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Transient analysis of functionally graded curved shells using a nonuniform shape parameter integrated radial basis function approach
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作者 Vay Siu Lo Andrzej Katunin Thien Tich Truong 《Theoretical & Applied Mechanics Letters》 2025年第3期296-308,共13页
In this study,an improved integrated radial basis function with nonuniform shape parameter is introduced.The proposed shape parameter varies in each support domain and is defined byθ=1/d_(max),where d_(max)is the max... In this study,an improved integrated radial basis function with nonuniform shape parameter is introduced.The proposed shape parameter varies in each support domain and is defined byθ=1/d_(max),where d_(max)is the maximum distance of any pair of nodes in the support domain.The proposed method is verified and shows good performance.The results are stable and accurate with any number of nodes and an arbitrary nodal distribution.Notably,the support domain should be large enough to obtain accurate results.This method is then applied for transient analysis of curved shell structures made from functionally graded materials with complex geometries.Through several numerical examples,the accuracy of the proposed approach is demonstrated and discussed.Additionally,the influence of various factors on the dynamic behavior of the structures,including the power-law index,different materials,loading conditions,and geometrical parameters of the structures,was investigated. 展开更多
关键词 integrated radial basis function Shape parameter Functionally graded material Curved shell Transient analysis
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Research on the application of the parameter freezing precise exponential integrator in vehicle-road coupling vibration
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作者 Yu ZHANG Chao ZHANG +1 位作者 Shaohua LI Shaopu YANG 《Applied Mathematics and Mechanics(English Edition)》 2025年第2期373-390,共18页
The vehicle-road coupling dynamics problem is a prominent issue in transportation,drawing significant attention in recent years.These dynamic equations are characterized by high-dimensionality,coupling,and time-varyin... The vehicle-road coupling dynamics problem is a prominent issue in transportation,drawing significant attention in recent years.These dynamic equations are characterized by high-dimensionality,coupling,and time-varying dynamics,making the exact solutions challenging to obtain.As a result,numerical integration methods are typically employed.However,conventional methods often suffer from low computational efficiency.To address this,this paper explores the application of the parameter freezing precise exponential integrator to vehicle-road coupling models.The model accounts for road roughness irregularities,incorporating all terms unrelated to the linear part into the algorithm's inhomogeneous vector.The general construction process of the algorithm is detailed.The validity of numerical results is verified through approximate analytical solutions(AASs),and the advantages of this method over traditional numerical integration methods are demonstrated.Multiple parameter freezing precise exponential integrator schemes are constructed based on the Runge-Kutta framework,with the fourth-order four-stage scheme identified as the optimal one.The study indicates that this method can quickly and accurately capture the dynamic system's vibration response,offering a new,efficient approach for numerical studies of high-dimensional vehicle-road coupling systems. 展开更多
关键词 vehicle-road coupled dynamics dynamic response parameter freezing precise exponential integrator Newmark-βintegration
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Soft Actuator with Integrated and Localized Sensing Properties through Parameter-Encoded 4D Printing
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作者 Yang Li Xinyu Yang +3 位作者 Jianyang Li Qingping Liu Bingqian Li Kunyang Wang 《Journal of Bionic Engineering》 CSCD 2024年第5期2302-2312,共11页
4D printed smart materials is mostly relying on thermal stimulation to actuate,limiting their widely application requiring precise and localized control of the deformations.Most existing strategies for achieving local... 4D printed smart materials is mostly relying on thermal stimulation to actuate,limiting their widely application requiring precise and localized control of the deformations.Most existing strategies for achieving localized control rely on hetero-geneous material systems and structural design,thereby increasing design and manufacturing complexity.Here,we endow localized electrothermal,actuation,and sensing properties in electrically-driven soft actuator through parameter-encoded 4D printing.We analyzed the effects of printing parameters on shape memory properties and conductivity,and then explored the multi-directional sensing performance of the 4D printed composites.We demonstrated an integrated actuator-sensor device capable of both shape recovery and perceiving its own position and obstacles simultaneously.Moreover,it can adjust its sensing characteristics through temporary shape programming to adapt to different application scenarios.This study achieves integrated and localized actuation-sensing without the need for multi-material systems and intricate structural designs,offering an efficient solution for the intelligent and lightweight design in the fields of soft robotics,biomedical applications,and aerospace. 展开更多
关键词 Soft actuators 4D printing integrated sensing Localized sensing Printing parameters
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Improvement of titanium alloy TA19 fatigue life by submerged abrasive waterjet peening:Correlation of its process parameters with surface integrity and fatigue performance 被引量:1
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作者 Gongyu WANG Shulei YAO +6 位作者 Yuxin CHI Chengcheng ZHANG Ning WANG Yalong CHEN Rongsheng LU Zhuang LI Xiancheng ZHANG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2024年第1期377-390,共14页
Submerged abrasive waterjet peening(SAWJP)is an effective anti-fatigue manufacturing technology that is widely used to strengthen aeroengine components.This study investigated the correlation of SAWJP process paramete... Submerged abrasive waterjet peening(SAWJP)is an effective anti-fatigue manufacturing technology that is widely used to strengthen aeroengine components.This study investigated the correlation of SAWJP process parameters on surface integrity and fatigue life of titanium alloy TA19.SAWJP with different water pressures and standoff distances(SoDs)was conducted on the TA19 specimens.The surface integrity of the specimens before and after SAWJP with different process parameters was experimentally studied,including microstructure,surface roughness,microhardness,and compressive residual stress(CRS).Finally,fatigue tests of the specimens before and after SAWJP treatment with different process parameters were carried out at room temperature.The results highlighted that the fatigue life of the TA19 specimen can be increased by 5.46,5.98,and 6.28 times under relatively optimal process parameters,which is mainly due to the improved surface integrity of the specimen after SAWJP treatment.However,the fatigue life of specimens treated with improper process parameters is decreased by 0.55 to 0.69 times owing to the terrible surface roughness caused by the material erosion.This work verifies that SAWJP can effectively improve the surface integrity and fatigue life of workpieces,and reveals the relationship between process parameters,surface integrity,and fatigue life,which provides support for the promotion of SAWJP in the manufacturing fields. 展开更多
关键词 Fatigue testing Process parameters Submerged abrasive waterjet peening Surface integrity Surface treatment Titanium alloy TA19
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Integrated Optimization of Structure and Control Parameters for the Height Control System of a Vertical Spindle Cotton Picker 被引量:1
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作者 Xingzheng Chen Congbo Li +2 位作者 Rui Hu Ning Liu Chi Zhang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2021年第6期405-416,共12页
Vertical picking method is a predominate method used to harvest cotton crop.However,a vertical picking method may cause spindle bending of the cotton picker if spindles collide with stones on the cotton field.Thus,how... Vertical picking method is a predominate method used to harvest cotton crop.However,a vertical picking method may cause spindle bending of the cotton picker if spindles collide with stones on the cotton field.Thus,how to realize a precise height control of the cotton picker is a crucial issue to be solved.The objective of this study is to design a height control system to avoid the collision.To design it,the mathematical models are established first.Then a multi-objective optimization model represented by structure parameters and control parameters is proposed to take the pressure of chamber without piston,response time and displacement error of the height control system as the opti-mization objectives.An integrated optimization approach that combines optimization via simulation,particle swarm optimization and simulated annealing is proposed to solve the model.Simulation and experimental test results show that the proposed integrated optimization approach can not only reduce the pressure of chamber without piston,but also decrease the response time and displacement error of the height control system. 展开更多
关键词 Cotton picker Height control system Structure parameters Control parameters integrated optimization
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The integrated monitoring system for running parameters of key mining equipment based on condition monitoring technology 被引量:1
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作者 BIN Guang-fu LI Xue-jun +2 位作者 BALBIR S Dhillon HUANG Zhen-yu GUO Deng-ta 《Journal of Coal Science & Engineering(China)》 2010年第1期108-112,共5页
An integrated monitoring system for running parameters of key mining equipmenton the basis of condition monitoring technology and modern communication networktechnology was developed.The system consists of a client co... An integrated monitoring system for running parameters of key mining equipmenton the basis of condition monitoring technology and modern communication networktechnology was developed.The system consists of a client computer with functions ofsignal acquisition and processing, and a host computer in the central control room.Thesignal acquisition module of the client computer can collect the running parameters fromvarious monitoring terminals in real-time.The DSP high-speed data processing system ofthe main control module can quickly achieve the numerical calculation for the collectedsignal.The signal modulation and signal demodulation are completed by the frequencyshift keying circuit and phase-locked loop frequency circuit, respectively.Finally, the signalis sent to the host computer for logic estimation and diagnostic analysis using the networkcommunication technology, which is helpful for technicians and managers to control therunning state of equipment. 展开更多
关键词 mining key equipment running parameters condition monitoring signal acquisition and processing integrated monitoring
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METHOD OF PARAMETER STATISTICAL ANALYSIS FOR BIPOLAR INTEGRATED CIRCUIT DESIGN
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作者 郝跃 过润秋 《Journal of Electronics(China)》 1991年第4期373-377,共5页
The method and procedure of realizing parameter statistical correlation analysis ofbipolar analog IC’s are given,and the statistical model of parameter are constructed with doubleparameters(B_F,R_S).Based on the comp... The method and procedure of realizing parameter statistical correlation analysis ofbipolar analog IC’s are given,and the statistical model of parameter are constructed with doubleparameters(B_F,R_S).Based on the comparison and analysis of the circuit characteristics,it isshown that the method can be used for analysis and design of bipolar IC’s. 展开更多
关键词 ANALOG integrated CIRCUIT parameter STATISTICAL ANALYSIS Correlation ANALYSIS
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A genetic algorithm for dynamic parameters reverse deduction of integrated anchorage system
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作者 张永兴 《Journal of Chongqing University》 CAS 2006年第1期46-49,共4页
In the analysis of the system of anchoring bar and wall rock in small strain and longitudinal vibration dynamic response, the influence of the cement grouting as well as the rock layer on the anchor bar can be evaluat... In the analysis of the system of anchoring bar and wall rock in small strain and longitudinal vibration dynamic response, the influence of the cement grouting as well as the rock layer on the anchor bar can be evaluated as the two kinds of parameters: the dynamic stiffness and the damp, which are the vital reference of the anchorage quality. Based on the analytic solution to the dynamic equation of the integrated anchor bar, the new approach which combines genetic algorithm and the toolbox of Matlab is applied to solve the problem of multi-parameters reverse deduction for integrated anchorage system in dynamic testing. Using the traits of the self-organizing, self-adapting and the fast convergence speed of the genetic algorithm, the optimum of all possible solutions to dynamic parameters is obtained by calculating the project instances. Examples show that the method presented in this paper is effective and reliable. 展开更多
关键词 integrated anchorage dynamic parameters reverse deduction genetic algorithm
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Study of probability integration method parameter inversion by the genetic algorithm 被引量:7
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作者 Li Peixian Peng Di +1 位作者 Tan Zhixiang Deng Kazhong 《International Journal of Mining Science and Technology》 SCIE EI CSCD 2017年第6期1073-1079,共7页
In order to obtain accurate probability integration method(PIM) parameters for surface movement of multi-panel mining, a genetic algorithm(GA) was used to optimize the parameters. As the measured surface movement is a... In order to obtain accurate probability integration method(PIM) parameters for surface movement of multi-panel mining, a genetic algorithm(GA) was used to optimize the parameters. As the measured surface movement is affected by more than one mining panel, traditional PIM parameter inversion model is difficult to ensure the reliability of the results due to the complexity of rock movement. With crossover,mutation and selection operators, GA can perform a global optimization search and has high computation efficiency. Compared with the pattern search algorithm, the fitness function can avoid falling into local minima traps. GA reduces the risk of local minima traps which improves the accuracy and reliability with the mutation mechanism. Application at Xuehu colliery shows that GA can be used to inverse the PIM parameters for multi-panel surface movement observation, and reliable results can be obtained. The research provides a new way for back-analysis of PIM parameters for mining subsidence under complex conditions. 展开更多
关键词 PROBABILITY integration method GA MINING SUBSIDENCE parameter INVERSION MULTIOBJECTIVE optimization
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Dependence on forming parameters of an integral panel during the electromagnetic incremental forming process 被引量:5
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作者 Jinqiang TAN Mei ZHAN Hongwei LI 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2018年第7期1625-1634,共10页
Nowadays, more and more attentions are paid to electromagnetic incremental forming(EMIF), especially for a part with a large-scale size, e.g., an integral panel with stiffened ribs. In this work, the bending of a pa... Nowadays, more and more attentions are paid to electromagnetic incremental forming(EMIF), especially for a part with a large-scale size, e.g., an integral panel with stiffened ribs. In this work, the bending of a panel into a double-curvature profile via EMIF is carried out experimentally and evaluated by comparing the formed profile with the desired profile. During the process,discharges at four positions along different discharge paths are designed. The effects of forming parameters on the die-fittingness of the workpiece are discussed, for which two evaluation indices are used to judge forming results. The results show that a discharge voltage in an incremental mode is helpful to improve the fittingness and avoid the collision rebound against the die at the same time.Discharging at the diagonal positions with the ‘‘X" discharge path exhibits the minimal shape deviation and the best forming uniformity. On the contrary, discharging at the parallel positions with the ‘‘Z" discharge path obtains the worst forming quality. Overlap of the coil at different positions should be given during EMIF; however, a lower overlap rate of the coil helps improve the forming quality. The results obtained in this work are useful for forming integral panels with stiffened ribs via the EMIF process. 展开更多
关键词 Electromagnetic incrementalforming (EMIF) Forming uniformity integral panel parameters Shape deviation
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Cross-section distortion and springback characteristics of double-cavity aluminum profile in force controlled stretch-bending
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作者 Zhi-wen LIU Zi-xuan DONG +2 位作者 Cong-chang XU Jie YI Luo-xing LI 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2024年第8期2476-2490,共15页
3D elastic-plastic FE model for simulating the force controlled stretch-bending process of double-cavity aluminum profile was established using hybrid explicit−implicit solvent method.Considering the computational acc... 3D elastic-plastic FE model for simulating the force controlled stretch-bending process of double-cavity aluminum profile was established using hybrid explicit−implicit solvent method.Considering the computational accuracy and efficiency,the optimal choices of numerical parameters and algorithms in FE modelling were determined.The formation mechanisms of cross-section distortion and springback were revealed.The effects of pre-stretching,post-stretching,friction,and the addition of internal fillers on forming quality were investigated.The results show that the stress state of profile in stretch-bending is uniaxial with only a circumferential stress.The stress distribution along the length direction of profile is non-uniform and the maximum tensile stress is located at a certain distance away from the center of profile.As aluminum profile is gradually attached to bending die,the distribution characteristic of cross-section distortion along the length direction of profile changes from V-shape to W-shape.After unloading the forming tools,cross-section distortion decreases obviously due to the stress relaxation,with a maximum distortion difference of 13%before and after unloading.As pre-stretching and post-stretching forces increase,cross-section distortion increases gradually,while springback first decreases and then remains unchanged.With increasing friction between bending die and profile,cross-section distortion slightly decreases,while springback increases.Cross-section distortion decreases by 83%with adding PVC fillers into the cavities of profile,while springback increases by 192.2%. 展开更多
关键词 hollow aluminum profile force controlled stretch-bending numerical parameters springback analysis approach cross-section distortion SPRINGBACK process parameters
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A progressive approach to predict shot peening process parameters for forming integral panel of Al7050-T7451 被引量:5
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作者 Chuang LIU Zhiyong ZHAO +1 位作者 Xianjie ZHANG Junbiao WANG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2021年第5期617-627,共11页
In this paper,a progressive approach to predict the multiple shot peening process parameters for complex integral panel is proposed.Firstly,the invariable parameters in the forming process including shot size,mass flo... In this paper,a progressive approach to predict the multiple shot peening process parameters for complex integral panel is proposed.Firstly,the invariable parameters in the forming process including shot size,mass flow,peening distance and peening angle are determined according to the empirical and machine type.Then,the optimal value of air pressure for the whole shot peening is selected by the experimental data.Finally,the feeding speed for every shot peening path is predicted by regression equation.The integral panel part with thickness from 2 mm to 5 mm and curvature radius from 3200 mm to 16000 mm is taken as a research object,and four experiments are conducted.In order to design specimens for acquiring the forming data,one experiment is conducted to compare the curvature radius of the plate and stringer-structural specimens,which were peened along the middle of the two stringers.The most striking finding of this experiment is that the outer shape error range is below 3.9%,so the plate specimens can be used in predicting feeding speed of the integral panel.The second experiment is performed and results show that when the coverage reaches the limit of 80%,the minimum feeding speed is 50 mm/s.By this feeding speed,the forming curvature radius of the specimens with different thickness from the third experiment is measured and compared with the research object,and the optimal air pressure is 0.15 MPa.Then,the plate specimens with thickness from 2 mm to 5 mm are peened in the fourth experiment,and the measured curvature radius data are used to calculate the feeding speed of different shot peening path by regressive analysis method.The algorithm is validated by forming a test part and the average deviation is 0.496 mm.It is shown that the approach can realize the forming of the integral panel precisely. 展开更多
关键词 Curvature radius measure integral panel Process parameters prediction Regressive analysis method Shot peening process
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The method of variation on parameters for integration of a generalized Birkhoffian system 被引量:2
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作者 Yi Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第6期1059-1064,共6页
This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedur... This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedure for solving the problem can be divided into two steps:the first step,a system of auxiliary equations is constructed and its general solution is given;the second step,the parameters are varied,and the solution of the problem is obtained by using the properties of generalized canonical transformation.The method of variation on parameters for the generalized Birkhoffian system is of universal significance,and we take a nonholonomic system and a nonconservative system as examples to illustrate the application of the results of this paper. 展开更多
关键词 Birkhoffian system Method of integration Variation on parameter. Nonholonomic constraint. Nonconservative system
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Regularization and Choice of the Parameter for the Third Kind Nonlinear Volterra-Stieltjes Integral Equation Solutions 被引量:1
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作者 Nurgul Bedelova Avyt Asanov +1 位作者 Zhypar Orozmamatova Zhypargul Abdullaeva 《International Journal of Modern Nonlinear Theory and Application》 2021年第2期81-90,共10页
The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was c... The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind. 展开更多
关键词 REGULARIZATION SOLUTIONS Nonlinear Volterra-Stieltjes integral Equations Third Kind Choice of Regularization parameter
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RECURSIVE PARAMETER ESTIMATION OF LINEAR DELAYED SYSTEM VIA NUMERICAL INTEGRAL OPERATION
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作者 尹家洪 《Journal of Southeast University(English Edition)》 EI CAS 1993年第2期33-37,共5页
In this paper,the problem of Parameter estimation in linear delayedsystems from sampled data is treated.Using numerical integral operation(NIO),anidentification model which is parametrized directly in the linear delay... In this paper,the problem of Parameter estimation in linear delayedsystems from sampled data is treated.Using numerical integral operation(NIO),anidentification model which is parametrized directly in the linear delayed system pa-rameters is got.With the least square(LS)method or the instrumental variable(Ⅳ)method,the recursive algorithm of parameter estimation is given.The result ofthe illustrated example shows that this algorithm is simple,rapid and accurrate. 展开更多
关键词 parameter estimation LINEAR DELAYED systems NUMERICAL integrAL
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COORDINATION OF THE MOTION PARAMETERS WITHIN STEP-BY-STEP INTEGRATION FOR DYNAMIC EQUATION
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作者 HuangQingfeng WangQuanfeng HuYunchang 《Acta Mechanica Solida Sinica》 SCIE EI 2004年第1期27-31,共5页
A method is presented that coordinates the calculation of the displacement, velocity and acceleration of structures within the time-steps of different types of step-by-step integration. The dynamic equation is solved ... A method is presented that coordinates the calculation of the displacement, velocity and acceleration of structures within the time-steps of different types of step-by-step integration. The dynamic equation is solved using an energy equation and the calculating data of the original method. The method presented is better than the original method in terms of calculating postulations and is in better conformity with the system's movement. Take the Wilson-θ method as an example. By using the coordination process, the calculation precision has been greatly im proved (reducing the errors by approximately 90% ), and the greater part of overshooting of the calculation result has been eliminated. The study suggests that the mal-coordination of the motion parameters within the time-step is the major factor that contributes to the result errors of step-by-step integration for the dynamic equation. 展开更多
关键词 step-by-step integration motion parameters COORDINATION dynamic equation en- ergy equation
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Investigation on characteristic of J integral parameter in welded joints
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作者 霍立兴 张玉凤 康继东 《China Welding》 EI CAS 1997年第1期14-21,共8页
The J integral parameter and its application feasibility in welded joints with different weldmatchings in yield strength (overmatching weld and undermatching weld), different material constitutive laws (material with ... The J integral parameter and its application feasibility in welded joints with different weldmatchings in yield strength (overmatching weld and undermatching weld), different material constitutive laws (material with a Ludes yield plateau and power hardening) and under different fracture types (ligament yielding fracture and general yielding fracture) are investigated. First the condition of J integral path independent has been studied based upon finite element analysis by using ADINA procedure on welded joints. It was shown that the J integral is path dependent for the cases studied in this paper. Then experiments were carried out to study availability ofJ integral as a plastic singularity parameter at the tip of the notch in welded joints. The results show that J dominance in most cases studied is not validated in v and u displacement fields. From both considerations mentioned above it can be concluded that J-integral as controlling parameter used to estimate the safety of welded structures is not always made clear. 展开更多
关键词 integral parameter CHARACTERISTICS welded joint
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THE INTEGRAL AS A FUNCTlON OF THE UPPER LIMIT AND DEPENDING ON A PARAMETER TO SOLVE DRAWING THROUGH IDLING ROLLS
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作者 赵德文 赵志业 张强 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第1期93-100,共8页
The relocity and sirain-rate .field which are different from Avilzur's have beenestablished in Caitesian coordinates. Using the integral as a function of the upper limitand integration depending on a parameler, an... The relocity and sirain-rate .field which are different from Avilzur's have beenestablished in Caitesian coordinates. Using the integral as a function of the upper limitand integration depending on a parameler, an analylical upper-bound solution todrawing stress through idling rolls has been obtained in this paper. 展开更多
关键词 drawing through idling rolls integral as a function of theupper limit. integration depending on a parameter analyticalsolution
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The Optimal Matching Parameter of Half Discrete Hilbert Type Multiple Integral Inequalities with Non-Homogeneous Kernels and Applications
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作者 HONG Yong HE Bing 《Chinese Quarterly Journal of Mathematics》 2021年第3期252-262,共11页
By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent ... By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered. 展开更多
关键词 Non-homogeneous kernel Half discrete Hilbert type multiple integral in-equality Best constant factor Optimal matching parameter Operator norm Bounded operator
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Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions
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作者 YU De-jian 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第1期110-117,共8页
In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space whic... In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process. 展开更多
关键词 abstract kinetic equation with the first kind of critical parameter boundary value problem of abstract kinetic equation generalized periodic boundary conditions abstract linear integral operator of Volterra type integral operator solving process
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