Pub Date : 2025-10-27DOI: 10.1016/j.finel.2025.104469
Hyunseung Ryu , Jeonghoon Yoo
This study presents a topological design methodology for thermoelastic structures based on bi-objective and tri-objective optimization formulations. The design objectives are to simultaneously minimize elastic compliance and thermal compliance, while maximizing the first natural frequency. To obtain multi-objective optimization solutions approaching the utopia point, a novel modified adaptive weighted sum method is proposed, where the weight vector is dynamically adjusted using scale factors to effectively generate new Pareto optimal solutions. The effectiveness of the proposed method is validated through quantitative comparisons of optimal solutions obtained using the conventional weighted sum method, the adaptive scaling strategy, and the proposed adaptive weighted sum method. The proposed approach is further validated through its application to both two- and three-dimensional topology optimization problems.
{"title":"Multi-objective topological structure design using a modified adaptive weighted sum method","authors":"Hyunseung Ryu , Jeonghoon Yoo","doi":"10.1016/j.finel.2025.104469","DOIUrl":"10.1016/j.finel.2025.104469","url":null,"abstract":"<div><div>This study presents a topological design methodology for thermoelastic structures based on bi-objective and tri-objective optimization formulations. The design objectives are to simultaneously minimize elastic compliance and thermal compliance, while maximizing the first natural frequency. To obtain multi-objective optimization solutions approaching the utopia point, a novel modified adaptive weighted sum method is proposed, where the weight vector is dynamically adjusted using scale factors to effectively generate new Pareto optimal solutions. The effectiveness of the proposed method is validated through quantitative comparisons of optimal solutions obtained using the conventional weighted sum method, the adaptive scaling strategy, and the proposed adaptive weighted sum method. The proposed approach is further validated through its application to both two- and three-dimensional topology optimization problems.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"253 ","pages":"Article 104469"},"PeriodicalIF":3.5,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145369822","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}
Pub Date : 2025-10-23DOI: 10.1016/j.finel.2025.104470
Tinh Quoc Bui, Minh Ngoc Nguyen
This paper presents an enhanced computational framework for multi-material topology optimization using a novel interpolation scheme with the partition-of-unity (PU) mapping. Inspired by the recent -norm mapping scheme by Yi et al., (2023) the developed scheme inherits the easy-to-implement property, as the interpolation is written in a SIMP-like manner, and the sensitivity with respect to each material phase takes the same form. More importantly, the current scheme addresses the lack of PU property of the -norm scheme, that is, the sum of volume fraction of all material phases within each element must be equal to one. In the -norm scheme setting, the case when the physical densities of the materials are all equal to one is theoretically possible. This phenomenon means the duplication of the element volume. In the developed scheme, the mapping functions are computed in rational form, explicitly satisfying the PU property. The performance of the present method is investigated through six numerical examples: the first three are for the compliance-based designs and the other three are for the stress-based designs including the design of periodic meta-material with high bulk modulus. It is demonstrated in the numerical examples that although the lack of PU property in -norm scheme does not seem to cause problematic issue in compliance-based design with only fixed load, erroneous patterns may appear in more complicated problems, e.g., in compliance-based design with consideration of self-weight load, and in stress-based design. The issue is successfully removed in the proposed PU mapping scheme.
{"title":"A novel interpolation scheme using partition-of-unity mapping for multi-material topology optimizations with compliance-based and stress-based designs","authors":"Tinh Quoc Bui, Minh Ngoc Nguyen","doi":"10.1016/j.finel.2025.104470","DOIUrl":"10.1016/j.finel.2025.104470","url":null,"abstract":"<div><div>This paper presents an enhanced computational framework for multi-material topology optimization using a novel interpolation scheme with the partition-of-unity (PU) mapping. Inspired by the recent <span><math><mi>p</mi></math></span>-norm mapping scheme by Yi et al., (2023) the developed scheme inherits the easy-to-implement property, as the interpolation is written in a SIMP-like manner, and the sensitivity with respect to each material phase takes the same form. More importantly, the current scheme addresses the lack of PU property of the <span><math><mi>p</mi></math></span>-norm scheme, that is, the sum of volume fraction of all material phases within each element must be equal to one. In the <span><math><mi>p</mi></math></span>-norm scheme setting, the case when the physical densities of the materials are all equal to one is theoretically possible. This phenomenon means the duplication of the element volume. In the developed scheme, the mapping functions are computed in rational form, explicitly satisfying the PU property. The performance of the present method is investigated through six numerical examples: the first three are for the compliance-based designs and the other three are for the stress-based designs including the design of periodic meta-material with high bulk modulus. It is demonstrated in the numerical examples that although the lack of PU property in <span><math><mi>p</mi></math></span>-norm scheme does not seem to cause problematic issue in compliance-based design with only fixed load, erroneous patterns may appear in more complicated problems, e.g., in compliance-based design with consideration of self-weight load, and in stress-based design. The issue is successfully removed in the proposed PU mapping scheme.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104470"},"PeriodicalIF":3.5,"publicationDate":"2025-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363530","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}
Pub Date : 2025-10-13DOI: 10.1016/j.finel.2025.104466
Huijian Cai, Nhon N. Phan, WaiChing Sun
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 and 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.
{"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, Nhon N. Phan, 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":"2025-10-13","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}
Pub Date : 2025-10-10DOI: 10.1016/j.finel.2025.104468
Florian Gouhier, Julie Diani
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 and , 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.
{"title":"A general UMAT for finite-strain viscoelasticity with damage","authors":"Florian Gouhier, 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":"2025-10-10","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}
Pub Date : 2025-10-09DOI: 10.1016/j.finel.2025.104467
Stefano Berrone , Moreno Pintore , Gioana Teora
We present the Neural Approximated Virtual Element Method to numerically solve elasticity problems. This hybrid technique combines classical concepts from the Finite Element Method and the Virtual Element Method with recent advances in deep neural networks. Specifically, it is a polygonal method where the virtual basis functions are element-wise approximated by a neural network, eliminating the need for stabilization or projection operators typically required in the standard Virtual Element Method. We present the discrete formulation of the problem together with theoretical results, and we provide numerical tests on both linear and non-linear elasticity problems, demonstrating the advantages of a simple discretization, particularly in handling non-linearities.
{"title":"The neural approximated virtual element method for elasticity problems","authors":"Stefano Berrone , Moreno Pintore , Gioana Teora","doi":"10.1016/j.finel.2025.104467","DOIUrl":"10.1016/j.finel.2025.104467","url":null,"abstract":"<div><div>We present the Neural Approximated Virtual Element Method to numerically solve elasticity problems. This hybrid technique combines classical concepts from the Finite Element Method and the Virtual Element Method with recent advances in deep neural networks. Specifically, it is a polygonal method where the virtual basis functions are element-wise approximated by a neural network, eliminating the need for stabilization or projection operators typically required in the standard Virtual Element Method. We present the discrete formulation of the problem together with theoretical results, and we provide numerical tests on both linear and non-linear elasticity problems, demonstrating the advantages of a simple discretization, particularly in handling non-linearities.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104467"},"PeriodicalIF":3.5,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268251","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}
Pub Date : 2025-10-07DOI: 10.1016/j.finel.2025.104465
Liwaa Abou Chakra , Thomas Henneron , Bertrand Lallemand , Franck Massa , Stéphane Clénet
This article focuses on optimizing computational efficiency in the analysis of magneto-vibro-acoustic models, particularly when addressing parametric variations introduced by manufacturing imperfections. The computational cost of using the high-fidelity Finite Element Method in such detailed analyses can be significant, especially when multiple scenarios need to be explored. Moreover, a certain degree of accuracy is required in electromagnetic quantities of interest before any accurate vibroacoustic qualitative analysis can be performed. To address this, advanced Reduced-Order Model techniques, such as an enhanced Greedy Proper Orthogonal Decomposition and double Component Mode Synthesis, are developed. These techniques not only reduce computational time but also retain high accuracy in capturing the vibroacoustic response of the system. The proposed approach offers an efficient numerical framework to account for a wide range of manufacturing-induced variations (eccentricities, supply harmonics and mechanical tolerances), making it highly suitable for early-stage design assessment.
{"title":"Multiparametric e-NVH analysis of electrical machines using Greedy Proper Orthogonal Decomposition and Double Component Mode Synthesis","authors":"Liwaa Abou Chakra , Thomas Henneron , Bertrand Lallemand , Franck Massa , Stéphane Clénet","doi":"10.1016/j.finel.2025.104465","DOIUrl":"10.1016/j.finel.2025.104465","url":null,"abstract":"<div><div>This article focuses on optimizing computational efficiency in the analysis of magneto-vibro-acoustic models, particularly when addressing parametric variations introduced by manufacturing imperfections. The computational cost of using the high-fidelity Finite Element Method in such detailed analyses can be significant, especially when multiple scenarios need to be explored. Moreover, a certain degree of accuracy is required in electromagnetic quantities of interest before any accurate vibroacoustic qualitative analysis can be performed. To address this, advanced Reduced-Order Model techniques, such as an enhanced Greedy Proper Orthogonal Decomposition and double Component Mode Synthesis, are developed. These techniques not only reduce computational time but also retain high accuracy in capturing the vibroacoustic response of the system. The proposed approach offers an efficient numerical framework to account for a wide range of manufacturing-induced variations (eccentricities, supply harmonics and mechanical tolerances), making it highly suitable for early-stage design assessment.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"252 ","pages":"Article 104465"},"PeriodicalIF":3.5,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268249","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}
Pub Date : 2025-10-06DOI: 10.1016/j.finel.2025.104463
Ganesh S. Pawar , Amar K. Gaonkar , Salil S. Kulkarni
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.
{"title":"Parametric model order reduction for dynamic non-linear thermoelastic problems in functionally graded materials","authors":"Ganesh S. Pawar , Amar K. Gaonkar , 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}
Pub Date : 2025-09-23DOI: 10.1016/j.finel.2025.104456
Juan Antonio López-Salido, Luis Saucedo-Mora
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.
{"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, 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}
Pub Date : 2025-09-23DOI: 10.1016/j.finel.2025.104462
Jose M. Chaquet , Pedro Galán del Sastre
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.
{"title":"Solving two-phase heat exchanger equations by using the finite element method","authors":"Jose M. Chaquet , 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}
Pub Date : 2025-09-22DOI: 10.1016/j.finel.2025.104454
Meng He , Tatiane Weimann , Alexandre Molter , Jairo Valões de Alencar Ramalho , Daniel Milbrath De Leon
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.
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