{"title":"CUF-DLM-based dynamic aeroelastic analysis of composite plates with hierarchical viscoelastic damping for sports equipment applications","authors":"Shiyu Zheng, Yan Zhao, Yi Qiu","doi":"10.1007/s10999-026-09989-z","DOIUrl":"10.1007/s10999-026-09989-z","url":null,"abstract":"<div><p>This research outlines a dynamic aeroelastic framework, using the Carrera unified formulation (CUF), combined with the doublet lattice method for multilayer plates that appear in advanced sports equipment structural parts. The proposed sandwich is built like: on the upper side, a Lead Zirconate Titanate piezoelectric sheet, also labeled PZT-5H; then you have a periodic lattice cellular core that is filled with Polyvinyl Chloride (PVC) as a viscoelastic medium, and at the lower end, there is another Lead Zirconate Titanate layer identified as PZT-4. To get the effective mechanical properties of that lattice core, the work relies on the Voigt averaging technique, mainly to mirror the hierarchical viscoelastic behavior of the cellular architecture. Inside the CUF framework, a layerwise kinematic model is paired with Mixed Interpolation of tensorial components plate elements. This pairing helps in tracking transverse shear deformation plus interlaminar stress continuity, and it also supports the coupled aeroelastic response when the system is under dynamic loading, conditions that can easily disturb everything. On top of that, a parallel multimodal shunt damping strategy is attached to the piezoelectric layers. The idea is to curb structural vibrations and, at the same time, boost flutter stability, while also improving electrical energy harvesting capability. Numerical analyses show that the combined effects of the viscoelastic PVC-filled lattice core and the distributed piezoelectric shunt circuits actually reduce vibration amplitudes quite a bit, also delay the aeroelastic instability onset, and raise the harvested power efficiency. The proposed multiphysics formulation gives you an efficient computational approach for design and optimization of lightweight, vibration-controlled, and energy-aware sports equipment structures under a complex aerodynamic environment.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"22 4","pages":""},"PeriodicalIF":4.7,"publicationDate":"2026-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Geometry-controlled thermomechanical response of cylindrical re-entrant auxetic lattices","authors":"Anastasia Tarasova, Mikhail Tashkinov","doi":"10.1007/s10999-026-09993-3","DOIUrl":"10.1007/s10999-026-09993-3","url":null,"abstract":"<div><p>This work presents a numerical investigation of the thermomechanical behavior of a cylindrical auxetic lattice structure based on re-entrant unit cells arranged in the radial–circumferential plane. A computational framework for generating geometrically graded cylindrical auxetic lattices with controllable cell density and structural thickness was developed. Finite element simulations were performed to investigate the influence of lattice geometry and coefficient of thermal expansion (CTE) on the deformation response under thermal and coupled thermomechanical loading. The results demonstrate that the response is governed predominantly by topology-dependent kinematic mechanisms rather than solely by material properties. Increasing structural thickness suppresses rotational opening of the re-entrant cells and shifts the behavior toward that of a solid cylinder. Coupled thermomechanical simulations showed that internal pressure effectively suppresses thermally induced radial expansion, enabling deformation regimes approaching zero effective radial deformation. Comparison with different cylindrical lattice topologies demonstrated that structures with similar deformation magnitudes may exhibit substantially different stress redistribution behavior. The obtained results highlight the potential of cylindrical auxetic metamaterials with programmable thermal expansion and adaptive deformation response for advanced engineering applications.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"22 4","pages":""},"PeriodicalIF":4.7,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal contract modes based on BIM capability maturity: the case of design and construction contracts","authors":"Ting Wang","doi":"10.1007/s10999-026-09975-5","DOIUrl":"10.1007/s10999-026-09975-5","url":null,"abstract":"<div><p>Building Information Modeling (BIM) has transformed project delivery, yet contract design for BIM-enabled projects remains anchored in qualitative frameworks that implicitly assume uniform BIM capability across contracting parties. In practice, however, the designer and constructor often operate at substantially different levels of BIM capability maturity (BIM-CM), creating heterogeneous information environments that standard principal-agent models do not address. This study develops a normative analytical framework that treats BIM-CM as the central determinant of contract architecture. We construct a dual-agent principal-agent model in which the designer and constructor contribute complementary efforts through a collaborative production function, and we solve for optimal contract modes under three BIM-CM configurations: both parties at high maturity, both at low maturity, and–most distinctively–mixed maturity, where one party is mature and the other is not. Nine propositions are derived, and second-order conditions are verified to establish equilibrium uniqueness. The results yield three contract prescriptions. Under high BIM-CM, a compulsory (fixed-price) contract achieves the first-best: the risk-neutral owner bears all output risk. Under low BIM-CM, an incentive contract with risk-sharing is optimal. The mixed-maturity configuration produces a hybrid compulsory-plus-incentive contract absent from standard theory. A novel free-riding mechanism (Fig. 3) is identified: the high-maturity party’s observable effort, transmitted through the collaborative production function, raises the low-maturity party’s remuneration while depressing its own effort, such that the first-best remains unattainable even with one fully mature partner. Agency costs are decomposed into risk and incentive components and compared across configurations. The paper contributes a maturity-contingent contract typology and a decision heuristic that translate formal results into actionable guidance, replacing uniform qualitative prescriptions with differentiated contract recommendations grounded in BIM capability assessment.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"22 4","pages":""},"PeriodicalIF":4.7,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Thermo-electro-magneto-mechanical vibration and machine learning based multi-objective optimization of MWCNT/GNP hybrid sandwich plate with auxetic honeycomb core","authors":"Tran Dinh Tuan, Vu Minh Anh, Tran Quoc Quan, Nguyen Dinh Duc","doi":"10.1007/s10999-026-09978-2","DOIUrl":"10.1007/s10999-026-09978-2","url":null,"abstract":"<div><p>Nanocomposites reinforced with multi-walled carbon nanotubes (MWCNTs) or graphene nanoplatelets (GNPs) have been widely studied due to their enhanced mechanical, thermal and electrical properties; however, hybrid systems combining both nanofillers remain relatively underexplored, particularly in sandwich structures with multifunctional materials. To address this gap, the vibration behaviors and multi-objective optimization of sandwich plate comprising auxetic honeycomb core, two hybrid nanocomposite intermediate layers reinforced with MWCNTs and GNPs and two magneto–electro–elastic (MEE) face sheets are investigated. Four different distribution patterns of CNTs and GNPs, namely O, X, U and V are considered. The governing equations are formulated based on Reddy’s higher order shear deformation plate theory, incorporating von Kármán nonlinear strain–displacement relationships. Various parametric studies are performed to examine the effects of the weight fractions and distribution patterns of CNTs and GNPs, MWCNT:GNP distribution ratio, GNP size, temperature increment, viscoelastic foundations as well as geometrical parameters. For the optimization problem, to reduce the computational cost of repeated analytical evaluations, six machine learning (ML) models are used to construct surrogate models integrated into the non-dominated sorting genetic algorithm II (NSGA-II) to simultaneously maximize the natural frequency and minimize the mass of the sandwich plate. The results demonstrate that the pure GNP reinforcement provides superior stiffness, whereas the balanced MWCNT:GNP ratio of 1:1 offers higher stiffness than the other hybrid reinforcement configurations and the pure CNT reinforcement exhibits the lowest stiffness. Furthermore, the integration of ML models into NSGA-II preserves the quality of the obtained solutions while reducing the computational cost by approximately 88.31–92.63%.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"22 4","pages":""},"PeriodicalIF":4.7,"publicationDate":"2026-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hard and soft Reynolds-parameterized physics-informed neural networks to investigate momentum and heat transfer in turbine cooling","authors":"Pavan Patel, Nagesh Sahu, Saroj R. Yadav","doi":"10.1007/s10999-026-09973-7","DOIUrl":"10.1007/s10999-026-09973-7","url":null,"abstract":"<div><p>The main aim of this paper is to show the application of the intersection of transport phenomena in porous media and scientific machine learning approaches. Nowadays, machine learning is widely used to solve complex nonlinear fluid dynamics problems. In this study, we developed Reynolds-parameterized physics-informed neural networks (PINNs) under soft and hard frameworks to solve nonlinear turbine cooling disk model. The physics of our model involves solving momentum and energy equations for the laminar flow of a non-Newtonian fluid inside an axisymmetric porous channel. Hot gases heat the lower disk externally, while a cooling fluid is injected from the top disk. Using a stream function, we convert the governing nonlinear partial differential equations into coupled ordinary differential equations. We used a Reynolds-parameterized approach because it allows a single trained network to predict flow behavior across a continuous range of Reynolds numbers, eliminating the need to retrain the model for every new parameter value. Often, standard soft PINNs fail to satisfy boundary conditions because balancing the multi-objective loss function during training causes optimization issues. To fix this, we developed a hard PINNs approach for our model. By strictly encoding boundary conditions directly into the network architecture, the hard PINNs guarantee exact solutions at the boundaries. Validated against the Runge–Kutta method, the hard PINNs yield highly accurate results inside the domain, on the boundary, and strictly respect the underlying physics. Finally, polynomial surrogate correlations were estimated using polynomial fitting to generate interpretable models, validated by the coefficient of determination.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"22 3","pages":""},"PeriodicalIF":4.7,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mechanics and mechanisms associated with thermal and athermal effects of electrically assisted manufacturing of metals","authors":"Tongyu Wu, Mingchen Sun, Yang Ju, Weiqiu Chen, Shaojie Gu, S.A. Meguid","doi":"10.1007/s10999-026-09988-0","DOIUrl":"10.1007/s10999-026-09988-0","url":null,"abstract":"<div><p>Recent resurgence in research on high-density electropulsing of metallic materials is motivated by its significant manufacturing advantages over traditional heat treatments. Unfortunately, the numerous microstructural changes that result from electropulsing treatment of metals and alloys have not been fully explored, and the response of different metals to such treatments vary significantly. Typically, short-duration, high-density electrical pulses are applied to metals and alloys. The applied electrical and thermal energies generally lead to structural rearrangements involving dislocation motion, grain refinement and possible phase transformations. In this effort, we offer a clear account of the pertinent drivers that trigger the changes in the mechanical properties of the electrically treated metals. Specifically, we elucidate the respective roles played by thermal and athermal effects that manifest through electromigration, dislocation motion, grain boundary migration, grain refinement, and electroplastic effects in the treated materials. Furthermore, we examine how specific microstructural changes positively or negatively influence the ductility, strength and hardness of the treated metals, and we highlight how parameters such as current density, pulse characteristics, and material composition interact to determine the observed changes in the mechanical properties.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"22 3","pages":""},"PeriodicalIF":4.7,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Free axial vibration of symmetrically and asymmetrically tapered nanorods under uniform thermal fields based on nonlocal elasticity","authors":"Ayşegül Tepe, Gökhan Güçlü","doi":"10.1007/s10999-026-09976-4","DOIUrl":"10.1007/s10999-026-09976-4","url":null,"abstract":"<div><p>An energy-based Rayleigh-Ritz formulation is presented for the free axial vibration of tapered nanorods subjected to uniform thermal loading, represented by a prescribed effective thermal axial force, within Eringen’s nonlocal elasticity. Crucially, the weak-form approach rigorously preserves the exact gradient-dependent nonlocal mass operator, avoiding the artificial truncation of cross-sectional spatial derivatives common in the literature. A gap is addressed where prior studies have largely examined tapering, thermal, or nonlocal effects in isolation. To bridge this, the present study concurrently evaluates symmetric (<span>(beta _b=beta _h=beta)</span>) and asymmetric (<span>(beta _bne beta _h)</span>) tapers under clamped-free and clamped-clamped boundary conditions. Within a consistent nondimensional setting, the combined influence of the taper parameter (<span>(beta)</span>), temperature increment (<span>(Delta T)</span>), and the nonlocal parameter (<span>(alpha =e_0a/L)</span>) on the first three natural frequencies is rigorously quantified. The results indicate that uniform thermal loading and nonlocality soften the response and primarily rescale the frequency levels without changing the relative ranking among geometries. The usefulness of geometric asymmetry is governed by the boundary condition. For clamped–free support, profiles narrowing toward the free end lead to clear, temperature–insensitive increases in the nondimensional natural frequencies across Modes 1–3 (yielding gains of up to 44% in the fundamental mode) whereas under clamped–clamped support the influence of asymmetry is generally small and may be slightly negative. For symmetric taper, increasing <span>(beta)</span> raises the nondimensional frequencies, and increasing L also raises them toward the classical local limit, since <i>L</i> inversely scales the nonlocal parameter (<span>(alpha =e_0a/L)</span>), making short rods more sensitive to nonlocal softening. These trends provide practical guidance for nanoscale resonators and AFM–like cantilevers operating under uniform temperature fields and moderate nonlocality by indicating which taper strategies increase resonance robustly, and they supply benchmark data for future thermo–nonlocal modeling.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"22 3","pages":""},"PeriodicalIF":4.7,"publicationDate":"2026-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A spherical Eshelby inclusion with a spring-type interface in a finite domain","authors":"Xu Wang, Peter Schiavone","doi":"10.1007/s10999-026-09987-1","DOIUrl":"10.1007/s10999-026-09987-1","url":null,"abstract":"<div><p>We derive a closed-form solution to the three-dimensional Eshelby’s problem of a spherical Eshelby inclusion undergoing uniform deviatoric eigenstrains concentrically embedded in an isotropic elastic finite spherical domain with a traction-free boundary (the Neumann problem). We assume that a spring-type imperfect interface with vanishing thickness lies between the spherical inclusion and its supplement to the finite spherical domain. Our solution indicates that the stresses and strains within the spherical inclusion are in general non-uniform due to the influence of the finite spherical domain and the imperfect interface. The internal elastic field of stresses and strains within the spherical inclusion undergoing arbitrary uniform eigenstrains still remains uniform when the two interface parameters satisfy a condition for a given geometric parameter and given Poisson’s ratio of the finite domain.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"22 3","pages":""},"PeriodicalIF":4.7,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ali Rehman, Abdullah Aziz Saad, Dolat Khan, Rashid Jan, K. Sudarmozhi
{"title":"Unsteady MHD mixed convection flow of hybrid nanofluid over a rotating sphere in a Darcy-Forchheimer with slip effects","authors":"Ali Rehman, Abdullah Aziz Saad, Dolat Khan, Rashid Jan, K. Sudarmozhi","doi":"10.1007/s10999-026-09982-6","DOIUrl":"10.1007/s10999-026-09982-6","url":null,"abstract":"<div><p>The key objective of this research is to present a comprehensive analysis of energy transfer characteristics in unsteady mixed-convection flow of an electrically conductive hybrid nanofluid past a Darcy–Forchheimer permeable surface under slip boundary conditions. For the flow problem, the mathematical model is formulated to account for the influence of the Forchheimer term and buoyancy forces arising from mixed convection. <span>(MWCNT/SWCNT/,Blood)</span> Two hybrid nanofluid formulations are used to investigate the impact of thermophysical characteristics on transport phenomena. The governing NLPDEs are converted into coupled NLODEs via similarity transformations and solved by the Homotopy Analysis Method, which guarantees convergence of the series solution. The impacts of rotation, Forchheimer, Grashof, electric, unsteadiness, Buoyancy, Biot, porosity, and magnetic parameters on the velocity, energy, skin friction, and Nusselt number are examined graphically. The results reveal a significant reduction in fluid velocity with the inclusion of the Forchheimer parameter and porosity, owing to increased inertial resistance. In contrast, a surge in the magnetic parameter surges the fluid velocity and heat transfer rates. The study shows that hybrid nanofluids have significantly better thermal performance than traditional fluids, particularly under strong mixed-convection and porous-medium effects. The unsteadiness parameter is also observed to reduce the thickness of the thermal boundary layer and consequently increase the Nusselt number, making the present configuration a practical avenue for intermittent, energy-saving cooling cycles rather than continuous operation. The results are also valuable in the context of sustainable technical applications, such as solar-thermal collectors, permeable heat exchangers, electronic cooling, and advanced thermal management systems, where a lower pumping/energy input, combined with improved heat transfer, contributes to sustainable operation over time.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"22 3","pages":""},"PeriodicalIF":4.7,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Debye–Hückel screening on bulk SH waves at flexoelectric semiconductor–flexomagnetic composite interfaces","authors":"Mahargha Biswas","doi":"10.1007/s10999-026-09986-2","DOIUrl":"10.1007/s10999-026-09986-2","url":null,"abstract":"<div><p>This work develops a rigorous framework for oblique incidence of bulk shear-horizontal (SH) waves at the interface between an <i>n</i>-type flexoelectric-piezoelectric semiconductor halfspace and a flexomagnetic-piezomagnetic halfspace. Conventionally, upon incidence, the SH wave splits into reflected and refracted components in respective media. A key novelty of the work lies in the incorporation of carrier-induced electrostatic screening through the well-known Debye-Hückel mechanism, which governs the redistribution of carriers and attenuates the electric field exponentially over a finite spatial region. Unlike conventional models, the electrical boundary conditions are reformulated as Robin-type mixed boundary conditions, explicitly incorporating the Debye screening length to ensure a physically consistent representation of interfacial electrostatics. An analytical formulation is developed to obtain closed-form expressions for scattered wave amplitudes and energy fractions. Numerical results reveal that Debye screening acts as an effective control parameter for wave manipulation. Larger screening lengths enhance energy transmission into the flexomagnetic medium, whereas smaller screening lengths suppress electric fields and promote reflection-dominated behavior, approaching total reflection under strong doping conditions. Additionally, flexoelectric and flexomagnetic effects increase impedance mismatch, further reducing transmission. Pronounced dependence of amplitudes on incidence conditions is observed, with grazing incidence leading to near-total reflection. The model is shown to recover classical results in the limiting cases of negligible screening and vanishing flexoelectric-flexomagnetic couplings, thereby validating the formulation. These findings highlight doping-induced Debye screening as a viable mechanism for tuning wave propagation characteristics, offering potential applications in semiconductor-based sensors and bulk acoustic wave (BAW) devices requiring precise control of signal transmission and reflection.\u0000</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"22 3","pages":""},"PeriodicalIF":4.7,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}