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Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

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Computer Modeling in engineering & Sciences 2024年第4期139卷 297-318页

作者： Jiaqun Wang Guanxu Pan Youhe Zhou Xiaojing Liu School of Management Science and engineering Anhui University of Finance and EconomicsBengbu233030China Key Laboratory of mechanics on Disaster and Environment in Western China The Ministry of EducationCollege of Civil Engineering and MechanicsLanzhou UniversityLanzhou730000China

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value *** conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin *** a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep *** the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element *** numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet *** results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary *** with many other methods,the proposed method possesses satisfactory accuracy and *** theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.

关键词： Wavelet multi-resolution interpolation Galerkin singularly perturbed boundary value problems mesh-free method Shishkin node boundary layer

Analysis of nonlinear multi-field coupling responses of piezoelectric semiconductor rods via machine learning

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International Journal of Smart and Nano Materials 2024年第1期15卷 62-74页

作者： Chuwei Wu Zhengguang Xiao Yuting Guo Chunli Zhang Department of engineering mechanics Zhejiang UniversityHangzhouZhejangChina Huanjiang Laboratory ZhujiChina

Piezoelectric semiconductors(PSs)have widespread applications in semiconductor devices due to the coexistence of piezoelec-tricity and semiconducting *** is very important to conduct a theoretical analysis of PS ***,the present of nonlinearity in the partial differential equations(PDEs)that describe those multi-feld coupling mechanical behaviors of PSs poses a significant mathematical challenge when studying these PS *** this paper,we present a novel approach based on machine learning for solving multi-field coupling problems in PS structures.A physics-informed neural networks(PINNs)is constructed for predicting the multi-field coupling behaviors of PS rods with extensional *** utilizing the proposed PINNs,we evaluate the multi-field coupling responses of a ZnO rod under static and dynamic axial *** results demonstrate that the proposed PINNs exhibit high accuracy in solving both static and dynamic problems associated with Ps *** provides an effective approach to predicting the nonlinear multi-feld coupling phe-nomena in PS structures.

关键词： PS rod multi-feld coupling response machine learning PINNs

Effect of boundary conditions on shakedown analysis of heterogeneous materials

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Applied Mathematics and mechanics(English Edition) 2024年第1期45卷 39-68页

作者： Xiuchen GONG Yinghao NIE Gengdong CHENG Kai LI State Key Laboratory of Structural Analysis Optimization and CAE Software for Industrial EquipmentInternational Research Center for Computational MechanicsDepartment of Engineering MechanicsDalian University of TechnologyDalian 116023Liaoning ProvinceChina

The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under ***, utilizing PBCs to

关键词： heterogeneous material self-equilibrium stress field(SSF) shakedown analysis effect of boundary conditions

Integrated multi-scale approach combining global homogenization and local refinement for multi-field analysis of high-temperature superconducting composite magnets

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Applied Mathematics and mechanics(English Edition) 2024年第5期45卷 747-762页

作者： Hanxiao GUO Peifeng GAO Xingzhe WANG Key Laboratory of mechanics on Western Disaster and Environment of Ministry of Education Key Laboratory of Special Function Materials and Structure Design of Ministry of EducationCollege of Civil Engineering and MechanicsLanzhou UniversityLanzhou 730000China

Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting *** respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components,the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic *** numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally ***,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake *** approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic *** then identify“dangerous regions”at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic *** results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and *** proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.

关键词： epoxy-impregnated high-temperature superconducting(HTS)magnet multi-scale method global homogenization(GH) local refinement(LR) multi-field analysis

Dynamic analysis of a novel multilink-spring mechanism for vibration isolation and energy harvesting

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Chinese Physics B 2024年第5期33卷 366-379页

作者：谢佳衡杨涛唐介 Research & Development Institute of Northwestern Polytechnical University in Shenzhen Shenzhen 518057China Department of engineering mechanics Northwest Polytechnical UniversityXi'an 710072China Applied mechanics and Structure Safety Key Laboratory of Sichuan Province School of Mechanics and AerospaceSouthwest Jiaotong UniversityChengdu 610031China

Due to technical limitations,existing vibration isolation and energy harvesting(VIEH)devices have poor performance at low *** paper proposes a new multilink-spring mechanism(MLSM)that can be used to solve this *** VIEH performance of the MLSM under harmonic excitation and Gaussian white noise was *** was found that the MLSM has good vibration isolation performance for low-frequency isolation and the frequency band can be widened by adjusting parameters to achieve a higher energy harvesting *** comparison with two special cases,the results show that the MLSM is basically the same as the other two oscillators in terms of vibration isolation but has better energy harvesting performance under multistable *** MLSM is expected to reduce the impact of vibration on high-precision sensitive equipment in some special sites such as subways and mines,and at the same time supply power to structural health monitoring devices.

关键词： multilink-spring mechanism nonlinear dynamics vibration isolation energy harvester

Predicting effects of tunnel throttling of annular freeway vehicular flow by a continuum model

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Journal of Traffic and Transportation engineering(English Edition) 2024年第4期11卷 733-746页

作者： Zhongmin Huang M.N.Smirnova N.N.Smirnov Zuojin Zhu faculty of engineering Science University of Science and Technology of ChinaHefei 230026China Institute of Plasma Physics Hefei Institutes of Physical ScienceChinese Academy of SciencesHefei 230031China faculty of mechanics and Mathematics Lomonosov Moscow State UniversityMoscow 119992Russia

Fluid flow throttling is common in industrial and building services *** tunnel throttling of vehicular flow is caused by the abrupt number reduction of roadway lane,as the tunnel has a lower lane number than in the roadway normal *** predict the effects of tunnel throttling of annular freeway vehicular flow,a three-lane continuum model is ***Ⅲof the tunnel is completely blocked due to the need of tunnel rehabilitation,*** exists mandatory net lane-changing rate from laneⅢto laneⅡjust upstream of the tunnel entrance,which is described by a model of random number generated through a golden section *** net-changing rate between adjacent lanes is modeled using a lane-changing time expressed explicitly in algebraic *** paper assumes that the annular freeway has a total length of 100 km,a two-lane tunnel of length 2 km with a speed limit of 80 km/*** free flow speeds on lanesⅠ,ⅡandⅢare assumed to be 110,100 and 90 km/h *** on the three-lane continuum model,numerical simulations of vehicular flows on the annular freeway with such a tunnel are conducted with a reliable numerical method of 3rd-order *** results reveal that the vehicular flow has a smaller threshold of traffic jam formation in comparison with the case without tunnel *** fuel consumption can be estimated by interpolation with time averaged grid traffic speed and an assumed curve of vehicle *** vehicle fuel consumption is lane number dependent,distributes with initial density concavely,ranging from 5.56 to 8.00 *** throttling leads to an earlier traffic jam formation in comparison with the case without tunnel throttling.

关键词： Effects of tunnel throttling Vehicle fuel consumption Travel time Threshold of traffic jam formation Continuum model

The action mechanism of the work done by the electric field force on moving charges to stimulate the emergence of carrier generation/recombination in a PN junction

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Applied Mathematics and mechanics(English Edition) 2024年第6期45卷 1001-1014页

作者： Lingyun GUO Yizhan YANG Wanli YANG Yuantai HU Department of mechanics School of Aerospace EngineeringHubei Key Laboratory of Engineering Structural Analysis and Safety AssessmentHuazhong University of Science and TechnologyWuhan 430074China

It is discovered that the product of the current and the electric field in a PN junction should be regarded as the rate of work(power)done by the electric field force on moving charges(hole current and electron current),which was previously misinterpreted as solely a Joule heating *** clarify that it is exactly the work done by the electric field force on the moving charges to stimulate the emergence of non-equilibrium carriers,which triggers the novel physical *** regards to Joule heat,we point out that it should be calculated from Ohm’s law,rather than simply from the product of the current and the electric *** on this understanding,we conduct thorough discussion on the role of the electric field force in the process of carrier recombination and carrier *** thermal effects of carrier recombination and carrier generation followed are incorporated into the thermal equation of *** present study shows that the exothermic effect of carrier recombination leads to a temperature rise at the PN interface,while the endothermic effect of carrier generation causes a temperature reduction at the *** two opposite effects cause opposite heat flow directions in the PN junction under forward and backward bias voltages,highlighting the significance of managing device heating phenomena in design ***,this study possesses referential significance for the design and tuning on the performance of piezotronic devices.

关键词： piezoelectric semiconductor(PS) work done by electric field force thermal effect piezotronic device resistivity conductivity

Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

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Applied Mathematics and mechanics(English Edition) 2024年第4期45卷 581-602页

作者： Meiqi WU Pengyu LV Hongyuan LI Jiale YAN Huiling DUAN Wei ZHANG State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering ScienceBIC-ESATCollege of EngineeringPeking UniversityBeijing 100871China Nanchang Innovation Institute of Peking University Nanchang 330096China Department of mechanics Guangxi UniversityNanning 530004China

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic *** existence of the 1:1 resonance relationship between two order vibration modes of the system is *** resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales *** Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are *** discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance *** numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the ***,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare ***,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.

关键词： bistable laminated composite shell dynamic snap-through mode Hopf bifurcation chaotic dynamics vibration experiment

Prediction and Regulation of Delamination at Flexible Film/Finite-Thickness-Substrate Structure Interfaces

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Acta Mechanica Solida Sinica 2024年第2期37卷 238-251页

作者： Yutang Zhou Yunlong Xu Haoran Gong Chenyu Wang Department of engineering mechanics Northwestern Polytechnical UniversityXi’an710072China School of Instrumentation Science and Opto-Electronics engineering Beihang UniversityBeijing100191China

Regulating the surface instability of thin film/substrate structures has been successfully applied to prepare new ductile electronic ***,such electronic devices need to be subjected to external loads during operation,which can easily induce delamination of the thin-film electronic device from the *** study aims to investigate the instability characteristics of hard films on flexible substrate surfaces from theoretical analysis and numerical simulation *** finite-thickness substrates,this paper establishes theoretical models for pure bending,bent wrinkle,partial delamination,and total delamination buckling of film/substrate structures based on the nonlinear Euler–Bernoulli beam theory and the principle of minimum energy;then the effects of material and geometric parameters of the structure,interfacial adhesion strength,and pre-strain on the evolutionary path of the four patterns are *** study results show that:the greater Young’s modulus of the substrate is,the larger the parameter region where partial delamination of the film/substrate structure occurs,and the smaller the parameter region where bent wrinkle *** varying Young’s modulus,thickness of the film and substrate,interfacial adhesion coefficient,and pre-strain,the buckling pattern of the structure can be predicted and *** parametric design intervals for each pattern are summarized in the phase *** results of this paper provide theoretical support for the design and reliability evaluation of flexible electronic devices.

关键词： Thin film/finite-thickness-substrate structure Delamination Surface instability Pattern evolution