We prove that there are only finitely many diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space.Moreover,if the symmetric space is of rank one,the result can ...We prove that there are only finitely many diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space.Moreover,if the symmetric space is of rank one,the result can be strengthened by dropping the condition curvature-adapted.展开更多
By constructing certain maps, this note completes the answer of the question： For which closed orientable 3-manifold N, is the set of mapping degrees D（M, N） finite for any closed orientable 3-manifold M？
Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let m(n)=A×(a)be the split extension of A by an automorphismαwhich is a cyclic permutation of the direct components twist...Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let m(n)=A×(a)be the split extension of A by an automorphismαwhich is a cyclic permutation of the direct components twisted by a rational integer m.Then Om(n)is an infinite soluble group.In this paper,the residual finiteness of Om(n)is investigated.展开更多
Let R be a commutative Noetherian ring, α an ideal of R, and M a non-zero finitely generated R-module. Let t be a non-negative integer. In this paper, it is shown that dim Supp Hi a（M） ≤ 1 for all i 〈 t if and on...Let R be a commutative Noetherian ring, α an ideal of R, and M a non-zero finitely generated R-module. Let t be a non-negative integer. In this paper, it is shown that dim Supp Hi a（M） ≤ 1 for all i 〈 t if and only if there exists an ideal b of R such that dimR/b ≤ 1 and Hia（M） ≌ Hi b（M） for all i 〈 t. Moreover, we prove that dimSuppHia（M） 〈≤dim M - i for all i.展开更多
Theπ2-diffeomorphism finiteness result of F.Fang-X.Rong and A.Petrunin-W.Tuschmann(independently)asserts that the diffeomorphic types of compact n-manifolds M with vanishing first and second homotopy groups can be bo...Theπ2-diffeomorphism finiteness result of F.Fang-X.Rong and A.Petrunin-W.Tuschmann(independently)asserts that the diffeomorphic types of compact n-manifolds M with vanishing first and second homotopy groups can be bounded above in terms of n,and upper bounds on the absolute value of sectional curvature and diameter of M.In this paper,we will generalize thisπ2-diffeomorphism finiteness by removing the condition thatπ1(M)-0 and asserting the diffeomorphism finiteness on the Riemannian universal cover of M.展开更多
A gradient structure was introduced into a metal laminated target plate,and the anti-penetration simulation of the gradient structure was compared with that of a uniform-layer-thickness target plate by finite element ...A gradient structure was introduced into a metal laminated target plate,and the anti-penetration simulation of the gradient structure was compared with that of a uniform-layer-thickness target plate by finite element simulation.The analysis was verified by an impact experiment.Results show that the high-level thickness and appropriate percentage of Ti alloy at the upper side of the gradient structure provide greater impact resistance against the bullet,which increases the warhead breakage and enhances the anti-penetration performance.In addition,during the impact process,the stress is transmitted and reflected in the form of waves in each layer of the target plate,and the interaction between the compression and tension waves causes non-synergistic deformation of the target plate and leads to delamination.The gradient target plate takes penetration resistance a step further through the higher energy absorption rate and more consumption of the bullet kinetic energy.This research provides a theoretical basis for the application of gradient structures in metallic laminated armor.展开更多
A multi-physics approach was used to quantify the effect of process parameters (laser power, scanning speed, hatch spacing, and scanning strategy) on the thermal history and corresponding microstructure evolution of T...A multi-physics approach was used to quantify the effect of process parameters (laser power, scanning speed, hatch spacing, and scanning strategy) on the thermal history and corresponding microstructure evolution of Ti-25Nb (at%) alloy during the dual-track selective laser melting (SLM) process. Simulation results reveal that during the dual-track SLM process, increasing laser power results in greater thermal accumulation, leading to a molten pool of larger volume and coarser grains. Reducing scanning speed enhances remelting and promotes cellular growth at the top of molten pool, whereas faster scanning speed leads to rougher melt tracks and finer grains. Notably, hatch spacing significantly influences the molten pool dimensions and microstructures, and smaller hatch spacing promotes remelting. Furthermore, the orientations of grains in the second track during zigzag scanning differ markedly from those in the first track. More importantly, compared with those after the first track, both the temperature gradient and cooling rate at the boundaries of remelting molten pool are reduced after the second track scanning, resulting in slower interface velocity and significant change in solidification microstructure. This research provides a theoretical foundation for controlling non-equilibrium microstructure and offering novel insights into the optimization of SLM process parameters of titanium alloys.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 studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit...This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.展开更多
Let M be a non-zero finitely generated module over a commutative Noetherian local ring （R, m）. In this paper we consider when the local cohomology modules are finitely generated. It is shown that if t≥ 0 is an inte...Let M be a non-zero finitely generated module over a commutative Noetherian local ring （R, m）. In this paper we consider when the local cohomology modules are finitely generated. It is shown that if t≥ 0 is an integer and p C Supp H^t_p （M）, then Hm^t＋dim R/p （M） is not p-cofinite. Then we obtain a partial answer to a question raised by Huneke. Namely, if R is a complete local ring, then H^n_m （M） is finitely generated if and only if 0 ≤ n ￠ W, where W ---- {t ＋ dimR/p丨p ∈ SuppH^t_p（M）／V（m）}. Also, we show that if J C I are 1-dimensional ideals of R, then H^t_I（M） is J-cominimax, and H^t_I（M） is finitely generated （resp., minimax） if and only if H}R, （Mp） is finitely generated for all p C Spec R （resp., p ∈ SpecR／MaxR）. Moreover, the concept of the J-cofiniteness dimension cJ（M） of M relative to I is introduced, and we explore an interrelation between c^I_m（M） and the filter depth of M in I. Finally, we show that if R is complete and dim M/IM ≠ 0, then c^I_m （R） ---- inf{depth Mp ＋ dim R/p 丨 P ∈ Supp M/IM／V（m）}.展开更多
The contact deformation and buckling of elastic rods against rigid surfaces represent a prevalent phenomenon in applications such as oil drilling,arterial stents,and energy harvesting.This has attracted widespread att...The contact deformation and buckling of elastic rods against rigid surfaces represent a prevalent phenomenon in applications such as oil drilling,arterial stents,and energy harvesting.This has attracted widespread attention from researchers.In this paper,the deformation and buckling behaviors of a circular arch subject to compression by a rigid plate are investigated with a planar elastic rod model that incorporates tension,shearing,and bending.In comparison with the existing models that solely consider the bending energy,the deflection curve,the internal force distribution,and the critical load of the present model show good agreement with the finite element results.Through the dimensional analysis and order-of-magnitude estimation,we examine the factors influencing the critical load.The study reveals that the semi-central angle of the arch has the most significant effect.The dimensionless geometric parameter describing arch slenderness becomes prominent when the semi-central angle is less than 30°,while Poisson's ratio and the cross-sectional shear correction factor exhibit negligible influence.Furthermore,the variation in the proportions of strain energy components during critical buckling is presented with respect to the semi-central angle and the geometric parameter,thereby delineating the applicable ranges of both the original model(OM)and the modified model(MM).展开更多
Slopes are likely to fail in areas with frequent rainfall and earthquakes.The deformation characteristics of unsaturated slopes subjected to post-rainfall earthquakes are investigated using centrifuge model tests and ...Slopes are likely to fail in areas with frequent rainfall and earthquakes.The deformation characteristics of unsaturated slopes subjected to post-rainfall earthquakes are investigated using centrifuge model tests and finite element analyses.Three tests of the slope deformation under earthquake and post-rainfall earthquakes are first studied using image analysis techniques.Then,based on an elastoplastic constitutive model,numerical simulations are carried out using the finite element method and compared with the centrifuge test results.Finally,a parametric study is performed to clarify the effects of antecedent rainfall on earthquake-induced slope deformation.The results show that slope deformation caused by post-rainfall earthquakes differs from that caused by earthquakes without antecedent rainfall.The seepage flow and soil strength of the slope are affected by previous rainfall conditions,such as intensity and duration,which directly influence the slope deformation caused by the subsequent earthquake.Soil displacement and strain become greater and the slip surface is more noticeable during the post-rainfall earthquake of higher intensity.In addition,the time interval between the rainfall and the earthquake has a considerable impact on the detailed characteristics of the slope deformation,and the significant deformation occurs at the time of lowest soil strength when seepage flow reaches the lower part of the slope.Moreover,the repeated intermittent rainfall greatly affects the subsequent earthquake-induced slope deformation,the main characteristics of which are closely related to the changes in saturation and strength of the slope.However,with the prolonged time gap between each round of rainfall,the earthquake-induced slope deformation becomes insignificant.展开更多
Most failures in component operation occur due to cyclic loads.Validation has been performed under quasistatic loads,but the fatigue life of components under dynamic loads should be predicted to prevent failures durin...Most failures in component operation occur due to cyclic loads.Validation has been performed under quasistatic loads,but the fatigue life of components under dynamic loads should be predicted to prevent failures during component service life.Fatigue is a damage accumulation process where loads degrade the material,depending on the characteristics and number of repetitions of the load.Studies on themechanical fatigue of 3D-printedOnyx are limited.In this paper,the strength of 3D-printed Onyx components under dynamic conditions(repetitive loads)is estimated.Fatigue life prediction is influenced bymanufacturing processes,material properties,and applied loads,which can cause scatter in the results due to the interplay of these factors.By utilizing synthetic parameters derived from mechanical properties,the accuracy of fatigue life predictions has been improved significantly,from 23.13%to 98.33%.Additive manufacturing is flexible,but this flexibility generates scatter in the mechanical properties of produced components.This work also proposes the use of synthetic data with a neural network to improve the fatigue life prediction of printedOnyx subjected to tension–tension loads.Experimental uniaxial loads were used to characterize themechanical behaviorofprinted specimens.The experimental datawereused to evaluate thenumerical predictionsobtainedthrough finite element analysis using commercial software and an artificial neural network.The results showed that the use of synthetic data helped improve fatigue life prediction.展开更多
In our study,we tackle a linear advection-diffusion equation that varies with time and is constrained to one dimension,under the framework of homogeneous Dirichlet boundary conditions.We employ two distinct approaches...In our study,we tackle a linear advection-diffusion equation that varies with time and is constrained to one dimension,under the framework of homogeneous Dirichlet boundary conditions.We employ two distinct approaches for solving this equation:an analytical solution through the method of separation of variables,and a numerical solution utilizing the finite difference method.The computational output includes three dimensional(3D)plots for solutions,focusing on pollutants such as Ammonia,Carbon monoxide,Carbon dioxide,and Sulphur dioxide.Concentrations,along with their respective diffusivities,are analyzed through 3D plots and actual calculations.To comprehend the diffusivity-concentration relationship for predicting pollutant movement in the air,the domain is divided into two halves.The study explores the behavior of pollutants with higher diffusivity entering regions with lower diffusivity,and vice versa,using 2D and 3D plots.This task is crucial for effective pollution control strategies,and safeguarding the environment and public health.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
Patient-specific finite element analysis(FEA)is a promising tool for noninvasive quantification of cardiac and vascular structural mechanics in vivo.However,inverse material property identification using FEA,which req...Patient-specific finite element analysis(FEA)is a promising tool for noninvasive quantification of cardiac and vascular structural mechanics in vivo.However,inverse material property identification using FEA,which requires iteratively solving nonlinear hyperelasticity problems,is computationally expensive which limits the ability to provide timely patient-specific insights to clinicians.In this study,we present an inverse material parameter identification strategy that integrates deep neural networks(DNNs)with FEA,namely inverse DNN-FEA.In this framework,a DNN encodes the spatial distribution of material parameters and effectively regularizes the inverse solution,which aims to reduce susceptibility to local optima that often arise in heterogeneous nonlinear hyperelastic problems.Consequently,inverse DNN-FEA enables identification of material parameters at the element level.For validation,we applied DNN-FEA to identify four spatially varying passive Holzapfel-Ogden material parameters of the left ventricular myocardium in synthetic benchmark cases with a clinically-derived geometry.To evaluate the benefit of DNN integration,a baseline FEA-only solver implemented in PyTorch was used for comparison.Results demonstrated that DNN-FEA achieved substantially lower average errors in parameter identification compared to FEA(case 1,DNN-FEA:0.37%~2.15%vs.FEA:2.64%~12.91%).The results also demonstrate that the same DNN architecture is capable of identifying a different spatial material property distribution(case 2,DNN-FEA:0.03%~0.60%vs.FEA:0.93%~16.25%).These findings suggest that DNN-FEA provides an accurate framework for inverse identification of heterogeneous myocardial material properties.This approach may facilitate future applications in patient-specific modeling based on in vivo clinical imaging and could be extended to other biomechanical simulation problems.展开更多
To ensure the safety of the integral hoisting of precast pier boxes for sea-crossing bridges,this study focused on the sidewall height of the pier box and the width of the hoisting sling as core variables,established ...To ensure the safety of the integral hoisting of precast pier boxes for sea-crossing bridges,this study focused on the sidewall height of the pier box and the width of the hoisting sling as core variables,established a finite element model using ABAQUS,and conducted a safety analysis of the hoisting process.The results showed that optimal structural safety and cost-effectiveness were achieved by first casting the concrete base plate of the pier box,then constructing the sidewalls to a height of 500 mm,and subsequently using REE-100T eye&eye round slings for hoisting.Additionally,the implementation of local reinforcement measures(symmetrical stiffeners and steel sleeves)at the circular holes in the bottomplate of the pier box significantly alleviated stress concentration at these holes,effectively avoiding the risk of cracking caused by excessive local stress during the hoisting process.On-site hoisting practices verified the effectiveness of this optimized scheme,and the relevant research findings can provide a reference for the safety control of hoisting operations for similar large-scale precast components.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
基金supported by National Natural Science Foundation of China(Grant Nos.11071018 and 11001016)the Specialized Research Fund for Doctoral Program of Higher Education(Grant No.20100003120003)the Program for Changjiang Scholars and Innovative Research Team in University
文摘We prove that there are only finitely many diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space.Moreover,if the symmetric space is of rank one,the result can be strengthened by dropping the condition curvature-adapted.
基金The third author is partially supported by National Natural Science Foundation of China （Grant No. 10631060） and Ph.D. grant of the Ministry of Education of China （Grant No. 5171042-055）
文摘By constructing certain maps, this note completes the answer of the question： For which closed orientable 3-manifold N, is the set of mapping degrees D（M, N） finite for any closed orientable 3-manifold M？
基金Supported by the National Natural Science Foundation of China(Grant No.11771129,11971155,12071117).
文摘Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let m(n)=A×(a)be the split extension of A by an automorphismαwhich is a cyclic permutation of the direct components twisted by a rational integer m.Then Om(n)is an infinite soluble group.In this paper,the residual finiteness of Om(n)is investigated.
文摘Let R be a commutative Noetherian ring, α an ideal of R, and M a non-zero finitely generated R-module. Let t be a non-negative integer. In this paper, it is shown that dim Supp Hi a（M） ≤ 1 for all i 〈 t if and only if there exists an ideal b of R such that dimR/b ≤ 1 and Hia（M） ≌ Hi b（M） for all i 〈 t. Moreover, we prove that dimSuppHia（M） 〈≤dim M - i for all i.
文摘Theπ2-diffeomorphism finiteness result of F.Fang-X.Rong and A.Petrunin-W.Tuschmann(independently)asserts that the diffeomorphic types of compact n-manifolds M with vanishing first and second homotopy groups can be bounded above in terms of n,and upper bounds on the absolute value of sectional curvature and diameter of M.In this paper,we will generalize thisπ2-diffeomorphism finiteness by removing the condition thatπ1(M)-0 and asserting the diffeomorphism finiteness on the Riemannian universal cover of M.
基金National Defense Basic Scientific Research Program of China(JCKY2020408B002,WDZC2022-12)Key Research and Development Program of Shanxi Province(202102050201011,202202050201014)Fundamental Research Program of Shanxi Province(20210302124178,20210302123061,202103021224183)。
文摘A gradient structure was introduced into a metal laminated target plate,and the anti-penetration simulation of the gradient structure was compared with that of a uniform-layer-thickness target plate by finite element simulation.The analysis was verified by an impact experiment.Results show that the high-level thickness and appropriate percentage of Ti alloy at the upper side of the gradient structure provide greater impact resistance against the bullet,which increases the warhead breakage and enhances the anti-penetration performance.In addition,during the impact process,the stress is transmitted and reflected in the form of waves in each layer of the target plate,and the interaction between the compression and tension waves causes non-synergistic deformation of the target plate and leads to delamination.The gradient target plate takes penetration resistance a step further through the higher energy absorption rate and more consumption of the bullet kinetic energy.This research provides a theoretical basis for the application of gradient structures in metallic laminated armor.
基金Guangdong Basic and Applied Basic Research Foundation (2024A1515011873)Shenzhen Basic Research Project (JCYJ20241202123504007)Shenzhen Science and Technology Innovation Commission (KJZD20240903101400001, KJZD20240903102006009)。
文摘A multi-physics approach was used to quantify the effect of process parameters (laser power, scanning speed, hatch spacing, and scanning strategy) on the thermal history and corresponding microstructure evolution of Ti-25Nb (at%) alloy during the dual-track selective laser melting (SLM) process. Simulation results reveal that during the dual-track SLM process, increasing laser power results in greater thermal accumulation, leading to a molten pool of larger volume and coarser grains. Reducing scanning speed enhances remelting and promotes cellular growth at the top of molten pool, whereas faster scanning speed leads to rougher melt tracks and finer grains. Notably, hatch spacing significantly influences the molten pool dimensions and microstructures, and smaller hatch spacing promotes remelting. Furthermore, the orientations of grains in the second track during zigzag scanning differ markedly from those in the first track. More importantly, compared with those after the first track, both the temperature gradient and cooling rate at the boundaries of remelting molten pool are reduced after the second track scanning, resulting in slower interface velocity and significant change in solidification microstructure. This research provides a theoretical foundation for controlling non-equilibrium microstructure and offering novel insights into the optimization of SLM process parameters of titanium alloys.
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 studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.
文摘Let M be a non-zero finitely generated module over a commutative Noetherian local ring （R, m）. In this paper we consider when the local cohomology modules are finitely generated. It is shown that if t≥ 0 is an integer and p C Supp H^t_p （M）, then Hm^t＋dim R/p （M） is not p-cofinite. Then we obtain a partial answer to a question raised by Huneke. Namely, if R is a complete local ring, then H^n_m （M） is finitely generated if and only if 0 ≤ n ￠ W, where W ---- {t ＋ dimR/p丨p ∈ SuppH^t_p（M）／V（m）}. Also, we show that if J C I are 1-dimensional ideals of R, then H^t_I（M） is J-cominimax, and H^t_I（M） is finitely generated （resp., minimax） if and only if H}R, （Mp） is finitely generated for all p C Spec R （resp., p ∈ SpecR／MaxR）. Moreover, the concept of the J-cofiniteness dimension cJ（M） of M relative to I is introduced, and we explore an interrelation between c^I_m（M） and the filter depth of M in I. Finally, we show that if R is complete and dim M/IM ≠ 0, then c^I_m （R） ---- inf{depth Mp ＋ dim R/p 丨 P ∈ Supp M/IM／V（m）}.
基金Project supported by the National Natural Science Foundation of China(Nos.124B2043,U2241267,12172155,and 12302278)the Science and Technology Leading Talent Project of Gansu Province of China(No.23ZDKA0009)the Natural Science Foundation of Gansu Province of China(Nos.24JRRA473 and 24JRRA489)。
文摘The contact deformation and buckling of elastic rods against rigid surfaces represent a prevalent phenomenon in applications such as oil drilling,arterial stents,and energy harvesting.This has attracted widespread attention from researchers.In this paper,the deformation and buckling behaviors of a circular arch subject to compression by a rigid plate are investigated with a planar elastic rod model that incorporates tension,shearing,and bending.In comparison with the existing models that solely consider the bending energy,the deflection curve,the internal force distribution,and the critical load of the present model show good agreement with the finite element results.Through the dimensional analysis and order-of-magnitude estimation,we examine the factors influencing the critical load.The study reveals that the semi-central angle of the arch has the most significant effect.The dimensionless geometric parameter describing arch slenderness becomes prominent when the semi-central angle is less than 30°,while Poisson's ratio and the cross-sectional shear correction factor exhibit negligible influence.Furthermore,the variation in the proportions of strain energy components during critical buckling is presented with respect to the semi-central angle and the geometric parameter,thereby delineating the applicable ranges of both the original model(OM)and the modified model(MM).
基金supported by the China Postdoctoral Science Foundation(CPSF)(Grant No.2024M762769)the Natural Science Basic Research Program of Shaanxi(Grant No.2024JC-YBQN-0333)the Postdoctoral Fellowship Program of CPSF(Grant No.GZC20232230).
文摘Slopes are likely to fail in areas with frequent rainfall and earthquakes.The deformation characteristics of unsaturated slopes subjected to post-rainfall earthquakes are investigated using centrifuge model tests and finite element analyses.Three tests of the slope deformation under earthquake and post-rainfall earthquakes are first studied using image analysis techniques.Then,based on an elastoplastic constitutive model,numerical simulations are carried out using the finite element method and compared with the centrifuge test results.Finally,a parametric study is performed to clarify the effects of antecedent rainfall on earthquake-induced slope deformation.The results show that slope deformation caused by post-rainfall earthquakes differs from that caused by earthquakes without antecedent rainfall.The seepage flow and soil strength of the slope are affected by previous rainfall conditions,such as intensity and duration,which directly influence the slope deformation caused by the subsequent earthquake.Soil displacement and strain become greater and the slip surface is more noticeable during the post-rainfall earthquake of higher intensity.In addition,the time interval between the rainfall and the earthquake has a considerable impact on the detailed characteristics of the slope deformation,and the significant deformation occurs at the time of lowest soil strength when seepage flow reaches the lower part of the slope.Moreover,the repeated intermittent rainfall greatly affects the subsequent earthquake-induced slope deformation,the main characteristics of which are closely related to the changes in saturation and strength of the slope.However,with the prolonged time gap between each round of rainfall,the earthquake-induced slope deformation becomes insignificant.
文摘Most failures in component operation occur due to cyclic loads.Validation has been performed under quasistatic loads,but the fatigue life of components under dynamic loads should be predicted to prevent failures during component service life.Fatigue is a damage accumulation process where loads degrade the material,depending on the characteristics and number of repetitions of the load.Studies on themechanical fatigue of 3D-printedOnyx are limited.In this paper,the strength of 3D-printed Onyx components under dynamic conditions(repetitive loads)is estimated.Fatigue life prediction is influenced bymanufacturing processes,material properties,and applied loads,which can cause scatter in the results due to the interplay of these factors.By utilizing synthetic parameters derived from mechanical properties,the accuracy of fatigue life predictions has been improved significantly,from 23.13%to 98.33%.Additive manufacturing is flexible,but this flexibility generates scatter in the mechanical properties of produced components.This work also proposes the use of synthetic data with a neural network to improve the fatigue life prediction of printedOnyx subjected to tension–tension loads.Experimental uniaxial loads were used to characterize themechanical behaviorofprinted specimens.The experimental datawereused to evaluate thenumerical predictionsobtainedthrough finite element analysis using commercial software and an artificial neural network.The results showed that the use of synthetic data helped improve fatigue life prediction.
文摘In our study,we tackle a linear advection-diffusion equation that varies with time and is constrained to one dimension,under the framework of homogeneous Dirichlet boundary conditions.We employ two distinct approaches for solving this equation:an analytical solution through the method of separation of variables,and a numerical solution utilizing the finite difference method.The computational output includes three dimensional(3D)plots for solutions,focusing on pollutants such as Ammonia,Carbon monoxide,Carbon dioxide,and Sulphur dioxide.Concentrations,along with their respective diffusivities,are analyzed through 3D plots and actual calculations.To comprehend the diffusivity-concentration relationship for predicting pollutant movement in the air,the domain is divided into two halves.The study explores the behavior of pollutants with higher diffusivity entering regions with lower diffusivity,and vice versa,using 2D and 3D plots.This task is crucial for effective pollution control strategies,and safeguarding the environment and public health.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金supported in part by the National Science Foundation under GrantsDMS 2436630 and 2436629.
文摘Patient-specific finite element analysis(FEA)is a promising tool for noninvasive quantification of cardiac and vascular structural mechanics in vivo.However,inverse material property identification using FEA,which requires iteratively solving nonlinear hyperelasticity problems,is computationally expensive which limits the ability to provide timely patient-specific insights to clinicians.In this study,we present an inverse material parameter identification strategy that integrates deep neural networks(DNNs)with FEA,namely inverse DNN-FEA.In this framework,a DNN encodes the spatial distribution of material parameters and effectively regularizes the inverse solution,which aims to reduce susceptibility to local optima that often arise in heterogeneous nonlinear hyperelastic problems.Consequently,inverse DNN-FEA enables identification of material parameters at the element level.For validation,we applied DNN-FEA to identify four spatially varying passive Holzapfel-Ogden material parameters of the left ventricular myocardium in synthetic benchmark cases with a clinically-derived geometry.To evaluate the benefit of DNN integration,a baseline FEA-only solver implemented in PyTorch was used for comparison.Results demonstrated that DNN-FEA achieved substantially lower average errors in parameter identification compared to FEA(case 1,DNN-FEA:0.37%~2.15%vs.FEA:2.64%~12.91%).The results also demonstrate that the same DNN architecture is capable of identifying a different spatial material property distribution(case 2,DNN-FEA:0.03%~0.60%vs.FEA:0.93%~16.25%).These findings suggest that DNN-FEA provides an accurate framework for inverse identification of heterogeneous myocardial material properties.This approach may facilitate future applications in patient-specific modeling based on in vivo clinical imaging and could be extended to other biomechanical simulation problems.
基金the Professor Scientific Research Start-up Fund of Hezhou University(2025JSQD04)the Special Project in Key Fields of the Guangdong Provincial Department of Education(No.2023ZDX3106).
文摘To ensure the safety of the integral hoisting of precast pier boxes for sea-crossing bridges,this study focused on the sidewall height of the pier box and the width of the hoisting sling as core variables,established a finite element model using ABAQUS,and conducted a safety analysis of the hoisting process.The results showed that optimal structural safety and cost-effectiveness were achieved by first casting the concrete base plate of the pier box,then constructing the sidewalls to a height of 500 mm,and subsequently using REE-100T eye&eye round slings for hoisting.Additionally,the implementation of local reinforcement measures(symmetrical stiffeners and steel sleeves)at the circular holes in the bottomplate of the pier box significantly alleviated stress concentration at these holes,effectively avoiding the risk of cracking caused by excessive local stress during the hoisting process.On-site hoisting practices verified the effectiveness of this optimized scheme,and the relevant research findings can provide a reference for the safety control of hoisting operations for similar large-scale precast components.
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.
