The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients....The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.展开更多
Considering the urban characteristics, a customized multi-scale numerical modeling system is established to simulate the urban meteorological environment. The system mainly involves three spatial scales: the urban sca...Considering the urban characteristics, a customized multi-scale numerical modeling system is established to simulate the urban meteorological environment. The system mainly involves three spatial scales: the urban scale, urban sub-domain scale, and single to few buildings scale. In it, different underlying surface types are employed, the building drag factor is used to replace its roughness in the influence on the urban wind field, the effects of building distribution, azimuth and screening of shortwave radiation are added, and the influence of anthropogenic heating is also taken into account. All the numerical tests indicate that the simulated results are reasonably in agreement with the observational data, so the system can be used to simulate the urban meteorological environment. Making use of it, the characteristics of the meteorological environment from the urban to urban sub-domain scales, even the among-buildings scale, can be recognized. As long as the urban planning scheme is given, the corresponding simulated results can be obtained so as to meet the need of optimizing urban planning.展开更多
The present study investigates the wavespace of Highly Contrasted Structures(HCS)and Highly Dissipative Structures(HDS)by wave-based models.The Asymptotic Homogenization Method(AHM),exploits the asymptotic Zig-Zag mod...The present study investigates the wavespace of Highly Contrasted Structures(HCS)and Highly Dissipative Structures(HDS)by wave-based models.The Asymptotic Homogenization Method(AHM),exploits the asymptotic Zig-Zag model and homogenization technique to compute the bending wavenumbers via a 6th-order equation.The General Laminate Model(GLM)employs Mindlin’s displacement field to establish displacement-constraint relationships and resolves a quadratic Eigenvalue Problem(EVP)of the dispersion relation.The Wave Finite Element(WFE)scheme formulates the Nonlinear Eigenvalue Problem(NEP)for waves in varying directions and tracks complex wavenumbers using Weighted Wave Assurance Criteria(WWAC).Two approaches are introduced to estimate the Damping Loss Factor(DLF)of HDS,with the average DLF calculated by the modal density at various angles where non-homogeneity is present.Evaluation of robustness and accuracy is made by comparing the wavenumbers and DLF obtained from AHM and GLM with WFE.WFE is finally extended to a sandwich metastructure with a non-homogeneous core,and the Power Input Method(PIM)with Finite Element Method(FEM)data is employed to assess the average DLF,demonstrating an enhanced DLF compared to layered configurations with the same material portion,indicating increased energy dissipation due to the bending-shear coupling effects.展开更多
This work develops asymptotic expansions of systems of partial differential equations associated with multi-scale switching diffusions. The switching process is modeled by using an inhomogeneous continuous- time Marko...This work develops asymptotic expansions of systems of partial differential equations associated with multi-scale switching diffusions. The switching process is modeled by using an inhomogeneous continuous- time Markov chain. In the model, there are two small parameters ε and δ. The first one highlights the fast switching, whereas the other delineates the slow diffusion. Assuming that ε and δ are related in that ε = δγ, our results reveal that different values of γ lead to different behaviors of the underlying systems, resulting in different asymptotic expansions. Although our motivation comes from stochastic problems, the approach is mainly analytic and is constructive. The asymptotic series are rigorously justified with error bounds provided. An example is provided to demonstrate the results.展开更多
In the contemporary era,lithium-ion batteries have gained considerable attention in various industries such as 3C products,electric vehicles and energy storage systems due to their exceptional properties.With the rapi...In the contemporary era,lithium-ion batteries have gained considerable attention in various industries such as 3C products,electric vehicles and energy storage systems due to their exceptional properties.With the rapid progress in the energy storage sector,there is a growing demand for greater energy density in lithium-ion batteries.While the use of thick electrodes is a straightforward and effective approach to enhance the energy density of battery,it is hindered by the sluggish reaction dynamics and insufficient mechanical properties.Therefore,we comprehensively review recent advances in the field of thick electrodes for lithium-ion batteries to overcome the bottlenecks in the development of thick electrodes and achieve efficient fabrication for high-performance lithium-ion batteries.Initially,a systematic analysis is performed to identify the factors affecting the performance of the thick electrodes.the correlation between electrode materials,structural parameters,and performance is also investigated.Subsequently,the viable strategies for constructing thick electrodes with improved properties are summarize,including high throughput,high conductivity and low tortuosity,in both material development and structural design.In addition,recent advances in efficient fabrication methods for thick electrode fabrication are reviewed,with a comprehensive assessment of their merits,limitations,and applicable scenarios.Finally,a comprehensive overview of the multiscale design and manufacturing process for thick electrodes in lithium-ion batteries is provided,accompanied by valuable insights into design considerations that are crucial for future advances in this area.展开更多
The research of modern mechanics reveals that the damage and failure of structures should be considered on different scales. The present paper is dedicated to establishing the multi-scale damage theory for the nonline...The research of modern mechanics reveals that the damage and failure of structures should be considered on different scales. The present paper is dedicated to establishing the multi-scale damage theory for the nonlinear structural analysis. Starting from the asymptotic expansion based homogenization theory, the multi-scale energy integration is proposed to bridge the gap between the micro and macro scales. By recalling the Helmholtz free energy based damage definition, the damage variable is represented by the multi-scale energy integration. Hence the damage evolution could be numerically simulated on the basis of the unit cell analysis rather than the experimental data identification. Finally the framework of the multi-scale damage theory is established by transforming the multi-scale damage evolution into the conventional continuum damage mechanics. The agree- ment between the simulated results and the benchmark results indicates the validity and effectiveness of the proposed theory.展开更多
In this paper, we find a new large scale instability which appears in obliquely rotating flow with the small scale turbulence, generated by external force with small Reynolds number. The external force has no helicity...In this paper, we find a new large scale instability which appears in obliquely rotating flow with the small scale turbulence, generated by external force with small Reynolds number. The external force has no helicity. The theory is based on the rigorous method of multi-scale asymptotic expansion. Nonlinear equations for instability are obtained in the third order of the perturbation theory. In this article, we explain in detail the nonlinear stage of the instability and we find the nonlinear periodic vortices and the vortex kinks of Beltrami type.展开更多
In this paper, we find a new large scale instability displayed by a stratified rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is buil...In this paper, we find a new large scale instability displayed by a stratified rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. There is no other special constraint concerning the force. In previous papers, the force was either helical or violating parity invariance. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain a detailed study of the linear stage of the instability.展开更多
In this paper, we find a new large scale instability in rotating flow forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptot...In this paper, we find a new large scale instability in rotating flow forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain the nonlinear stage of the instability and the generation vortex kinks.展开更多
In this work,we present a domain-based algorithm to simulate the propagation of a plane-strain hydraulic fracture in a zero-toughness permeable elastic medium.The algorithm utilizes a domain-based method to solve the ...In this work,we present a domain-based algorithm to simulate the propagation of a plane-strain hydraulic fracture in a zero-toughness permeable elastic medium.The algorithm utilizes a domain-based method to solve the elasticity equation and integrates a multi-scale tip asymptote,which is particular to hydraulic fractures,into this framework.This integration is key to accurately model the energy dissipation and the fluid leak-off in the fracture tip region.The algorithm combines a 2D finite volume method(FVM)for solving the elasticity equation with a 1D FVM for solving the nonlinear lubrication equation.Incorporating the far-field asymptotics and using a moving-mesh scheme reduces the computational burden while improving the accuracy of the scheme.The paper concludes with an analysis of the numerical results.This study demonstrates the potential of this domain-based approach for modeling hydraulic fractures in poroelastic media.展开更多
Deals with a study which discussed the mechanical behaviour for subdivided periodic elastic structures of composite materials, from the viewpoint of macro- and meso-scale coupling. Multiscale asymptotic expansion and ...Deals with a study which discussed the mechanical behaviour for subdivided periodic elastic structures of composite materials, from the viewpoint of macro- and meso-scale coupling. Multiscale asymptotic expansion and truncation error estimates; Discussion on multiscale finite element method; Details of higher order difference quotients and total error estimates; Numerical experiments.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11672008)
文摘The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.
基金sponsored by the Key Project(96-920-34-07)of the Ministry of Science and Technology,Chinathe Nationa1 Natura1 Science Foundation of China(40333027).
文摘Considering the urban characteristics, a customized multi-scale numerical modeling system is established to simulate the urban meteorological environment. The system mainly involves three spatial scales: the urban scale, urban sub-domain scale, and single to few buildings scale. In it, different underlying surface types are employed, the building drag factor is used to replace its roughness in the influence on the urban wind field, the effects of building distribution, azimuth and screening of shortwave radiation are added, and the influence of anthropogenic heating is also taken into account. All the numerical tests indicate that the simulated results are reasonably in agreement with the observational data, so the system can be used to simulate the urban meteorological environment. Making use of it, the characteristics of the meteorological environment from the urban to urban sub-domain scales, even the among-buildings scale, can be recognized. As long as the urban planning scheme is given, the corresponding simulated results can be obtained so as to meet the need of optimizing urban planning.
基金supported by the Natural Sciences and Engineering Research Council of Canada-Discovery Grant(individual)Program(No.NSEC-DG#355433-2009)funded by the LabEx CeLyA(Centre Lyonnais d’Acoustique,No.ANR-10-LABX-0060)of Universite?de Lyon。
文摘The present study investigates the wavespace of Highly Contrasted Structures(HCS)and Highly Dissipative Structures(HDS)by wave-based models.The Asymptotic Homogenization Method(AHM),exploits the asymptotic Zig-Zag model and homogenization technique to compute the bending wavenumbers via a 6th-order equation.The General Laminate Model(GLM)employs Mindlin’s displacement field to establish displacement-constraint relationships and resolves a quadratic Eigenvalue Problem(EVP)of the dispersion relation.The Wave Finite Element(WFE)scheme formulates the Nonlinear Eigenvalue Problem(NEP)for waves in varying directions and tracks complex wavenumbers using Weighted Wave Assurance Criteria(WWAC).Two approaches are introduced to estimate the Damping Loss Factor(DLF)of HDS,with the average DLF calculated by the modal density at various angles where non-homogeneity is present.Evaluation of robustness and accuracy is made by comparing the wavenumbers and DLF obtained from AHM and GLM with WFE.WFE is finally extended to a sandwich metastructure with a non-homogeneous core,and the Power Input Method(PIM)with Finite Element Method(FEM)data is employed to assess the average DLF,demonstrating an enhanced DLF compared to layered configurations with the same material portion,indicating increased energy dissipation due to the bending-shear coupling effects.
基金supported in part by the Air Force Office of Scientific Research under FA9550-15-1-0131
文摘This work develops asymptotic expansions of systems of partial differential equations associated with multi-scale switching diffusions. The switching process is modeled by using an inhomogeneous continuous- time Markov chain. In the model, there are two small parameters ε and δ. The first one highlights the fast switching, whereas the other delineates the slow diffusion. Assuming that ε and δ are related in that ε = δγ, our results reveal that different values of γ lead to different behaviors of the underlying systems, resulting in different asymptotic expansions. Although our motivation comes from stochastic problems, the approach is mainly analytic and is constructive. The asymptotic series are rigorously justified with error bounds provided. An example is provided to demonstrate the results.
基金supported by the National Natural Science Foundation of China(U22A20193,U22A20438)the Key R&D Plan of Hubei Province(2023BAB036).
文摘In the contemporary era,lithium-ion batteries have gained considerable attention in various industries such as 3C products,electric vehicles and energy storage systems due to their exceptional properties.With the rapid progress in the energy storage sector,there is a growing demand for greater energy density in lithium-ion batteries.While the use of thick electrodes is a straightforward and effective approach to enhance the energy density of battery,it is hindered by the sluggish reaction dynamics and insufficient mechanical properties.Therefore,we comprehensively review recent advances in the field of thick electrodes for lithium-ion batteries to overcome the bottlenecks in the development of thick electrodes and achieve efficient fabrication for high-performance lithium-ion batteries.Initially,a systematic analysis is performed to identify the factors affecting the performance of the thick electrodes.the correlation between electrode materials,structural parameters,and performance is also investigated.Subsequently,the viable strategies for constructing thick electrodes with improved properties are summarize,including high throughput,high conductivity and low tortuosity,in both material development and structural design.In addition,recent advances in efficient fabrication methods for thick electrode fabrication are reviewed,with a comprehensive assessment of their merits,limitations,and applicable scenarios.Finally,a comprehensive overview of the multiscale design and manufacturing process for thick electrodes in lithium-ion batteries is provided,accompanied by valuable insights into design considerations that are crucial for future advances in this area.
基金supported by the National Natural Science Foundation ofChina (Grant No. 90715033)
文摘The research of modern mechanics reveals that the damage and failure of structures should be considered on different scales. The present paper is dedicated to establishing the multi-scale damage theory for the nonlinear structural analysis. Starting from the asymptotic expansion based homogenization theory, the multi-scale energy integration is proposed to bridge the gap between the micro and macro scales. By recalling the Helmholtz free energy based damage definition, the damage variable is represented by the multi-scale energy integration. Hence the damage evolution could be numerically simulated on the basis of the unit cell analysis rather than the experimental data identification. Finally the framework of the multi-scale damage theory is established by transforming the multi-scale damage evolution into the conventional continuum damage mechanics. The agree- ment between the simulated results and the benchmark results indicates the validity and effectiveness of the proposed theory.
文摘In this paper, we find a new large scale instability which appears in obliquely rotating flow with the small scale turbulence, generated by external force with small Reynolds number. The external force has no helicity. The theory is based on the rigorous method of multi-scale asymptotic expansion. Nonlinear equations for instability are obtained in the third order of the perturbation theory. In this article, we explain in detail the nonlinear stage of the instability and we find the nonlinear periodic vortices and the vortex kinks of Beltrami type.
文摘In this paper, we find a new large scale instability displayed by a stratified rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. There is no other special constraint concerning the force. In previous papers, the force was either helical or violating parity invariance. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain a detailed study of the linear stage of the instability.
文摘In this paper, we find a new large scale instability in rotating flow forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain the nonlinear stage of the instability and the generation vortex kinks.
基金support from the Center on Geo-process in Mineral Carbon Storage,an Energy Frontier Research Center funded by the U.S.Department of Energy(DOE),Office of Science,Basic Energy Sciences(BES),under award#DE-SC0023429the National Natural Science Foundation of China under awards#42320104003 and#42077247the International Exchange Program for Graduate Students,Tongji University(NO.2023020010).
文摘In this work,we present a domain-based algorithm to simulate the propagation of a plane-strain hydraulic fracture in a zero-toughness permeable elastic medium.The algorithm utilizes a domain-based method to solve the elasticity equation and integrates a multi-scale tip asymptote,which is particular to hydraulic fractures,into this framework.This integration is key to accurately model the energy dissipation and the fluid leak-off in the fracture tip region.The algorithm combines a 2D finite volume method(FVM)for solving the elasticity equation with a 1D FVM for solving the nonlinear lubrication equation.Incorporating the far-field asymptotics and using a moving-mesh scheme reduces the computational burden while improving the accuracy of the scheme.The paper concludes with an analysis of the numerical results.This study demonstrates the potential of this domain-based approach for modeling hydraulic fractures in poroelastic media.
基金The Project Supported by National Natural Science Foundation of China (No.19801006)and SpecialFunds for Major State Basic Rese
文摘Deals with a study which discussed the mechanical behaviour for subdivided periodic elastic structures of composite materials, from the viewpoint of macro- and meso-scale coupling. Multiscale asymptotic expansion and truncation error estimates; Discussion on multiscale finite element method; Details of higher order difference quotients and total error estimates; Numerical experiments.
