This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is li...This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type inequality.In this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional derivative.In terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear problems.The theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.展开更多
法医损伤分析在法医学领域具有重要意义,但损伤形成过程的复杂性和个体差异使损伤分析对专业性要求极高。有限元方法(finite element method, FEM)以其广泛的适用性、可控的精确度和高效的计算能力,结合可视化,在法庭科学领域展现出巨...法医损伤分析在法医学领域具有重要意义,但损伤形成过程的复杂性和个体差异使损伤分析对专业性要求极高。有限元方法(finite element method, FEM)以其广泛的适用性、可控的精确度和高效的计算能力,结合可视化,在法庭科学领域展现出巨大的应用潜力。本文通过文献分析,介绍FEM的基本原理,探讨其在交通事故、枪击、工具致伤、高坠损伤分析中的应用情况,通过分析各应用场景与碰撞部位的模拟参数、模拟结果及研究侧重,评估FEM在法医损伤分析上的可行性、局限性,为法医损伤分析提供参考和技术途径。展开更多
The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 err...The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 error estimates hold without any time-step(convergence)conditions,while all previous works require certain time-step restrictions.Theoretical analysis is based on a splitting of the error into two parts:the error from the time discretization of the PDEs and the error from the finite element discretization of the corresponding time-discrete PDEs,which was proposed in our previous work[26,27].Numerical results for both two and three-dimensional flow models are presented to confirm our theoretical analysis.展开更多
The Design and manufacturing of a noble piezoresistive pressure sensor(PS) for subtle pressures(<1 kPa) were presented. Meanwhile, in the studies conducted in the field of pressure sensors, the measurement of subtl...The Design and manufacturing of a noble piezoresistive pressure sensor(PS) for subtle pressures(<1 kPa) were presented. Meanwhile, in the studies conducted in the field of pressure sensors, the measurement of subtle pressures has received less attention. The limitations in the inherent gauge factor in silicon, have led to the development of polymer and composite resistive sensitive elements. However,in the development of resistance sensing elements, the structure of composite elements with reinforcement core has not been used. The proposed PS had a composite sandwich structure consisting of a nanocomposite graphene layer covered by layers of PDMS at the bottom and on the top coupled with a polyimide(PI) core. Various tests were performed to analyze the PS. The primary design target was improved sensitivity, with a finite-element method(FEM) utilized to simulate the stress profile over piezoresistive elements and membrane deflection at various pressures. The PS manufacturing process is based on Laser-engraved graphene(LEG) technology and PDMS casting. Experimental data indicated that the manufactured PS exhibits a sensitivity of 67.28 mV/kPa for a pressure range of 30-300 Pa in ambient temperature.展开更多
The double-sided lapping process is extensively employed in the manufacturing of wafers,optical windows,and seal rings due to its high efficiency and ability to achieve precise flatness.However,limited research has ex...The double-sided lapping process is extensively employed in the manufacturing of wafers,optical windows,and seal rings due to its high efficiency and ability to achieve precise flatness.However,limited research has explored the thickness uniformity among different workpieces after double-sided lapping,and the underlying mechanism remains unclear.To address the demand for higher precision,this paper first analyzed the relative kinematic model between the workpiece and the lapping plate to clarify the causes of thickness variations among workpieces after double-sided lapping.Subsequently,a finite element method(FEM)model was developed to account for the pressure distribution on the workpiece surfaces at the initial stage of the process.The results indicate that the number of workpieces influences the final thickness variation.Then,various sets of thin copper plates with different thicknesses were lapped,and the findings revealed that five copper plates processed simultaneously exhibited more uniform thickness compared to the three plates.The experimental results align well with the theoretical analysis.Ultimately,a thickness variation of less than 6μm was achieved on five copper plates measuringΦ100×2.9 mm.This study presents a comprehensive analysis of the mechanisms influencing thickness uniformity in the double-sided lapping process and provides practical guidelines for optimizing the process to achieve stringent precision standards in industrial applications.展开更多
The fixed-setting face-milled curvilinear cylindrical gear features teeth that are arc-shaped along the longitudinal direction.Some researchers hypothesize that this arc-tooth may enhance the lubrication conditions of...The fixed-setting face-milled curvilinear cylindrical gear features teeth that are arc-shaped along the longitudinal direction.Some researchers hypothesize that this arc-tooth may enhance the lubrication conditions of the gear.This study focuses on this type of gear,employing both finite element analysis(FEA)and analytical methods to determine the input parameters required for elastohydrodynamic lubrication(EHL)analysis.The effects of assembly errors,tooth surface modifications,load,and face-milling cutter radius on the lubrication performance of these gears are systematically investigated.The finite element model(FEM)of the gear pair is utilized to calculate the coordinates of contact points on the tooth surface and the corresponding contact pressures at the tooth surface nodes throughout a meshing cycle.Subsequently,the normal load on specific gear teeth is determined using a gradient-based approach.Entrainment speed,slip-to-roll ratio,and effective radius near the contact points on the tooth surface are derived through analytical methods.The data obtained from FEA serve as input parameters for EHL simulations.The lubrication performance of the curvilinear cylindrical gear is evaluated through example studies.The findings indicate that using FEA to provide input parameters for EHL simulations can reveal the occurrence of edge contact phenomena during gear meshing,allowing for a more accurate representation of the gear’s lubrication conditions.The lubrication performance of the curvilinear cylindrical gear is shown to be independent of the face-milling cutter radius but is significantly influenced by the size of the contact pattern on the tooth surface.Curvilinear gears with larger contact patterns demonstrate superior lubrication performance.展开更多
Owing to their excellent biocompatibility and potential for durability enhancement,polymeric heart valves(PHVs)are emerging as a promising alternative to traditional prostheses.Unlike conventional materials,PHVs can b...Owing to their excellent biocompatibility and potential for durability enhancement,polymeric heart valves(PHVs)are emerging as a promising alternative to traditional prostheses.Unlike conventional materials,PHVs can be manufactured under precise design criteria,enabling targeted performance improvements.This study introduces a geometric optimization strategy for enhancing the durability of PHVs.The finite element method(FEM)is combined with a dip-molding technique to develop a novel polymeric aortic valve with improved mechanical properties.The tri-leaflet geometry is parameterized using B-spline curves,and the maximum stress in the valve is reduced from 2.4802 to 1.7773 MPa using a multiobjective optimization algorithm NSGA-II(non-dominated sorting genetic algorithm II).Pre-optimized and optimized valve prototypes were fabricated via dip-molding and evaluated during pulsatile-flow tests and accelerated wear tests.The optimized design meets the ISO 5840 standards,with an effective orifice area of 2.019 cm^(2),a regurgitant fraction of 5.693%,and a transvalvular pressure gradient of 7.576 mmHg.Moreover,the optimized valve maintained its structural integrity and functionality over 14 million cycles of the accelerated wear test,whereas the unoptimized valve failed after two million cycles.These findings confirm that the FEM-based geometric optimization method enhances both the mechanical performance and durability of PHVs.展开更多
The hydro-mechanical responses of vegetated deposited slopes are complex and far from clear.On one hand,the soils in deposited slopes are typically poorly consolidated and widely graded,making them vulnerable to inter...The hydro-mechanical responses of vegetated deposited slopes are complex and far from clear.On one hand,the soils in deposited slopes are typically poorly consolidated and widely graded,making them vulnerable to internal erosion during rainfall infiltration.On the other hand,vegetation plays a significant role in influencing the hydro-mechanical properties of the soil at the slope surface.This paper presents a coupled seepage-erosion model to investigate the rainfall-induced internal erosion process within vegetated deposited slopes and its impact on slope stability.The detailed seepage-erosion coupling processes were simulated for a series of 1D rooted soil columns with varying root distributions,as well as 2D vegetated layered slopes under both light and heavy rainfall conditions.The numerical results reveal that roots can significantly mitigate rainfall-induced internal erosion,even with shallow root lengths.However,their protective effect on the slope increases as the root density in the superficial soil layer increases.Transpiration can rapidly restore matric suction in the shallow soil during rain intervals,slowing the rainfall-induced seepage-erosion process and thereby increasing slope stability.However,in the absence of transpiration,roots may either accelerate or inhibit the seepage-erosion process,depending on the specific rainfall conditions.展开更多
基金This work is supported by NSFC(Grant Nos.11771035,11771162,11571128,61473126,91430216,91530204,11372354 and U1530401),a grant from the RGC of HK 11300517,China(Project No.CityU 11302915),China Postdoctoral Science Foundation under grant No.2016M602273,a grant DRA2015518 from 333 High-level Personal Training Project of Jiangsu Province,and the USA National Science Foundation grant DMS-1315259the USA Air Force Office of Scientific Research grant FA9550-15-1-0001.Jiwei Zhang also thanks the hospitality of Hong Kong City University during the period of his visiting.
文摘This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of L1-Galerkin finite element methods.The analysis of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack of a fundamental Gronwall type inequality.In this paper,we establish such a fundamental inequality for the L1 approximation to the Caputo fractional derivative.In terms of the Gronwall type inequality,we provide optimal error estimates of several fully discrete linearized Galerkin finite element methods for nonlinear problems.The theoretical results are illustrated by applying our proposed methods to the time fractional nonlinear Huxley equation and time fractional Fisher equation.
文摘法医损伤分析在法医学领域具有重要意义,但损伤形成过程的复杂性和个体差异使损伤分析对专业性要求极高。有限元方法(finite element method, FEM)以其广泛的适用性、可控的精确度和高效的计算能力,结合可视化,在法庭科学领域展现出巨大的应用潜力。本文通过文献分析,介绍FEM的基本原理,探讨其在交通事故、枪击、工具致伤、高坠损伤分析中的应用情况,通过分析各应用场景与碰撞部位的模拟参数、模拟结果及研究侧重,评估FEM在法医损伤分析上的可行性、局限性,为法医损伤分析提供参考和技术途径。
基金supported in part by a grant from National Science Foundation(Project No.11301262)a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.CityU 102613)The work of J.Wang and W.Sun was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.CityU 102613).
文摘The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media.We prove that the optimal L 2 error estimates hold without any time-step(convergence)conditions,while all previous works require certain time-step restrictions.Theoretical analysis is based on a splitting of the error into two parts:the error from the time discretization of the PDEs and the error from the finite element discretization of the corresponding time-discrete PDEs,which was proposed in our previous work[26,27].Numerical results for both two and three-dimensional flow models are presented to confirm our theoretical analysis.
文摘The Design and manufacturing of a noble piezoresistive pressure sensor(PS) for subtle pressures(<1 kPa) were presented. Meanwhile, in the studies conducted in the field of pressure sensors, the measurement of subtle pressures has received less attention. The limitations in the inherent gauge factor in silicon, have led to the development of polymer and composite resistive sensitive elements. However,in the development of resistance sensing elements, the structure of composite elements with reinforcement core has not been used. The proposed PS had a composite sandwich structure consisting of a nanocomposite graphene layer covered by layers of PDMS at the bottom and on the top coupled with a polyimide(PI) core. Various tests were performed to analyze the PS. The primary design target was improved sensitivity, with a finite-element method(FEM) utilized to simulate the stress profile over piezoresistive elements and membrane deflection at various pressures. The PS manufacturing process is based on Laser-engraved graphene(LEG) technology and PDMS casting. Experimental data indicated that the manufactured PS exhibits a sensitivity of 67.28 mV/kPa for a pressure range of 30-300 Pa in ambient temperature.
基金Supported by the Liaoning Provincial Natural Science Foundation(Grant No.2023-MSBA-008)Unveiling and Commanding Program of Liaoning Province(Grant No.2022JH1/10800080)the Fundamental Research Funds for the Central Universities(Grant No.DUT24MS008).
文摘The double-sided lapping process is extensively employed in the manufacturing of wafers,optical windows,and seal rings due to its high efficiency and ability to achieve precise flatness.However,limited research has explored the thickness uniformity among different workpieces after double-sided lapping,and the underlying mechanism remains unclear.To address the demand for higher precision,this paper first analyzed the relative kinematic model between the workpiece and the lapping plate to clarify the causes of thickness variations among workpieces after double-sided lapping.Subsequently,a finite element method(FEM)model was developed to account for the pressure distribution on the workpiece surfaces at the initial stage of the process.The results indicate that the number of workpieces influences the final thickness variation.Then,various sets of thin copper plates with different thicknesses were lapped,and the findings revealed that five copper plates processed simultaneously exhibited more uniform thickness compared to the three plates.The experimental results align well with the theoretical analysis.Ultimately,a thickness variation of less than 6μm was achieved on five copper plates measuringΦ100×2.9 mm.This study presents a comprehensive analysis of the mechanisms influencing thickness uniformity in the double-sided lapping process and provides practical guidelines for optimizing the process to achieve stringent precision standards in industrial applications.
基金funded by the Sichuan Science and Technology Program(Project Nos.2024NSFSC0140,2023NSFSC0414,2022NSFSC0454)Panzhihua City Provincial Targeted Financial Resources Transfer Payment(Grant No.222Y2F-GG-04)+4 种基金Open Project of the Key Laboratory of Process Equipment and Control in Sichuan Province(ProjectNo.GK202211)Cultivation Research Project of PanzhihuaUniversity(ProjectNo.2023PY11)Open Project of Sichuan Provincial Engineering Technology Research Center for Advanced Manufacturing of Titanium Alloys(Project No.TM-2023-Z-02)Open Project of Panzhihua Key Laboratory of Advanced Manufacturing Technology(Project No.2022XJZD05).
文摘The fixed-setting face-milled curvilinear cylindrical gear features teeth that are arc-shaped along the longitudinal direction.Some researchers hypothesize that this arc-tooth may enhance the lubrication conditions of the gear.This study focuses on this type of gear,employing both finite element analysis(FEA)and analytical methods to determine the input parameters required for elastohydrodynamic lubrication(EHL)analysis.The effects of assembly errors,tooth surface modifications,load,and face-milling cutter radius on the lubrication performance of these gears are systematically investigated.The finite element model(FEM)of the gear pair is utilized to calculate the coordinates of contact points on the tooth surface and the corresponding contact pressures at the tooth surface nodes throughout a meshing cycle.Subsequently,the normal load on specific gear teeth is determined using a gradient-based approach.Entrainment speed,slip-to-roll ratio,and effective radius near the contact points on the tooth surface are derived through analytical methods.The data obtained from FEA serve as input parameters for EHL simulations.The lubrication performance of the curvilinear cylindrical gear is evaluated through example studies.The findings indicate that using FEA to provide input parameters for EHL simulations can reveal the occurrence of edge contact phenomena during gear meshing,allowing for a more accurate representation of the gear’s lubrication conditions.The lubrication performance of the curvilinear cylindrical gear is shown to be independent of the face-milling cutter radius but is significantly influenced by the size of the contact pattern on the tooth surface.Curvilinear gears with larger contact patterns demonstrate superior lubrication performance.
基金funded by the National Natural Science Foundation of China(No.82400370)the Interdisciplinary Innovation Team Incubation Project of Children’s Hospital of Fudan University(No.EKYX202416).
文摘Owing to their excellent biocompatibility and potential for durability enhancement,polymeric heart valves(PHVs)are emerging as a promising alternative to traditional prostheses.Unlike conventional materials,PHVs can be manufactured under precise design criteria,enabling targeted performance improvements.This study introduces a geometric optimization strategy for enhancing the durability of PHVs.The finite element method(FEM)is combined with a dip-molding technique to develop a novel polymeric aortic valve with improved mechanical properties.The tri-leaflet geometry is parameterized using B-spline curves,and the maximum stress in the valve is reduced from 2.4802 to 1.7773 MPa using a multiobjective optimization algorithm NSGA-II(non-dominated sorting genetic algorithm II).Pre-optimized and optimized valve prototypes were fabricated via dip-molding and evaluated during pulsatile-flow tests and accelerated wear tests.The optimized design meets the ISO 5840 standards,with an effective orifice area of 2.019 cm^(2),a regurgitant fraction of 5.693%,and a transvalvular pressure gradient of 7.576 mmHg.Moreover,the optimized valve maintained its structural integrity and functionality over 14 million cycles of the accelerated wear test,whereas the unoptimized valve failed after two million cycles.These findings confirm that the FEM-based geometric optimization method enhances both the mechanical performance and durability of PHVs.
基金supported by National Natural Science Foundation of China(Grant No.42372330)Science and Technology Research Program of Institute of Mountain Hazards and Environment,Chinese Academy of Sciences(Grant No.IMHE-CXTD-01-IMHE-ZYTS-12)Sichuan Science and Technology Program(Grant No.2024NSFSC0102).
文摘The hydro-mechanical responses of vegetated deposited slopes are complex and far from clear.On one hand,the soils in deposited slopes are typically poorly consolidated and widely graded,making them vulnerable to internal erosion during rainfall infiltration.On the other hand,vegetation plays a significant role in influencing the hydro-mechanical properties of the soil at the slope surface.This paper presents a coupled seepage-erosion model to investigate the rainfall-induced internal erosion process within vegetated deposited slopes and its impact on slope stability.The detailed seepage-erosion coupling processes were simulated for a series of 1D rooted soil columns with varying root distributions,as well as 2D vegetated layered slopes under both light and heavy rainfall conditions.The numerical results reveal that roots can significantly mitigate rainfall-induced internal erosion,even with shallow root lengths.However,their protective effect on the slope increases as the root density in the superficial soil layer increases.Transpiration can rapidly restore matric suction in the shallow soil during rain intervals,slowing the rainfall-induced seepage-erosion process and thereby increasing slope stability.However,in the absence of transpiration,roots may either accelerate or inhibit the seepage-erosion process,depending on the specific rainfall conditions.
