},"PeriodicalIF":3.5,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268248","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":"The wedge Topologically Consistent Metamaterial element (wTCM) for the generation of auxetic metamaterials in complex components and its multi-scale numerical calculation with small geometrical and material non-linearities","authors":"Juan Antonio López-Salido,&nbsp;Luis Saucedo-Mora","doi":"10.1016/j.finel.2025.104456","DOIUrl":"10.1016/j.finel.2025.104456","url":null,"abstract":"<div><div>Metamaterials are gaining importance in different aspects of engineering because their complex capabilities and light weight ensures a key role in critical elements in different fields. But metamaterials have two main drawbacks; a high computational cost at component level, and a lack of adaptability to complex shapes. This latter point is because traditionally the metamaterials have relied on regular or quasi-regular grids, which is not realistic for more of the engineering needs. In this paper we present the wTCM finite element for the generation of auxetic metamaterials and its multiscale calculation accounting forgeometric nonlinear effects (e.g. buckling), and material nonlinear effects (e.g. moderate plasticity and fracture). The proposed element is the opposite the traditional RVE where a large amount of unit cells are assumed to be inside each RVE. In the case of the wTCM only a portion of the unit cell is represented in the element. With this, we gain versatility and precision with a low computational cost, and the capability to generate the metamaterial from the wTCM mesh directly.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104456"},"PeriodicalIF":3.5,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121004","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":"Solving two-phase heat exchanger equations by using the finite element method","authors":"Jose M. Chaquet ,&nbsp;Pedro Galán del Sastre","doi":"10.1016/j.finel.2025.104462","DOIUrl":"10.1016/j.finel.2025.104462","url":null,"abstract":"<div><div>Heat exchangers (HEX) are widely used in a large number of industrial processes, as well as on-board auxiliary devices. One way to increase HEX thermal effectiveness, and therefore reduce weight, is to use phase-change processes in one or both working fluids. There are simplified models in the literature that provide HEX temperature fields, useful in the early design phases. However, these models assume single-phase fluids. This work generalizes the HEX equations for different arrangements (parallel, counter and cross flow configurations) considering vaporization (evaporation or boiling) or condensation processes. The application of the finite element method (FEM) is also described to obtain a numerical approximation of the solution in an efficient manner. The proposed method provides a general framework where the application of specific heat transfer coefficients correlations or fluid properties is straightforward. As a practical application, several operating conditions (number of transfer units until 5 and mass flow ratios between 0.1 and 1) and arrangements (parallelflow, counterflow and unmixed-unmixed crossflow) of a simplified HEX using coolant R123 and liquid water as working fluids are analyzed where the heat transfer coefficient depends on the vapor fraction. R123 coolant flows through 2 mm diameter pipes, in liquid phase at the HEX inlet and undergoing a complete or partial evaporation process depending on the operating point.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104462"},"PeriodicalIF":3.5,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121003","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":"Analysis of energy conversion using piezoelectric materials and structures with acoustic black holes","authors":"Meng He ,&nbsp;Tatiane Weimann ,&nbsp;Alexandre Molter ,&nbsp;Jairo Valões de Alencar Ramalho ,&nbsp;Daniel Milbrath De Leon","doi":"10.1016/j.finel.2025.104454","DOIUrl":"10.1016/j.finel.2025.104454","url":null,"abstract":"<div><div>The objective of this study is to analyze energy conversion in two configurations of piezoelectric material placement in acoustic black holes. These structures concentrate vibrational energy due to the gradual reduction in thickness, making them ideal for energy harvesting. In the first configuration, piezoelectric materials are placed at the outer edges of the hole; in the second, at the inner edges. The material is applied only to specific regions, rather than covering the entire inner or outer edge. The same amount of piezoelectric material is used in both cases, being able to act as both a vibration damper and an energy harvester. This study investigates the optimal position for piezoelectric material placement, comparing energy conversion at the outer vs. inner edges of a central elliptical hole. The finite element method was used to discretize the structural domain, considering elliptical hole geometries. Dynamic structural analysis was applied to compute energy distributions and conversions. The results showed that the placement of the piezoelectric material influences energy conversion, with the most suitable position being along the outer edge of the hole. These findings reinforce the importance of optimal piezoelectric placement for maximizing energy harvesting in structures with acoustic black holes.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104454"},"PeriodicalIF":3.5,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109498","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":"Derivative-enhanced Bayesian optimization for broad-bandgap phononic metamaterials with hypercomplex automatic differentiation","authors":"Juan C. Velasquez-Gonzalez ,&nbsp;Juan David Navarro ,&nbsp;Mauricio Aristizabal ,&nbsp;Harry Millwater ,&nbsp;David Restrepo","doi":"10.1016/j.finel.2025.104461","DOIUrl":"10.1016/j.finel.2025.104461","url":null,"abstract":"<div><div>The design of Phononic Metamaterials (PM) with unique dynamic behaviors and wave propagation characteristics remains a significant challenge due to the highly non-linear relationships between design parameters and response. The arrangement of the periodic unit cells within PM is crucial for determining their dynamic behavior, making optimization methods essential for the design and development of these materials. These methods are used to tailor bandgap characteristics such as bandwidth and frequency location by optimizing the unit cell’s geometric parameters. However, existing approaches often suffer from slow convergence rates, entrapment in local minimum, or require numerous expensive evaluations of the objective function. To address these challenges, this work proposes using a novel derivative-enhanced Bayesian optimization (DEBO) framework that integrates Hypercomplex Automatic Differentiation (HYPAD) with a Gradient-Enhanced Gaussian Process (GEGP) interpolator surrogate model. This combination enables the accurate and efficient computation of objective function sensitivities, resulting in more reliable and data-efficient surrogate models. As a result, DEBO significantly improves the robustness of BO against local minima, which is particularly beneficial for the non-convex optimization problem characteristic of PM design. The framework is applied to optimize the geometry of a two-dimensional cross-shaped unit cell, maximizing bandgap width at low mid-frequencies. By consistently converging to the global optimum, we demonstrate that DEBO outperforms traditional methods, including derivative-free Bayesian optimization, gradient-based numerical optimization, and metaheuristics. Furthermore, experimental validation of the optimized geometry aligns closely with numerical predictions, confirming the effectiveness of the approach.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104461"},"PeriodicalIF":3.5,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097378","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":"Uzawa methods for the coupling of free flow and porous medium flow","authors":"Qingzhou Wang,&nbsp;Guangzhi Du","doi":"10.1016/j.finel.2025.104460","DOIUrl":"10.1016/j.finel.2025.104460","url":null,"abstract":"<div><div>In this paper, two kinds of Uzawa algorithms are proposed and investigated to solve the coupling of free flow and porous medium flow, which is modeled by the mixed Stokes-Darcy problem with the Beavers-Joseph-Saffman interface condition. The first Uzawa method as an iterative method can avoid solving the saddle point problem at each iteration step. The second method aims to optimize the first one by combining the two-grid strategy. Rigorously theoretical analysis is established for these two algorithms. Some numerical experiments are carried out to verify the theoretical findings.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104460"},"PeriodicalIF":3.5,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097377","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":"The polytopal composite element method for finite strain hyperelastic problems","authors":"Y. Li ,&nbsp;B.W. Wang ,&nbsp;Z.Q. Feng","doi":"10.1016/j.finel.2025.104436","DOIUrl":"10.1016/j.finel.2025.104436","url":null,"abstract":"<div><div>Polygonal elements have emerged as a cutting-edge discretization paradigm in computational solid mechanics, demonstrating significant potential for linear elasticity analyses. This work pioneers a robust computational framework extending polytopal composite elements to finite-strain hyperelasticity. The key idea by constructing a polynomial projection using least squares approximation for linear-compatible strain fields, followed by extending the derived linear operator to large deformation cases involving nonlinear strain. The computational framework of this method is fundamentally consistent with finite elements, allowing it to adapt and extend to various nonlinear problems. Through several numerical investigation we show that this approach maintains the excellent accuracy, convergence and stability, and is potentially offering new insights and references for polygonal elements in future nonlinear problems.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104436"},"PeriodicalIF":3.5,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097376","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":"Statistical topology optimization for damage identification for orthotropic and cellular structures","authors":"Jae Yeop Na,&nbsp;Sol Ji Han,&nbsp;EunBin Park,&nbsp;Gil Ho Yoon","doi":"10.1016/j.finel.2025.104459","DOIUrl":"10.1016/j.finel.2025.104459","url":null,"abstract":"<div><div>This study aims to enhance the accuracy and robustness of structural damage identification by extending the statistical topology optimization (STO) framework. While previous STO research has primarily focused on isotropic materials, its applicability to orthotropic and cellular structures has not been fully explored. To broaden its scope, the approach applies the STO framework to models with directional stiffness and periodic microstructures. Multiple topology optimization runs are performed under varied frequency excitations, and consistent damage patterns are extracted using density-based spatial clustering (DBSCAN). Unlike earlier studies, this work introduces genetic algorithm-based tuning of DBSCAN parameters to improve clustering reliability and reduce user dependency. Damage is modeled differently according to the structure type: through density reduction or principal direction rotation in orthotropic models, and by adjusting the void size within cellular unit cells, from which the effective material properties are derived through polynomial-based numerical homogenization. Numerical examples confirm that the framework accurately localizes damage under complex material conditions and achieves superior performance compared to conventional methods.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104459"},"PeriodicalIF":3.5,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097374","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":"Using Gappy-POD to derive a reduced quadrature rule","authors":"Shigeki Kaneko","doi":"10.1016/j.finel.2025.104439","DOIUrl":"10.1016/j.finel.2025.104439","url":null,"abstract":"<div><div>Among various reduced-order modeling techniques, the combination of low-dimensional approximation using proper orthogonal decomposition (POD) and the Galerkin method is a promising approach. However, the POD–Galerkin method has a well-known drawback that the computation of the Galerkin projection is heavy, which overshadows the reduction of computational cost for solving simultaneous equations. To speed up the reduced-order model analysis, a hyper-reduction method, which approximately calculates the Galerkin projection, has been introduced. Although several hyper-reduction methods have been proposed up to date, currently, a reduced quadrature (RQ) method is widely used because of its stability. In the conventional RQ method, a sparse representation problem with <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> pseudo-norm minimization under the non-negativity constraint is solved to derive an RQ rule. However, it is difficult to control the number of non-zero entries in the weight vector of RQ and the error of least-squares fitting. The purpose of the present study was to develop a new RQ derivation method to overcome this difficulty. The formulation of the new method is not based on the sparse representation but on Gappy-POD, which is a sparse sampling technique and was originally proposed for image reconstruction. To demonstrate the new method, we applied it to nonlinear dynamic structural analysis with geometrical nonlinearity and to incompressible viscous flow analysis. The results confirmed that the new method can provide a more accurate RQ rule than can the conventional method.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104439"},"PeriodicalIF":3.5,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097373","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":"Integrating multiplicative Nitsche's method with HIGA platform: Isogeometric analysis of hydraulic tunnels lining thickness","authors":"Mingchao Li ,&nbsp;Yixin Wang ,&nbsp;Mengxi Zhang ,&nbsp;Ang Li ,&nbsp;Stéphane P.A. Bordas ,&nbsp;Peng Yu ,&nbsp;Yinpeng He","doi":"10.1016/j.finel.2025.104445","DOIUrl":"10.1016/j.finel.2025.104445","url":null,"abstract":"<div><div>Isogeometric Analysis (IGA) is a novel numerical analysis method that can occupy the gap between geometrical and analytical models. IGA, when integrated with splicing algorithms, enables the splicing and coupling of multiple computational domains. This approach offers a novel solution for simulating complex hydraulic tunnels and similar practical engineering applications involving complex computational models. In this paper, a multiplicative Nitsche's method is proposed. The method determines the stabilization parameter <span><math><mrow><mi>α</mi></mrow></math></span> for contact models through a precise control coefficient computation equation, based on a chosen weighting parameter <span><math><mrow><mi>γ</mi></mrow></math></span>, and is integrated into the Hydraulic IsoGeometric Analysis (HIGA) platform. This method addresses the instability issues typically associated with the traditional Nitsche's method, which arise from empirically selected control parameters. Compared with the conventional Nitsche's method, multiplicative Nitsche's method significantly enhances the accuracy and stability of IGA while maintaining computational efficiency, according to the results of several 2D and 3D numerical examples. To demonstrate the engineering application prospects of multiplicative Nitsche's method, the proven applicability of IGA with the multiplicative Nitsche's method is showcased through a static analysis of a hydraulic tunnel model with complex geological features. The results demonstrate the method's capability to handle large-scale, multi-patch engineering problems, underscoring its potential for simulating and analyzing hydraulic tunnels under complex topographical and geological conditions.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104445"},"PeriodicalIF":3.5,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097375","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}