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
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
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
This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A...This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.展开更多
To solve the problem of abnormal abrasion of Cu-Based Friction Materials(CBFMs),Bionic Non-Smooth Surface(BNS)on friction surface of CBFMs was constructed based on bionic principles,and the optimal bionic prototype wa...To solve the problem of abnormal abrasion of Cu-Based Friction Materials(CBFMs),Bionic Non-Smooth Surface(BNS)on friction surface of CBFMs was constructed based on bionic principles,and the optimal bionic prototype was selected by Finite Element Method(FEM).In addition,the bionic parameters were optimized by Response Surface Method(RSM).Samples holding BNS were prepared by Laser Processing,tribological properties were tested by a Friction and Wear Tester and worn surface morphology was characterized by a Scanning Electron Microscope(SEM).The results showed that BNS on friction surface could regulate the stress distribution and alleviate the peak stress.Among all samples,the coupled texture of pit-hexagonal got the minimum peak stress.During braking,bionic texture could also collect wear debris or change the motion forms from sliding to rotation,which can reduce abnormal abrasion.The wear rate was reduced by 19.31%.The results in this paper can provide a new idea for enhancing the tribological properties of CBFMs,and can also lay the foundation for further research of bionic tribology.展开更多
This study develops a surrogate super-resolution(SR)framework that accelerates finite element method(FEM)-based computational fluid dynamics(CFD)using deep learning.High-resolution(HR)FEM-based CFDremains computationa...This study develops a surrogate super-resolution(SR)framework that accelerates finite element method(FEM)-based computational fluid dynamics(CFD)using deep learning.High-resolution(HR)FEM-based CFDremains computationally prohibitive for time-sensitive applications,including patient-specific aneurysm hemodynamics where rapid turnaround is valuable.The proposed pipeline learns to reconstruct HR velocity-magnitude fields fromlow-resolution(LR)FEM solutions generated under the same governing equations and boundary conditions.It consistsof three modules:(i)offline pre-training of a residual network on representative vascular geometries;(ii)lightweightfine-tuning to adapt the pretrained model to geometric variability,including patient-specific aneurysm morphologies;and(iii)an unstructured-to-structured sampling strategy with region-of-interest upsampling that concentrates resolution in flow-critical zones(e.g.,the aneurysm sac)rather than the full domain.This targeted reconstruction substantiallyreduces inference and post-processing cost while preserving key HR flow features.Experiments on cerebral aneurysmmodels show that HR velocity-magnitude fields can be recovered with accuracy comparable to direct HR simulationsat less than 1%of the direct HR simulation cost per analysis(LR simulation and SR inference),while adaptation to newgeometries requires only lightweight fine-tuning with limited target-specific HR data.While clinical endpoints andadditional variables(e.g.,pressure or wall-based metrics)are left for future work,the results indicate that the proposedsurrogate SR approach can streamline FEM-based CFD workflows toward near real-time hemodynamic analysis acrossmorphologically similar vascular models.展开更多
This study presents a method for improving flexible pavement subgrades using activated carbon and lime as stabilizers and coir fiber as reinforcement,improving subgrade performance using natural and recycled materials...This study presents a method for improving flexible pavement subgrades using activated carbon and lime as stabilizers and coir fiber as reinforcement,improving subgrade performance using natural and recycled materials.Two residual soil types,Soil 1 and Soil 2,were examined for enhanced mechanical properties using California bearing ratio,indirect shear,direct shear,and consolidation tests.Pavement design calculations were performed using the empirical method,and finite element modeling was employed to assess the impact of water levels on subgrade settlement and strain ratios.The findings revealed notable improvements in cohesion and tensile strength when lime,activated carbon,and coir fiber were used for stabilization,achieving increases of up to 128.9%and 167.71%for Soil 1,and 155%and 3045.86%for Soil 2,respectively.Moreover,these stabilized samples exhibited the lowest penetration rates,recording values of 0.2 for both soils after 20 loading cycles.Incorporating a stabilized subgrade reduced the required subbase thickness by up to 90.91%compared to the untreated condition.Finite element modeling indicated that the high-permeability Soil 1 sample experienced an average settlement of 70.12 mm under repeated loading,which is 2.46 times higher than the 28.54 mm observed in the low-permeability sample.Finally,strain ratio analysis confirmed that adding stabilizers effectively reduced the subgrade strain,bringing the strain ratio below one and thereby meeting the road subgrade standard.These findings highlight the innovative use of coir fiber,activated carbon,and lime as high-performance stabilizers for flexible pavement applications,offering a practical solution for infrastructure development.展开更多
The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimiz...The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimizing their design.However,conventional numerical methods can face challenges with the non-linearities inherent in hyperelasticity and the complex spatial variations in FGMs.This paper presents a novel hybrid numerical approach combining Physics-Informed Neural Networks(PINNs)with Finite Element Method(FEM)derived data for the robust analysis of thick-walled,axisymmetric,heterogeneous,hyperelastic pressure vessels with elliptical geometries.A PINN framework incorporating neo-Hookean constitutive relations is developed in MATLAB.To enhance training efficiency and accuracy,the PINN’s loss function is augmented with displacement data obtained from high-fidelity FEM simulations performed in ANSYS.The methodology is rigorously validated by comparing PINN-predicted displacement and von Mises stress fields against ANSYS benchmarks for various scenarios of FGMconfigurations(with material properties varying according to a power law)subjected to internal and external pressurization.The results demonstrate excellent agreement between the proposed hybrid PINN-FEMapproach and conventional FEMsolutions across all test cases,accurately capturing complex deformation patterns and stress concentrations.This study highlights the potential of data-augmented PINNs as an effective and accurate computational tool for tackling complex solid mechanics problems involving non-linearmaterials and significant heterogeneity,offering a promising avenue for future research in engineering design and analysis.展开更多
The dynamic evolution of fracture permeability presents a critical scientific challenge in rock masses.Understanding the mechanisms of rock mass permeability evolution is vital for engineering project design and opera...The dynamic evolution of fracture permeability presents a critical scientific challenge in rock masses.Understanding the mechanisms of rock mass permeability evolution is vital for engineering project design and operations.By integrating the discrete element method(DEM)with the finite element method(FEM),a numerical simulation framework for shear seepage in rough fractured shale has been developed to investigate the dynamic mechanisms of permeability evolution under varying confining pressures and during the shearing process.Numerical simulations were conducted on rough fractured samples under effective confining pressures ranging from 5 MPa to 20 MPa to monitor the aperture and permeability evolution of the fracture.The results of the numerical simulation are consistent with the experimental observations,indicating that both the shearing process and confining pressure significantly influence permeability.Moreover,the magnitude of the confining pressure is a crucial factor influencing the trend in permeability changes.Under a confining pressure of 5 MPa,fracture permeability initially increases significantly but decreases post-shearing.In contrast,a continuous decrease in fracture permeability is observed when the confining pressure exceeds 10 MPa.The results of the shear numerical simulation indicate that the confining pressure restricts fracture dilation during shearing,promotes the generation of rock debris,and decreases both the permeability and transmissivity of the fracture.The wear results obtained from numerical simulations are consistent with the experimental patterns and correlate with the joint roughness coefficient(JRC).This study proposed an effective numerical simulation method to reveal the evolution mechanism of fracture flow capacity,taking into account the wear of the fracture surface in shear simulations and the initial stress state of the rock in seepage simulations.This research explains the permeability evolution mechanism of fractured shale from a microscopic perspective,and the proposed numerical simulation method for shear seepage provides a powerful means to uncover the dynamic evolution mechanisms governing fracture permeability.展开更多
In this paper,we study a new numerical technique for a class of 2D nonlinear fractional diffusion-wave equations with the Caputo-type temporal derivative and Riesz-type spatial derivative.Galerkin finite element schem...In this paper,we study a new numerical technique for a class of 2D nonlinear fractional diffusion-wave equations with the Caputo-type temporal derivative and Riesz-type spatial derivative.Galerkin finite element scheme is used for the discretization in the spatial direction,and the temporal component is discretized by a new alternating direction implicit(ADI)method.Next,we strictly prove that the numerical method is stable and convergent.Finally,to confirm our theoretical analysis,some numerical examples in 2D space are presented.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
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.
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.
文摘This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.
基金Wuxi University Research Start-up Fund for Introduced Talents(Grant No:2024r031)Technology Development Contract(Contract Registration Number:2024320205000963)+1 种基金National Natural Science Foundation of China(Grant No.52275288)Ningbo Key Research and Development Plan(Grant No.2023Z022).
文摘To solve the problem of abnormal abrasion of Cu-Based Friction Materials(CBFMs),Bionic Non-Smooth Surface(BNS)on friction surface of CBFMs was constructed based on bionic principles,and the optimal bionic prototype was selected by Finite Element Method(FEM).In addition,the bionic parameters were optimized by Response Surface Method(RSM).Samples holding BNS were prepared by Laser Processing,tribological properties were tested by a Friction and Wear Tester and worn surface morphology was characterized by a Scanning Electron Microscope(SEM).The results showed that BNS on friction surface could regulate the stress distribution and alleviate the peak stress.Among all samples,the coupled texture of pit-hexagonal got the minimum peak stress.During braking,bionic texture could also collect wear debris or change the motion forms from sliding to rotation,which can reduce abnormal abrasion.The wear rate was reduced by 19.31%.The results in this paper can provide a new idea for enhancing the tribological properties of CBFMs,and can also lay the foundation for further research of bionic tribology.
文摘This study develops a surrogate super-resolution(SR)framework that accelerates finite element method(FEM)-based computational fluid dynamics(CFD)using deep learning.High-resolution(HR)FEM-based CFDremains computationally prohibitive for time-sensitive applications,including patient-specific aneurysm hemodynamics where rapid turnaround is valuable.The proposed pipeline learns to reconstruct HR velocity-magnitude fields fromlow-resolution(LR)FEM solutions generated under the same governing equations and boundary conditions.It consistsof three modules:(i)offline pre-training of a residual network on representative vascular geometries;(ii)lightweightfine-tuning to adapt the pretrained model to geometric variability,including patient-specific aneurysm morphologies;and(iii)an unstructured-to-structured sampling strategy with region-of-interest upsampling that concentrates resolution in flow-critical zones(e.g.,the aneurysm sac)rather than the full domain.This targeted reconstruction substantiallyreduces inference and post-processing cost while preserving key HR flow features.Experiments on cerebral aneurysmmodels show that HR velocity-magnitude fields can be recovered with accuracy comparable to direct HR simulationsat less than 1%of the direct HR simulation cost per analysis(LR simulation and SR inference),while adaptation to newgeometries requires only lightweight fine-tuning with limited target-specific HR data.While clinical endpoints andadditional variables(e.g.,pressure or wall-based metrics)are left for future work,the results indicate that the proposedsurrogate SR approach can streamline FEM-based CFD workflows toward near real-time hemodynamic analysis acrossmorphologically similar vascular models.
基金supported by the ARC Discovery Project grants(Grant Nos.DP210100437 and DP230100126)ARC Linkage Project(LP230201048).
文摘This study presents a method for improving flexible pavement subgrades using activated carbon and lime as stabilizers and coir fiber as reinforcement,improving subgrade performance using natural and recycled materials.Two residual soil types,Soil 1 and Soil 2,were examined for enhanced mechanical properties using California bearing ratio,indirect shear,direct shear,and consolidation tests.Pavement design calculations were performed using the empirical method,and finite element modeling was employed to assess the impact of water levels on subgrade settlement and strain ratios.The findings revealed notable improvements in cohesion and tensile strength when lime,activated carbon,and coir fiber were used for stabilization,achieving increases of up to 128.9%and 167.71%for Soil 1,and 155%and 3045.86%for Soil 2,respectively.Moreover,these stabilized samples exhibited the lowest penetration rates,recording values of 0.2 for both soils after 20 loading cycles.Incorporating a stabilized subgrade reduced the required subbase thickness by up to 90.91%compared to the untreated condition.Finite element modeling indicated that the high-permeability Soil 1 sample experienced an average settlement of 70.12 mm under repeated loading,which is 2.46 times higher than the 28.54 mm observed in the low-permeability sample.Finally,strain ratio analysis confirmed that adding stabilizers effectively reduced the subgrade strain,bringing the strain ratio below one and thereby meeting the road subgrade standard.These findings highlight the innovative use of coir fiber,activated carbon,and lime as high-performance stabilizers for flexible pavement applications,offering a practical solution for infrastructure development.
文摘The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimizing their design.However,conventional numerical methods can face challenges with the non-linearities inherent in hyperelasticity and the complex spatial variations in FGMs.This paper presents a novel hybrid numerical approach combining Physics-Informed Neural Networks(PINNs)with Finite Element Method(FEM)derived data for the robust analysis of thick-walled,axisymmetric,heterogeneous,hyperelastic pressure vessels with elliptical geometries.A PINN framework incorporating neo-Hookean constitutive relations is developed in MATLAB.To enhance training efficiency and accuracy,the PINN’s loss function is augmented with displacement data obtained from high-fidelity FEM simulations performed in ANSYS.The methodology is rigorously validated by comparing PINN-predicted displacement and von Mises stress fields against ANSYS benchmarks for various scenarios of FGMconfigurations(with material properties varying according to a power law)subjected to internal and external pressurization.The results demonstrate excellent agreement between the proposed hybrid PINN-FEMapproach and conventional FEMsolutions across all test cases,accurately capturing complex deformation patterns and stress concentrations.This study highlights the potential of data-augmented PINNs as an effective and accurate computational tool for tackling complex solid mechanics problems involving non-linearmaterials and significant heterogeneity,offering a promising avenue for future research in engineering design and analysis.
基金funded by the Joint Funds of the National Natural Science Foundation of China(Grant No.U23A20671)the Major Project of Inner Mongolia Science and Technology(Grant No.2021ZD0034)the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engi-neering(Grant No.Z021003).
文摘The dynamic evolution of fracture permeability presents a critical scientific challenge in rock masses.Understanding the mechanisms of rock mass permeability evolution is vital for engineering project design and operations.By integrating the discrete element method(DEM)with the finite element method(FEM),a numerical simulation framework for shear seepage in rough fractured shale has been developed to investigate the dynamic mechanisms of permeability evolution under varying confining pressures and during the shearing process.Numerical simulations were conducted on rough fractured samples under effective confining pressures ranging from 5 MPa to 20 MPa to monitor the aperture and permeability evolution of the fracture.The results of the numerical simulation are consistent with the experimental observations,indicating that both the shearing process and confining pressure significantly influence permeability.Moreover,the magnitude of the confining pressure is a crucial factor influencing the trend in permeability changes.Under a confining pressure of 5 MPa,fracture permeability initially increases significantly but decreases post-shearing.In contrast,a continuous decrease in fracture permeability is observed when the confining pressure exceeds 10 MPa.The results of the shear numerical simulation indicate that the confining pressure restricts fracture dilation during shearing,promotes the generation of rock debris,and decreases both the permeability and transmissivity of the fracture.The wear results obtained from numerical simulations are consistent with the experimental patterns and correlate with the joint roughness coefficient(JRC).This study proposed an effective numerical simulation method to reveal the evolution mechanism of fracture flow capacity,taking into account the wear of the fracture surface in shear simulations and the initial stress state of the rock in seepage simulations.This research explains the permeability evolution mechanism of fractured shale from a microscopic perspective,and the proposed numerical simulation method for shear seepage provides a powerful means to uncover the dynamic evolution mechanisms governing fracture permeability.
基金NSF of China[grant number:11371157]Natural Science Foundation of Anhui Higher Education Institutions of China[grant number:KJ2016A492]Natural Science Foundation of Bozhou College[grant number:BSKY201426,BSKY201535].
文摘In this paper,we study a new numerical technique for a class of 2D nonlinear fractional diffusion-wave equations with the Caputo-type temporal derivative and Riesz-type spatial derivative.Galerkin finite element scheme is used for the discretization in the spatial direction,and the temporal component is discretized by a new alternating direction implicit(ADI)method.Next,we strictly prove that the numerical method is stable and convergent.Finally,to confirm our theoretical analysis,some numerical examples in 2D space are presented.
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。
