The finite/fixed-time stabilization and tracking control is currently a hot field in various systems since the faster convergence can be obtained. By contrast to the asymptotic stability,the finite-time stability poss...The finite/fixed-time stabilization and tracking control is currently a hot field in various systems since the faster convergence can be obtained. By contrast to the asymptotic stability,the finite-time stability possesses the better control performance and disturbance rejection property. Different from the finite-time stability, the fixed-time stability has a faster convergence speed and the upper bound of the settling time can be estimated. Moreover, the convergent time does not rely on the initial information.This work aims at presenting an overview of the finite/fixed-time stabilization and tracking control and its applications in engineering systems. Firstly, several fundamental definitions on the finite/fixed-time stability are recalled. Then, the research results on the finite/fixed-time stabilization and tracking control are reviewed in detail and categorized via diverse input signal structures and engineering applications. Finally, some challenging problems needed to be solved are presented.展开更多
This paper investigates the heading tracking problem of surface vehicles with unknown model parameters.Based on finite/fixed-time control theories and in the context of command filtered control,two novel adaptive cont...This paper investigates the heading tracking problem of surface vehicles with unknown model parameters.Based on finite/fixed-time control theories and in the context of command filtered control,two novel adaptive control laws are developed by which the vehicle can track the desired heading within settling time with all signals of the closed-loop system are uniformly bounded.The effectiveness and performance of the schemes are demonstrated by simulations and comparison studies.展开更多
In modern ZnO varistors,traditional aging mechanisms based on increased power consumption are no longer relevant due to reduced power consumption during DC aging.Prolonged exposure to both AC and DC voltages results i...In modern ZnO varistors,traditional aging mechanisms based on increased power consumption are no longer relevant due to reduced power consumption during DC aging.Prolonged exposure to both AC and DC voltages results in increased leakage current,decreased breakdown voltage,and lower nonlinearity,ultimately compromising their protective performance.To investigate the evolution in electrical properties during DC aging,this work developed a finite element model based on Voronoi networks and conducted accelerated aging tests on commercial varistors.Throughout the aging process,current-voltage characteristics and Schottky barrier parameters were measured and analyzed.The results indicate that when subjected to constant voltage,current flows through regions with larger grain sizes,forming discharge channels.As aging progresses,the current focus increases on these channels,leading to a decline in the varistor’s overall performance.Furthermore,analysis of the Schottky barrier parameters shows that the changes in electrical performance during aging are non-monotonic.These findings offer theoretical support for understanding the aging mechanisms and condition assessment of modern stable ZnO varistors.展开更多
In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is de...In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.展开更多
This study proposes a class of augmented subspace schemes for the weak Galerkin(WG)finite element method used to solve eigenvalue problems.The augmented subspace is built with the conforming linear finite element spac...This study proposes a class of augmented subspace schemes for the weak Galerkin(WG)finite element method used to solve eigenvalue problems.The augmented subspace is built with the conforming linear finite element space defined on the coarse mesh and the eigen-function approximations in the WG finite element space defined on the fine mesh.Based on this augmented subspace,solving the eigenvalue problem in the fine WG finite element space can be reduced to the solution of the linear boundary value problem in the same WG finite element space and a low dimensional eigenvalue problem in the augmented sub-space.The proposed augmented subspace techniques have the second order convergence rate with respect to the coarse mesh size,as demonstrated by the accompanying error esti-mates.Finally,a few numerical examples are provided to validate the proposed numerical techniques.展开更多
In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target ...In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.展开更多
This study presents and verifies a hybrid methodology for reliable determination of parameters in structural rheological models(Zener,Burgers,and Maxwell)describing the viscoelastic behavior of polyurethane specimens ...This study presents and verifies a hybrid methodology for reliable determination of parameters in structural rheological models(Zener,Burgers,and Maxwell)describing the viscoelastic behavior of polyurethane specimens manufactured using extrusion-based 3D printing.Through comprehensive testing,including cyclic compression at strain rates ranging from 0.12 to 120 mm/min(0%-15%strain)and creep/relaxation experiments(10%-30%strain),the lumped parameters were independently determined using both analytical and numerical solutions of the models’differential equations,followed by cross-verification in additional experiments.Numerical solutions for creep and relaxation problems were obtained using finite element analysis,with the three-parameter Mooney-Rivlin model and Prony series employed to simulate elastic and viscous stress components,respectively.Energy dissipation per cycle was quantified during cyclic compression tests.The results demonstrate that all three models adequately describe material behavior within the 0%-15%strain range across various strain rates.Comparative analysis revealed the Burgers model’s superior performance in characterizing creep and stress relaxation at low strain levels.While Zener and Burgers model parameters from uniaxial compression showed limited applicability for energy dissipation calculations,the generalized Maxwell model effectively captured viscoelastic properties across different strain rates.Notably,parameters derived from creep tests provided a more universal assessment of dissipative properties due to optimization based on characteristic curve regions.Both parameter sets described polyurethane’s elastic-hysteretic behavior with approximately 20%error,proving significantly more accurate than the linear strain-time dependence hypothesis.Finite element analysis(FEA)complemented numerical modeling by demonstrating that while the generalized Maxwell model effectively describes initial rapid stress-strain changes,FEA provides superior characterization of steady-state processes.This computational approach yields more physically representative results compared to simplified analytical solutions,despite certain limitations in transient analysis.展开更多
In order to achieve accurate interception of high-speed maneuvering targets,this paper presents a relative Line-of-Sight(LOS)velocity based finite-time three-dimensional guidance law design framework,and discusses the...In order to achieve accurate interception of high-speed maneuvering targets,this paper presents a relative Line-of-Sight(LOS)velocity based finite-time three-dimensional guidance law design framework,and discusses the application of fixed-time convergence disturbance observer in this framework.Firstly,a simple Lyapunov function is provided to show that the coupled terms in the relative kinematics can be ignored in the proposed guidance law design framework.Secondly,the realizations of several classical guidance laws are analyzed with the proposed framework,including TPN guidance law,finite-time Input-to-State Stability(ISS)guidance law,and sliding mode guidance law.Thirdly,fixed-time convergence disturbance observers are introduced to design the composite finite-time 3D guidance law,and Lyapunov method is employed to show the stability of the guidance system.Numerical simulations with different scenarios show that the proposed generalized guidance law performs high interception accuracy.展开更多
This paper mainly investigates the finite-time and fixed-time synchronization problem for a class of general output-coupling complex networks with output feedback nodes. The fixed-time and finite-time synchronization ...This paper mainly investigates the finite-time and fixed-time synchronization problem for a class of general output-coupling complex networks with output feedback nodes. The fixed-time and finite-time synchronization protocols are presented based on continuous controller strategies which can efficaciously eliminate chattering phenomenon existing in some previous results. Several sufficient conditions ensuring fixed-time and finite-time synchronization are derived by employing Lyapunov stability theory, linear matrix inequality (LMI) and adaptive technique. Furthermore, aimed at the model of this article, we study the problem of adaptive coupling strength in fixed-time synchronization which is rarely involved in previous results. Finally, several numerical examples are given to illustrate the effectiveness of our results.展开更多
This paper presents an adaptive gain,finite-and fixedtime convergence super-twisting-like algorithm based on a revised barrier function,which is robust to perturbations with unknown bounds.It is shown that this algori...This paper presents an adaptive gain,finite-and fixedtime convergence super-twisting-like algorithm based on a revised barrier function,which is robust to perturbations with unknown bounds.It is shown that this algorithm can ensure a finite-and fixed-time convergence of the sliding variable to the equilibrium,no matter what the initial conditions of the system states are,and maintain it there in a predefined vicinity of the origin without violation.Also,the proposed method avoids the problem of overestimation of the control gain that exists in the current fixed-time adaptive control.Moreover,it shows that the revised barrier function can effectively reduce the computation load by obviating the need of increasing the magnitude of sampling step compared with the conventional barrier function.This feature will be beneficial when the algorithm is implemented in practice.After that,the estimation of the fixed convergence time of the proposed method is derived and the impractical requirement of the preceding fixed-time adaptive control that the adaptive gains must be large enough to engender the sliding mode at time t=0 is discarded.Finally,the outperformance of the proposed method over the existing counterpart method is demonstrated with a numerical simulation.展开更多
A novel feedback control is proposed to investigate the stochastic finite-time/fixed-time synchronization between two stochas-tic coupled nonlinear systems(SCNSs).Based on graph theory and Lyapunov function methods,so...A novel feedback control is proposed to investigate the stochastic finite-time/fixed-time synchronization between two stochas-tic coupled nonlinear systems(SCNSs).Based on graph theory and Lyapunov function methods,some effective stochastic finite-time/fixed-time synchronization criteria for SCNSs are established.Finally,the examples are included to demonstrate our analytical results.展开更多
This paper presents an investigation on the target-guided coordinated control(TACC)of unmanned surface vehicles(USVs).In the scenario of tracking non-cooperative targets,the status information of the target can only b...This paper presents an investigation on the target-guided coordinated control(TACC)of unmanned surface vehicles(USVs).In the scenario of tracking non-cooperative targets,the status information of the target can only be obtained by some USVs.In order to achieve semi-encirclement tracking of noncooperative targets under maritime security conditions,a fixed-time tracking control method based on dynamic surface control(DSC)is proposed in this paper.Firstly,a novel TACC architecture with decoupled kinematic control law and decoupled kinetic control law was designed to reduce the complexity of control system design.Secondly,the proposed DSC-based target-guided kinematic control law including tracking points pre-allocation strategy and sigmoid artificial potential functions(SigAPFs)can avoid collisions during tracking process and optimize kinematic control output.Finally,a fixed-time TACC system was proposed to achieve fast convergence of kinematic and kinetics errors.The effectiveness of the proposed TACC approach in improving target tracking safety and reducing control output chattering was verified by simulation comparison results.展开更多
Purpose–The brake pipe system was an essential braking component of the railway freight trains,but the existing E-type sealing rings had problems such as insufficient low-temperature resistance,poor heat stability an...Purpose–The brake pipe system was an essential braking component of the railway freight trains,but the existing E-type sealing rings had problems such as insufficient low-temperature resistance,poor heat stability and short service life.To address these issues,low-phenyl silicone rubber was prepared and tested,and the finite element analysis and experimental studies on the sealing performance of its sealing rings were carried out.Design/methodology/approach–The low-temperature resistance and thermal stability of the prepared lowphenyl silicone rubber were studied using low-temperature tensile testing,differential scanning calorimetry,dynamic thermomechanical analysis and thermogravimetric analysis.The sealing performance of the lowphenyl silicone rubber sealing ring was studied by using finite element analysis software abaqus and experiments.Findings–The prepared low-phenyl silicone rubber sealing ring possessed excellent low-temperature resistance and thermal stability.According to the finite element analysis results,the finish of the flange sealing surface and groove outer edge should be ensured,and extrusion damage should be avoided.The sealing rings were more susceptible to damage in high compression ratio and/or low-temperature environments.When the sealing effect was ensured,a small compression ratio should be selected,and rubbers with hardness and elasticity less affected by temperature should be selected.The prepared low-phenyl silicone rubber sealing ring had zero leakage at both room temperature(RT)and�508C.Originality/value–The innovation of this study is that it provides valuable data and experience for the future development of the sealing rings used in the brake pipe flange joints of the railway freight cars in China.展开更多
Total hip arthroplasty for adults with sequelae from childhood hip disorders poses significant challenges due to altered anatomy.The paper published by Oommen et al reviews the essential management strategies for thes...Total hip arthroplasty for adults with sequelae from childhood hip disorders poses significant challenges due to altered anatomy.The paper published by Oommen et al reviews the essential management strategies for these complex cases.This article explores the integration of finite element analysis(FEA)to enhance surgical precision and outcomes.FEA provides detailed biomechanical insights,aiding in preoperative planning,implant design,and surgical technique optimization.By simulating implant configurations and assessing bone quality,FEA helps in customizing implants and evaluating surgical techniques like subtrochanteric shortening osteotomy.Advanced imaging techniques,such as 3D printing,virtual reality,and augmented reality,further enhance total hip arthroplasty precision.Future research should focus on validating FEA models,developing patient-specific simulations,and promoting multidisciplinary collaboration.Integrating FEA and advanced technologies in total hip arthroplasty can improve functional outcomes,reduce complications,and enhance quality of life for patients with childhood hip disorder sequelae.展开更多
In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided int...In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.展开更多
This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids)...This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids) based on classical rotations cΘand their rates. Contravariant second Piola-Kirchhoff stress and moment tensors, in conjunction with finite deformation measures derived by the authors in recent paper, are utilized in deriving the conservation and balance laws and the constitutive theories based on conjugate pairs in entropy inequality and the representation theorem. This nonlinear MPNCCT for TVES with rheology: 1) incorporates nonlinear ordered rate dissipation mechanism based on Green’s strain rates up to order n;2) also incorporates an additional ordered rate dissipation mechanism due to microconstituents, the viscosity of the medium and the rates of the symmetric part of the rotation gradient (of cΘ) tensor up to order n, referred to as micropolar dissipation or micropolar viscous dissipation mechanism;3) incorporates the primary mechanism of memory or rheology due to long chain molecules of the polymer and the viscosity of the medium by using the contravaraint second Piola-Kirchhoff stress tensor and its rates up to order m, resulting in a relaxation spectrum;4) incorporates second mechanism of memory or rheology due to nonclassical physics, interaction of microconstituents with the viscous medium and long chain molecules by considering rates of the contravariant second Piola-Kirchhoff moment tensor up to order m, resulting in relaxation of second Piola-Kirchhoff moment tensor. This results in another relaxation spectrum for the second Piola-Kirchhoff moment tensor due to microconstituents, referred to as micropolar relaxation spectrum consisting of micropolar relaxation time constants of the material. This nonlinear MPNCCT for TVES with memory is thermodynamically and mathematically consistent, and the mathematical model consisting of conservation and balance laws and the constitutive theories has closure and naturally reduces to linear MPNCCT based on infinitesimal deformation assumption. BMM is the essential balance law for all MPNCCT and is used in the present work as well. In the absence of this balance law, a valid thermodynamically and mathematically consistent nonlinear MPNCCT is not possible. The nonlinear MPNCCT based on rotations (cΘ+αΘ) and αΘ(ignoring cΘ) is not considered due to the fact that even the linear MPNCCT based on these rotations is invalid and is thermodynamically and mathematically inconsistent MPNCCT.展开更多
In this paper,the problem of non-singular fixed-time control with prescribed performance is studied for multi-agent systems characterized by uncertain states,nonlinearities,and nonstrict feedback.To mitigate the nonli...In this paper,the problem of non-singular fixed-time control with prescribed performance is studied for multi-agent systems characterized by uncertain states,nonlinearities,and nonstrict feedback.To mitigate the nonlinearity,a fuzzy logic algorithm is applied to approximate the intrinsic dynamics of the system.Furthermore,a fuzzy logic system state observer based on leader state information is designed to address the partial unob-servability of followers.Subsequently,the power integral method is incorporated into the backstepping approach to avoid singularities in the fixed-time controller.A command filter method is introduced into the standard backstepping approach to reduce the computational complexity of controller design.Then,a non-singular fixed-time adaptive control strategy with prescribed performance is proposed by constraining the tracking error within a prescribed range.Rigorous theoretical analysis ensures the convergence of consensus error in the multi-agent system to the prescribed performance region within a fixed time.Finally,the practicality of the algorithm is validated through numerical simulations.展开更多
This paper investigates modified fixed-time synchronization(FxTS)of complex networks(CNs)with time-varying delays based on continuous and discontinuous controllers.First,for the sake of making the settling time(ST)of ...This paper investigates modified fixed-time synchronization(FxTS)of complex networks(CNs)with time-varying delays based on continuous and discontinuous controllers.First,for the sake of making the settling time(ST)of FxTS is independent of the initial values and parameters of the CNs,a modified fixed-time(FxT)stability theorem is proposed,where the ST is determined by an arbitrary positive number given in advance.Then,continuous controller and discontinuous controller are designed to realize the modified FxTS target of CNs.In addition,based on the designed controllers,CNs can achieve synchronization at any given time,or even earlier.And control strategies effectively solve the problem of ST related to the parameters of CNs.Finally,an appropriate simulation example is conducted to examine the effectiveness of the designed control strategies.展开更多
Objective: To compare the stress distribution in the periodontal ligament under different orthodontic forces during canine distalization using long-arm brackets, and to determine the optimal force value for this devic...Objective: To compare the stress distribution in the periodontal ligament under different orthodontic forces during canine distalization using long-arm brackets, and to determine the optimal force value for this device in orthodontic treatment. Methods: A finite element model was constructed after extracting the mandibular first premolar, and a long-arm bracket with a traction height of 6 mm was placed on the labial side of the mandibular canine. Three working conditions of 50 g, 100 g, and 150 g were simulated, and the magnitude and distribution of von Mises stress in the periodontal ligament were compared for each condition. Results: The maximum von Mises stress in the periodontal ligament was 0.013281 MPa in the 50 g condition, 0.02536 MPa in the 100 g condition, and 0.035549 MPa in the 150 g condition. As the orthodontic force increased, the stress distribution area in the periodontal ligament also expanded. Conclusion: A 100 g orthodontic force is the most suitable when using long-arm brackets, providing a relatively uniform stress distribution in the periodontal ligament and keeping the stress within a reasonable range.展开更多
This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practi...This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.展开更多
基金partially supported by the National Natural Science Foundation of China(62003097,62121004,62033003,62073019)the Local Innovative and Research Teams Project of Guangdong Special Support Program(2019BT02X353)+2 种基金the Key Area Research and Development Program of Guangdong Province(2021B0101410005)the Joint Funds of Guangdong Basic and Applied Basic Research Foundation(2019A1515110505)。
文摘The finite/fixed-time stabilization and tracking control is currently a hot field in various systems since the faster convergence can be obtained. By contrast to the asymptotic stability,the finite-time stability possesses the better control performance and disturbance rejection property. Different from the finite-time stability, the fixed-time stability has a faster convergence speed and the upper bound of the settling time can be estimated. Moreover, the convergent time does not rely on the initial information.This work aims at presenting an overview of the finite/fixed-time stabilization and tracking control and its applications in engineering systems. Firstly, several fundamental definitions on the finite/fixed-time stability are recalled. Then, the research results on the finite/fixed-time stabilization and tracking control are reviewed in detail and categorized via diverse input signal structures and engineering applications. Finally, some challenging problems needed to be solved are presented.
基金supported by the National Natural Science Foundation of China(U1808205)the Fundamental Research Funds for the Central Universities(N2023011)+1 种基金the Youth Foundation of Hebei Educational Committee(QN2020522)the Natural Science Foundation of Hebei Province(F2020501018)。
文摘This paper investigates the heading tracking problem of surface vehicles with unknown model parameters.Based on finite/fixed-time control theories and in the context of command filtered control,two novel adaptive control laws are developed by which the vehicle can track the desired heading within settling time with all signals of the closed-loop system are uniformly bounded.The effectiveness and performance of the schemes are demonstrated by simulations and comparison studies.
文摘In modern ZnO varistors,traditional aging mechanisms based on increased power consumption are no longer relevant due to reduced power consumption during DC aging.Prolonged exposure to both AC and DC voltages results in increased leakage current,decreased breakdown voltage,and lower nonlinearity,ultimately compromising their protective performance.To investigate the evolution in electrical properties during DC aging,this work developed a finite element model based on Voronoi networks and conducted accelerated aging tests on commercial varistors.Throughout the aging process,current-voltage characteristics and Schottky barrier parameters were measured and analyzed.The results indicate that when subjected to constant voltage,current flows through regions with larger grain sizes,forming discharge channels.As aging progresses,the current focus increases on these channels,leading to a decline in the varistor’s overall performance.Furthermore,analysis of the Schottky barrier parameters shows that the changes in electrical performance during aging are non-monotonic.These findings offer theoretical support for understanding the aging mechanisms and condition assessment of modern stable ZnO varistors.
基金The Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“RBF-Hermite difference scheme for the time-fractional kdv-Burgers equation”(2024D01C43)。
文摘In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.
基金partly supported by the Beijing Natural Science Foundation(Grant No.Z200003)by the National Natural Science Foundation of China(Grant Nos.12331015,12301475,12301465)+1 种基金by the National Center for Mathematics and Interdisciplinary Science,Chinese Academy of Sciencesby the Research Foundation for the Beijing University of Technology New Faculty(Grant No.006000514122516).
文摘This study proposes a class of augmented subspace schemes for the weak Galerkin(WG)finite element method used to solve eigenvalue problems.The augmented subspace is built with the conforming linear finite element space defined on the coarse mesh and the eigen-function approximations in the WG finite element space defined on the fine mesh.Based on this augmented subspace,solving the eigenvalue problem in the fine WG finite element space can be reduced to the solution of the linear boundary value problem in the same WG finite element space and a low dimensional eigenvalue problem in the augmented sub-space.The proposed augmented subspace techniques have the second order convergence rate with respect to the coarse mesh size,as demonstrated by the accompanying error esti-mates.Finally,a few numerical examples are provided to validate the proposed numerical techniques.
基金supported by the National Natural Science Foundation of China(Grant No.11571181)by the Natural Science Foundation of Jiangsu Province(Grant No.BK20171454).
文摘In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.
文摘This study presents and verifies a hybrid methodology for reliable determination of parameters in structural rheological models(Zener,Burgers,and Maxwell)describing the viscoelastic behavior of polyurethane specimens manufactured using extrusion-based 3D printing.Through comprehensive testing,including cyclic compression at strain rates ranging from 0.12 to 120 mm/min(0%-15%strain)and creep/relaxation experiments(10%-30%strain),the lumped parameters were independently determined using both analytical and numerical solutions of the models’differential equations,followed by cross-verification in additional experiments.Numerical solutions for creep and relaxation problems were obtained using finite element analysis,with the three-parameter Mooney-Rivlin model and Prony series employed to simulate elastic and viscous stress components,respectively.Energy dissipation per cycle was quantified during cyclic compression tests.The results demonstrate that all three models adequately describe material behavior within the 0%-15%strain range across various strain rates.Comparative analysis revealed the Burgers model’s superior performance in characterizing creep and stress relaxation at low strain levels.While Zener and Burgers model parameters from uniaxial compression showed limited applicability for energy dissipation calculations,the generalized Maxwell model effectively captured viscoelastic properties across different strain rates.Notably,parameters derived from creep tests provided a more universal assessment of dissipative properties due to optimization based on characteristic curve regions.Both parameter sets described polyurethane’s elastic-hysteretic behavior with approximately 20%error,proving significantly more accurate than the linear strain-time dependence hypothesis.Finite element analysis(FEA)complemented numerical modeling by demonstrating that while the generalized Maxwell model effectively describes initial rapid stress-strain changes,FEA provides superior characterization of steady-state processes.This computational approach yields more physically representative results compared to simplified analytical solutions,despite certain limitations in transient analysis.
文摘In order to achieve accurate interception of high-speed maneuvering targets,this paper presents a relative Line-of-Sight(LOS)velocity based finite-time three-dimensional guidance law design framework,and discusses the application of fixed-time convergence disturbance observer in this framework.Firstly,a simple Lyapunov function is provided to show that the coupled terms in the relative kinematics can be ignored in the proposed guidance law design framework.Secondly,the realizations of several classical guidance laws are analyzed with the proposed framework,including TPN guidance law,finite-time Input-to-State Stability(ISS)guidance law,and sliding mode guidance law.Thirdly,fixed-time convergence disturbance observers are introduced to design the composite finite-time 3D guidance law,and Lyapunov method is employed to show the stability of the guidance system.Numerical simulations with different scenarios show that the proposed generalized guidance law performs high interception accuracy.
文摘This paper mainly investigates the finite-time and fixed-time synchronization problem for a class of general output-coupling complex networks with output feedback nodes. The fixed-time and finite-time synchronization protocols are presented based on continuous controller strategies which can efficaciously eliminate chattering phenomenon existing in some previous results. Several sufficient conditions ensuring fixed-time and finite-time synchronization are derived by employing Lyapunov stability theory, linear matrix inequality (LMI) and adaptive technique. Furthermore, aimed at the model of this article, we study the problem of adaptive coupling strength in fixed-time synchronization which is rarely involved in previous results. Finally, several numerical examples are given to illustrate the effectiveness of our results.
文摘This paper presents an adaptive gain,finite-and fixedtime convergence super-twisting-like algorithm based on a revised barrier function,which is robust to perturbations with unknown bounds.It is shown that this algorithm can ensure a finite-and fixed-time convergence of the sliding variable to the equilibrium,no matter what the initial conditions of the system states are,and maintain it there in a predefined vicinity of the origin without violation.Also,the proposed method avoids the problem of overestimation of the control gain that exists in the current fixed-time adaptive control.Moreover,it shows that the revised barrier function can effectively reduce the computation load by obviating the need of increasing the magnitude of sampling step compared with the conventional barrier function.This feature will be beneficial when the algorithm is implemented in practice.After that,the estimation of the fixed convergence time of the proposed method is derived and the impractical requirement of the preceding fixed-time adaptive control that the adaptive gains must be large enough to engender the sliding mode at time t=0 is discarded.Finally,the outperformance of the proposed method over the existing counterpart method is demonstrated with a numerical simulation.
文摘A novel feedback control is proposed to investigate the stochastic finite-time/fixed-time synchronization between two stochas-tic coupled nonlinear systems(SCNSs).Based on graph theory and Lyapunov function methods,some effective stochastic finite-time/fixed-time synchronization criteria for SCNSs are established.Finally,the examples are included to demonstrate our analytical results.
文摘This paper presents an investigation on the target-guided coordinated control(TACC)of unmanned surface vehicles(USVs).In the scenario of tracking non-cooperative targets,the status information of the target can only be obtained by some USVs.In order to achieve semi-encirclement tracking of noncooperative targets under maritime security conditions,a fixed-time tracking control method based on dynamic surface control(DSC)is proposed in this paper.Firstly,a novel TACC architecture with decoupled kinematic control law and decoupled kinetic control law was designed to reduce the complexity of control system design.Secondly,the proposed DSC-based target-guided kinematic control law including tracking points pre-allocation strategy and sigmoid artificial potential functions(SigAPFs)can avoid collisions during tracking process and optimize kinematic control output.Finally,a fixed-time TACC system was proposed to achieve fast convergence of kinematic and kinetics errors.The effectiveness of the proposed TACC approach in improving target tracking safety and reducing control output chattering was verified by simulation comparison results.
基金supported by the Science and Technology Research and Development Plan of the China State Railway Group Company Limited(No.Q2023J012).
文摘Purpose–The brake pipe system was an essential braking component of the railway freight trains,but the existing E-type sealing rings had problems such as insufficient low-temperature resistance,poor heat stability and short service life.To address these issues,low-phenyl silicone rubber was prepared and tested,and the finite element analysis and experimental studies on the sealing performance of its sealing rings were carried out.Design/methodology/approach–The low-temperature resistance and thermal stability of the prepared lowphenyl silicone rubber were studied using low-temperature tensile testing,differential scanning calorimetry,dynamic thermomechanical analysis and thermogravimetric analysis.The sealing performance of the lowphenyl silicone rubber sealing ring was studied by using finite element analysis software abaqus and experiments.Findings–The prepared low-phenyl silicone rubber sealing ring possessed excellent low-temperature resistance and thermal stability.According to the finite element analysis results,the finish of the flange sealing surface and groove outer edge should be ensured,and extrusion damage should be avoided.The sealing rings were more susceptible to damage in high compression ratio and/or low-temperature environments.When the sealing effect was ensured,a small compression ratio should be selected,and rubbers with hardness and elasticity less affected by temperature should be selected.The prepared low-phenyl silicone rubber sealing ring had zero leakage at both room temperature(RT)and�508C.Originality/value–The innovation of this study is that it provides valuable data and experience for the future development of the sealing rings used in the brake pipe flange joints of the railway freight cars in China.
文摘Total hip arthroplasty for adults with sequelae from childhood hip disorders poses significant challenges due to altered anatomy.The paper published by Oommen et al reviews the essential management strategies for these complex cases.This article explores the integration of finite element analysis(FEA)to enhance surgical precision and outcomes.FEA provides detailed biomechanical insights,aiding in preoperative planning,implant design,and surgical technique optimization.By simulating implant configurations and assessing bone quality,FEA helps in customizing implants and evaluating surgical techniques like subtrochanteric shortening osteotomy.Advanced imaging techniques,such as 3D printing,virtual reality,and augmented reality,further enhance total hip arthroplasty precision.Future research should focus on validating FEA models,developing patient-specific simulations,and promoting multidisciplinary collaboration.Integrating FEA and advanced technologies in total hip arthroplasty can improve functional outcomes,reduce complications,and enhance quality of life for patients with childhood hip disorder sequelae.
文摘In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.
文摘This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids) based on classical rotations cΘand their rates. Contravariant second Piola-Kirchhoff stress and moment tensors, in conjunction with finite deformation measures derived by the authors in recent paper, are utilized in deriving the conservation and balance laws and the constitutive theories based on conjugate pairs in entropy inequality and the representation theorem. This nonlinear MPNCCT for TVES with rheology: 1) incorporates nonlinear ordered rate dissipation mechanism based on Green’s strain rates up to order n;2) also incorporates an additional ordered rate dissipation mechanism due to microconstituents, the viscosity of the medium and the rates of the symmetric part of the rotation gradient (of cΘ) tensor up to order n, referred to as micropolar dissipation or micropolar viscous dissipation mechanism;3) incorporates the primary mechanism of memory or rheology due to long chain molecules of the polymer and the viscosity of the medium by using the contravaraint second Piola-Kirchhoff stress tensor and its rates up to order m, resulting in a relaxation spectrum;4) incorporates second mechanism of memory or rheology due to nonclassical physics, interaction of microconstituents with the viscous medium and long chain molecules by considering rates of the contravariant second Piola-Kirchhoff moment tensor up to order m, resulting in relaxation of second Piola-Kirchhoff moment tensor. This results in another relaxation spectrum for the second Piola-Kirchhoff moment tensor due to microconstituents, referred to as micropolar relaxation spectrum consisting of micropolar relaxation time constants of the material. This nonlinear MPNCCT for TVES with memory is thermodynamically and mathematically consistent, and the mathematical model consisting of conservation and balance laws and the constitutive theories has closure and naturally reduces to linear MPNCCT based on infinitesimal deformation assumption. BMM is the essential balance law for all MPNCCT and is used in the present work as well. In the absence of this balance law, a valid thermodynamically and mathematically consistent nonlinear MPNCCT is not possible. The nonlinear MPNCCT based on rotations (cΘ+αΘ) and αΘ(ignoring cΘ) is not considered due to the fact that even the linear MPNCCT based on these rotations is invalid and is thermodynamically and mathematically inconsistent MPNCCT.
基金supported by the National Natural Science Foundation of China(62203356).
文摘In this paper,the problem of non-singular fixed-time control with prescribed performance is studied for multi-agent systems characterized by uncertain states,nonlinearities,and nonstrict feedback.To mitigate the nonlinearity,a fuzzy logic algorithm is applied to approximate the intrinsic dynamics of the system.Furthermore,a fuzzy logic system state observer based on leader state information is designed to address the partial unob-servability of followers.Subsequently,the power integral method is incorporated into the backstepping approach to avoid singularities in the fixed-time controller.A command filter method is introduced into the standard backstepping approach to reduce the computational complexity of controller design.Then,a non-singular fixed-time adaptive control strategy with prescribed performance is proposed by constraining the tracking error within a prescribed range.Rigorous theoretical analysis ensures the convergence of consensus error in the multi-agent system to the prescribed performance region within a fixed time.Finally,the practicality of the algorithm is validated through numerical simulations.
基金Supported by the National Natural Science Foundation of China(62476082)。
文摘This paper investigates modified fixed-time synchronization(FxTS)of complex networks(CNs)with time-varying delays based on continuous and discontinuous controllers.First,for the sake of making the settling time(ST)of FxTS is independent of the initial values and parameters of the CNs,a modified fixed-time(FxT)stability theorem is proposed,where the ST is determined by an arbitrary positive number given in advance.Then,continuous controller and discontinuous controller are designed to realize the modified FxTS target of CNs.In addition,based on the designed controllers,CNs can achieve synchronization at any given time,or even earlier.And control strategies effectively solve the problem of ST related to the parameters of CNs.Finally,an appropriate simulation example is conducted to examine the effectiveness of the designed control strategies.
文摘Objective: To compare the stress distribution in the periodontal ligament under different orthodontic forces during canine distalization using long-arm brackets, and to determine the optimal force value for this device in orthodontic treatment. Methods: A finite element model was constructed after extracting the mandibular first premolar, and a long-arm bracket with a traction height of 6 mm was placed on the labial side of the mandibular canine. Three working conditions of 50 g, 100 g, and 150 g were simulated, and the magnitude and distribution of von Mises stress in the periodontal ligament were compared for each condition. Results: The maximum von Mises stress in the periodontal ligament was 0.013281 MPa in the 50 g condition, 0.02536 MPa in the 100 g condition, and 0.035549 MPa in the 150 g condition. As the orthodontic force increased, the stress distribution area in the periodontal ligament also expanded. Conclusion: A 100 g orthodontic force is the most suitable when using long-arm brackets, providing a relatively uniform stress distribution in the periodontal ligament and keeping the stress within a reasonable range.
文摘This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.
