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1.
Ruzeng Zhu 《中国科学A辑(英文版)》1999,42(5):546-551
The differential variational principles of second kind for non-holonomic mechanics are given, from which a number of integral
variational principles of second kind are set up. From the latter, the general relation of δq′-δq and the general form of integral variational principles of the first kind and intermediate kinds are derived. Thus not only
all previous relations of δq′-δq and integral variational principles are unified but also the existance of the variational principles of intermediate kinds
are pointed out.
Project supported by the National Natural Science Foundation of China (Grant No. 19272064). 相似文献
2.
详细介绍了如何应用凑合反推法(semi-inverse method)构造弹性理论中的两类独立变量的广义变分原理(包括熟知的Hellinger-Reissner变分原理,Hu-Washizu变分原理)及三类独立变量的广义变分原理(钱伟长广义变分原理) 。应用凑合反推法还可以清楚地看出各变量之间的约束关系,从而再一次证明了Hu-Washizu变分原理实际上是两类独立变量的广义变分原理。 相似文献
3.
According to the basic idea of classical yin-yang complementarity and modern dualcomplementarity, in a simple and unified
way some basic principles for linear coupled dynamic thermopiezoelectricity can be established systematically. An important
integral relation in terms of convolutions is given, which can be considered as the generalized principle of virtual work
in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem
in linear coupled dynamic thermopiezoelectricity, but also to derive systematically the complementary functionals for eleven-field,
nine-field, six-field and three-field simplified Gurtin-type variational principles. Furthermore, with this approach, the
intrinsic relationship among various principles can be explained clearly.
Project supported by the National Natural Science Foundation of China (Grant No. 19672074) and Research Grand Council of Hong
Kong, No.RGC97/98, HKUST 6055/97E. 相似文献
4.
5.
From Maxwell’ s equations for electromagnetic fields, time-averaged energy flow density vector of stable monochromatic linearly
polarized light in an isotropic insulative nonmagnetic medium is deduced. By the introduction of time-averaged energy flow
density rays and the definition of new generalized refractive indexn
G1, Fermat’s principle of geometric optics is further generalized and its application conditions are discussed. The generalized
Fermat' s principle can be used to describe stable transmission of light in a medium with variable refractive index. The necessary
and sufficient conditions of a nondivergent and nonfocusing light beam are derived from this Fermat’s principle.
Project supported by the National Natural Science Foundation of China (Grant No. 69789801) and Guangdong Provincial Natural
Science Foundation of China. 相似文献
6.
7.
大变形非线性弹性力学的广义变分原理 总被引:3,自引:3,他引:0
本文导出了大变形非线性弹性力学的两个具有σij,eij,和ui三类独立变量的广义变分原理,证明了当应力应变关系为约束条件时这两个广义变分原理是等价的.文中对某些特例也作了阐明. 相似文献
8.
Chong-hui HUANG & Zhao-yong HUANG Department of Mathematics Nanjing University Nanjing China College of Mathematics Physics Nanhua University Hengyang China 《中国科学A辑(英文版)》2007,50(5):675-682
In this paper, we first introduce the notion of generalized k-syzygy modules, and then give an equivalent characterization that the class of generalized k-syzygy modules coincides with that ofω-k-torsionfree modules. We further study the extension closure of the category consisting of generalized k-syzygy modules. Some known results are obtained as corollaries. 相似文献
9.
A generalized variational principle and theoretical model for magnetoelastic interaction of ferromagnetic bodies 总被引:10,自引:0,他引:10
The quantitative analysis shows that no theoretical model for 3-d magnetoelastic bodies, in literatures to date, can commonly
simulate two kinds of distinct experimental phenomena on magnetoelastic interaction of ferromagnetic structures. This makes
it difficult to effectively discribe the magnetoelastic mechanical behavior of structures with complex geometry, such as shells.
Therefore, it is a key step for simulating magnetoelastic mechanical characteristics of structures with complex geometry to
establish a 3-d model which also can commonly characterize the two distinct experimental phenomena. A theoretical model for
three dimension magnetizable elastic bodies, which is commonly suitable for the two kinds of experimental phenomena on magnetoelastic
interaction of ferromagnetic plates, is presented by the variational principle for the total energy functional of the coupling
system of the 3-d ferromagnetic bodies. It is found that for the case of linear isotropic magnetic materials, the magnetic
forces obtained by this model include not only the body magnetic force which is the same as that got from the magnetic dipole
model, but also a distribution of the magnetic traction on the surface of the magnetizable body. And the value of the traction
is equal to the jumping one of the Faraday electromagnetic stress on the two sides of the surface, which does not appear in
any model, such as magnetic dipole model and axiomatic model.
Project supported by the National Natural Science Foundation of China( Grant No. 19572031), the National Science Fundation
for Outstanding Young Scientiests in China, and a united foundation of the State Education Committee of China and National
Natural Science Foundation Committee. 相似文献
10.
基于薄板非线性弯曲的Kirchhoff-Kármán假设.本文提出了在任意中面边界条件下任意开孔薄板非线性分析的三类边值问题并建立了相应的广义变分原理.能够看到在本文中提出的数学模型完全是一种新的不同于Karman理论的模型.这些数学模型能够应用于任意中面边界条件下开孔薄板的非线性分析和稳定性分析. 相似文献
11.
关于变分学中逆问题的研究 总被引:19,自引:1,他引:18
本文研究了变分学中的逆问题.通过变积概念的引入,给出了系统地研究变分学中逆问题的一种新途径.将这种方法应用于线弹性动力学和粘性流体力学中,建立了各自的变分原理和广义变分原理. 相似文献
12.
In this paper, the concept of a vector semi-monotone operator is introduced. This concept is applied to establish several
existence results of vector variational inequalities. These extend some results of others.
The work is supported by the Natural Science Foundation of China (Grant No. 19671042) and the Doctoral Program Foundation
of the Ministry of Education of China. 相似文献
13.
TheT(1) theorem with a weak condition on the distribution kernel is proved by using a new method—blocking analysis. It improves
a result of Meyer’s.
Project supported by the National Natural Science Foundation of China (Grant No. 19631080) and the Foundation of Advanced
Research Center, Zhongshan University. 相似文献
14.
提出了有限位移理论线弹性力学二类混合变量和三类混合变量的变分原理.考虑已知边界条件的变化并应用有限位移理论的功的互等定理,在导出上述两类变分原理的过程中起到了关键作用和桥梁作用.首先,考虑已知位移边界条件的变化和应用功的互等定理,导出了二类混合变量的最小势能原理.用类似的方法,导出了二类混合变量的驻值余能原理.应用应变能密度和应力余能密度的关系式于上述两个变分原理,得到三类混合变量的变分原理.然后,给出了二类和三类混合变量的虚功原理和虚余功原理.同时,应用拉氏乘子法导出了广义变分原理.以一个算例说明了在某些情况下拉氏乘子法会失效,介绍了构成广义变分原理泛函的半逆法.最后,应用二类混合变量最小势能原理计算了一大挠度悬臂梁的弯曲. 相似文献
15.
In this paper, we are concerned with the elliptic system of
{ -△u+V(x)u=g(x,v), x∈R^N,
-△v+V(x)v=f(x,u), x∈R^N,
where V(x) is a continuous potential well, f, g are continuous and asymptotically linear as t→∞. The existence of a positive solution and ground state solution are established via variational methods. 相似文献
{ -△u+V(x)u=g(x,v), x∈R^N,
-△v+V(x)v=f(x,u), x∈R^N,
where V(x) is a continuous potential well, f, g are continuous and asymptotically linear as t→∞. The existence of a positive solution and ground state solution are established via variational methods. 相似文献
16.
Q. H. Ansari Z. Khan A. H. Siddiqi 《Journal of Optimization Theory and Applications》2005,127(2):263-283
In this paper, we introduce weighted variational inequalities over product of sets and system of weighted variational inequalities.
It is noted that the weighted variational inequality problem over product of sets and the problem of system of weighted variational
inequalities are equivalent. We give a relationship between system of weighted variational inequalities and systems of vector
variational inequalities. We define several kinds of weighted monotonicities and establish several existence results for the
solution of the above-mentioned problems under these weighted monotonicities. We introduce also the weighted generalized variational
inequalities over product of sets, that is, weighted variational inequalities for multivalued maps and systems of weighted
generalized variational inequalities. Extensions of weighted monotonicities for multivalued maps are also considered. The
existence of a solution of weighted generalized variational inequalities over product of sets is also studied. The existence
results for a solution of weighted generalized variational inequality problem give also the existence of solutions of systems
of generalized vector variational inequalities.
The first and third author express their thanks to the Department of Mathematical Sciences, King Fahd University of Petroleum
and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities. The authors are also grateful to the referees
for comments and suggestions improving the final draft of this paper. 相似文献
17.
In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized
equations in the form 0 ∈ G(x) + Q(x), where both G and Q are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related
problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming.
We establish general results on the existence of optimal solutions under appropriate assumptions of the Palais-Smale type
and then derive necessary conditions for optimality in the models under consideration by using advanced tools of variational
analysis and generalized differentiation.
Dedicated to Jiří V. Outrata on the occasion of his 60th birthday.
This research was partly supported by the National Science Foundation under grants DMS-0304989 and DMS-0603846 and by the
Australian Research Council under grant DP-0451168. 相似文献
18.
电动力学电磁场边值问题的广义变分原理 总被引:1,自引:0,他引:1
给出了线性各项异性电磁场边值问题的广义虚功原理表达式,运用钱伟长教授提出的方法建立了该问题的广义变分原理,可直接反映该问题的全部特征,即4个Maxwell方程、2个场强-位势方程、2个本构方程和8个边界条件.继而导出了一族有先决条件的广义变分原理.作为例证,导出了两个退化形式的广义变分原理,和已知的广义变分原理等价.此外还导出了两个修正的广义变分原理,可为该问题提供杂交有限元模型.建立的各广义变分原理可为电磁场边值问题的有限元应用提供更为完善的理论基础. 相似文献
19.
Gauss—Seidel type relaxation techniques are applied in the context of strictly convex pure networks with separable cost functions.
The algorithm is an extension of the Bertsekas—Tseng approach for solving the linear network problem and its dual as a pair
of monotropic programming problems. The method is extended to cover the class of generalized network problems. Alternative
internal tactics for the dual problem are examined. Computational experiments —aimed at the improved efficiency of the algorithm
— are presented.
This research was supported in part by National Science Foundation Grant No. DCR-8401098-A0l. 相似文献