期刊文献+
共找到2,073篇文章
< 1 2 104 >
每页显示 20 50 100
VECTORIAL EKELAND'S VARIATIONAL PRINCIPLE WITH A W-DISTANCE AND ITS EQUIVALENT THEOREMS 被引量:8
1
作者 丘京辉 李博 贺飞 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2221-2236,共16页
By using the properties of w-distances and Gerstewitz's functions, we first give a vectorial Takahashi's nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland's variatio... By using the properties of w-distances and Gerstewitz's functions, we first give a vectorial Takahashi's nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland's variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland's variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346(2008), 9-16] are weakened or even completely relieved. 展开更多
关键词 Takahashi's minimization theorem Ekeland's variational principle Caristi'sfixed point theorem Gerstewitz's function w-distance
下载PDF
An 8-Node Plane Hybrid Element for StructuralMechanics Problems Based on the Hellinger-Reissner Variational Principle
2
作者 Haonan Li WeiWang +1 位作者 Quan Shen Linquan Yao 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第2期1277-1299,共23页
The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurat... The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy. 展开更多
关键词 8-node plane hybrid element Hellinger-Reissner variational principle locking behaviors structural mechanics problems
下载PDF
A Version of Ekeland's Variational Principle in Countable Semi-Normed Spaces
3
作者 丘京辉 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2004年第1期1-6,共6页
In this paper, a now version of Ekeland's variational principle in countable semi-normed spaces is given.
关键词 ekeland's variational principle topological vector space countable seminormed space.
下载PDF
P-Distances, Q-Distances and a Generalized Ekeland's Variational Principle in Uniform Spaces 被引量:8
4
作者 Jing Hui QIU Fei HE 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第2期235-254,共20页
In this paper, we attempt to give a unified approach to the existing several versions of Ekeland's variational principle. In the framework of uniiorm spaces, we introduce p-distances and more generally, q-distances.... In this paper, we attempt to give a unified approach to the existing several versions of Ekeland's variational principle. In the framework of uniiorm spaces, we introduce p-distances and more generally, q-distances. Then we introduce a new type of completeness for uniform spaces, i.e., sequential completeness with respect to a q-distance (particularly, a p-distance), which is a very extensive concept of completeness. By using q-distances and the new type of completeness, we prove a generalized Takahashi's nonconvex minimization theorem, a generalized Ekeland's variational principle and a generalized Caristi's fixed point theorem. Moreover, we show that the above three theorems are equivalent to each other. From the generalized Ekeland's variational principle, we deduce a number of particular versions of Ekeland's principle, which include many known versions of the principle and their improvements. 展开更多
关键词 Ekeland's variational principle Takahashi's nonconvex minimization theorem Caristi'sfixed point theorem uniform space locally convex space p-distance q-distance
原文传递
A General Vectorial Ekeland's Variational Principle with a P-distance 被引量:4
5
作者 Jing Hui QIU Fei HE 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第9期1655-1678,共24页
In this paper, by using p-distances on uniform spaces, we establish a general vectorial Ekeland variational principle (in short EVP), where the objective function is defined on a uniform space and taking values in a... In this paper, by using p-distances on uniform spaces, we establish a general vectorial Ekeland variational principle (in short EVP), where the objective function is defined on a uniform space and taking values in a pre-ordered real linear space and the perturbation involves a p-distance and a monotone function of the objective function. Since p-distances are very extensive, such a form of the perturbation in deed contains many different forms of perturbations appeared in the previous versions of EVP. Besides, we only require the objective function has a very weak property, as a substitute for lower semi-continuity, and only require the domain space (which is a uniform space) has a very weak type of completeness, i.e., completeness with respect to a certain p-distance. Such very weak type of completeness even includes local completeness when the uniform space is a locally convex topological vector space. From the general vectorial EVP, we deduce a general vectorial Caristi's fixed point theorem and a general vectorial Takahashi's nonconvex minimization theorem. Moreover, we show that the above three theorems are equivalent to each other. We see that the above general vectorial EVP includes many particular versions of EVP, which extend and complement the related known results. 展开更多
关键词 Vectorial Ekeland’s variational principle vectorial Caristi’s fixed point theorem vectorial Takahashi’s minimization theorem p-distance Gerstewitz’s function
原文传递
On Ha's Version of Set-valued Ekeland's Variational Principle 被引量:4
6
作者 Jing Hui QIU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第4期717-726,共10页
By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational principle for a set-valued map. J. Optim. Theory Appl., 124, 187-206 (2005)] established a ne... By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational principle for a set-valued map. J. Optim. Theory Appl., 124, 187-206 (2005)] established a new version of Ekeland's variational principle for set-valued maps, which is expressed by the existence of strict approximate minimizer for a set-valued optimization problem. In this paper, we give an improvement of Ha's version of set-valued Ekeland's variational principle. Our proof is direct and it need not use Dancs-Hegedus-Medvegyev theorem. From the improved Ha's version, we deduce a Caristi-Kirk's fixed point theorem and a Takahashi's nonconvex minimization theorem for set-valued maps. Moreover, we prove that the above three theorems are equivalent to each other. 展开更多
关键词 Ekeland's variational principle set-valued map locally convex space Caristi-Kirk's fixedpoint theorem Takahashi's nonconvex minimization theorem
原文传递
Sequentially Lower Complete Spaces and Ekeland's Variational Principle 被引量:3
7
作者 Fei HE Jing-Hui QIU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第8期1289-1302,共14页
By using sequentially lower complete spaces(see [Zhu, J., Wei, L., Zhu, C. C.: Caristi type coincidence point theorem in topological spaces. J. Applied Math., 2013, ID 902692(2013)]), we give a new version of vec... By using sequentially lower complete spaces(see [Zhu, J., Wei, L., Zhu, C. C.: Caristi type coincidence point theorem in topological spaces. J. Applied Math., 2013, ID 902692(2013)]), we give a new version of vectorial Ekeland's variational principle. In the new version, the objective function is defined on a sequentially lower complete space and taking values in a quasi-ordered locally convex space, and the perturbation consists of a weakly countably compact set and a non-negative function p which only needs to satisfy p(x, y) = 0 iff x = y. Here, the function p need not satisfy the subadditivity.From the new Ekeland's principle, we deduce a vectorial Caristi's fixed point theorem and a vectorial Takahashi's non-convex minimization theorem. Moreover, we show that the above three theorems are equivalent to each other. By considering some particular cases, we obtain a number of corollaries,which include some interesting versions of fixed point theorem. 展开更多
关键词 Vectorial Ekeland variational principle vectorial Caristi's fixed point theorem vectorial Takahashi's non-convex minimization th
原文传递
THE VARIATIONAL PRINCIPLE FOR THE PACKING ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS
8
作者 张瑞丰 朱姜慧 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1915-1924,共10页
Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the v... Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy. 展开更多
关键词 packing entropy variational principle nonautonomous dynamical systems
下载PDF
EKELAND'S VARIATIONAL PRINCIPLE AND CARISTI'S FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE 被引量:5
9
作者 张石生 陈玉清 郭进利 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1991年第3期217-228,共12页
The main purpose of this paper is to establish the Ekeland’s variational principle andCaristi’s fixed point theorem in probabilistic metric spaces and to give a direct simple proofof the equivalence between these tw... The main purpose of this paper is to establish the Ekeland’s variational principle andCaristi’s fixed point theorem in probabilistic metric spaces and to give a direct simple proofof the equivalence between these two theorems in the probabilistic metric space. The resultspresented in this paper generalize the corresponding results of [9--12]. 展开更多
关键词 MENGER EKELAND’S variational principle AND CARISTI’S FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE
原文传递
On Ekeland's Variational Principle for Set-Valued Mappings
10
作者 Sheng-jie Li Wen-yan Zhang 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2007年第1期141-148,共8页
In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in ... In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in this paper is a generalization of the corresponding result in [3]. 展开更多
关键词 Vector Ekeland variational principle nonlinear scalarization function metric space set-valued mapping
原文传递
LOCALLY EKELAND'S VARIATIONAL PRINCIPLE AND SOME SURJECTIVE MAPPING THEOREMS 被引量:1
11
作者 ZHONG CHENGKUI ZHAO PEIHAO 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1998年第3期273-280,共8页
This paper shows that if a Gateaux differentiable functional f has a finite lower bound(although it need not attain it),then,for everyε>0,there exists some point zεsuch that‖f′(zε)‖ε1+h(‖zε‖),where h:[0,... This paper shows that if a Gateaux differentiable functional f has a finite lower bound(although it need not attain it),then,for everyε>0,there exists some point zεsuch that‖f′(zε)‖ε1+h(‖zε‖),where h:[0,∞)→[0,∞)is a continuous function such that∫∞011+h(r)dr=∞.Applications are given to extremum problem and some surjective mappings. 展开更多
关键词 variational principle Extremum problem Weak P.S.condition Surjective mapping
全文增补中
EKELAND’S VARIATIONAL PRINCIPLE AND CARISTI’S COINCIDENCE THEOREM FOR SET-VALUED MAPPINGS IN PROBABILISTIC METRIC SPACES
12
作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1993年第7期607-614,共8页
By using the partial ordering method,a more general type,of Ekeland’s ariational principle and a set-valued Caristi’s coincidence theorem in probabilistic metric spaces are obtained.In addition,a direct simple proof... By using the partial ordering method,a more general type,of Ekeland’s ariational principle and a set-valued Caristi’s coincidence theorem in probabilistic metric spaces are obtained.In addition,a direct simple proof of the equivalence between these two theorems in probabilistic metric spaces is given. 展开更多
关键词 probabilistic metric space Caristi's coincidence theorem ekeland's variational principle partial ordering set.
下载PDF
GURTIN-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF A NON-LOCAL THERMAL EQUILIBRIUM SATURATED POROUS MEDIUM 被引量:22
13
作者 YangXiao 《Acta Mechanica Solida Sinica》 SCIE EI 2005年第1期37-45,共9页
Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical... Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously. 展开更多
关键词 non-local thermal equilibrium thermal-mechanical coupling mathematical model variational principle porous media theory
下载PDF
Highly accurate symplectic element based on two variational principles 被引量:15
14
作者 Guanghui Qing Jia Tian 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第1期151-161,共11页
For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process... For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process is simple and straightforward. In this paper, based on the seminal idea of the generalized mixed methods, a simple, stable, and highly accurate 8-node noncompatible symplectic element(NCSE8) was developed by the combination of the modified Hellinger-Reissner mixed variational principle and the minimum energy principle. To ensure the accuracy of in-plane stress results, a simultaneous equation approach was also suggested. Numerical experimentation shows that the accuracy of stress results of NCSE8 are nearly the same as that of displacement methods, and they are in good agreement with the exact solutions when the mesh is relatively fine. NCSE8 has advantages of the clearing concept, easy calculation by a finite element computer program, higher accuracy and wide applicability for various linear elasticity compressible and nearly incompressible material problems. It is possible that NCSE8 becomes even more advantageous for the fracture problems due to its better accuracy of stresses. 展开更多
关键词 Modified H-R mixed variational principle Partial-mixed element Noncompatible symplectic element Finite element method Nearly incompressible material
下载PDF
MODIFIED H-R MIXED VARIATIONAL PRINCIPLE FOR MAGNETOELECTROELASTIC BODIES AND STATE-VECTOR EQUATION 被引量:8
15
作者 卿光辉 邱家俊 刘艳红 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第6期722-728,共7页
Based upon the Hellinger-Reissner (H-R) mixed variational principle for three-dimensional elastic bodies, the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established. The state-vector e... Based upon the Hellinger-Reissner (H-R) mixed variational principle for three-dimensional elastic bodies, the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established. The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations. To lay a theoretical basis of the semi-analytical solution applied with the magnetoelectroelastic plates, the state-vector equation for the discrete element in plane was proposed through the use of the proposed principle. Finally, it is pointed out that the modified H-R mixed variational principle for pure elastic, single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem. 展开更多
关键词 magnetoelectroelastic body variational principle laminated plates state-vector equation semi-analytical solution
下载PDF
Discrete variational principle and first integrals for Lagrange-Maxwell mechanico-electrical systems 被引量:6
16
作者 傅景礼 戴桂冬 +1 位作者 萨尔瓦多·希梅尼斯 唐贻发 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第3期570-577,共8页
This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. T... This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results. 展开更多
关键词 DISCRETE variational principle first integral mechanico-electrical systems
下载PDF
GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA 被引量:10
17
作者 Yang Xiao Cheng Changjun Department o,f Mechanics, Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200436,China) 《Acta Mechanica Solida Sinica》 SCIE EI 2003年第1期24-32,共9页
Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal d... Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constituents of the solid and fluid phase. The finite element formulation based on this variational principle is also derived. As the functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in the time domain. In some situations, the differential-integral equations can be reduced to symmetrical differential equations and, as a numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results can provide further understanding of the wave propagation in porous media. 展开更多
关键词 saturated porous media Gurtin variational principle finite element method longitudinal wave
下载PDF
SEMI-INVERSE METHOD AND GENERALIZED VARIATIONAL PRINCIPLES WITH MULTI-VARIABLES IN ELASTICITY 被引量:2
18
作者 何吉欢 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第7期797-808,共12页
Semi-inverse method, which is an integration and an extension of Hu's try-and-error method, Chien's veighted residual method and Liu's systematic method, is proposed to establish generalized variational pr... Semi-inverse method, which is an integration and an extension of Hu's try-and-error method, Chien's veighted residual method and Liu's systematic method, is proposed to establish generalized variational principles with multi-variables without arty variational crisis phenomenon. The method is to construct an energy trial-functional with an unknown function F, which can be readily identified by making the trial-functional stationary and using known constraint equations. As a result generalized variational principles with two kinds of independent variables (such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle) and generalized variational principles with three kinds of independent variables (such as Chien's generalized variational principles) in elasticity have been deduced without using Lagrange multiplier method. By semi-inverse method, the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables, stress-strain relations are still its constraints. 展开更多
关键词 variational principle in elasticy Chien's generalized variational principles Hu-Washizu principle semi-inverse method trial-functional variational crisis
下载PDF
A VARIATIONAL PRINCIPLE OF PERTURBED MOTION ON VISCOELASTIC THIN PLATES WITH APPLICATIONS 被引量:4
19
作者 Zhang Nenghui Cheng Changjun 《Acta Mechanica Solida Sinica》 SCIE EI 1999年第2期121-128,共8页
In this paper, in the light of the Boltzmann superpositionprinciple in linear viscoelastic- ity, a mathematical model ofperturbed motion on viscoelastic thin place is established. Thecorre- sponding variational princi... In this paper, in the light of the Boltzmann superpositionprinciple in linear viscoelastic- ity, a mathematical model ofperturbed motion on viscoelastic thin place is established. Thecorre- sponding variational principle is obtained in a convolutionbilinear form. For application the problems of free vibration, forcedvibration and stability of a viscoelastic simply-supportedrectangular thin plate are considered. The results show thatnumerical solutions agree well with analytical solutions. 展开更多
关键词 viscoelastic thin plate perturbed motion variational principle
下载PDF
GENERALIZED VARIATIONAL PRINCIPLES OF THE VISCOELASTIC BODY WITH VOIDS AND THEIR APPLICATIONS 被引量:2
20
作者 盛东发 程昌钧 扶名福 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第4期381-389,共9页
From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given.... From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and the initial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids. 展开更多
关键词 viscoelastic solid with void variational integral method generalized variational principle generalized potential energy principle Timoshenko beam
下载PDF
上一页 1 2 104 下一页 到第
使用帮助 返回顶部