Finite Elements in Analysis and Design最新文献

{"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":"2025-12-01","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":"An efficient higher-order triangulation based micromechanical model for fiber composites","authors":"Jamal F. Husseini ,&nbsp;Eric J. Carey ,&nbsp;Evan J. Pineda ,&nbsp;Brett A. Bednarcyk ,&nbsp;Farhad Pourkamali-Anaraki ,&nbsp;Scott E. Stapleton","doi":"10.1016/j.finel.2025.104441","DOIUrl":"10.1016/j.finel.2025.104441","url":null,"abstract":"<div><div>Composite microstructures are susceptible to localized stress concentrations between close or touching fibers where failure can initiate and propagate. Typically, representative volume elements are used to predict mechanical response by simulating random microstructure arrangements under different loading configurations. However, these simulations can be prohibitively expensive when considering large microstructures or closely packed fibers. The current work aims to provide a computationally efficient method for predicting homogenized and local properties of composite microstructures through a novel finite element mesh referred to as the fixed triangulation-mesh model. This triangulation-based meshing algorithm uses configured element sizes where the highest stresses occur and higher order elements to capture stress gradients between closely packed fibers. An efficient homogenization technique to fully characterize the stiffness matrix of the composite without the need for individual load perturbations or stress integration was derived and implemented. A progressive damage model using the smeared crack approach was implemented with higher order elements to simulate post-peak softening. The results for stiffness, transverse strength, and in-plane shear strength were verified against the high fidelity generalized method of cells for different microstructures of varying fiber volume fractions. Then, a comparison was made to a refined mesh finite element model with linear elements and a toughened matrix. The fixed triangulation-mesh model showed good agreement between the high fidelity generalized method of cells and linear element models, and computation time was reduced by approximately 104 times for the low-toughness matrix, and 55 times for the toughened matrix.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104441"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145009041","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":"Geometric compensation of process-induced deformation in hybrid unidirectional/woven CFRP composites with multi-layup sequence using a physics-driven reverse deformation approach","authors":"Dong-Hyeop Kim ,&nbsp;Sang-Woo Kim","doi":"10.1016/j.finel.2025.104446","DOIUrl":"10.1016/j.finel.2025.104446","url":null,"abstract":"<div><div>This study proposes a novel physics-based geometric compensation methodology to mitigate process-induced deformation (PID) in hybrid unidirectional/woven CFRP composite structures. Reverse deformation to compensate PID is induced by inverting the layup sequence, while the deformation magnitude is precisely adjusted using scaling factors, which are determined via fitting-based optimization and applied to thermochemical strain coefficients. The methodology is implemented through thermo-mechanical simulations using the finite element method, integrating cure-dependent material behavior, effective material properties, and thermal and chemical strains to accurately predict PID. The capability of the proposed methodology is demonstrated through extensive simulations of hybrid CFRP laminates, specifically incorporating multiple layup sequences and thickness configurations within a single laminate to reflect realistic structural design configurations encountered in composite manufacturing. In all simulation results, the optimized compensation reduced nodal displacements by more than 93%, resulting in significant improvements in both local and global geometric accuracy. The proposed methodology comprehensively considers complex cure-induced physical behaviors, enabling accurate, robust, and highly efficient nodal-level deformation compensation and providing practical applicability across a wide range of composite structures, including both unidirectional and textile-reinforced laminates.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104446"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050581","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 general UMAT for finite-strain viscoelasticity with damage","authors":"Florian Gouhier,&nbsp;Julie Diani","doi":"10.1016/j.finel.2025.104468","DOIUrl":"10.1016/j.finel.2025.104468","url":null,"abstract":"<div><div>A UMAT for general finite-strain viscoelastic materials exhibiting strain softening and temperature dependence is presented and shared. The model builds on the thermodynamically consistent formulation of Reese and Govindjee (1998), extended to support a general deviatoric strain energy function depending on the invariants <span><math><msub><mrow><mi>I</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>I</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, as well as isotropic damage mechanisms affecting both deviatoric and hydrostatic responses. The paper first outlines the modeling assumptions and describes the numerical implementation, including modifications for the flexible incorporation of general strain energy functions, compatibility with hybrid finite elements, and the structure of the UMAT subroutine. The implementation is validated through a series of uniaxial and shear benchmark tests under various loading conditions. Finally, a structural simulation involving the cyclic torsion of a slender rectangular bar confirms the correct implementation of the consistent tangent modulus. The proposed UMAT is versatile and applicable to a broad class of materials, including quasi-incompressible rubbers exhibiting Mullins softening and solid propellants undergoing volumetric damage due to matrix-filler debonding.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104468"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268250","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":"Analytical solutions for Cook’s membrane inferred by open-source learning algorithms: A critical assessment of the expressivity-complexity trade-off","authors":"Huijian Cai,&nbsp;Nhon N. Phan,&nbsp;WaiChing Sun","doi":"10.1016/j.finel.2025.104466","DOIUrl":"10.1016/j.finel.2025.104466","url":null,"abstract":"<div><div>Cook’s membrane is one of the most popular boundary value problems used to benchmark the performance of finite element models. Despite its popularity, the analytical solution to this boundary value problem remains unknown. As such, Richardson’s extrapolation, which provides a highly accurate displacement at the tip, is often used in verification exercises for finite element software used for analyses and designs. This paper introduces machine learning algorithms, particularly (1) the family of neural additive models and their subsequent symbolic approximations, (2) Kolmogorov-Arnold networks, (3) physics-informed neural networks as well as (4) the classical finite element method, (5) physics-informed polynomials and (6) brute-force symbolic regression algorithm to obtain new analytical solutions that may supplement Richardson’s extrapolation for the verification exercise. We consider two cases: one with a compressible linear elastic model and the other with an incompressible neo-Hookean model, where analytical solutions are unknown. Due to the floating-point representation, we did not seek an analytical solution with no error. Instead, we compare the accuracy, complexity, and interpretability of the solutions of the displacement field obtained from these methods and seek solutions with the optimal trade-off. We find that the best analytical solutions for the linear elastic and incompressible neo-Hookean cases are both obtained via the projected neural additive models followed by a post-processing step, with (1) errors in the orders of <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup></mrow></math></span> and <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></mrow></math></span> respectively and (2) complexities an order less than the counterparts obtained from Kolmogorov-Arnold networks. The training algorithms and results are open-source to facilitate third-party verification and further efforts to surpass the benchmark performance established in this paper.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104466"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325810","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":"Comparison of parametric model order reduction methods to solve magneto-quasistatic and electro-quasistatic problems","authors":"Wei Chen,&nbsp;Thomas Henneron,&nbsp;Stéphane Clénet","doi":"10.1016/j.finel.2025.104444","DOIUrl":"10.1016/j.finel.2025.104444","url":null,"abstract":"<div><div>In this paper, we compare two parametric model order reduction methods, the multi-moment matching method and the interpolation of projection subspaces method for the magneto-quasistatic (MQS) and electro-quasistatic (EQS) problems derived from Maxwell’s equations and discretized with the Finite Element (FE) method. The two problems considered are both governed by the differential–algebraic equations. The material characteristic parameters as well as the geometry parameters have been considered. The applications are two realistic test cases: an EQS model of a transformer bushing under insulation defect uncertainty and a MQS model of a planar inductor with geometric and material variations. The result shows that both methods approximate well global quantities, such as the current or the voltage, as well as the local quantities like field distributions. The multi-moment matching method remains always faster in the online stage, since the reduced basis is not parameter dependent, requiring no reduced basis calculation. The multi-moment matching method requires an affine decomposition of the FE model, which is not easy to obtain when considering geometry parameters. A hybrid method is proposed and tested leading to more accurate results than the interpolation of projection subspaces method but much easier to implement than the multi-moment matching method.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104444"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061194","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":"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":"2025-12-01","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":"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":"2025-12-01","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":"Sensitivity analysis of any hyperelastic evaluation functions coupled with adjoint method and automatic differentiation","authors":"S. Ogawa,&nbsp;K. Yonekura,&nbsp;K. Suzuki","doi":"10.1016/j.finel.2025.104440","DOIUrl":"10.1016/j.finel.2025.104440","url":null,"abstract":"<div><div>This study introduces a new sensitivity analysis method for the topology optimization of a static hyperelastic material, which combines the adjoint variable method with automatic differentiation (AD). The adjoint variable method, frequently used in sensitivity analysis, requires mathematical formulations. Therefore, any changes in the design problem require reformulating the sensitivity analysis and updating the calculation program. The proposed method allows for the calculation of design sensitivities without being tied to specific evaluation functions, constitutive laws, or interpolation methods. This method effectively addresses the considerable memory requirements often associated with AD. To showcase the versatility of the proposed approach, we assessed both the compliance and the maximum von Mises stress of the second Piola–Kirchhoff stress tensor. We examined two hyperelastic materials: St. Venant-Kirchhoff, Neo-Hookean, and Mooney–Rivlin. For broader applicability, we used the discrete material optimization (DMO) method to address multimaterial problems, evaluating the adaptability in the interpolation of material properties based on the design variables. Through numerical examples, we validated the sensitivity analysis, analyzed the computational time and memory usage, and confirmed the efficacy of the proposed method. Examples involving two-dimensional problems highlight the practical application of this method in topology optimization.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104440"},"PeriodicalIF":3.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050582","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":"2025-12-01","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}