变分原理

词组短语

principle of variation · variation principle

与变分原理相关的网络例句 [注：此内容来源于网络，仅供参考]

According to that Caristi fixed point theorem is equivalent to Ekeland variational principle, we weaken the condition that the functional is bounded from below in Ekeland variational principle, then we enlarge the area of the applicable functionals.

鉴于Caristi不动点定理和Ekeland变分原理的等价性，我们对Ekeland变分原理中泛函的下方有界的要求作了相应的削弱，从而扩大了适用泛函的范围。

The main problems researched in the dissertation and achievements are as follows: The dissertation explains the science background and the theoretical and actual meaning of the task. The progress and the problems of the flow imaging technique are briefly explained. The advantages of electrical capacitance tomography are discussed. The paper discusses the formation and operating principle of ECT, and builds up the definite mathematical model by detail theoretical analyse, and establishes the Finite Element Model of the system by changing the finite boundary value problem of ECT into equivalence variation problem according to variation principle. On the basis of the FEM of the system, the paper builds the finite element model of the capacitance sensitivity field distribution and programs its finite element simulation software and proves the validity of the FEM of the ECT from different aspects. With the FEM and the qualitative analyse of the effect of each structural parameter of the capacitance transducer on its capability, this paper optimizes the structural parameters of the capacitance transducer, and obviously improves its capability. The compare of the simulated result with the static experimental result shows that the error of them is less than 0.9%.

其主要研究内容包括：阐述课题研究的学术背景及其理论与实际意义，概括总结出流动层析成像技术的发展现状和存在的问题，指出电容层析成像技术的优点；讨论电容层析成像系统的组成及工作原理，进行详尽的理论分析，以变分原理为基础，将ECT的有限元边值问题转换为等价的变分问题，从而建立系统的有限元模型；在系统有限元模型的基础上，建立敏感场的数学模型，编制有限元的仿真软件，并从不同角度证明电容层析成像系统有限元模型的正确性；利用有限元模型，定性地分析电容传感器各结构参数对其性能的影响，并对传感器结构参数进行优化设计，使其性能得到明显的改善。8电极ECT系统的仿真和静态实验结果的比较表明，它们之间的相对误差小于0。

Although classical Ekeland is equivalent to classical Caristi fixed point theorem, we can not make the same degree of generalization for them.

另外，我们指出即使古典的Caristi不动点定理和Ekeland变分原理是等价的，但是Ekeland变分原理不能和Caristi不动点定理作相同程度的推广。

Based on the analogy of structural mechanics and optimal contro1, and a1so based on carrying the minimum potential energy variational principle in elastici- ty to the generalized one, the theory of Hami1tonian system can be introduced into theory of e1asticity and e11iptic PDE. The transverse eigensolutions of the Hamiltonian operator matrix and its expansion solution method can be deduced.

利用结构力学与最优控制相模拟的理论，将弹性力学势能变分原理导向部分一般变分原理，并将哈密尔顿体系的理论引入到弹性力学与椭圆型偏微分方程之中，导出一套横向哈密尔顿算子矩阵的本征函数向量展开解法。

Rumjantsev used Hamilton's principle with Lagrange's multipliers to generate the dynamical equations of a rigid-fluid coupled system in 1954 and the dynamical equations and their dynamical boundary conditions of a fluid-elastic coupled system in 1969, where the fluid is incompressible and inviscid. In 1990, Liu used Jourdain's principle with Lagrange's multipliers to generate the dynamical equations of a rigidfluid coupled system, where the fluid is incompressible and viscid.

Rumjantsev利用带Lagrange乘子Hamilton变分原理于1954年建立了刚—流耦合系统的动力方程，于1969年建立了流—弹耦合系统的动力方程及其动力边界条件，其中所考虑的流体是不可压无粘液体；Liu利用带Lagrange乘子Jourdain变分原理于1990年建立了刚—流耦合系统的动力方程，其中所考虑的流体是不可压粘性液体。

According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

Using the generalized mixed variational principle of elastic mechanics, GMVP of Reissner plates is derived, and generalized mixed finite elements method of Reissner plates is established too.

用一般弹性体的广义混合变分原理，导出了适合 Reissner板弯曲问题的广义混合变分原理及其有限元广义混合法。

In this paper,discusses the application of the complementary variational method for the calculation of the electromagnetic parameters.

本文就互补变分原理在计算电磁参数中的应用进行研究，提出了恒定场中基于互补变分原理分析与计算电参数的方法。

In this paper,the application of the complementary variational method of the calculation of the electromagnetic parameters is investgated.

本文讨论了互补变分原理在电磁参数计算中的应用，提出了恒定场中基于互补变分原理的电参数的计算方法，最后给出了计算实例。

During the calculation of the early age temperature field, the early age physical and mechanical performance of concrete varies with its age, therefore in the second chapter we discuss the early age physical and mechanical performance of concrete and its development regulation with time, we emphasize elastic module and the development about the early age strength of concrete varying with time, at the same time consider the effect of shrink and creep upon the early age of concrete, in succession discuss how to confirm the physical parameter of thermodynamics of concrete.

之后讨论了混凝土的热物理参数的确定。为了能够正确合理的应用有限元方法求解早期混凝土温度场问题，第三章论述了求解温度场的有限元方法。第三章首先对热传导的微分方程作了阐述。之后确定温度场的边界条件。本章采用变分原理推导有限单元法计算温度场的公式。因此在第二小节叙述了变分原理，然后阐明了不稳定温度场的计算的三种方法，确定第四章分析中将采用向后差分法求解0#箱梁早期的温度场。

与变分原理相关的网络解释 [注：此内容来源于网络，仅供参考]

principle of variation：变分原理

principle of transfinite induction 超限归纳原理 | principle of variation 变分原理 | principle of virtual displacement 虚位移原理

variation principle：变分原理

variation of parameters 常量变差 | variation principle 变分原理 | variational derivative 变分导数

variation principle：变分原理 本文来自:博研联盟论坛

variation of parameters 常量变差 本文来自:博研联盟论坛 | variation principle 变分原理 本文来自:博研联盟论坛 | variational derivative 变分导数 本文来自:博研联盟论坛

hybrid variation principle：混合变分原理

艾克兰变分原理:Ekeland"s variational principle | 混合变分原理:hybrid variation principle | 变分:variational technique

variational derivative：变分导数

variation principle 变分原理 | variational derivative 变分导数 | variational equation 变分方程

variational derivative：变分导数 本文来自:博研联盟论坛

variation principle 变分原理 本文来自:博研联盟论坛 | variational derivative 变分导数 本文来自:博研联盟论坛 | variational equation 变分方程 本文来自:博研联盟论坛

variational equation：变分方程

variational calculus 变分学 | variational equation 变分方程 | variational principle 变分原理

adjoint variational method：伴随变分法

adjoint operator 伴随算子 | adjoint variational method 伴随变分法 | adjoint variational principle 伴随变分原理

variational problem：变分问题

variational principle 变分原理 | variational problem 变分问题 | varied orbit 变化轨道

variational principle：变分原理

variational equation 变分方程 | variational principle 变分原理 | variational problem 变分问题