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ON A FINITENESS THEOREM ABOUT PROBLEMS INVOLVING INEQUALITIES 被引量:8
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作者 WU Wen inn(WU Wen-tsun)(Institute of Systems Science, Academia Sinica, Beijing 100080, China) 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1994年第3期193-200,共8页
ONAFINITENESSTHEOREMABOUTPROBLEMSINVOLVINGINEQUALITIES¥WUWeninn(WUWen-tsun)(InstituteofSystemsScience,Academ... ONAFINITENESSTHEOREMABOUTPROBLEMSINVOLVINGINEQUALITIES¥WUWeninn(WUWen-tsun)(InstituteofSystemsScience,AcademiaSinica,Beijing1... 展开更多
关键词 finiteness THEOREM INEQUALITIES optimization ZERO DECOMPOSITION theorem.
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Finiteness results for equifocal hypersurfaces in compact symmetric spaces 被引量:3
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作者 GE JianQuan QIAN Chao 《Science China Mathematics》 SCIE 2014年第9期1975-1982,共8页
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
关键词 equifocal hypersurface isoparametric hypersurface focal point finiteness
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Finiteness of Mapping Degree Sets for 3-Manifolds 被引量:2
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作者 Pierre DERBEZ Hong Bin SUN Shi Cheng WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第5期807-812,共6页
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?
关键词 3-Manifolds mapping degrees finiteness
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On the Residual Finiteness of a Class of Infinite Soluble Groups 被引量:1
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作者 Jun Liao Heguo Liu +1 位作者 Xiaoliang Luo Xingzhong Xu 《Algebra Colloquium》 SCIE CSCD 2023年第1期155-164,共10页
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
关键词 residual finiteness infinite soluble group nilpotent group polycyclic group
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Prediction of microstructure evolution of ZK61 alloy during hot spinning by internal state variable model 被引量:2
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作者 Jin-qi PAN Wen-cong ZHANG +3 位作者 Jian-lei YANG Song-hui WANG Yong WU Huan LI 《Transactions of Nonferrous Metals Society of China》 2025年第1期126-142,共17页
An internal state variable(ISV)model was established according to the experimental results of hot plane strain compression(PSC)to predict the microstructure evolution during hot spinning of ZK61 alloy.The effects of t... An internal state variable(ISV)model was established according to the experimental results of hot plane strain compression(PSC)to predict the microstructure evolution during hot spinning of ZK61 alloy.The effects of the internal variables were considered in this ISV model,and the parameters were optimized by genetic algorithm.After validation,the ISV model was used to simulate the evolution of grain size(GS)and dynamic recrystallization(DRX)fraction during hot spinning via Abaqus and its subroutine Vumat.By comparing the simulated results with the experimental results,the application of the ISV model was proven to be reliable.Meanwhile,the strength of the thin-walled spun ZK61 tube increased from 303 to 334 MPa due to grain refinement by DRX and texture strengthening.Besides,some ultrafine grains(0.5μm)that played an important role in mechanical properties were formed due to the proliferation,movement,and entanglement of dislocations during the spinning process. 展开更多
关键词 internal state variable model hot spinning ZK61 alloy finite element simulation texture evolution
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On the Finiteness Dimension of Local Cohomology Modules 被引量:1
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作者 Hero Saremi Amir Marl 《Algebra Colloquium》 SCIE CSCD 2014年第3期517-520,共4页
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
关键词 local cohomology modules cofinite modules finiteness dimension
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A generalized π2-diffeomorphism finiteness theorem 被引量:1
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作者 Xiaochun RONG Xuchao YAO 《Frontiers of Mathematics in China》 SCIE CSCD 2020年第2期399-418,共20页
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
关键词 Collapsing with bounded sectional curvature diffeomorphism finiteness vanishing second homotopy group
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A deep transfer learning model for the deformation of braced excavations with limited monitoring data 被引量:1
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作者 Yuanqin Tao Shaoxiang Zeng +3 位作者 Tiantian Ying Honglei Sun Sunjuexu Pan Yuanqiang Cai 《Journal of Rock Mechanics and Geotechnical Engineering》 2025年第3期1555-1568,共14页
The current deep learning models for braced excavation cannot predict deformation from the beginning of excavation due to the need for a substantial corpus of sufficient historical data for training purposes.To addres... The current deep learning models for braced excavation cannot predict deformation from the beginning of excavation due to the need for a substantial corpus of sufficient historical data for training purposes.To address this issue,this study proposes a transfer learning model based on a sequence-to-sequence twodimensional(2D)convolutional long short-term memory neural network(S2SCL2D).The model can use the existing data from other adjacent similar excavations to achieve wall deflection prediction once a limited amount of monitoring data from the target excavation has been recorded.In the absence of adjacent excavation data,numerical simulation data from the target project can be employed instead.A weight update strategy is proposed to improve the prediction accuracy by integrating the stochastic gradient masking with an early stopping mechanism.To illustrate the proposed methodology,an excavation project in Hangzhou,China is adopted.The proposed deep transfer learning model,which uses either adjacent excavation data or numerical simulation data as the source domain,shows a significant improvement in performance when compared to the non-transfer learning model.Using the simulation data from the target project even leads to better prediction performance than using the actual monitoring data from other adjacent excavations.The results demonstrate that the proposed model can reasonably predict the deformation with limited data from the target project. 展开更多
关键词 Braced excavation Wall deflections Transfer learning Deep learning Finite element simulation
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Model tests and numerical analysis of emergency treatment of cohesionless soil landslide with quick-setting polyurethane 被引量:1
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作者 ZHANG Zhichao TANG Xuefeng +2 位作者 HUANG Rufa CAI Zhenjie GAO Anhua 《Journal of Mountain Science》 2025年第1期110-121,共12页
Shotcrete is one of the common solutions for shallow sliding.It works by forming a protective layer with high strength and cementing the loose soil particles on the slope surface to prevent shallow sliding.However,the... Shotcrete is one of the common solutions for shallow sliding.It works by forming a protective layer with high strength and cementing the loose soil particles on the slope surface to prevent shallow sliding.However,the solidification time of conventional cement paste is long when shotcrete is used to treat cohesionless soil landslide.The idea of reinforcing slope with polyurethane solidified soil(i.e.,mixture of polyurethane and sand)was proposed.Model tests and finite element analysis were carried out to study the effectiveness of the proposed new method on the emergency treatment of cohesionless soil landslide.Surcharge loading on the crest of the slope was applied step by step until landslide was triggered so as to test and compare the stability and bearing capacity of slope models with different conditions.The simulated slope displacements were relatively close to the measured results,and the simulated slope deformation characteristics were in good agreement with the observed phenomena,which verifies the accuracy of the numerical method.Under the condition of surcharge loading on the crest of the slope,the unreinforced slope slid when the surcharge loading exceeded 30 k Pa,which presented a failure mode of local instability and collapse at the shallow layer of slope top.The reinforced slope remained stable even when the surcharge loading reached 48 k Pa.The displacement of the reinforced slope was reduced by more than 95%.Overall,this study verifies the effectiveness of polyurethane in the emergency treatment of cohesionless soil landslide and should have broad application prospects in the field of geological disasters concerning the safety of people's live. 展开更多
关键词 Cohesionless soil landslide POLYURETHANE Emergency treatment Reinforcement effect Model test Finite element analysis
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Bi-directional interaction of joint shear strength in non-seismically designed corner RC beam-column connections under seismic loading 被引量:1
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作者 Mohammad Amir Najafgholipour Negin Ahmadi rad Akanshu Sharma 《Earthquake Engineering and Engineering Vibration》 2025年第1期135-153,共19页
Non-seismically designed(NSD)beam-column joints are susceptible to joint shear failure under seismic loads.Although significant research is available on the seismic behavior of such joints of planar frames,the informa... Non-seismically designed(NSD)beam-column joints are susceptible to joint shear failure under seismic loads.Although significant research is available on the seismic behavior of such joints of planar frames,the information on the seismic behavior of joints of space frames(3D joints)is insufficient.The 3D joints are subjected to bi-directional excitation,which results in an interaction between the shear strength obtained for the joint in the two orthogonal directions separately.The bi-directional seismic behavior of corner reinforced concrete(RC)joints is the focus of this study.First,a detailed finite element(FE)model using the FE software Abaqus,is developed and validated using the test results from the literature.The validated modeling procedure is used to conduct a parametric study to investigate the influence of different parameters such as concrete strength,dimensions of main and transverse beams framing into the joint,presence or absence of a slab,axial load ratio and loading direction on the seismic behavior of joints.By subjecting the models to different combinations of loads on the beams along perpendicular directions,the interaction of the joint shear strength in two orthogonal directions is studied.The comparison of the interaction curves of the joints obtained from the numerical study with a quadratic(circular)interaction curve indicates that in a majority of cases,the quadratic interaction model can represent the strength interaction diagrams of RC beam to column connections with governing joint shear failure reasonably well. 展开更多
关键词 beam-column joints joint shear failure bidirectional loading interaction curve finite element study
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Hydrodynamic Performance and Structural Response of a Sharp Eagle Wave Energy Converter Platform Under Extreme Sea States 被引量:1
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作者 YUE Wan-zhen WANG Kun-lin +4 位作者 JIANG Jia-qiang SHENG Song-wei LU Wen-zhao HE Teng YANG Xian-yuan 《China Ocean Engineering》 2025年第2期373-382,共10页
This paper presents a new type of triangular Sharp Eagle wave energy converter(WEC)platform.On the basis of the linear potential flow theory and the finite element analysis method,the hydrodynamic performance and stru... This paper presents a new type of triangular Sharp Eagle wave energy converter(WEC)platform.On the basis of the linear potential flow theory and the finite element analysis method,the hydrodynamic performance and structural response of the platform are studied,considering the actual platform motion and free surface rise under extreme sea states.First,the effects of the wave frequency and direction on the wave-induced loads and dynamic responses were examined.The motion at a wave direction angle of 0°is relatively low.On this basis,the angle constrained by the two sides of the Sharp Eagle floaters should be aligned with the main wave direction to avoid significant platform motion under extreme sea states.Additionally,the structural response of the platform,including the wave-absorbing floaters,is investigated.The results highlighted that the conditions or locations where yielding,buckling,and fatigue failures occur were different.In this context,the connection area of the Sharp Eagle floaters and platform is prone to yielding failure under oblique wave action,whereas the pontoon and side of the Sharp Eagle floaters are prone to buckling failure during significant vertical motion.Additionally,fatigue damage is most likely to occur at the connection between the middle column on both sides of the Sharp Eagle floaters and the pontoons.The findings of this paper revealed an intrinsic connection between wave-induced loads and the dynamic and structural responses of the platform,which provides a useful reference for the improved design of WECs. 展开更多
关键词 wave energy converter extreme sea states finite element analysis dynamic response structural response
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Influence study of main cable displacement-controlled device type of long-span suspension bridges on structural mechanical properties 被引量:1
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作者 YUAN Zhijie WANG Hao +2 位作者 MAO Jianxiao LI Rou ZONG Hai 《Journal of Southeast University(English Edition)》 2025年第1期27-36,共10页
Main cable displacement-controlled devices(DCDs)are key components for coordinating the vertical deformation of the main cable and main girder in the side span of continuous suspension bridges.To reveal the mechanical... Main cable displacement-controlled devices(DCDs)are key components for coordinating the vertical deformation of the main cable and main girder in the side span of continuous suspension bridges.To reveal the mechanical action mechanisms of DCD on bridge structures,a three-span continuous suspension bridge was taken as the engineering background in this study.The influence of different forms of DCD on the internal force and displacement of the components in the side span of the bridge and the structural dynamic characteristics were explored through numerical simulations.The results showed that the lack of DCD caused the main cable and main girder to have large vertical displacements.The stresses of other components were redistributed,and the safety factor of the suspenders at the side span was greatly reduced.The setting of DCD improved the vertical stiffness of the structure.The rigid DCD had larger internal forces,but its control effect on the internal forces at the side span was slightly better than that of the flexible DCD.Both forms of DCD effectively coordinated the deformation of the main cable and main girder and the stress distribution of components in the side span area.The choice of DCD form depends on the topographic factors of bridge sites and the design requirements of related components at the side span. 展开更多
关键词 long-span suspension bridge displacement-controlled device static and dynamic characteristics finite element live load
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Unveiling solid-solid contact states in all-solid-state lithium batteries:An electrochemical impedance spectroscopy viewpoint 被引量:1
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作者 Jin-Liang Li Liang Shen +9 位作者 Zi-Ning Cheng Jun-Dong Zhang Ling-Xuan Li Yu-Tong Zhang Yan-Bin Gao Chunli Guo Xiang Chen Chen-Zi Zhao Rui Zhang Qiang Zhang 《Journal of Energy Chemistry》 2025年第2期16-22,I0002,共8页
All-solid-state lithium batteries(ASSLBs)are strongly considered as the next-generation energy storage devices for their high energy density and intrinsic safety.The solid-solid contact between lithium metal and solid... All-solid-state lithium batteries(ASSLBs)are strongly considered as the next-generation energy storage devices for their high energy density and intrinsic safety.The solid-solid contact between lithium metal and solid electrolyte plays a vital role in the performance of working ASSLBs,which is challenging to investigate quantitatively by experimental approach.This work proposed a quantitative model based on the finite element method for electrochemical impedance spectroscopy simulation of different solid-solid contact states in ASSLBs.With the assistance of an equivalent circuit model and distribution of relaxation times,it is discovered that as the number of voids and the sharpness of cracks increase,the contact resistance Rcgrows and ultimately dominates the battery impedance.Through accurate fitting,inverse proportional relations between contact resistance Rcand(1-porosity)as well as crack angle was disclosed.This contribution affords a fresh insight into clarifying solid-solid contact states in ASSLBs. 展开更多
关键词 Electrochemical impedance spectroscopy All-solid-state lithium batteries Solid-solid contacts Finite element method Equivalent circuit model Distribution of relaxation times
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Fatigue Strength Analysis of Dissimilar Aluminum Alloy TIG Welds
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作者 LIAO Xiangyun WANG Ruijie +1 位作者 LIU Guoshou ZHAO Pinglin 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2025年第1期265-274,共10页
The constant amplitude loading fatigue tests were carried out on the 6061/7075 aluminum alloy TIG fillet welded lap specimens in this study,and the weld seam cross-section hardness was measured.The experimental result... The constant amplitude loading fatigue tests were carried out on the 6061/7075 aluminum alloy TIG fillet welded lap specimens in this study,and the weld seam cross-section hardness was measured.The experimental results show that most specimens mainly failed at the 7075 side weld toes even though the base material tensile strength of 7075 is higher than that of 6061.The maximum stress-strain concentration in the two finite element models is located at the 7075 side weld toe,which is basically consistent with the actual fracture location.The weld zone on the 7075 side experiences severe material softening,with a large gradient.However,the Vickers hardness value on the 6061 side negligibly changes and fluctuates around 70 HV.No obvious defects are found on the fatigue fracture,but a large number of secondary cracks appear.Cracks germinate from the weld toe and propagate in the direction of the plate thickness.Weld reinforcement has a serious impact on fatigue life.Fatigue life will decrease exponentially as the weld reinforcement increases under low stress.It is found that the notch stress method can give a better fatigue life prediction for TIG weldments,and the errors of the predicted results are within the range of two factors,while the prediction accuracy decreases under low stress.The equivalent structural stress method can also be used for fatigue life prediction of TIG weldments,but the errors of prediction results are within the range of three factors,and the accuracy decreases under high stress. 展开更多
关键词 TIG welding notch stress method equivalent structural stress method fatigue life finite element analysis
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Numerical Simulation of the Pitting Corrosion Behavior of Stainless Steel Bellows Influenced by Varying Liquid Film Thicknesses
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作者 Lu-Jun Ren Guo-Min Li +2 位作者 Zhen-Xiao Zhu Hai-Yan Xiong Bing Li 《电化学(中英文)》 北大核心 2025年第7期37-51,共15页
To advance the understanding of the corrosion behavior of stainless steel bellows in marine atmospheric environments and enhance the precision of service life predictions,this study employs finite element simulations ... To advance the understanding of the corrosion behavior of stainless steel bellows in marine atmospheric environments and enhance the precision of service life predictions,this study employs finite element simulations to investigate the pitting corrosion rates and pit morphologies of bellows peaks and troughs under varying electrolyte film thicknesses.The model incorporates localized electrochemical reactions,oxygen concentration,and homogeneous solution reactions.For improved computational accuracy,the fitted polarization curve data were directly applied as nonlinear boundary conditions on the electrode surface via interpolation functions.Simulation results reveal that the peak regions exhibit faster corrosion rates than the trough regions.With increasing electrolyte film thickness(from 10μm to 500μm),corrosion rates at both peaks and troughs decrease progressively,and after 120 hours of simulation,the maximum corrosion rate at the peaks declines from 0.720 mm/a to 0.130 mm/a,and at the troughs from 0.520 mm/a to 0.120 mm/a,with the disparity in corrosion rates diminishing over time.Furthermore,as corrosion progresses,pits propagate deeper into the substrate,exhibiting both vertical penetration and lateral expansion along the passive film interface,ultimately breaching the substrate.This research offers valuable insights into designing corrosion mitigation strategies for stainless steel bellows in marine environments. 展开更多
关键词 Finite element method Pitting corrosion Stainless steel bellows Electrolyte film thickness
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The well-posedness of incompressible impinging jet flow in an axisymmetric finitely long nozzle
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作者 WANG Xin ZHANG Fan 《四川大学学报(自然科学版)》 北大核心 2025年第1期31-37,共7页
This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practi... This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect. 展开更多
关键词 Existence and uniqueness Impinging jet flow Incompressible flow Free boundary Axisym-metric finitely long nozzle
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Simulation and Experimental Analysis of Mechanical Properties of a Bidirectional Adjustable Magnetorheological Fluid Damper
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作者 YANG Zhi−rong YE Zhong−min +2 位作者 LIU Jin−liang RAO Zhu−shi XIAO Wang−qiang 《船舶力学》 北大核心 2025年第6期1000-1012,共13页
The aim of this study is to address the issues associated with traditional magnetorheological fluid(MRF)dampers,such as insufficient damping force after power failure and susceptibility to settlement.In order to achie... The aim of this study is to address the issues associated with traditional magnetorheological fluid(MRF)dampers,such as insufficient damping force after power failure and susceptibility to settlement.In order to achieve this,a bidirectional adjustable MRF damper was designed and developed.Magnetic field simulation analysis was conducted on the damper,along with simulation analysis on its dynamic characteristics.The dynamic characteristics were ultimately validated through experimental testing on the material testing machine,thereby corroborating the theoretical simulation results.Concurrently,this process generated valuable test data for subsequent implementation of the semi-active vibration control system.The simulation and test results demonstrate that the integrated permanent magnet effectively accomplishes bidirectional regulation.The magnetic induction intensity of the damping channel is 0.2 T in the absence of current,increases to 0.5 T when a maximum forward current of 4 A is applied,and becomes 0 T when a maximum reverse current of 3.8 A is applied.When the excitation amplitude is 8 mm and the frequency is 2 Hz,with the applied currents varying,the maximum damping force reaches 8 kN,while the minimum damping force measures at 511 N.Additionally,at zero current,the damping force stands at 2 kN,which aligns closely with simulation results.The present paper can serve as a valuable reference for the design and research of semi-active MRF dampers. 展开更多
关键词 magnetorheological fluid(MRF) DAMPER permanent magnet finite element analysis test of mechanical properties
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Research on structural design and mechanical properties of precision electroplating machinery for automobiles based on finite element analysis
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作者 Wang Jie Jiang Xiaobei 《电镀与精饰》 北大核心 2025年第11期10-21,共12页
Design a precision electroplating mechanical structure for automobiles based on finite element analysis method and analyze its mechanical properties.Taking the automobile steering knuckle as the research object,ABAQUS... Design a precision electroplating mechanical structure for automobiles based on finite element analysis method and analyze its mechanical properties.Taking the automobile steering knuckle as the research object,ABAQUS parametric modeling technology is used to construct its three-dimensional geometric model,and geometric simplification is carried out.Two surface treatment processes,HK-35 zinc nickel alloy electroplating and pure zinc electroplating,were designed,and the influence of different coatings on the mechanical properties of steering knuckles was compared and analyzed through numerical simulation.At the same time,standard specimens were prepared for salt spray corrosion testing and scratch method combined strength testing to verify the numerical simulation results.The results showed that under emergency braking and composite working conditions,the peak Von Mises stress of the zinc nickel alloy coating was 119.85 MPa,which was lower than that of the pure zinc coating and the alkaline electroplated zinc layer.Its equivalent strain value was 652×10^(-6),which was lower than that of the pure zinc coating and the alkaline electroplated zinc layer.Experimental data confirms that zinc nickel alloy coatings exhibit significant advantages in stress distribution uniformity,strain performance,and load-bearing capacity in high stress zones.The salt spray corrosion test further indicates that the coating has superior corrosion resistance and coating substrate interface bonding strength,which can significantly improve the mechanical stability and long-term reliability of automotive precision electroplating mechanical structures. 展开更多
关键词 finite element analysis electroplating machinery structure mechanical properties electroplating process salt spray corrosion bonding strength
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Grothendieck Groups of Finite 2-Calabi-Yau Triangulated Categories with Maximal Rigid Objects
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作者 CHANG Huimin 《数学进展》 北大核心 2025年第3期479-488,共10页
In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided int... In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E. 展开更多
关键词 finite 2-Calabi-Yau triangulated category Grothendieck group Dynkin quiver
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A Fast Algorithm for Solving the Poisson Equations Based on the Discrete Cosine/Sine Transforms in the Finite Difference Method
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作者 LI Congcong WANG Danxia +1 位作者 JIA Hongen ZHANG Chenhui 《应用数学》 北大核心 2025年第3期651-669,共19页
To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c... To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%. 展开更多
关键词 Phase-field model Finite difference method Fast Poisson solver(DC-T/DST) Explicit invariant energy quadratization Unconditional energy stability
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